random walk

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Beyond the Random Walk: A Guide to Stock Market Anomalies and Low Risk Investing by Vijay Singal

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Andrei Shleifer, asset allocation, capital asset pricing model, correlation coefficient, cross-subsidies, Daniel Kahneman / Amos Tversky, diversified portfolio, endowment effect, index arbitrage, index fund, locking in a profit, Long Term Capital Management, loss aversion, margin call, market friction, market microstructure, mental accounting, merger arbitrage, new economy, prediction markets, price stability, profit motive, random walk, Richard Thaler, risk-adjusted returns, risk/return, Sharpe ratio, short selling, transaction costs, Vanguard fund

Using all three quality-identifying proxies simultaneously should improve the detection of price patterns. The idea is that if a stock experiences a large price change unaccompanied by high volume or a public announcement, then that price change may get reversed. On the other hand, a price change accompanied by high volume and a public announcement is likely to be permanent. Indeed, if large price changes are accompanied by an increase in volume and a public announcement by the management or analysts, then a price continuation is likely to result in a one-month abnormal return of about 3.5 percent for positive events and –2.25 percent for negative events. A trading strategy set up to exploit these price patterns can earn an abnormal return of 1.25 percent to 3 percent after transaction costs, that is, 15–36 percent annually. 57 58 Beyond the Random Walk Evidence The evidence on the short-term price drift begins with a large price change as an indicator of a strong signal of new information.

Since an individual stock’s volume, like its return, depends on market volume, it is appropriate to adjust the stock’s trading volume by market volume. The results in panel A of Table 4.2 reveal two return patterns. First, price changes that are accompanied by high volume have price continuations. Price increases with high volume are followed by subsequent increases of 0.20 percent and 0.95 percent over five-day 61 62 Beyond the Random Walk Table 4.2 Returns Following Large Price Changes, High Volume, and News Price Change High Volume Public News Sample Size Abnormal Return: Days 1–5 (%) Abnormal Return: Days 1–20 (%) Panel A: Large price changes with and without high volume 1. 2. 3. 4. Increase Increase Decrease Decrease Yes No Yes No — — — — 1,477 1,442 1,142 812 0.20 –0.71 –0.66 0.49 0.95 –0.67 –0.65 –0.13 Panel B: Large price changes, high volume, and public news 5. 6. 7. 8. Increase Increase Decrease Decrease Yes Yes Yes Yes Yes No Yes No 603 874 653 489 0.54 –0.09 –1.26 0.63 1.98 0.03 –1.68 0.52 Large price change is based on relative return.

Second, the explanation requires a positive return after both positive and negative events in order to compensate for the extra risk. The continuation of the negative price drift after price declines is inconsistent with this explanation. Finally, prices may not react fully to new information because of investor behavior (see Chapter 12 for a discussion). As investors are slow to change their deeply held beliefs about a stock’s value, they tend to underreact. According to this explanation, as investors realize their mistakes, they trade, but with a time lag, resulting in the 67 68 Beyond the Random Walk price drift. In addition, investors are averse to selling at a loss and will continue to delay selling in the hope that the stock price will recover. As a result of this characteristic of investor behavior, the negative drift in price would be less than the positive drift in price. This prediction is supported by the data in Table 4.3.

 

pages: 209 words: 13,138

Empirical Market Microstructure: The Institutions, Economics and Econometrics of Securities Trading by Joel Hasbrouck

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barriers to entry, conceptual framework, correlation coefficient, discrete time, disintermediation, distributed generation, experimental economics, financial intermediation, index arbitrage, interest rate swap, inventory management, market clearing, market design, market friction, market microstructure, martingale, price discovery process, price discrimination, quantitative trading / quantitative finance, random walk, Richard Thaler, second-price auction, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, two-sided market, ultimatum game

Later chapters explore multivariate extensions and cointegration. In macroeconomics applications, random-walk decompositions are usually called permanent/transitory. The random-walk terminology is used here to stress the financial economics connection to the random-walk efficient prices. The permanent/transitory distinction is in some respects more descriptive, however, of the attributions that we’re actually making. From a microstructure perspective, the key results expand on those demonstrated for the generalized Roll model: The moving average representation for the price changes suffices to identify the variance of the 2 , the projection of the efficient price on past price implicit efficient price σw changes, and a lower bound on the variance of the difference between the transaction price and the efficient price. The development in this section is heuristic and intuitive.

The discussion then turns to bid and ask quotes, order arrivals, and the resulting transaction price process. 3.2 The Random-Walk Model of Security Prices Before financial economists began to concentrate on the trading process, the standard statistical model for a security price was the random walk. THE ROLL MODEL OF TRADE PRICES The random-walk model is no longer considered to be a complete and valid description of short-term price dynamics, but it nevertheless retains an important role as a model for the fundamental security value. Furthermore, some of the lessons learned from early statistical tests of the randomwalk hypothesis have ongoing relevance in modeling market data. Let pt denote the transaction price at time t, where t indexes regular points of real (“calendar” or “wall-clock”) time, for example, end-of-day, end-of-hour, and so on.

Equation (10.13) suggests a recursive procedure for forecasting. To construct impulse response functions, we set lagged price changes and disturbances to zero and work forward from an initial specified shock εt . By successively computing the impulse response functions for unit shocks in each variable, we may obtain the VMA representation for the price changes pt = θ(L)εt . We may posit for the n prices a random-walk decomposition of the form pt = mt × ι + st (n×1) (n×1) (n×1) where mt = mt−1 + wt , (10.15) where ι is a vector of ones. It is important to note that mt is a scalar: The random-walk (“efficient price”) component is the same for all prices in 2 = [θ(1)] [θ(1)]′ , where [ · ] the model. The random-walk variance is: σw 1 1 1 denotes the first row of the matrix. One property developed earlier for the structural model, however, is general: The rows of θ(1) are identical.

 

pages: 345 words: 86,394

Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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Albert Einstein, asset allocation, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Norbert Wiener, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

BM is a very simple yet very rich process, extremely useful for representing many random processes especially those in finance. Its simplicity allows calculations and analysis that would not be possible with other processes. For example, in option pricing it results in simple closed-form formulæ for the prices of vanilla options. It can be used as a building block for random walks with characteristics beyond those of BM itself. For example, it is used in the modelling of interest rates via mean-reverting random walks. Higher-dimensional versions of BM can be used to represent multi-factor random walks, such as stock prices under stochastic volatility. One of the unfortunate features of BM is that it gives returns distributions with tails that are unrealistically shallow. In practice, asset returns have tails that are much fatter than that given by the normal distribution of BM.

• Finding the value of derivatives by exploiting the theoretical relationship between option values and expected payoff under a risk-neutral random walk. Exploring portfolio statistics The most successful quantitative models represent investments as random walks. There is a whole mathematical theory behind these models, but to appreciate the role they play in portfolio analysis you just need to understand three simple concepts. First, you need an algorithm for how the most basic investments evolve randomly. In equities this is often the lognormal random walk. (If you know about the real/risk-neutral distinction then you should know that you will be using the real random walk here.) This can be represented on a spreadsheet or in code as how a stock price changes from one period to the next by adding on a random return. In the fixed-income world you may be using the BGM model to model how interest rates of various maturities evolve.

You would expect equity prices to follow a random walk around an exponentially growing average. So take the logarithm of the stock price and you might expect that to be normal about some mean. That is the non-mathematical explanation for the appearance of the lognormal distribution. More mathematically we could argue for lognormality via the Central Limit Theorem. Using Ri to represent the random return on a stock price from day i - 1 to day i we haveS1 = S0(1 + R1), the stock price grows by the return from day zero, its starting value, to day 1. After the second day we also haveS2 = S1(1 + R2 ) = S0(1 + R1)(1 + R2). After n days we have Figure 2-12: The probability density function for the lognormal random walk evolving through time. the stock price is the initial value multiplied by n factors, the factors being one plus the random returns.

 

pages: 338 words: 106,936

The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall

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Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, butterfly effect, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, new economy, Paul Lévy, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, V2 rocket, volatility smile

To see how this kind of mathematics can be helpful in understanding financial markets, you just have to see that a stock price is a lot like our man in Cancun. At any instant, there is a chance that the price will go up, and a chance that the price will go down. These two possibilities are directly analogous to the drunkard stumbling toward room 700, or toward room 799, working his way up or down the hallway. And so, the question that mathematics can answer in this case is the following: If the stock begins at a certain price, and it undergoes a random walk, what is the probability that the price will be a particular value after some fixed period of time? In other words, which door will the price have stumbled to after one hundred, or one thousand, ticks? This is the question Bachelier answered in his thesis. He showed that if a stock price undergoes a random walk, the probability of its taking any given value after a certain period of time is given by a curve known as a normal distribution, or a bell curve.

As its name suggests, this curve looks like a bell, rounded at the top and widening at the bottom. The tallest part of this curve is centered at the starting price, which means that the most likely scenario is that the price will be somewhere near where it began. Farther out from this center peak, the curve drops off quickly, indicating that large changes in price are less likely. As the stock price takes more steps on the random walk, however, the curve progressively widens and becomes less tall overall, indicating that over time, the chances that the stock will vary from its initial value increase. A picture is priceless here, so look at Figure 1 to see how this works. Figure 1: Bachelier discovered that if the price of a stock undergoes a random walk, the probability that the price will take a particular value in the future can be calculated from a curve known as a normal distribution.

By the time the Cootner book was published in 1964, the idea that market prices follow a random walk was well entrenched, and many economists recognized that Bachelier was responsible for it. But the random walk model wasn’t the punch line of Bachelier’s thesis. He thought of it as preliminary work in the service of his real goal, which was developing a model for pricing options. An option is a kind of derivative that gives the person who owns the option the right to buy (or sometimes sell) a specific security, such as a stock or bond, at a predetermined price (called the strike price), at some future time (the expiration date). When you buy an option, you don’t buy the underlying stock directly. You buy the right to trade that stock at some point in the future, but at a price that you agree to in the present. So the price of an option should correspond to the value of the right to buy something at some time in the future.

 

pages: 461 words: 128,421

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street by Justin Fox

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, invisible hand, Isaac Newton, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, New Journalism, Nikolai Kondratiev, Paul Lévy, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, volatility smile, Yogi Berra

Morgenstern wasn’t enough of a mathematician to do this himself, but he hired young British statistician Clive Granger and put him to work examining stock prices. In 1963, Morgenstern and Granger published a paper confirming that, according to their tests, stock prices moved in a short-term random walk (over the longer run, the movements didn’t look quite so random).13 Morgenstern had connections at Fortune that dated back to the magazine’s coverage of game theory fifteen years before, and his was thus the first of the random walk papers to receive attention in the mainstream press. The headline of the brief item in the magazine’s personal investing section in February 1963 was “A Random Walk in Wall Street.”14 THE HEADQUARTERS OF THIS EARLY random walk movement was Samuelson’s MIT. The university’s new Sloan School of Industrial Management shared a building with the Economics Department.

Over the forty-two years of data he examined, Working found that the speculators had, as a group, lost money.32 Moving on, Working began to study the movements of futures prices. He found a few interesting patterns. “Wheat prices tend strongly to rise during a season following three of low average price and to decline during a season following three of high average price,” he reported in 1931. “The relation is attributed partly to a tendency for price judgments of wheat traders to be unduly influenced by memory of prices in recent years.”33 Much of what Working saw in price movements, though, seemed random. The phrase “random walk” appears to have been coined in 1905, in an exchange in the letters pages of the English journal Nature concerning the mathematical description of the meanderings of a hypothetical drunkard.34 Most early studies of economic data had been a search not for drunken meanderings but for recognizable patterns and, not surprisingly, many were found.

“It’s easier to win than lose,” Business Week, May 29, 1965, 122. 20. Arnold Moore, interview with the author. Moore finished his dissertation in 1962, and it was published as “Some Characteristics of Changes in Common Stock Prices,” in The Random Character of Stock Prices, Paul Cootner, ed. (Cambridge, Mass.: MIT Press, 1964), 139–61. 21. Robert A. Levy, “Random Walks: Reality or Myth,” Financial Analysts Journal (Nov.–Dec. 1967): 69–77. 22. Michael C. Jensen, “Random Walks: Reality or Myth—Comment,” Financial Analysts Journal (Nov.–Dec. 1967): 84. 23. Jensen, “Random Walks,” 81. 24. Eugene F. Fama, Lawrence Fisher, Michael C. Jensen, Richard Roll, “The Adjustment of Stock Prices to New Information,” International Economic Review (Feb. 1969): 1–21. It took the paper years to get to print because Fama was set on publishing it somewhere other than the Chicago Business School’s Journal of Business, where all his previous papers had ended up, and it was a struggle to find another journal willing to take it.

 

pages: 442 words: 39,064

Why Stock Markets Crash: Critical Events in Complex Financial Systems by Didier Sornette

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Asian financial crisis, asset allocation, Berlin Wall, Bretton Woods, Brownian motion, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, market design, market fundamentalism, mental accounting, moral hazard, Network effects, new economy, oil shock, open economy, pattern recognition, Paul Erdős, quantitative trading / quantitative finance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, Tacoma Narrows Bridge, technological singularity, The Coming Technological Singularity, The Wealth of Nations by Adam Smith, Tobin tax, total factor productivity, transaction costs, tulip mania, VA Linux, Y2K, yield curve

This corresponds to a specific realization of the random numbers used in generating the random walks W t represented in the second panel. The top panel is obtained by taking a power of the inverse of a constant Wc , here taken equal to 1 minus the random walk shown in the second panel. In this case, when the random walk approaches 1, the bubble diverges. Notice the similarity between the trajectories shown in the top (Bt) and second (W t) panels as long as the random walk W t does not approach the value Wc = 1 too much. It is free to wander, but when it approaches 1, the bubble price Bt shows much greater sensitivity and eventually diverges when W t reaches 1. Before this happens, Bt can exhibit local peaks, that is, local bubbles, which come back smoothly. This corresponds to realizations of when the random walk approaches Wc without touching it and then spontaneously recedes away from it.

We can conclude that the residual correlations are those little enough not to be profitable by strategies such as those described above due to “imperfect” market conditions. In other words, the liquidity and efficiency of markets control the degree of correlation that is compatible with a near absence of arbitrage opportunity. THE EFFICIENT MARKET HYPOTHESIS AND THE RANDOM WALK Such observations have been made for a long time. A pillar of modern finance is the 1900 Ph.D. thesis dissertation of Louis Bachelier, in Paris, and his subsequent work, especially in 1906 and 1913 [25]. To account for the apparent erratic motion of stock market prices, he proposed that price trajectories are identical to random walks. The Random Walk The concept of a random walk is simple but rich for its many applications, not only in finance but also in physics and the description of natural phenomena. It is arguably one of the most important founding concepts in modern physics as well as in finance, as it underlies the theories of elementary particles, which are the building blocks of our universe, as well as those describing the complex organization of matter around us.

Figure 5.8 shows a typical trajectory of the bubble component of the price generated by the nonlinear positive feedback model [396], starting from some initial value up to the time just before the price starts to blow up. The simplest version of this model consists in a bubble price Bt being essentially a power of the inverse of a random walk W t in the following sense. Starting from B0 = W 0 = 0 at the origin of time, when the random walk approaches some value Wc , here 165 model ing bubbles a n d c r a s h e s B(t) 4.0 2.0 0 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 W(t) 1.0 0.5 0 dB(t) 0.2 0 -0.2 dW(t) 0.1 0 -0.1 t Fig. 5.8. Top panel: Realization of a bubble price Bt as a function of time constructed from the “singular inverse random walk.” This corresponds to a specific realization of the random numbers used in generating the random walks W t represented in the second panel.

 

The Armchair Economist: Economics and Everyday Life by Steven E. Landsburg

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Albert Einstein, Arthur Eddington, diversified portfolio, first-price auction, German hyperinflation, Golden Gate Park, invisible hand, means of production, price discrimination, profit maximization, Ralph Nader, random walk, Ronald Coase, sealed-bid auction, second-price auction, second-price sealed-bid, statistical model, the scientific method, Unsafe at Any Speed

I had misinterpreted the word random to mean "unrelated to anything else in the world," which is why I thought that the random walk theory denied that IBM's behavior could affect its stock price. But one random event can be perfectly correlated with another. Great corporate blunders arrive randomly, and the corresponding stock price changes arrive along with them. Economists believe that stock market prices behave a lot like random walks most of the time. That is, we believe that price changes (not prices) usually have the same statistical characteristics as the series of numbers generated by a roulette wheel. If prices were random, as I once erroneously believed, then today's price would be useless as a predictor of tomorrow's. Because price changes are random, the opposite is true. Today's price is the best possible predictor of tomorrow's. Tomorrow's price is today's price, plus a (usually small) random adjustment. 190 HOW MARKETS WORK Imagine a simple game of chance.

I'll be in my well-worn armchair, thinking about things. CHAPTER 20 RANDOM WALKS AND STOCK MARKET PRICES A Primer for Investors When I was young and first heard that stock market prices follow random walks, I was incredulous. Did this mean that IBM might as well replace its corporate officers with underprivileged eight-year-olds? My question was born of naivete', and of considerable ignorance. I've learned a lot in the interim. One thing I've learned is that a random walk is not a theory of prices; it is a theory of price changes. In that distinction lies a world of difference. My original (entirely wrong) conception invoked a roulette wheel as its central image. One day the little ball lands on 10, and the stock price is $10; the next day it lands on 8, and the price falls to $8, or it lands on 20 and the stockholders get rich.

Or that because it has recently risen, it is likely to fall soon or to rise further. But if stock prices are like random walks, as economists believe they usually are, then future price changes are quite independent of past history. The current price predicts the future price. The commentators notwithstanding, past price changes predict nothing. Those who play the market like to believe that they are more sophisticated than those who play casino games. Yet only the most naive roulette player would suggest that because his cash balance has fallen over the last several plays, it is now due for a "correction" upward. Experienced gamblers know what to expect from a random walk. When I was young, I harbored many misconceptions (not all of them related to finance). Another was that in the presence of a random walk, there can be no role for investment strategy.

 

pages: 416 words: 118,592

A Random Walk Down Wall Street: The Time-Tested Strategy for Successful Investing by Burton G. Malkiel

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accounting loophole / creative accounting, Albert Einstein, asset allocation, asset-backed security, backtesting, Bernie Madoff, BRICs, capital asset pricing model, compound rate of return, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Elliott wave, Eugene Fama: efficient market hypothesis, experimental subject, feminist movement, financial innovation, fixed income, framing effect, hindsight bias, Home mortgage interest deduction, index fund, invisible hand, Isaac Newton, Long Term Capital Management, loss aversion, margin call, market bubble, mortgage tax deduction, new economy, Own Your Own Home, passive investing, pets.com, Ponzi scheme, price stability, profit maximization, publish or perish, purchasing power parity, RAND corporation, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, short selling, Silicon Valley, South Sea Bubble, The Myth of the Rational Market, The Wisdom of Crowds, transaction costs, Vanguard fund, zero-coupon bond

Slow adjustment can make stock prices rise steadily for a period, imparting a degree of momentum. The failure of stock prices to measure up perfectly to the definition of a random walk led the financial economists Andrew Lo and A. Craig MacKinlay to publish a book entitled A Non-Random Walk Down Wall Street. In addition to some evidence of short-term momentum, there has been a long-run uptrend in most averages of stock prices in line with the long-run growth of earnings and dividends. But don’t count on short-term momentum to give you some sure-fire strategy to allow you to beat the market. For one thing, stock prices don’t always underreact to news—sometimes they overreact and price reversals can occur with terrifying suddenness. Two mutual funds managed in accordance with a momentum strategy started off with distinctly subpar returns. And even during periods when momentum is present (and the market fails to behave like a random walk), the systematic relationships that exist are often so small that they are not useful to investors.

Participants were faced with a choice—sell their cards at some negotiated price or hold on to them and hope to win. Obviously, each card had the same probability of winning. Nevertheless, the prices at which players were willing to sell their cards were systematically higher for those who chose their cards than for the group who had simply been given a card. Insights such as this led to the decision to let state lottery buyers pick their own numbers even though luck alone determines lottery winners. It is this illusion of control that can lead investors to see trends that do not exist or to believe that they can spot a stock-price pattern that will predict future prices. In fact, despite considerable efforts to tease some form of predictability out of stock-price data, the development of stock prices from period to period is very close to a random walk, where price changes in the future are essentially unrelated to changes in the past.

The life-cycle investment guide described in Part Four gives individuals of all age groups specific portfolio recommendations for meeting their financial goals, including advice on how to invest in retirement. WHAT IS A RANDOM WALK? A random walk is one in which future steps or directions cannot be predicted on the basis of past history. When the term is applied to the stock market, it means that short-run changes in stock prices are unpredictable. Investment advisory services, earnings forecasts, and complicated chart patterns are useless. On Wall Street, the term “random walk” is an obscenity. It is an epithet coined by the academic world and hurled insultingly at the professional soothsayers. Taken to its logical extreme, it means that a blindfolded monkey throwing darts at the stock listings could select a portfolio that would do just as well as one selected by the experts.

 

pages: 389 words: 109,207

Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street by William Poundstone

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Albert Einstein, anti-communist, asset allocation, Benoit Mandelbrot, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, en.wikipedia.org, Eugene Fama: efficient market hypothesis, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, New Journalism, Norbert Wiener, offshore financial centre, publish or perish, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, short selling, speech recognition, statistical arbitrage, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond

The butterfly whose flapping causes a hurricane could lead to the sinking of a yacht full of Sperry executives, pummeling the stock’s price. How can anyone predict such contingencies systematically? Then Thorp thought of the random walk model. Assume that there is no possible way of predicting the events that move stock prices. Then buying a stock option is placing a bet on a random walk. Thorp knew that there were already precise methods for calculating the probability distributions of random walks. They depend on the average size of the random motions—in this case, how much a stock’s price changes, up or down, per day. Thorp did some computations. He found that most warrants were priced like carnival games. They cost too much, given what you can win and your chance of winning it. This was especially true of warrants that were within a couple of years of expiring.

The mathematical treatment of Brownian motion that Einstein published in 1905 was similar to, but less advanced than, the one that Bachelier had already derived for stock prices. Einstein, like practically everyone else, had never heard of Bachelier. The Random Walk Cosa Nostra SAMUELSON ADOPTED Bachelier’s ideas into his own thinking. Characteristically, he did everything he could to acquaint people with Bachelier’s genius. Just as characteristically, Samuelson called Bachelier’s views “ridiculous.” Huh? Samuelson spotted a mistake in Bachelier’s work. Bachelier’s model had failed to consider that stock prices cannot fall below zero. Were stock price changes described by a conventional random walk, it would be possible for prices to wander below zero, ending up negative. That can’t happen in the real world. Investors are protected by limited liability.

No matter what goes wrong with a company, the investors do not end up owing money. This spoiled Bachelier’s neat model. Samuelson found a simple fix. He suggested that each day, a stock’s price is multiplied by a random factor (like 98 or 105 percent) rather than increased or decreased by a random amount. A stock might, for instance, be just as likely to double in price as to halve in price over a certain time frame. This model, called a log-normal or geometric random walk, prevents stocks from taking on negative values. To Samuelson, the random walk suggested that the stock market was a glorified casino. If the daily movements of stock prices are as unpredictable as the daily lotto numbers, then maybe people who make fortunes in the market are like people who win lotteries. They are lucky, not smart. It follows that all the people who advise clients on which stocks to buy are quacks.

 

pages: 364 words: 101,286

The Misbehavior of Markets by Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

On average—just as in the coin-toss game—he gets nowhere. So if you consider only that average, his random walk across the field will be forever stuck at his starting point. And that would be the best possible forecast of his future position at any time, if you had to make such a guess. The same reasoning applies to a bond price: In the absence of new information that might change the balance of supply and demand, what is the best possible forecast of the price tomorrow? Again, the price can go up or down, by big increments or small. But, with no new information to push the price decisively in one direction or another, the price on average will fluctuate around its starting point. So again, the best forecast is the price today. Moreover, each variation in price is unrelated to the last, and is generated by the same unchanging but mysterious process that drives the markets.

It takes no great leap of the imagination to see how such spurious patterns could also appear in otherwise random financial data. This is not to say that price charts are meaningless, or that prices all vary by the whim of luck. But it does say that, when examining price charts, we should guard against jumping to conclusions that the invisible hand of Adam Smith is somehow guiding them. It is a bold investor who would try to forecast a specific price level based solely on a pattern in the charts. 9. Forecasting Prices May Be Perilous, but You Can Estimate the Odds of Future Volatility. All is not hopeless. Markets are turbulent, deceptive, prone to bubbles, infested by false trends. It may well be that you cannot forecast prices. But evaluating risk is another matter entirely. Step back a moment. The classic Random Walk model makes three essential claims. First is the so-called martingale condition: that your best guess of tomorrow’s price is today’s price.

What a company does today—a merger, a spin-off, a critical product launch—shapes what the company will look like a decade hence; in the same way, its stock-price movements today will influence movements tomorrow. Others suggest that the market may take a long time to absorb and fully price information. When confronted by bad news, some quick-triggered investors react immediately while others, with different financial goals and longer time-horizons, may not react for another month or year. Whatever the explanation, we can confirm the phenomenon exists—and it contradicts the random-walk model. Second, contrary to orthodoxy, price changes are very far from following the bell curve. If they did, you should be able to run any market’s price records through a computer, analyze the changes, and watch them fall into the approximate “normality” assumed by Bachelier’s random walk. They should cluster about the mean, or average, of no change. In fact, the bell curve fits reality very poorly.

 

Commodity Trading Advisors: Risk, Performance Analysis, and Selection by Greg N. Gregoriou, Vassilios Karavas, François-Serge Lhabitant, Fabrice Douglas Rouah

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Asian financial crisis, asset allocation, backtesting, capital asset pricing model, collateralized debt obligation, commodity trading advisor, compound rate of return, constrained optimization, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, discrete time, distributed generation, diversification, diversified portfolio, dividend-yielding stocks, fixed income, high net worth, implied volatility, index arbitrage, index fund, interest rate swap, iterative process, linear programming, London Interbank Offered Rate, Long Term Capital Management, market fundamentalism, merger arbitrage, Mexican peso crisis / tequila crisis, p-value, Ponzi scheme, quantitative trading / quantitative finance, random walk, risk-adjusted returns, risk/return, Sharpe ratio, short selling, stochastic process, systematic trading, technology bubble, transaction costs, value at risk

Some authors have suggested that unit root tests suffer from low power and that the test does not discriminate very 328 PROGRAM EVALUATION, SELECTION, AND RETURNS well between mean reverting series and series that do not mean revert at all (Kennedy 1998). However, the robustness of the ADF test is increased when lags are used. If a series is found to be nonstationary by the ADF test, it does not necessarily imply that it behaves like a random walk, because random walks are but one example of nonstationary time series. Fortunately, the ADF test also can be used to test specifically for random walks. No CTA strategy that relies solely on historical prices can be continuously profitable if markets are efficient and the random walk hypothesis holds true. In this case, future percent changes in NAVs would be entirely unrelated by the historical performance (Pindyck and Rubinfeld 1998). Recent studies have shown that a minimal amount of performance persistence is found in CTAs and there could exist some advantages in selecting CTAs based on past performance when a long time series of data is available and accurate methods are used (Brorsen and Townsend 2002).

T INTRODUCTION This chapter investigates whether monthly percent changes in net asset values (NAVs) of commodity trading advisor (CTA) classifications follow random walks. Previous econometric studies of financial time series have employed unit root tests, such as the Augmented Dickey-Fuller test (ADF), to identify random walk behavior in stock prices and market indices, for example. The characteristics of CTAs are such that investment into this alternative investment class can enhance portfolio returns, but these characteristics are likely to be mitigated if pure random walk behavior is present because that would imply a lack of evidence of value added to the portfolio (differential manager skill). Research into the performance persistence of CTAs is sparse, so there is little information on the long-term diligence of these managers (Edwards This article previously appeared in Journal of Alternative Investments, No. 2, 2003.

CTAs assume both long and short market positions, and realize profits when there are persistent trends in markets and when those trends can be identified early enough. Thus, the performance of CTAs depends not only on price movements, but also on the managers’ ability to identify them. One possible explanation for random walk behavior during the examination period is due to the fact that traditional CTAs make large profits during extreme market movements, themselves random events. Their correlations may be more accurate and stable if they are used as a hedge against short volatility exposure. The discretionary, currency, and European traders trade in periods of high liquidity, which has been the case since 1995. We found that only one class, diversified, did not behave as a random walk, likely since trends in a diversified portfolio are stable, although they may not produce sufficient profits to satisfy the expectations of all investors.

 

Evidence-Based Technical Analysis: Applying the Scientific Method and Statistical Inference to Trading Signals by David Aronson

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Albert Einstein, Andrew Wiles, asset allocation, availability heuristic, backtesting, Black Swan, capital asset pricing model, cognitive dissonance, compound rate of return, Daniel Kahneman / Amos Tversky, distributed generation, Elliott wave, en.wikipedia.org, feminist movement, hindsight bias, index fund, invention of the telescope, invisible hand, Long Term Capital Management, mental accounting, meta analysis, meta-analysis, p-value, pattern recognition, Ponzi scheme, price anchoring, price stability, quantitative trading / quantitative finance, Ralph Nelson Elliott, random walk, retrograde motion, revision control, risk tolerance, risk-adjusted returns, riskless arbitrage, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, statistical model, systematic trading, the scientific method, transfer pricing, unbiased observer, yield curve, Yogi Berra

First, “the usual method of graphing stock prices gives a picture of successive (price) levels rather than of price changes and levels can give an artificial appearance of pattern or trend. Second, chance behavior itself produces patterns that invite spurious interpretations.”128 Roberts showed that the same chart patterns to which TA attaches importance129 appear with great regularity in random walks. A random walk is, by definition, devoid of authentic trends, patterns, or exploitable order of any kind. However, Roberts’ random-walk charts displayed headand-shoulder tops and bottoms, triangle tops and bottoms, triple tops and bottoms, trend channels, and so forth. You can create a random-walk chart from a sequence of coin flips by starting with an arbitrary price, say $100, and adding one dollar for each head and subtracting one dollar for each tail.

It occurs when an observer has no prior belief about whether the process generating the data is random or nonrandom The clustering illusion is the misperception of order (nonrandomness) in data that is actually a random walk. Again, imagine someone observing the outcomes of a process that is truly a random walk trying to determine if the process is random or nonrandom (orderly, systematic).71 Recall that small samples of random walks often appear more trended (clustered) than common sense would lead us to expect (the hot hand in basketball). As a result of the clustering illusion, a sequence of positive price or earnings changes is wrongly interpreted as a legitimate trend, when it is nothing more than an ordinary streak in a random walk. Social Factors: Imitative Behavior, Herding, and Information Cascades72 We have just seen how investor behavior viewed at the level of the individual investor can explain several types of systematic price movement. This section examines investor behavior at the group level to explain systematic price movements.

So it is hard to imagine that the market as a whole reflects the emotions described by these psychological theories.”7 We will need to look beyond the platitudes of popular texts for TA’s justification. Fortunately, theories developed in the field of behavioral finance and elsewhere are beginning to offer the theoretical support TA needs. THE ENEMY’S POSITION: EFFICIENT MARKETS AND RANDOM WALKS Before discussing theories that explain why nonrandom price movements should exist, we need to consider the enemy’s position, the EMH. Recently, some have argued that EMH does not necessarily imply that prices follow unpredictable random walks,8 and that efficient markets and price predictability can coexist. However, the pioneers of EMH asserted that random walks were a necessary consequence of efficient markets. This section states their case and examines its weaknesses. What Is an Efficient Market? An efficient market is a market that cannot be beaten. In such a market, no fundamental or technical analysis strategy, formula, or system can earn a risk-adjusted rate of return that beats the market defined by a benchmark index.

 

The Intelligent Asset Allocator: How to Build Your Portfolio to Maximize Returns and Minimize Risk by William J. Bernstein

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asset allocation, backtesting, capital asset pricing model, computer age, correlation coefficient, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, fixed income, index arbitrage, index fund, Long Term Capital Management, p-value, passive investing, prediction markets, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, South Sea Bubble, the scientific method, time value of money, transaction costs, Vanguard fund, Yogi Berra, zero-coupon bond

.): correlation coefficients, 71–74 international diversification with small stocks, 74–75 risk tolerance and, 79–80, 143 three-step approach to, 75–83 Out of sample, 87 Overbalancing, 138 Overconfidence, 139–140 P/B ratio (See Book value) P/E ratio: data on ranges of, 113, 114 earnings yield as reverse of, 119 in new era of investing, 124 in value investing, 112, 119–120 Pacific Rim stocks, 19, 20, 21, 25, 55–59, 147, 156 Pension funds, 103 (See also Institutional investors) Perfectly reasonable price (PRP), 127–128 Performance measurement: alpha in, 89–90, 98 three-factor model in, 123–124 (See also Benchmarking) Perold, Andre, 141 Persistence of performance, 85–88 Peters, Tom, 118 Piscataqua Research, 103 Policy allocation, 59 Portfolio insurance, 141 Portfolio Selection (Markowitz), 177–178 Precious metals stocks, 19–20, 21, 48, 55, 57, 59 Price, Michael, 162 Professional investors (See Institutional investors) Prudent man test, 60 Random Walk Down Wall Street, A (Malkiel), 101–102, 175 Random walk theory, 106–108, 119 positive autocorrelation and, 106–108 204 Index Random walk theory (Cont.): random walk defined, 106 rebalancing and, 109 Raskob, John J., 16–17 Real estate investment trusts (REITs), 38, 40, 100, 145 defined, 19 index fund, 148 returns on, 19, 21, 25 Real return, 26, 80, 168, 170 Rebalancing: frequency of, 108–109 importance of, 32–33, 35–36, 59, 63, 174 and mean-variance optimizer (MVO), 65 overbalancing in, 138 random walk theory and, 109 rebalancing bonus, 74, 159–160 of tax-sheltered accounts, 159–160 of taxable accounts, 160–161 Recency effects, 47–48, 52, 53, 58–59, 140–141 Regression analysis, 89–90 Reinvestment risk, 23 Representativeness, 118 Research expenses, 92, 95 Residual return, 98 Retirement, 165–172 asset allocation for, 153–154 duration risk and, 165–167 shortfall risk and, 167–172 (See also Tax-sheltered accounts) Return: annualized, 2–3, 5 average, 2–3 coin toss and, 1–5 company size and, 116–117 correlation between risk and, 21 dividend discount method, 23–24, 26, 127–132 efficient frontier and, 55–58 expected investment, 26 historical, problems with, 21–27 Return (Cont.): impact of diversification on, 31–36, 63 market, 168 real, 26, 80, 168, 170 return and risk plot, 31–36, 41–45 risk and high, 18 uncorrelated, 29–31 variation in, 116–117 Risk: common stock, 1–5 correlation between return and, 21 currency, 132–137 duration, 165–167 efficient frontier and, 55–58 excess, 12–13 high returns and, 18 impact of diversification on, 31–36, 63 nonsystematic, 12–13 reinvestment, 23 return and risk plot, 31–36, 41–45 shortfall, 167–172 sovereign, 72 systematic, 13 (See also Standard deviation) Risk aversion myopia, 141–142 Risk dilution, 45–46 Risk-free investments, 10, 15, 152 Risk-free rate, 121 Risk time horizon, 130, 131, 143–144, 167 Risk tolerance, 79–80, 143 Roth IRA, 172 Rukeyser, Lou, 174 Rule of 72, 27 Sanborn, Robert, 88–90 Securities Act of 1933, 92–93 Security Analysis (Graham and Dodd), 93, 118, 125, 176 Selling forward, 132–133 Semivariance, 7 Sharpe, William, 141 Shortfall risk, 167–172 Siegel, Jeremy, 19, 136 Index Simple portfolios, 31–36 Sinquefield, Rex, 148 Small-cap premium, 53, 121, 122 Small-company stocks, 13–16, 25 correlation with large-company stocks, 53–55 efficient frontier and, 55–59 indexing, 101, 102, 148–149 international diversification with, 74–75 January effect and, 92–94 large-company stocks versus, 53–55, 75 “lottery ticket” premium and, 127 tracking error of, 75 Small investors, institutional investors versus, 59–61 Solnik, Bruno, 72 Sovereign risk, 72 S&P 500, 13, 38, 39, 55 as benchmark, 60, 78, 79, 80, 86, 88–89, 145 efficient frontier, 56–57 Spiders (SPDRS), 149 Spot rate, 135 Spread, 91, 92, 93, 96 Standard deviation, 5–8 defined, 6, 63 limitations of, 7 of manager returns, 96 in mean-variance analysis, 65 Standard error (SE), 87 Standard normal cumulative distribution function, 7 Stocks, Bonds, Bills, and Inflation (Ibbotson Associates), 9–10, 41–42, 178 Stocks for the Long Run (Siegel), 19, 136 Strategic asset allocation, 58–59 Survivorship bias, 101–102 Systematic risk, 13 t distribution function, 87 Tax-sheltered accounts: asset allocation for, 153–154 rebalancing, 108–109, 159–160 (See also Retirement accounts) 205 Taxable accounts: asset allocation for, 153–154 rebalancing, 160–161 Taxes: in asset allocation strategy, 145 capital gains capture, 102, 108 foreign tax credits, 161 market efficiency and, 102–103 Technological change: historical, impact of, 125 in new era of investing, 125 Templeton, John, 164 Thaler, Richard, 131, 142 Three-factor model (Fama and French), 120–124 Time horizon, 130, 131, 143–144, 167 Tracking error: defined, 75 determining tolerance for, 83, 145 of small-company stocks, 75 of various equity mixes, 79 Treasury bills: 1926–1998, 10–11 returns on, 25–26 as risk-free investments, 10, 15, 152 Treasury bonds: 1926–1998, 11–13, 42–45 ladders, 152 Treasury Inflation Protected Security (TIPS), 80, 131–132, 172 Treasury notes, 11 Turnover, 95, 102, 130–131, 145 Tweedy, Browne, 148–149, 162, 176 Utility functions, 7 Value averaging, 155–159 Value Averaging (Edleson), 176 Value index funds, 145 Value investing, 77, 111–124 defined, 118 growth investing versus, 117, 118–120 measures used in, 112–114 studies on, 115–118 three-factor model of, 120–124 Value premium, 121–123 206 Index VanEck Gold Fund, 21 Vanguard Group, 97–100, 146–148, 149, 150, 152, 156, 161–163 Variance, 7, 108–109 mean-variance analysis, 44–45, 64–71, 181–182 minimum-variance portfolios, 65–69 Variance drag, 69 Walz, Daniel T., 169 Websites, 178–180 Wilkinson, David, 56, 57, 181–182 Williams, John Burr, 127 Wilshire Associates, 120, 147, 162 World Equity Benchmark Securities (WEBS), 149–151 z values, 87 Zero correlation, 31 About the Author William Bernstein, Ph.D, M.D., is a practicing neurologist in Oregon.

Momentum in foreign and domestic equity asset classes exists, resulting in periodic asset overvaluation and undervaluation. Eventually long-term mean reversion occurs to correct these excesses. Over 2 decades ago, Eugene Fama made a powerful case that security price changes could not be predicted, and Burton Malkiel introduced the words “random walk” into the popular investing lexicon. Unfortunately, in a truly random-walk world, there is no advantage to portfolio rebalancing. If you rebalance, you profit only when the frogs in your portfolio turn into princes, and vice versa. In the real world, fortunately, there are subtle departures in random-walk behavior that the asset allocator-investor can exploit. Writer and money manager Ken Fisher calls this change in asset desirability, and the resultant short-term momentum and long-term mean reversion, the “Wall Street Waltz.”

Efficient-market theorists are fond of pointing out that there is no pattern to stock or market prices. (As we have already seen, this is not Odds and Ends 119 strictly true.) Growth-stock investors believe that they can pick those companies which will have persistent earnings growth and thus reap the benefits of their ever-increasing earnings stream. Unfortunately, established growth companies are very expensive, often selling at P/Es two or three times that of the market as a whole. A company growing 5% faster than the rest of the market and selling at a P/E twice the market’s will have to continue growing for another 14 years at that rate before the shareholder is fairly compensated. As we’ve already seen, stock price movements are essentially an unpredictable “random walk.” Interestingly, it turns out that earnings growth also exhibits random-walk behavior; a company with good earnings growth this year is quite likely to have poor earnings growth next year (and vice versa).

 

pages: 295 words: 66,824

A Mathematician Plays the Stock Market by John Allen Paulos

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Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Nash equilibrium, Network effects, passive investing, Paul Erdős, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, transaction costs, ultimatum game, Vanguard fund, Yogi Berra

By starting with the basic up-down-up and down-up-down patterns of a stock’s possible movements, continually replacing each of these patterns’ three segments with smaller versions of one of the basic patterns chosen at random, and then altering the spikiness of the patterns to reflect changes in the stock’s volatility, Mandelbrot has constructed what he calls multifractal “forgeries.” The forgeries are patterns of price movement whose general look is indistinguishable from that of real stock price movements. In contrast, more conventional assumptions about price movements, say those of a strict random-walk theorist, lead to patterns that are noticeably different from real price movements. These multifractal patterns are so far merely descriptive, not predictive of specific price changes. In their modesty, as well as in their mathematical sophistication, they differ from the Elliott waves mentioned in chapter 3. Even this does not prove that chaos (in the mathematical sense) reigns in (part of) the market, but it is clearly a bit more than suggestive.

Weeding out some of the details, let’s assume for the sake of the argument (although Lo and MacKinlay don’t) that the thesis of Burton Malkiel’s classic book, A Random Walk Down Wall Street, is true and that the movement of the market as a whole is entirely random. Let’s also assume that each stock, when its fluctuations are examined in isolation, moves randomly. Given these assumptions it would nevertheless still be possible that the price movements of, say, 5 percent of stocks accurately predict the price movements of a different 5 percent of stocks one week later. The predictability comes from cross-correlations over time between stocks. (These associations needn’t be causal, but might merely be brute facts.) More concretely, let’s say stock X, when looked at in isolation, fluctuates randomly from week to week, as does stock Y. Yet if X’s price this week often predicts Y’s next week, this would be an exploitable opportunity and the strict random-walk hypothesis would be wrong.

Yet if X’s price this week often predicts Y’s next week, this would be an exploitable opportunity and the strict random-walk hypothesis would be wrong. Unless we delved deeply into such possible cross-correlations among stocks, all we would see would be a randomly fluctuating market populated by randomly fluctuating stocks. Of course, I’ve employed the typical mathematical gambit of considering an extreme case, but the example does suggest that there may be relatively simple elements of order in a market that appears to fluctuate randomly. There are other sorts of stock price anomalies that can lead to exploitable opportunities. Among the most well-known are so-called calendar effects whereby the prices of stocks, primarily small-firm stocks, rise disproportionately in January, especially during the first week of January. (The price of WCOM rose significantly in January 2001, and I was hoping this rise would repeat itself in January 2002.

 

pages: 206 words: 70,924

The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton by Colin Read

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Albert Einstein, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, David Ricardo: comparative advantage, discovery of penicillin, discrete time, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John von Neumann, Joseph Schumpeter, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, naked short selling, price stability, principal–agent problem, quantitative trading / quantitative finance, RAND corporation, random walk, risk tolerance, risk/return, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

Bachelier had already discovered this, though. His statement that stock prices could be modeled as a random walk according to a Weiner process was amenable to empirical verification. Alfred Cowles, who would found the Cowles Commission, and Herbert Jones explored and subsequently vindicated this notion that there is no memory effect in the price of stocks in a 1937 paper together.8 While the notion of the random walk has since been replaced with the less restrictive concept of a martingale process, much of finance pricing theory still retains the random walk because of its simple first and second moment characterization of price movements. The random walk of absolute prices Bachelier constructed a theory of absolute rather than relative price movements. Now we recognize it as some of the most analytically and theoretically complex work in stochastic calculus in finance until the late 1950s or 1960s.

Bachelier aimed to provide the theory behind these rather complex instruments that must be treated not only based on their prices but also on their expiration date, the exercise price, and the right to either buy (calls) or sell (puts) at that price. Bachelier modeled options pricing by noting how increments to the stock price would affect the price of the option derived from it. He assumed that the stock experienced identically and independently distributed random movements, which allowed him to use the central limit theorem to describe the probability distribution of these movements by the normal distribution. He also allowed a drift of zero mean of the security price and assumed that the variance of the price drift is proportional to the length of time of the random walk. In combination, he had described what we now call a Weiner process. The Times 105 While Bachelier was the first to apply Brownian motion to finance, the methodology is now commonplace.

Einstein and Bachelier both noted that, beyond a common drift element, the movement of a particle or a stock from one period to the next is uncorrelated. We now know this phenomenon as the random walk. We return to Bachelier’s model later in our discussion of options pricing theory, and more fully in the next volume of our series on Applications 33 the random walk and the efficient market hypothesis. Without fully anticipating the profound impact, he nonetheless created a wave of scientific innovation in finance. Others continued the tradition that he helped to establish. In Britain, the Financial Review of Reviews began analyzing the prices and volatility of various stocks and bonds. The precursors of the ratings agencies Standard & Poor’s, Fitch, and Moody’s began researching and analyzing the fundamental profitability of companies as a way of assuring investors that corporate bonds were sound.

 

pages: 752 words: 131,533

Python for Data Analysis by Wes McKinney

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backtesting, cognitive dissonance, crowdsourcing, Debian, Firefox, Google Chrome, index card, random walk, recommendation engine, revision control, sentiment analysis, Sharpe ratio, side project, sorting algorithm, statistical model, type inference

Partial list of numpy.random functions FunctionDescription seed Seed the random number generator permutation Return a random permutation of a sequence, or return a permuted range shuffle Randomly permute a sequence in place rand Draw samples from a uniform distribution randint Draw random integers from a given low-to-high range randn Draw samples from a normal distribution with mean 0 and standard deviation 1 (MATLAB-like interface) binomial Draw samples a binomial distribution normal Draw samples from a normal (Gaussian) distribution beta Draw samples from a beta distribution chisquare Draw samples from a chi-square distribution gamma Draw samples from a gamma distribution uniform Draw samples from a uniform [0, 1) distribution Example: Random Walks An illustrative application of utilizing array operations is in the simulation of random walks. Let’s first consider a simple random walk starting at 0 with steps of 1 and -1 occurring with equal probability. A pure Python way to implement a single random walk with 1,000 steps using the built-in random module: import random position = 0 walk = [position] steps = 1000 for i in xrange(steps): step = 1 if random.randint(0, 1) else -1 position += step walk.append(position) See Figure 4-4 for an example plot of the first 100 values on one of these random walks. Figure 4-4. A simple random walk You might make the observation that walk is simply the cumulative sum of the random steps and could be evaluated as an array expression.

First, I’ll use scaled prices for the SPY exchange-traded fund as a proxy for the S&P 500 index: In [127]: import pandas.io.data as web # Approximate price of S&P 500 index In [128]: px = web.get_data_yahoo('SPY')['Adj Close'] * 10 In [129]: px Out[129]: Date 2011-08-01 1261.0 2011-08-02 1228.8 2011-08-03 1235.5 ... 2012-07-25 1339.6 2012-07-26 1361.7 2012-07-27 1386.8 Name: Adj Close, Length: 251 Now, a little bit of setup. I put a couple of S&P 500 future contracts and expiry dates in a Series: from datetime import datetime expiry = {'ESU2': datetime(2012, 9, 21), 'ESZ2': datetime(2012, 12, 21)} expiry = Series(expiry).order() expiry then looks like: In [131]: expiry Out[131]: ESU2 2012-09-21 00:00:00 ESZ2 2012-12-21 00:00:00 Then, I use the Yahoo! Finance prices along with a random walk and some noise to simulate the two contracts into the future: np.random.seed(12347) N = 200 walk = (np.random.randint(0, 200, size=N) - 100) * 0.25 perturb = (np.random.randint(0, 20, size=N) - 10) * 0.25 walk = walk.cumsum() rng = pd.date_range(px.index[0], periods=len(px) + N, freq='B') near = np.concatenate([px.values, px.values[-1] + walk]) far = np.concatenate([px.values, px.values[-1] + walk + perturb]) prices = DataFrame({'ESU2': near, 'ESZ2': far}, index=rng) prices then has two time series for the contracts that differ from each other by a random amount: In [133]: prices.tail() Out[133]: ESU2 ESZ2 2013-04-16 1416.05 1417.80 2013-04-17 1402.30 1404.55 2013-04-18 1410.30 1412.05 2013-04-19 1426.80 1426.05 2013-04-22 1406.80 1404.55 One way to splice time series together into a single continuous series is to construct a weighting matrix.

Thus, I use the np.random module to draw 1,000 coin flips at once, set these to 1 and -1, and compute the cumulative sum: In [215]: nsteps = 1000 In [216]: draws = np.random.randint(0, 2, size=nsteps) In [217]: steps = np.where(draws > 0, 1, -1) In [218]: walk = steps.cumsum() From this we can begin to extract statistics like the minimum and maximum value along the walk’s trajectory: In [219]: walk.min() In [220]: walk.max() Out[219]: -3 Out[220]: 31 A more complicated statistic is the first crossing time, the step at which the random walk reaches a particular value. Here we might want to know how long it took the random walk to get at least 10 steps away from the origin 0 in either direction. np.abs(walk) >= 10 gives us a boolean array indicating where the walk has reached or exceeded 10, but we want the index of the first 10 or -10. Turns out this can be computed using argmax, which returns the first index of the maximum value in the boolean array (True is the maximum value): In [221]: (np.abs(walk) >= 10).argmax() Out[221]: 37 Note that using argmax here is not always efficient because it always makes a full scan of the array. In this special case once a True is observed we know it to be the maximum value. Simulating Many Random Walks at Once If your goal was to simulate many random walks, say 5,000 of them, you can generate all of the random walks with minor modifications to the above code.

 

pages: 425 words: 122,223

Capital Ideas: The Improbable Origins of Modern Wall Street by Peter L. Bernstein

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Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buy low sell high, capital asset pricing model, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, new economy, New Journalism, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, stochastic process, the market place, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, transfer pricing, zero-coupon bond

See also Capital Asset Pricing Model; Random price fluctuations; specific types of securities arbitrage Black/Scholes formula of: see Black/Scholes formula earnings ratio efficient markets and future of growth stocks information and interest rates and intrinsic value and manipulation risk and security analysis and shadow transfer trends value differentiation zero downside limit on “Price Movements in Speculative Markets: Trends or Random Walks” (Alexander) “Pricing of Options and Corporate Liabilities, The” (Black/Scholes) Probability theory Procter & Gamble Profit maximization Program trading Prospective yield “Proposal for a Smog Tax, A” (Sharpe) Puts: see Options Railroads RAND Random Character of Stock Prices, The (Cootner) “Random Difference Series for Use in the Analysis of Time Series, A” (Working) Random price fluctuations/random walks selection of securities and “Random Walks in Stock Market Prices” (Fama) Rational Expectations Hypothesis “Rational Theory of Warrant Pricing” (Samuelson) Regulation of markets Return analysis: see Risk/return ratios Review of Economics and Statistics Review of Economic Studies, The “RHM Warrant and Low-Price Stock Survey, The” Risk arbitrage calculations diversification and dominant expected return and minimalization portfolio premium return ratios Rosenberg’s model stock prices and of stocks vs. bonds systematic (beta) trade-offs valuation of assets and “Risk and the Evaluation of Pension Fund Performance” (Fama) Risk-free assets Rosenberg Institutional Equity Management (RIEM) “Safety First and the Holding of Assets” (Roy) Samsonite Savings rates Scott Paper Securities analysis Securities and Exchange Commission Security Analysis (Graham/Dodd) Security selection Separation Theorem Shadow prices “Simplified Model for Portfolio Analysis, A” (Sharpe) Singer Manufacturing Company Single-index model Sloan School of Management Standard & Poor’s 500 index “State of the Art in Our Profession, The” (Vertin) Stock(s) cash ratios common expected return on growth income international legal restrictions on market value variance volatility Stock market (general discussion) Black Monday (October, 1987, crash) “Stock Market ‘Patterns’ and Financial Analysis” (Roberts) Supply and demand theory Swaps Tactical asset allocation theory Tampax Taxes.

He then throws down the gauntlet to the chartists and technical analysts who believe that the past pattern of stock prices makes future prices predictable: The chartist must admit that the evidence in favor of the random walk model is both consistent and voluminous, whereas there is precious little published in discussion of rigorous empirical tests of the various technical theories. If the chartist rejects the evidence of the random walk model, his position is weak if his own theories have not been subjected to equally rigorous tests. This, I believe, is the challenge that the random walk theory makes.14 Now Fama moves to a deeper matter: the uses and value of information itself. This is a more serious issue than the accomplishments of the technical analysts, who eschew information and believe that market prices tell their own story of what is to come. It is also an intensely controversial issue.

The mathematical formula that describes this phenomenon was one of Bachelier’s crowning achievements. Over time, in the literature on finance, Brownian motion came to be called the random walk, which someone once described as the path a drunk might follow at night in the light of a lamppost. No one knows who first used this expression, but it became increasingly familiar among academics during the 1960s, much to the annoyance of financial practitioners. Eugene Fama of the University of Chicago, one of the first and most enthusiastic proponents of the concept, tells me that random walk “is an ancient statistical term; nobody alive can claim it.”13 In later years, the primary focus of research on capital markets was on determining whether or not the random walk is a valid description of security price movements. Bachelier himself, hardly a modest man, ended his dissertation with this flat statement: “It is evident that the present theory resolves the majority of problems in the study of speculation by the calculus of probability.”14 Despite its importance, Bachelier’s thesis was lost until it was rediscovered quite by accident in the 1950s by Jimmie Savage, a mathematical statistician at Chicago.

 

pages: 1,088 words: 228,743

Expected Returns: An Investor's Guide to Harvesting Market Rewards by Antti Ilmanen

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Andrei Shleifer, asset allocation, asset-backed security, availability heuristic, backtesting, balance sheet recession, bank run, banking crisis, barriers to entry, Bernie Madoff, Black Swan, Bretton Woods, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, central bank independence, collateralized debt obligation, commodity trading advisor, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, debt deflation, deglobalization, delta neutral, demand response, discounted cash flows, disintermediation, diversification, diversified portfolio, dividend-yielding stocks, equity premium, Eugene Fama: efficient market hypothesis, fiat currency, financial deregulation, financial innovation, financial intermediation, fixed income, Flash crash, framing effect, frictionless, frictionless market, George Akerlof, global reserve currency, Google Earth, high net worth, hindsight bias, Hyman Minsky, implied volatility, income inequality, incomplete markets, index fund, inflation targeting, interest rate swap, invisible hand, Kenneth Rogoff, laissez-faire capitalism, law of one price, Long Term Capital Management, loss aversion, margin call, market bubble, market clearing, market friction, market fundamentalism, market microstructure, mental accounting, merger arbitrage, mittelstand, moral hazard, New Journalism, oil shock, p-value, passive investing, performance metric, Ponzi scheme, prediction markets, price anchoring, price stability, principal–agent problem, private sector deleveraging, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, random walk, reserve currency, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Robert Shiller, Robert Shiller, savings glut, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, stochastic volatility, systematic trading, The Great Moderation, The Myth of the Rational Market, too big to fail, transaction costs, tulip mania, value at risk, volatility arbitrage, volatility smile, working-age population, Y2K, yield curve, zero-coupon bond

The model assumes that earnings streams follow a random walk; yet investors mistakenly believe that observed earnings come from either of two regimes—a normal mean-reverting regime or a momentum regime—and they switch back and forth between the two mindsets. They try to infer the prevailing regime from the data, predicting earnings reversals when they believe that normal conditions apply, but extrapolating apparent earnings trends when they observe a string of same sign shocks and infer that a momentum regime is more likely. The first type of mistake (proxying for conservatism) leads to price underreactions and momentum, while the second type of mistake leads to (delayed) price overreactions. Because the true earnings process is a random walk, the extrapolating investor will eventually be disappointed, resulting in long-term price reversal and value effects [8]

Adding the evidence that estimated ex ante bond risk premia track expected inflation, it seems fair to assume that inflation uncertainty and the IRP are both level dependent. Inflation persistence rose with inflation level until 1980. During the gold standard, prices could go persistently up or down but the best long-term forecasts used to be for no change. That is, the price level followed a random walk and recent inflation had no ability to predict future inflation. Between the 1950s and the 1970s, as inflation’s persistence gradually rose, the best time series forecast of future inflation shifted from zero to the most recent inflation rate. That is, instead of the price level following a random walk, the inflation rate did so (the statistical persistence parameter rose from 0 to 1, before reversing after 1980). At least the process did not become more explosive in developed markets, as it does when hyperinflation psychology takes hold.

Antti Ilmanen Bad Homburg, November 2010 Abbreviations and acronyms AM Arithmetic Mean ATM At The Money (option) AUM Assets Under Management BEI Break-Even Inflation BF Behavioral Finance B/P Book/Price, book-to-market ratio BRP Bond Risk Premium, term premium B-S Black–Scholes C-P BRP Cochrane–Piazzesi Bond Risk Premium CAPM Capital Asset Pricing Model CAY Consumption wealth ratio CB Central Bank CCW Covered Call Writing CDO Collateralized Debt Obligation CDS Credit Default Swap CF Cash Flow CFNAI Chicago Fed National Activity Index CFO Chief Financial Officer CMD Commodity (futures) CPIyoy Consumer Price Inflation year on year CRB Commodity Research Bureau CRP Credit Risk Premium (over Treasury bond) CRRA Constant Relative Risk Aversion CTA Commodity Trading Advisor DDM Dividend Discount Model DJ CS Dow Jones Credit Suisse DMS Dimson–Marsh–Staunton D/P Dividend/Price (ratio), dividend yield DR Diversification Return E( ) Expected (conditional expectation) EMH Efficient Markets Hypothesis E/P Earnings/Price ratio, earnings yield EPS Earnings Per Share ERP Equity Risk Premium ERPB Equity Risk Premium over Bond (Treasury) ERPC Equity Risk Premium over Cash (Treasury bill) F Forward price or futures price FF Fama–French FI Fixed Income FoF Fund of Funds FX Foreign eXchange G Growth rate GARCH Generalized AutoRegressive Conditional Heteroskedasticity GC General Collateral repo rate (money market interest rate) GDP Gross Domestic Product GM Geometric Mean, also compound annual return GP General Partner GSCI Goldman Sachs Commodity Index H Holding-period return HF Hedge Fund HFR Hedge Fund Research HML High Minus Low, a value measure, also VMG HNWI High Net Worth Individual HPA House Price Appreciation (rate) HY High Yield, speculative-rated debt IG Investment Grade (rated debt) ILLIQ Measure of a stock’s illiquidity: average absolute daily return over a month divided by dollar volume IPO Initial Public Offering IR Information Ratio IRP Inflation Risk Premium ISM Business confidence index ITM In The Money (option) JGB Japanese Government Bond K-W BRP Kim–Wright Bond Risk Premium LIBOR London InterBank Offered Rate, a popular bank deposit rate LP Limited Partner LSV Lakonishok–Shleifer–Vishny LtA Limits to Arbitrage LTCM Long-Term Capital Management MA Moving Average MBS (fixed rate, residential) Mortgage-Backed Securities MIT-CRE MIT Center for Real Estate MOM Equity MOMentum proxy MSCI Morgan Stanley Capital International MU Marginal Utility NBER National Bureau of Economic Research NCREIF National Council of Real Estate Investment Fiduciaries OAS Option-Adjusted (credit) Spread OTM Out of The Money (option) P Price P/B Price/Book (valuation ratio) P/E Price/Earnings (valuation ratio) PE Private Equity PEH Pure Expectations Hypothesis PT Prospect Theory r Excess return R Real (rate) RE Real Estate REITs Real Estate Investment Trusts RWH Random Walk Hypothesis S Spot price, spot rate SBRP Survey-based Bond Risk Premium SDF Stochastic Discount Factor SMB Small Minus Big, size premium proxy SR Sharpe Ratio SWF Sovereign Wealth Fund TED Treasury–Eurodollar (deposit) rate spread in money markets TIPS Treasury Inflation-Protected Securities, real bonds UIP Uncovered Interest Parity (hypothesis) VaR Value at Risk VC Venture Capital VIX A popular measure of the implied volatility of S&P 500 index options VMG Value Minus Growth, equity value premium proxy WDRA Wealth-Dependent Risk Aversion X Cash flow Y Yield YC Yield Curve (steepness), term spread YTM Yield To Maturity YTW Yield To Worst Disclaimer Antti Ilmanen is a Senior Portfolio Manager at Brevan Howard, one of Europe’s largest hedge fund managers.

 

pages: 320 words: 33,385

Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

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asset allocation, backtesting, barriers to entry, Brownian motion, capital asset pricing model, constrained optimization, credit crunch, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, implied volatility, interest rate swap, market friction, market microstructure, p-value, performance metric, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, yield curve

In Section II.5.3.7 we prove that the discrete time version of (I.3.142) is a stationary AR(1) model. I.3.7.3 Stochastic Models for Asset Prices and Returns Time series of asset prices behave quite differently from time series of returns. In efficient markets a time series of prices or log prices will follow a random walk. More generally, even in the presence of market frictions and inefficiencies, prices and log prices of tradable assets are integrated stochastic processes. These are fundamentally different from the associated returns, which are generated by stationary stochastic processes. Figures I.3.28 and I.3.29 illustrate the fact that prices and returns are generated by very different types of stochastic process. Figure I.3.28 shows time series of daily prices (lefthand scale) and log prices (right-hand scale) of the Dow Jones Industrial Average (DJIA) DJIA 12000 9.4 Log DJIA 9.3 11000 9.2 10000 9.1 9000 9 8000 8.9 Sep-01 May-01 Jan-01 Sep-00 May-00 Jan-00 Sep-99 May-99 Jan-99 Sep-98 May-98 8.8 Jan-98 7000 Figure I.3.28 Daily prices and log prices of DJIA index 56 This is not the only possible discretization of a continuous increment.

Probability and Statistics 139 Application of Itô’s lemma with f = ln S shows that a continuous time representation of geometric Brownian motion that is equivalent to the geometric Brownian motion (I.3.143) but is translated into a process for log prices is the arithmetic Brownian motion, d ln St = − 21 2 dt + dWt (I.3.145) We already know what a discretization of (I.3.145) looks like. The change in the log price is the log return, so using the standard discrete time notation Pt for a price at time t we have d ln St → ln Pt Hence the discrete time equivalent of (I.3.145) is ln Pt = + $t $t ∼ NID 0 2 (I.3.146) where = − 21 2 . This is equivalent to a discrete time random walk model for the log prices, i.e. ln Pt = + ln Pt−1 + $t $t ∼ NID 0 2 (I.3.147) To summarize, the assumption of geometric Brownian motion for prices in continuous time is equivalent to the assumption of a random walk for log prices in discrete time. I.3.7.4 Jumps and the Poisson Process A Poisson process, introduced in Section I.3.3.2, is a stochastic process governing the occurrences of events through time.

. • Continuous time stochastic processes are represented as stochastic differential equations (SDEs). The most famous example of an SDE in finance is geometric Brownian motion. This is introduced below, but its application to option pricing is not discussed until Chapter III.3. The first two subsections define what is meant by a stationary or ‘mean-reverting’ stochastic process in discrete and continuous time. We contrast this with a particular type of nonstationary process which is called a ‘random walk’. Then Section I.3.7.3 focuses on some standard discrete and continuous time models for the evolution of financial asset prices and returns. The most basic assumption in both types of models is that the prices of traded assets follow a random walk, and from this it follows that their returns follow a stationary process. I.3.7.1 Stationary and Integrated Processes in Discrete Time This section introduces the time series models that are used to model stationary and integrated processes in discrete time.

 

pages: 374 words: 114,600

The Quants by Scott Patterson

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Albert Einstein, asset allocation, automated trading system, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, NetJets, new economy, offshore financial centre, Paul Lévy, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

It would also give birth to its own destructive forces and pave the way to a series of financial catastrophes, culminating in an earthshaking collapse that erupted in August 2007. Like Thorp’s methodology for pricing warrants, an essential component of the Black-Scholes formula was the assumption that stocks moved in a random walk. Stocks, in other words, are assumed to move in antlike zigzag patterns just like the pollen particles observed by Brown in 1827. In their 1973 paper, Black and Scholes wrote that they assumed that the “stock price follows a random walk in continuous time.” Just as Thorp had already discovered, this allowed investors to determine the relevant probabilities for volatility—how high or low a stock or option would move in a certain time frame. Hence, the theory that had begun with Robert Brown’s scrutiny of plants, then led to Bachelier’s observations about bond prices, finally reached a most pragmatic conclusion—a formula that Wall Street would use to trade billions of dollars’ worth of stock and options.

“It is not easy to get rich in Las Vegas, at Churchill Downs, or at the local Merrill Lynch office,” he wrote. At the time, Samuelson was becoming an éminence grise of the economic community. If he thought the market followed a random walk, that meant everyone had to get on board or have a damn good reason not to. Most agreed, including one of Samuelson’s star students, Robert Merton, one of the co-creators of the Black-Scholes option-pricing formula. Another acolyte was Burton Malkiel, who went on to write A Random Walk Down Wall Street. It was Fama, however, who connected all of the dots and put the efficient-market hypothesis on the map as a central feature of modern portfolio theory. The idea that the market is an efficient, randomly churning price-processing machine has many odd consequences. Fama postulates a vast, swarming world of investors constantly searching for inefficiencies—those hungry piranhas circling in wait of fresh meat.

The future movement of a stock—a variable known to quants as volatility—is random, and therefore quantifiable. And if the warrant is priced in a way that underestimates, or overestimates, its likely volatility, money can be made. Discovering how to price volatility was the key to unlocking the stock warrant treasure trove. Say you own a warrant for IBM. The current value of IBM’s stock is $100. The warrant, which expires in twelve months, will be valuable only if IBM is worth $110 at some point during that twelve-month period. If you can determine how volatile IBM’s stock is—how likely it is that it will hit $110 during that time period—you then know how much the warrant is worth. Thorp discovered that by plugging in the formula for Brownian motion, the random walk model, in addition to an extra variable for whether the stock itself tends to rise more or less than other stocks, he could know better than almost anyone else in the market what the IBM warrant was worth.

 

Analysis of Financial Time Series by Ruey S. Tsay

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Asian financial crisis, asset allocation, Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, correlation coefficient, data acquisition, discrete time, frictionless, frictionless market, implied volatility, index arbitrage, Long Term Capital Management, market microstructure, martingale, p-value, pattern recognition, random walk, risk tolerance, short selling, statistical model, stochastic process, stochastic volatility, telemarketer, transaction costs, value at risk, volatility smile, Wiener process, yield curve

In some studies, interest rates, foreign exchange rates, or the price series of an asset are of interest. These series tend to be nonstationary. For a price series, the nonstationarity is mainly due to the fact that there is no fixed level for the price. In the time series literature, such a nonstationary series is called unit-root nonstationary time series. The best known example of unit-root nonstationary time series is the random-walk model. 2.7.1 Random Walk A time series { pt } is a random walk if it satisfies pt = pt−1 + at , (2.32) where p0 is a real number denoting the starting value of the process and {at } is a white noise series. If pt is the log price of a particular stock at date t, then p0 could be the log price of the stock at its initial public offering (i.e., the logged IPO price). If at has a symmetric distribution around zero, then conditional on pt−1 , pt has a 50–50 chance to go up or down, implying that pt would go up or down at random.

If at has a symmetric distribution around zero, then conditional on pt−1 , pt has a 50–50 chance to go up or down, implying that pt would go up or down at random. If we treat the random-walk model as a special AR(1) model, then the coefficient of pt−1 is unity, which does not satisfy the weak stationarity condition of an AR(1) model. A random-walk series is, therefore, not weakly stationary, and we call it a unit-root nonstationary time series. The random-walk model has been widely considered as a statistical model for the movement of logged stock prices. Under such a model, the stock price is not predictable or mean reverting. To see this, the 1-step ahead forecast of model (2.32) at the forecast origin h is p̂h (1) = E( ph+1 | ph , ph−1 , . . .) = ph , which is the log price of the stock at the forecast origin. Such a forecast has no practical value. The 2-step ahead forecast is UNIT- ROOT NONSTATIONARITY 57 p̂h (2) = E( ph+2 | ph , ph−1 , . . .) = E( ph+1 + ah+2 | ph , ph−1 , . . .) = E( ph+1 | ph , ph−1 , . . .) = p̂h (1) = ph , which again is the log price at the forecast origin.

Theoretically, this means that pt can assume any real value for a sufficiently large t. For the log price pt of an individual stock, this is plausible. Yet for market indexes, negative log price is very rare if it happens at all. In this sense, the adequacy of a random-walk model for market indexes is questionable. Third, from the representation, ψi = 1 for all i. Thus, the impact of any past shock at−i on pt does not decay over time. Consequently, the series has a strong memory as it remembers all of the past shocks. In economics, the shocks are said to have a permanent effect on the series. 2.7.2 Random Walk with a Drift As shown by empirical examples considered so far, the log return series of a market index tends to have a small and positive mean. This implies that the model for the log price is pt = µ + pt−1 + at , (2.33) where µ = E( pt − pt−1 ) and {at } is a white noise series.

 

Stocks for the Long Run, 4th Edition: The Definitive Guide to Financial Market Returns & Long Term Investment Strategies by Jeremy J. Siegel

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asset allocation, backtesting, Black-Scholes formula, Bretton Woods, buy low sell high, California gold rush, capital asset pricing model, cognitive dissonance, compound rate of return, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, dividend-yielding stocks, equity premium, Eugene Fama: efficient market hypothesis, fixed income, German hyperinflation, implied volatility, index arbitrage, index fund, Isaac Newton, joint-stock company, Long Term Capital Management, loss aversion, market bubble, mental accounting, new economy, oil shock, passive investing, prediction markets, price anchoring, price stability, purchasing power parity, random walk, Richard Thaler, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, South Sea Bubble, technology bubble, The Great Moderation, The Wisdom of Crowds, transaction costs, tulip mania, Vanguard fund

In 1965, Professor Paul Samuelson of MIT showed that the randomness in security prices did not contradict the laws of supply and demand.4 In fact, such randomness was a result of a free and efficient market in which investors had already incorporated all the known factors influencing the price of the stock. This is the crux of the efficient market hypothesis. If the market is efficient, prices will change only when new, unanticipated information is released to the market. Since unanticipated information is as likely to be good as it is to be bad, the resulting movement in stock prices is random. Price charts will look like a random walk since the probability that stocks go up or down is completely random and cannot be predicted.5 SIMULATIONS OF RANDOM STOCK PRICES If stock prices are indeed random, their movements should not be distinguishable from counterfeits generated randomly by a computer.

TABLE 2–2 Portfolio Allocation: Percentage of Portfolio Recommended in Stocks Based on All Historical Data Risk Tolerance 1 Year Holding Period 5 Years 10 Years 30 Years Ultraconservative (Minimum Risk) 9.0% 22.0% 39.3% 71.4% Conservative 25.0% 38.7% 59.6% 89.5% Moderate 50.0% 61.6% 88.0% 116.2% Aggressive Risk Taker 75.0% 78.5% 110.1% 139.1% CHAPTER 2 Risk, Return, and Portfolio Allocation 35 because modern portfolio theory was established when the academic profession believed in the random walk theory of security prices. As noted earlier, under a random walk, the relative risk of various securities does not change for different holding periods, so portfolio allocations do not depend on how long one holds the asset. The holding period becomes a crucial issue in portfolio theory when the data reveal the mean reversion of stock returns.8 INFLATION-INDEXED BONDS Until the last decade, there was no U.S. government bond whose return was guaranteed against changes in the price level. But in January 1997, the U.S. Treasury issued the first government-guaranteed inflation-indexed bond. The coupons and principal repayment of this inflation-protected bond are automatically increased when the price level rises, so bondholders suffer no loss of purchasing power when they receive the coupons or final principal.

With the remaining seven charts, the brokers showed 4 Paul Samuelson, “Proof That Properly Anticipated Prices Fluctuate Randomly,” Industrial Management Review, vol. 6 (1965), p. 49. 5 More generally, the sum of the product of each possible price change times the probability of its occurrence is zero. This is called a martingale, of which a random walk (50 percent probability up, 50 percent probability down) is a special case. CHAPTER 17 Technical Analysis and Investing with the Trend FIGURE 293 17–1 Real and Simulated Stock Indexes Figure A Figure B Figure C Figure D Figure E Figure F Figure G Figure H 294 PART 4 Stock Fluctuations in the Short Run no ability to distinguish actual from counterfeit data. The true historical prices are represented by charts b, d, e, and h, while the computer-generated data are charts a, c, f, and g.6 TRENDING MARKETS AND PRICE REVERSALS Despite the fact that many “trends” are in fact the result of the totally random movement of stock prices, many traders will not invest against a trend that they believe they have identified.

 

Monte Carlo Simulation and Finance by Don L. McLeish

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Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, discrete time, distributed generation, finite state, frictionless, frictionless market, implied volatility, incomplete markets, invention of the printing press, martingale, p-value, random walk, Sharpe ratio, short selling, stochastic process, stochastic volatility, the market place, transaction costs, value at risk, Wiener process, zero-coupon bond

Equivalently, we generate X = V1 /V2 where Vi ∼ U [−1, 1] conditional on V12 + V22 · 1 to produce a standard Cauchy variate X. Example: Stable random walk. A stable random walk may be used to model a stock price but the closest analogy to the Black Scholes model would be a logstable process St under which the distribution of ln(St ) has a symmetric stable distribution. Unfortunately, this specification renders impotent many of our tools of analysis, since except in 158 CHAPTER 3. BASIC MONTE CARLO METHODS the case α = 2 or the case β = −1, such a stock price process St has no finite moments at all. Nevertheless, we may attempt to fit stable laws to the distribution of ln(St ) for a variety of stocks and except in the extreme tails, symmetric stable laws with index α ' 1.7 often provide a reasonably good fit. To see what such a returns process looks like, we generate a random walk with 10,000 time steps where each increment is distributed as independent stable random variables having parameter 1.7.

It has been an important part of the literature in Physics, Probability and Finance at least since the papers of Bachelier and Einstein, about 100 years ago. A Brownian motion process also has some interesting and remarkable theoretical properties; it is continuous with probability one but the probability that the process has finite 10 68 CHAPTER 2. SOME BASIC THEORY OF FINANCE Random Walk 4 3 2 Sn 1 0 -1 -2 -3 0 2 4 6 8 10 n 12 14 16 18 Figure 2.7: A sample path of a Random Walk variation in any interval is 0. With probability one it is nowhere differentiable. Of course one might ask how a process with such apparently bizarre properties can be used to approximate real-world phenomena, where we expect functions to be built either from continuous and differentiable segments or jumps in the process. The answer is that a very wide class of functions constructed from those that are quite well-behaved (e.g. step functions) and that have independent increments converge as the scale on which they move is refined either to a Brownian motion process or to a process defined as an integral with respect to a Brownian motion process and so this is a useful approximation to a broad range of continuous time processes.

The answer is that a very wide class of functions constructed from those that are quite well-behaved (e.g. step functions) and that have independent increments converge as the scale on which they move is refined either to a Brownian motion process or to a process defined as an integral with respect to a Brownian motion process and so this is a useful approximation to a broad range of continuous time processes. For example, consider a random walk process Pn Sn = i=1 Xi where the random variables Xi are independent identically distributed with expected value E(Xi ) = 0 and var(Xi ) = 1. Suppose we plot the graph of this random walk (n, Sn ) as below. Notice that we have linearly interpolated the graph so that the function is defined for all n, whether integer or not. [FIGURE 2.7 ABOUT HERE] 20 MODELS IN CONTINUOUS TIME 69 Now if we increase the sample size and decrease the scale appropriately on both axes, the result is, in the limit, a Brownian motion process.

 

pages: 119 words: 10,356

Topics in Market Microstructure by Ilija I. Zovko

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Brownian motion, continuous double auction, correlation coefficient, financial intermediation, Gini coefficient, market design, market friction, market microstructure, Murray Gell-Mann, p-value, quantitative trading / quantitative finance, random walk, stochastic process, stochastic volatility, transaction costs

One of the predictions of the model, that to our knowledge has not been hypothesized elsewhere in the literature, is that the order size σ is an important determinant of the spread. Another prediction of the model concerns the price diffusion rate, which drives the volatility of prices and is the primary determinant of financial risk. If we assume that prices make a random walk, then the diffusion rate measures the size and frequency of its increments. The variance V of a random walk grows as V (t) = Dt, where D is the diffusion rate and t is time. This is the main free parameter in the Bachelier model of prices (Bachelier, 1964). While its value is essential for risk estimation and derivative pricing there is very little fundamental understanding of what actually determines it. In standard models it is often assumed to depend on “information arrival” (Clark, 1973), which has the disadvantage that it is impossible to measure directly.

We have done several studies, which will be reported in a future work, testing the importance of this effect. These show that while daily variations in W do give additional predictability for the spread, other aspects of the model are substantially responsible for these results. Measuring the price diffusion rate The measurement of the price diffusion rate requires some discussion. We measure the intraday price diffusion by computing the mid-point price variance V (τ ) = Var{m(t + τ ) − m(t)}, for different time scales τ . The averaging over t includes all events that change the mid-point price. The plot of V (τ ) against τ is called a diffusion curve and for an IID random walk is a straight line with slope D, the diffusion coefficient. 46 CHAPTER 3. THE PREDICTIVE POWER OF ZERO INTELLIGENCE IN FINANCIAL MARKETS 0.00008 0.00006 0.00004 Vodafone, August 4 1998 D=1.498e!06, R^2=0.998 0.00000 0.00002 <(m(t + τ) − m(t))2> 0.00010 0.00012 In our case, the computation of D is as follows: For each day we compute the diffusion curve.

One must bear in mind that the price diffusion rate from day to day has substantial correlations, as illustrated in Fig. 3.6. 0 20 40 60 80 τ Figure 3.5: Illustration of the procedure for measuring the price diffusion rate for Vodafone (VOD) on August 4th, 1998. On the x axis we plot the time τ in units of ticks, and on the y axis the variance of mid-price diffusion V (τ ). According to the hypothesis that mid-price diffusion is an uncorrelated Gaussian random walk, the plot should obey V (τ ) = Dτ . To cope with the fact that points with larger values of τ have fewer independent intervals and are less statistically significant, we use a weighted regression to compute the slope D. 47 !6.5 !7.5 !7.0 log(D) !6.0 !5.5 CHAPTER 3. THE PREDICTIVE POWER OF ZERO INTELLIGENCE IN FINANCIAL MARKETS 0 100 200 300 400 ACF 0.0 0.4 0.8 days 0 20 40 60 80 100 Lag Figure 3.6: Time series (top) and autocorrelation function (bottom) for daily price diffusion rate Dt for Vodafone. Because of longmemory effects and the short length of the series, the long-lag coefficients are poorly determined; the figure is just to demonstrate that the correlations are quite large. 3.5.6 Estimating the errors for the regressions The error bars presented in the text are based on a bootstrapping method.

 

pages: 354 words: 26,550

High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems by Irene Aldridge

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algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business process, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, diversification, equity premium, fault tolerance, financial intermediation, fixed income, high net worth, implied volatility, index arbitrage, interest rate swap, inventory management, law of one price, Long Term Capital Management, Louis Bachelier, margin call, market friction, market microstructure, martingale, New Journalism, p-value, paper trading, performance metric, profit motive, purchasing power parity, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, Small Order Execution System, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic trading, trade route, transaction costs, value at risk, yield curve

As Table 7.4 shows, the runs test rejects randomness of price changes at 1-minute frequencies, except for prices on S&P 500 Depository Receipts (SPY). The results imply strong market inefficiency in 1-minute data for the securities shown. Market inefficiency measured by runs test decreases or disappears entirely at a frequency lower than 10 minutes. Tests of Random Walks Other, more advanced tests for market efficiency have been developed over the years. These tests help traders evaluate the state of the markets and reallocate trading capital to the markets with the most inefficiencies—that is, the most opportunities for reaping profits. When price changes are random, they are said to follow a “random walk.” Formally, a random walk process is specified as follows: ln Pt = ln Pt−1 + εt (7.2) where ln Pt is the logarithm of the price of the financial security of interest at time t, ln Pt-1 is the logarithm of the price of the security one time TABLE 7.4 Non-Parametric Runs Test Applied to Data on Various Securities and Frequencies Recorded on June 8, 2009.

From equation (7.2), log price changes ln Pt are obtained as follows: ln Pt = ln Pt − ln Pt−1 = εt At any given time, the change in log price is equally likely to be positive and negative. The logarithmic price specification ensures that the model does not allow prices to become negative (logarithm of a negative number does not exist). The random walk process can drift, and be specified as shown in equation (7.3): ln Pt = µ + ln Pt−1 + εt (7.3) In this case, the average change in prices equals the drift rather than 0, since ln Pt = ln Pt − ln Pt−1 = µ + εt . The drift can be due to a variety of factors; persistent inflation, for example, would uniformly lower the value of the U.S. dollar, inflicting a small positive drift on prices of all U.S. equities. At very high frequencies, however, drifts are seldom noticeable. Lo and MacKinlay (1988) developed a popular test for whether or not a given price follows a random walk.

Harris, 1988. “Estimating the Components of the Bid-Ask Spread.” Journal of Financial Economics 21, 123–142. Glosten, Lawrence and P. Milgrom, 1985. “Bid, Ask, and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders.” Journal of Financial Economics 13, 71–100. Goettler, R., C. Parlour and U. Rajan, 2005. “Equilibrium in a Dynamic Limit Order Market.” Journal of Finance 60, 2149–2192. Goettler, R., C. Parlour and U. Rajan, 2007. “Microstructure Effects and Asset Pricing.” Working paper, University of California—Berkeley. References 313 Goodhart, Charles A.E., 1988. “The Foreign Exchange Market: A Random Walk with a Dragging Anchor.” Economica 55, 437–460. Goodhart, Charles A.E. and Maureen O’Hara, 1997. “High Frequency Data in Financial Markets: Issues and Applications.” Journal of Empirical Finance 4, 73– 114.

 

pages: 389 words: 98,487

The Undercover Economist: Exposing Why the Rich Are Rich, the Poor Are Poor, and Why You Can Never Buy a Decent Used Car by Tim Harford

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Albert Einstein, barriers to entry, Berlin Wall, collective bargaining, congestion charging, Corn Laws, David Ricardo: comparative advantage, decarbonisation, Deng Xiaoping, Fall of the Berlin Wall, George Akerlof, invention of movable type, John Nash: game theory, John von Neumann, market design, Martin Wolf, moral hazard, new economy, price discrimination, Productivity paradox, race to the bottom, random walk, rent-seeking, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, sealed-bid auction, second-price auction, second-price sealed-bid, Shenzhen was a fishing village, special economic zone, spectrum auction, The Market for Lemons, Thomas Malthus, trade liberalization, Vickrey auction

In fact, rational investors should be able to second-guess any predictable movements in the stock market or in the price of any particular share—if it’s predictable then, given the money at stake, they will predict it. But that means that if investors really are rational, there won’t be any predictable share movements at all. All the predictability should be sucked out of the stock market very quickly because all trends will be anticipated. The only thing that is left is unpredictable news. As a result of the fact that only random news moves share prices, those prices, and the indices measuring the stock market as a whole, should fluctuate completely at random. Math- • 138 • R A T I O N A L I N S A N I T Y ematicians call the behavior “a random walk”—equally likely on any day to rise as to fall. More correctly, the stock market should exhibit a “random walk with a trend,” meaning that it should on average edge up as the months go past, so that it is competitive compared with other potential investments such as money in a savings account, or property.

But if enough experts knew that, it wouldn’t be the shortest any more. The truth is that busy, smart, agile, and experienced shoppers are a bit better at calling the fastest lines and can probably average a quicker time than the rest of us. But not by much. Value and price— beyond the random walk Assuming that what is true of supermarket lines is also true of stock-market prices, economists should be able to throw some light on the market, but not very much. Many economists do work for investment funds. They are as wrong nearly as often as they are right, but not quite. Our modified random walk theory tells us that this is what we should expect. So, what do these economists do to provide investment funds with such tiny edges over the market? The starting point is to view stock shares for what they are: a claim on the future profits of a company.

The answer would be useful, not least because Amazon’s roller-coaster performance is common. So can the Undercover Economist say anything about why share prices acted the way they did, and how they might behave in the future? A random walk Economists face a serious problem in trying to say anything sensible about stock prices. Economists work by studying rational behavior, but the more rational the behavior of stock-market investors, the more erratic the behavior of the stock market becomes. Here’s why. Rational people would buy shares today if it was obvious that they would go up tomorrow, and sell them if it was obvious that they would fall. But this means that any forecast that shares will obviously rise tomorrow will be wrong: shares will rise today instead because people will buy them, and keep buying them until they are no longer so cheap that they will obviously rise tomorrow.

 

The Smartest Investment Book You'll Ever Read: The Simple, Stress-Free Way to Reach Your Investment Goals by Daniel R. Solin

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asset allocation, corporate governance, diversification, diversified portfolio, index fund, market fundamentalism, passive investing, prediction markets, random walk, risk tolerance, risk-adjusted returns, risk/return, transaction costs, Vanguard fund

While a number of books have been written about the virtues of being a Smart Investor, few have achieved commercial 90 Your Broker or Advisor Is Keeping You from Being a Smart Investor success. One exception is A Random Walk Down Wall Street, a superb book by Bunon Malkiel, now in its eighth edition. Malkiel, a professor of econom ics at Princeton University, was one of the first to show that the history of the price of a stock cannot be used to predict how it will move in the future, and therefore that stock price movement is, in the language of economists. "random." In other words, he completely debunked the belief that anyone can consistently predict [he future prices of stocks (which is the core belief of Hyperactive Investors!). Most of the books and anicles written on the merits of being a Smarr Investor are, unfortunately, dense and difficult to understand-thus seemingly validating the myth that being a Smart Investor is somehow elitist, complex and beyond the ability of the ordinary investor.

See "Will Active Mutual Funds Continue [ 0 Underperform the Market in the Future?" by John Bogle. in Scott Simon's book Inda Mutual Funds: Profiting from an In mtmmt Rrvolution; see also the article by Edward S. O'Neal, discussed in Chapter 13. and a study by Dalbar, Inc .• a well~ respected research firm. Reported at http://www.dalbarinc.com/ con ten tIshowpage.asp ?page=200 1062 100. Burton Malkiel summarizes these studies in A Random Walk Down Wall Strut, p. 187. In Mark Hebner's book, Index Funds: Tht i2-Sup Program for Actiw InvtstorJ (pp. 47-53), he sets forth the studies showing the lack of consistency of mutual fund performance and the daunting odds of picking an actively managed fund that will outperform its benchmark index. One particularly compelling study referenced by Hebner indicated that, for the 1O~year period ending October 2004, oo1y 2.4% of the 1446 funds that had as a goal beating the S&P 500 Index succeeded in doing so.

The reprehensible conduct of hyperactive funds touting the "sizzle" of their past performance was recently exposed by the outstanding journalist Jonathan Clements of the Wall Street Journal in an online column entitled "Those PerformanceTouting Fund Ads Are Back-And That Could Mean Trouble." It is summarized at: http://socialize.morningstar.com/New Socialize/asp/FullConv.asp?forumId=F 1000000 15&lastConv Seq=41356 . Clements is the rare exception to those financial journalists who routinely peddle "financial pornography." Too Good 10 Be True? 153 Here is what Burton Malkid has to say about charting (wh ich he likens to "alchemy") in his sem inal book, A Random Walk Down Wall Strut, (p. 165): "There has been a rematkable unjformity in the conclusions of studies done on all forms of technical ana1ysis. Not one has consistently outperformed the placebo of a buy-and-hold strategy. Technical methods cannot be used to make useful investment strategies ... Ma1kiel believes that chartistS simply provide cover fo r hyperactive brokers to encourage more trading-generating more fees-by their unsuspecting clients.

 

pages: 695 words: 194,693

Money Changes Everything: How Finance Made Civilization Possible by William N. Goetzmann

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money: store of value / unit of account / medium of exchange, moral hazard, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, transatlantic slave trade, tulip mania, wage slave

These solutions to the option pricing problem linked finance and physics together forever afterward. In fact, it turned out that the Black-Scholes option pricing model was the same as a problem in thermodynamics—a “heat” equation, in which molecules—not stock prices—were drifting randomly. The foundation of the science of thermodynamics is entropy—the tendency toward disorder. Time only goes in one direction, and with it, the universe tends toward less organization, not more. The option pricing model is based on the principle of forecasting the range of future outcomes of the stock price by assuming it will follow a random walk that conforms to Regnault’s square-root of time insight. However, the Black-Scholes formula gives a solution to the option price today by mathematically rolling time backward. It reverses entropy. In this, it echoes the most basic trait of finance—it uses mathematics to transcend time.

For example, we saw in Chapter 15 that Jules Regnault proposed and tested a stochastic process that varied randomly, which resulted in a rule about risk increasing with the square root of time. Likewise, Louis Bachelier more formally developed a random-walk stochastic process. Paul Lévy formalized these prior random walk models into a very general family of stochastic processes referred to as Lévy processes. Brownian motion was just one process in the family of Lévy processes—and perhaps the best behaved of them. Other stochastic processes have such things as discontinuous jumps and unusually large shocks (which might, for example, explain the crash of 1987, when the US stock market lost 22.6% of its value in a single day). In the 1960s, Benoit Mandelbrot began to investigate whether Lévy processes described economic time series like cotton prices and stock prices. He found that the ones that generated jumps and extreme events better described financial markets.

It nearly, but not exactly, solved the problem of how to value an option—and thanks to Lefèvre, that means he came close to being able to value a complex portfolio of options, hedges, and speculations. The option pricing problem would not be solved precisely until much later in the twentieth century. The scholars who did so, Myron Scholes, Fischer Black, and Robert Merton, recognized Bachelier’s contribution. Scholes and Merton accepted the Nobel Prize in Economic Sciences in 1997 for their work on this important financial problem. Fischer Black had passed away before he could share in the award. MODELS AND MODERN MARKETS Scholes and Merton were professors of financial economics at the Massachusetts Institute of Technology in 1970, where they met the economist Fischer Black. Evidently none knew of Bachelier, and thus they had to retrace the mathematical logic of fair prices and random walks when they began work on the problem of option pricing in the late 1960s. Like Bachelier, they relied on a model of variation in prices—Brownian motion—although unlike Bachelier, they chose one that did not allow prices to become negative—a limitation of Bachelier’s work.

 

Mathematical Finance: Core Theory, Problems and Statistical Algorithms by Nikolai Dokuchaev

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Black-Scholes formula, Brownian motion, buy low sell high, discrete time, fixed income, implied volatility, incomplete markets, martingale, random walk, short selling, stochastic process, stochastic volatility, transaction costs, volatility smile, Wiener process, zero-coupon bond

Proposition 2.24 Under the assumptions and notations of Definition 2.23, for all measurable deterministic functions F such that the corresponding random variables are integrable. Problem 2.25 Prove that a discrete time random walk is a Markov process. Vector processes Let ξ(t)=(ξ1(t),…, ξn(t)) be a vector process such that all its components are random processes. Then ξ is said to be an n-dimensional (vector) random process. All definitions given above can be extended for these vector processes. Sometimes, we can convert a process that is not a Markov process to a Markov process of higher dimension. Example 2.26 Let ηt be a random walk, t=0, 1, 2,…, and let Then ψt is not a Markov process, but the vector process (ηt,ψt) is a Markov process. 2.5 Problems Problem 2.27 Let ζ be a random variable, and let 0≤a<b≤1. Let a continuous time random process ξ(t) be such that Find the filtration when a=1/4, b=2/3

For simplicity, we shall use below stationary processes and white noise in the sense of Definitions 8.1–8.3, but all results are valid for wide-sense stationary processes and for the white noise defined as a wide-sense stationary process with no correlation and zero mean. 8.2 Simplest regression and autoregression The first-order regression model can be described by a one-dimensional equation © 2007 Nikolai Dokuchaev Review of Statistical Estimation 141 yt=β0+βxt+εt, t=1, 2,…. (8.1) Here yt and xt represent observable discrete time processes; yt is called the regressand, or dependent variable, xt is called the regressor, or explanatory variable, εt is an unobserved and are parameters that are usually unknown. error term, The standard assumption is that (8.2) Special case: autoregression (AR) Let us describe the first-order autoregressive process, AR(1), as yt=β0+βyt−1+εt, (8.3) where εt is a white noise process, are parameters. The AR(1) model is a special case of the simplest regression (8.1), where xt= yt−1. It can be shown that εt is uncorrelated with {ys}s<t. If −1<β<1, then there exists a stationary process such that as t→+∞. If β=1 and β0=0 in (8.3), then yt is a random walk (see Definition 2.6). A random walk is non-stationary and it does not converge to any stationary process. In fact, if |β|≥1, then Var yt→+∞ as t→+∞. This implies that many standard tools for forecasting and testing coefficients etc. are invalid. To avoid this, we can try to study changes in yt instead: for example, the differences zt=yt−yt−1 may converge to a stationary process. If not, the differences zt−zt−1 (i.e., the second differences yt−2yt−1+yt−2) may converge to a stationary process. 8.3 Least squares (LS) estimation Consider again the basic regression model (8.1)–(8.2).

Problem 8.40 Let yk=R(tk), where R(t)=ln S(tk), and where S(tk) are the daily prices for some stock, k=1, …, N, for some large enough N. (Find some prices on the internet or in newspapers.) (i) Using the LS estimator, forecast yk for N+2, N+10, N+100 days. Use this result to forecast the corresponding R(t). (ii) Estimate intervals that contain these increments of log of prices (and/or prices) with probability 0.7. © 2007 Nikolai Dokuchaev 9 Estimation of models for stock prices In this chapter, methods of statistical analysis are applied to historical stock prices. We show how to estimate the appreciation rate and the volatility for some continuous time stock price models. Some generic methods of forecast of evolution of prices and parameters are also given. 9.1 Review of the continuous time model Let us consider again the stock price equation dS(t)=a(t)S(t)dt+σ(t)S(t)dw(t), (9.1) where a(t) is the appreciation rate, σ(t) is the volatility, w(t) is a Wiener process, w(t)~N(0, t).

 

pages: 240 words: 60,660

Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life by Emanuel Derman

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Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, Henri Poincaré, Isaac Newton, law of one price, Mikhail Gorbachev, quantitative trading / quantitative finance, random walk, Richard Feynman, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve

(a) A single stock path simulated via a random walk. (b) Four typical simulated stock paths. (c) An actual four-year path for the level of the S&P 500 index. The EMM Isn’t Wild Enough Figure 5.4 compares the paths of stock prices generated from the EMM model with the level of the S&P 500 from late 2006 to late 2010. The apparently naïve either-up-or-down model does superficially mimic the riskiness of a stock’s price. But only more or less. The mimicry fails because the stock paths in the model are just too smooth when compared with the observed movements of actual stock prices. When examined closely, the stock price trajectory in Figure 5.4c is jerkier than those in Figure 5.4b. Actual stock prices are more wildly random than those of the model, as becomes very obvious during stock market crashes, when stock prices cascade downward in giant leaps, and volatility spikes beyond belief.

A MODEL FOR RISK Risk = The Uncertain Return on an Investment If you buy a stock for $100, you can imagine its price going up to $110 for a return of 10%, or down to $90 for a return of -10%. The risk of the stock is reflected in the range of possible returns you can envisage. A Random Walk for Stock Prices A company is a complex organism. How can one model the range of possible returns that a share of its stock might accrue? The Efficient Market Model’s answer to this question is radical: ignore complexity! It hypothesizes that the market, anthropomorphically speaking, has used all available knowledge about the company to determine the stock price. Therefore the next change in the stock price will arise only from new information, which will arrive randomly and therefore be equally likely to be good or bad as far as the company’s future returns are concerned.

The second assumption is pure model. The EMM’s picture of price movements goes by several names: a random walk, diffusion, and Brownian motion. One of its origins is in the description of the drift of pollen particles through a liquid as they collide with its molecules. Einstein used the diffusion model to successfully predict the square root of the average distance the pollen particles move through the liquid as a function of temperature and time, thus lending credence to the existence of hypothetical molecules and atoms too small to be seen. For particles of pollen, the model is also a theory, and pretty close to a true one. For stock prices, however, it’s only a model. It’s how we choose to imagine the way changes in stock prices occur, not what actually happens. It is naïve to imagine that the risk of every stock in the market can be condensed into just one quantity, its volatility σ.

 

Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernie Chan

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algorithmic trading, asset allocation, automated trading system, backtesting, Black Swan, Brownian motion, business continuity plan, compound rate of return, Elliott wave, endowment effect, fixed income, general-purpose programming language, index fund, Long Term Capital Management, loss aversion, p-value, paper trading, price discovery process, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Ray Kurzweil, Renaissance Technologies, risk-adjusted returns, Sharpe ratio, short selling, statistical arbitrage, statistical model, systematic trading, transaction costs

T 115 P1: JYS c07 JWBK321-Chan September 24, 2008 14:4 116 Printer: Yet to come QUANTITATIVE TRADING MEAN-REVERTING VERSUS MOMENTUM STRATEGIES Trading strategies can be profitable only if securities prices are either mean-reverting or trending. Otherwise, they are randomwalking, and trading will be futile. If you believe that prices are mean reverting and that they are currently low relative to some reference price, you should buy now and plan to sell higher later. However, if you believe the prices are trending and that they are currently low, you should (short) sell now and plan to buy at an even lower price later. The opposite is true if you believe prices are high. Academic research has indicated that stock prices are on average very close to random walking. However, this does not mean that under certain special conditions, they cannot exhibit some degree of mean reversion or trending behavior. Furthermore, at any given time, stock prices can be both mean reverting and trending depending on the time horizon you are interested in.

Unfortunately, most stock price series are not stationary—they exhibit a geometric random walk that gets them farther and farther away from their starting (i.e., initial public offering) values. However, you can often find P1: JYS c07 JWBK321-Chan September 24, 2008 14:4 Printer: Yet to come 127 Special Topics in Quantitative Trading a pair of stocks such that if you long one and short the other, the market value of the pair is stationary. If this is the case, then the two individual time series are said to be cointegrated. They are so described because a linear combination of them is integrated of order zero. Typically, two stocks that form a cointegrating pair are from the same industry group. Traders have long been familiar with this so-called pair-trading strategy. They buy the pair portfolio when the spread of the stock prices formed by these pairs is low, and sell/short the pair when the spread is high—in other words, a classic mean-reverting strategy.

Example 6.1: An Interesting Puzzle (or Why Risk Is Bad for You)* Here is a little puzzle that may stymie many a professional trader. Suppose a certain stock exhibits a true (geometric) random walk, by which I mean there is a 50–50 chance that the stock is going up 1 percent or down 1 percent every minute. If you buy this stock, are you most likely—in the long run and ignoring financing costs—to make money, lose money, or be flat? Most traders will blurt out the answer “Flat!,” and that is wrong. The correct answer is that you will lose money, at the rate of 0.005 percent (or 0.5 basis point) every minute! This is because for a geometric random walk, the average compounded rate of return is not the short-term (or one-period) return m (0 here), but is g = m − s 2 /2. This follows from the general formula for compounded growth g(f ) given in the appendix to this chapter, with the leverage f set to 1 and risk-free rate r set to 0.

 

pages: 236 words: 77,735

Rigged Money: Beating Wall Street at Its Own Game by Lee Munson

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affirmative action, asset allocation, backtesting, barriers to entry, Bernie Madoff, Bretton Woods, buy low sell high, California gold rush, call centre, Credit Default Swap, diversification, diversified portfolio, estate planning, fiat currency, financial innovation, fixed income, Flash crash, follow your passion, German hyperinflation, High speed trading, housing crisis, index fund, joint-stock company, moral hazard, passive investing, Ponzi scheme, price discovery process, random walk, risk tolerance, risk-adjusted returns, risk/return, too big to fail, trade route, Vanguard fund, walking around money

See national best bid and offer New York Stock Exchange Regulation (NYSE Regulation) no-transaction-fee funds (NTFs) noise non-correlated assets A Non-Random Walk Down Wall Street NTFs. See no-transaction-fee funds NYSE Regulation. See New York Stock Exchange Regulation O OER. See operating expense ratio OneSourse Select List operating cost operating expense ratio (OER) opinion, strong OPRA. See Options Price Reporting Authority Options Price Reporting Authority (OPRA) options strategies trading OTC. See Over-the-Counter Over-the-Counter (OTC) P Panic of 1907 passive investing Pay-Up Amendment. See Section 28(e) penny stocks pension pension manager Philip Morris pie charts bar charts versus Pit Bull play-it-safe investment portfolio, moderate risk premium price compression price discovery The Price Is Right price, best prime broker prognostication reports Q QQQ.

Usually used by advisers to impress clients with the broad diversification of terms a single asset class can be split up into. This aids in selling more mutual funds with different asset classes. For example, U.S. stocks can be split up into large-cap growth, large-cap value, large-cap high-dividend yield, and large-cap sector-that-is-currently-going-up which you don’t own because your sector is going down. The pitch continues that the classes do not move in tandem, but in a random walk unrelated to each other. A random walk is an overused term. Does anyone really think global markets are just walking around aimlessly with no rhyme or reason? Several people have been awarded the Nobel Prize in Economics for suggesting this. Perhaps the winners are chosen randomly as well. Of course, all of these asset classes are expected to go up over time. You wouldn’t buy something if it wasn’t designed to make a profit, right?

This is one reason many exchanges have circuit breakers to halt trading in a particular security or the whole exchange if prices go beyond a corridor or 5 to 10 percent in a short period of time. If prices move too fast, the risk increases that liquidity will disappear right at the moment it is needed the most. So, what changes the price? If you have more people who are willing to sell at the current market price than people who are willing to buy at a set limit, the price goes down. Think of it this way. Say you want to sell your house today for $100 (yes, you live in Detroit). If only one person walks by and offers $50, that’s the price you can sell for. If two people will pay $100, the price might rise until one backs down. In each case, the transaction price is based on what the other person is willing to pay; either a limit they set, or the market price you accept. When the market declines quickly, as we saw in the Flash Crash of May 6, 2010, many orders were placed to sell at the market price.

 

pages: 335 words: 94,657

The Bogleheads' Guide to Investing by Taylor Larimore, Michael Leboeuf, Mel Lindauer

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asset allocation, buy low sell high, corporate governance, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, endowment effect, estate planning, financial independence, financial innovation, high net worth, index fund, late fees, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, market bubble, mental accounting, passive investing, random walk, risk tolerance, risk/return, Sharpe ratio, statistical model, transaction costs, Vanguard fund, yield curve

The study again found "no evidence of ability to predict successfully the direction of the stock market. " In the 1960s, a University of Chicago Professor, Eugene E Fama, performed a detailed analysis of the ever-increasing volume of stock price data. He concluded that stock prices are very efficient and that it's extremely difficult to pick winning stocks-especially after factoring in the costs of transaction fees. In 1973, Princeton professor Burton Malkiel, after extensive research, came to the same conclusion as Bachelier, Cowles, and Fama. Professor Malkiel published a book with the catchy title Random Walk Down Wall Street. The book is now an investment classic, and updated revisions are published on a regular basis. We think it deserves a place on the bookshelf of every serious investor. Professor Malkiel describes a random walk this way: "One in which future steps or directions cannot be predicted on the basis of past action.

When the term is applicable to the stock market, it means that short-run changes in stock prices cannot be predicted. " Another, more vivid, description of a random walk: A drunk standing in the middle of the road whose future movements can only be guessed. " Few academics argue that the stock market is totally efficient. Nevertheless, they agree that stocks and bonds are so efficiently priced that the majority of investors, including full-time professional fund managers, will not outperform an unmanaged index fund after transaction costs. Jack Bogle wrote: I know of no serious academic, professional money manager, trained security analyst, or intelligent individual investor who would disagree with the thrust of EMT The stock market itself is a demanding taskmaster. It sets a high hurdle that few investors can leap. Efficient markets and random walk are obscenities on Wall Street, where investors are constantly told that Wall Street's superior knowledge can make it easy to beat the market (for a fee).

Rebalancing may also improve your returns, since asset classes have had a tendency to revert to the mean (RTM) over time. By rebalancing, you're selling a portion of your winning asset classes before they revert to the mean (drop in price) and you're buying more of your underperforming asset classes when their prices are lower, before they revert to the mean (increase in value). So, you're selling high and buying low. If you believe in RTM, rebalancing could increase your returns. Jack Bogle believes in RTM, and we do, too. Even if you don't believe that RTM will occur in the future, but rather, believe that the market is a random walk and that each market move is independent of previous moves, remember that you'll still benefit from rebalancing because you're controlling the level of risk in your portfolio. Experienced investors have learned that risk control helps to keep your emotions in check and that in turn keeps your portfolio in line with your long-term plan.

 

pages: 512 words: 162,977

New Market Wizards: Conversations With America's Top Traders by Jack D. Schwager

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backtesting, Benoit Mandelbrot, Berlin Wall, Black-Scholes formula, butterfly effect, commodity trading advisor, Elliott wave, fixed income, full employment, implied volatility, interest rate swap, Louis Bachelier, margin call, market clearing, market fundamentalism, paper trading, pattern recognition, placebo effect, prediction markets, Ralph Nelson Elliott, random walk, risk tolerance, risk/return, Saturday Night Live, Sharpe ratio, the map is not the territory, transaction costs, War on Poverty

using both “Toward” and “Away From” motivation; having a goal of full capability plus, with anything less being unacceptable; breaking down potentially overwhelming goals into chunks, with satisfaction garnered from the completion of each individual step; keeping full concentration on the present moment—that is, the single task at hand rather than the long-term goal; being personally involved in achieving goals (as opposed to depending on others); and making self-to-self comparisons to measure progress. 41. PRICES ARE NONRANDOM = THE MARKETS CAN BE BEAT In reference to academicians who believe market prices are random, Trout says, “That’s probably why they’re professors and why Fin making money doing what I’m doing.” The debate over whether prices are random is not yet over. However, my experience with the interviews conducted for this book and its predecessor leaves me with little doubt that the random walk theory is wrong. It is not the magnitude of the winnings registered by the Market Wizards but the consistency of these winnings in some cases that underpin my belief. As a particularly compelling example, consider Blake’s 25:1 ratio of winning to losing months and his average annual return of 45 percent compared with a worst drawdown of only 5 percent.

And since cybernetic devices lack many of our human limitations, someday they’ll be able to do it better. I have no doubt that eventually the world’s best trader will be an automaton. I’m not saying this will happen soon, but probably within the next few generations. A good part of the academic community insists that the random nature of price behavior means that it’s impossible to develop trading systems that can beat the market over the long run. What’s your response? 124 / The New Market Wizard The evidence against the random walk theory of market action is staggering. Hundreds of traders and managers have profited from price-based mechanical systems. What about the argument that if you have enough people trading, some of them are going to do well, even if just because of chance? That may be true, but the probability of experiencing the kind of success that we have had and continue to have by chance alone has to be near zero.

Since then, there has been a steadily increasing number of papers providing evidence that the random walk theory is false. System trading has gone from a fringe idea to being a new kind of orthodoxy. I don’t think this could have happened if there weren’t something to it. However, I have to admit that I find it unsettling that what began as a renegade idea has become an element of the conventional wisdom. Of course, you can’t actually prove that price behavior is random. That’s right. You’re up against the problem of trying to prove a negative proposition. Although the contention that the markets are random is an affirmative proposition, in fact you’re trying to prove a negative. You’re trying to prove that there’s no systematic component in the price. Any negative proposition is very difficult to confirm because you’re trying to prove that something doesn’t exist.

 

pages: 545 words: 137,789

How Markets Fail: The Logic of Economic Calamities by John Cassidy

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Albert Einstein, Andrei Shleifer, anti-communist, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black-Scholes formula, Bretton Woods, British Empire, capital asset pricing model, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, global supply chain, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, laissez-faire capitalism, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Network effects, Nick Leeson, Northern Rock, paradox of thrift, Ponzi scheme, price discrimination, price stability, principal–agent problem, profit maximization, quantitative trading / quantitative finance, race to the bottom, Ralph Nader, RAND corporation, random walk, Renaissance Technologies, rent control, Richard Thaler, risk tolerance, risk-adjusted returns, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, unorthodox policies, value at risk, Vanguard fund

The coin-tossing model was resurrected: by the early 1960s, Samuelson and a number of other economists were publishing papers claiming that stock prices followed a random walk. One of these authors was Eugene Fama, an Italian American from Boston who was still in his early twenties. After paying his way through Tufts, Fama went to the University of Chicago, where he did his Ph.D. thesis on the behavior of stock prices, using the school’s spiffy new IBM mainframe to analyze data covering the period from 1926 to 1960. After providing a critical survey of previous research that had purported to find some predictability in stock returns, Fama reported details of his own statistical tests, which supported the random walk model. What made Fama’s paper especially distinctive was the criticism it contained of “fundamental analysis”—the type of stock research that many Wall Street professionals relied on, which involved deconstructing companies’ earnings reports, visiting factories, and so on.

(For many years, Malkiel served as a director of the Vanguard Group, which pioneered index funds. Fama joined another firm that manages index funds, Dimensional Fund Advisors.) The rise of efficient market theory also signaled the beginning of quantitative finance. In addition to the random walk model of stock prices, the period between 1950 and 1970 saw the development of the mean-variance approach to portfolio diversification, which Harry Markowitz, another Chicago economist, pioneered; the capital asset pricing model, which a number of different scholars developed independently of one another; and the Black-Scholes option pricing formula, which Fischer Black, an applied mathematician from Harvard, and Myron Scholes, a finance Ph.D. from Chicago, developed. Some of the mathematics used in these theories is pretty befuddling, which helps explain why there are so many physicists and mathematicians working on Wall Street, but the basic ideas underpinning them aren’t so difficult.

Posner, Richard Poulakakos, Harry Poulakakos, Peter Poundstone, William Prechter, Robert predictability, illusion of Prescott, Edward C. President’s Economic Policy Advisory Board Priceline Prices and Production (Hayek) Prince, Charles “Chuck” Princeton University Institute for Advanced Study Principles of Economics (Marshall) Principles of Political Economy (Mill) prisoner’s dilemma “Problem of Social Cost, The” (Coase) productivity agricultural growth of, random fluctuations in wages and Proud Decades, The (Diggins) Prudential Securities Quantum Fund Quarterly Journal of Economics, The Quesnay, François Rabin, Matt Radner, Roy Rajan, Raghuram G. Ramsey, Frank Rand, Ayn RAND Institute Random Walk Down Wall Street, A (Malkiel) random walk theory Ranieri, Lewis rational expectations theory RBS Greenwich Capital Reader’s Digest Reagan, Ronald reality-based economics RealtyTrac Reinhart, Vincent Renaissance Technologies “Report on Social Insurance and Allied Services” (Beveridge) Republican Party Reserve Primary Fund residential mortgage-backed securities (RMBSs) Resolution Trust Corporation Review of Economic Studies, The Revolution (Anderson) Revolutionary era Ricardo, David Rigas, John RiskMetrics Roach, Stephen S.

 

pages: 415 words: 125,089

Against the Gods: The Remarkable Story of Risk by Peter L. Bernstein

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Albert Einstein, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Big bang: deregulation of the City of London, Bretton Woods, buttonwood tree, capital asset pricing model, cognitive dissonance, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Lloyd's coffeehouse, endowment effect, experimental economics, fear of failure, Fellow of the Royal Society, Fermat's Last Theorem, financial deregulation, financial innovation, full employment, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Nash equilibrium, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Thaler, Robert Shiller, Robert Shiller, spectrum auction, statistical model, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, trade route, transaction costs, tulip mania, Vanguard fund

The normal distribution provides a more rigorous test of the random-walk hypothesis. But one qualification is important. Even if the random walk is a valid description of reality in the stock market-even if changes in stock prices fall into a perfect normal distribution-the mean will be something different from zero. The upward bias should come as no surprise. The wealth of owners of common stocks has risen over the long run as the economy and the revenues and profits of corporations have grown. Since more stock-price movements have been up than down, the average change in stock prices should work out to more than zero. In fact, the average increase in stock prices (excluding dividend income) was 7.7% a year. The standard deviation was 19.3%; if the future will resemble the past, this means that two-thirds of the time stock prices in any one year are likely to move within a range of +27.0% and -12.1%.

How closely do changes in the prices of stocks resemble a normal distribution? Some authorities on market behavior insist that stock prices follow a random walk-that they resemble the aimless and unplanned lurches of a drunk trying to grab hold of a lamppost. They believe that stock prices have no more memory than a roulette wheel or a pair of dice, and that each observation is independent of the preceding observation. Today's price move will be whatever it is going to be, regardless of what happened a minute ago, yesterday, the day before, or the day before that. The best way to determine whether changes in stock prices are in fact independent is to find out whether they fall into a normal distribution. Impressive evidence exists to support the case that changes in stock prices are normally distributed.

The charts in Chapter 8 (page 147) show that market performance over periods of a year or more does not look much like a normal distribution, but that performance by the month and by the quarter does, though not precisely. Quetelet would interpret that evidence as proof that stock-price movements in the short run are independent-that today's changes tell us nothing about what tomorrow's prices will be. The stock market is unpredictable. The notion of the random walk was evoked to explain why this should be so. But what about the longer view? After all, most investors, even impatient ones, stay in the market for more than a month, a quarter, or a year. Even though the contents of their portfolios change over time, serious investors tend to keep their money in the stock market for many years, even decades. Does the long run in the stock market really differ from the short run? If the random-walk view is correct, today's stock prices embody all relevant information. The only thing that would make them change is the availability of new information.

 

Mathematics for Finance: An Introduction to Financial Engineering by Marek Capinski, Tomasz Zastawniak

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Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative finance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

Glossary of Symbols A B β c C C CA CE E C Cov delta div div0 D D DA E E∗ f F gamma Φ k K i m fixed income (risk free) security price; money market account bond price beta factor covariance call price; coupon value covariance matrix American call price European call price discounted European call price covariance Greek parameter delta dividend present value of dividends derivative security price; duration discounted derivative security price price of an American type derivative security expectation risk-neutral expectation futures price; payoff of an option; forward rate forward price; future value; face value Greek parameter gamma cumulative binomial distribution logarithmic return return coupon rate compounding frequency; expected logarithmic return 305 306 Mathematics for Finance M m µ N N k ω Ω p p∗ P PA PE P E PA r rdiv re rF rho ρ S S σ t T τ theta u V Var VaR vega w w W x X y z market portfolio expected returns as a row matrix expected return cumulative normal distribution the number of k-element combinations out of N elements scenario probability space branching probability in a binomial tree risk-neutral probability put price; principal American put price European put price discounted European put price present value factor of an annuity interest rate dividend yield effective rate risk-free return Greek parameter rho correlation risky security (stock) price discounted risky security (stock) price standard deviation; risk; volatility current time maturity time; expiry time; exercise time; delivery time time step Greek parameter theta row matrix with all entries 1 portfolio value; forward contract value, futures contract value variance value at risk Greek parameter vega symmetric random walk; weights in a portfolio weights in a portfolio as a row matrix Wiener process, Brownian motion position in a risky security strike price position in a fixed income (risk free) security; yield of a bond position in a derivative security Index admissible – portfolio 5 – strategy 79, 88 American – call option 147 – derivative security – put option 147 amortised loan 30 annuity 29 arbitrage 7 at the money 169 attainable – portfolio 107 – set 107 183 basis – of a forward contract 128 – of a futures contract 140 basis point 218 bear spread 208 beta factor 121 binomial – distribution 57, 180 – tree model 7, 55, 81, 174, 238 Black–Derman–Toy model 260 Black–Scholes – equation 198 – formula 188 bond – at par 42, 249 – callable 255 – face value 39 – fixed-coupon 255 – floating-coupon 255 – maturity date 39 – stripped 230 – unit 39 – with coupons 41 – zero-coupon 39 Brownian motion 69 bull spread 208 butterfly 208 – reversed 209 call option 13, 181 – American 147 – European 147, 188 callable bond 255 cap 258 Capital Asset Pricing Model 118 capital market line 118 caplet 258 CAPM 118 Central Limit Theorem 70 characteristic line 120 compounding – continuous 32 – discrete 25 – equivalent 36 – periodic 25 – preferable 36 conditional expectation 62 contingent claim 18, 85, 148 – American 183 – European 173 continuous compounding 32 continuous time limit 66 correlation coefficient 99 coupon bond 41 coupon rate 249 307 308 covariance matrix 107 Cox–Ingersoll–Ross model 260 Cox–Ross–Rubinstein formula 181 cum-dividend price 292 delta 174, 192, 193, 197 delta hedging 192 delta neutral portfolio 192 delta-gamma hedging 199 delta-gamma neutral portfolio 198 delta-vega hedging 200 delta-vega neutral portfolio 198 derivative security 18, 85, 253 – American 183 – European 173 discount factor 24, 27, 33 discounted stock price 63 discounted value 24, 27 discrete compounding 25 distribution – binomial 57, 180 – log normal 71, 186 – normal 70, 186 diversifiable risk 122 dividend yield 131 divisibility 4, 74, 76, 87 duration 222 dynamic hedging 226 effective rate 36 efficient – frontier 115 – portfolio 115 equivalent compounding 36 European – call option 147, 181, 188 – derivative security 173 – put option 147, 181, 189 ex-coupon price 248 ex-dividend price 292 exercise – price 13, 147 – time 13, 147 expected return 10, 53, 97, 108 expiry time 147 face value 39 fixed interest 255 fixed-coupon bond 255 flat term structure 229 floating interest 255 floating-coupon bond 255 floor 259 floorlet 259 Mathematics for Finance forward – contract 11, 125 – price 11, 125 – rate 233 fundamental theorem of asset pricing 83, 88 future value 22, 25 futures – contract 134 – price 134 gamma 197 Girsanov theorem 187 Greek parameters 197 growth factor 22, 25, 32 Heath–Jarrow–Morton model hedging – delta 192 – delta-gamma 199 – delta-vega 200 – dynamic 226 in the money 169 initial – forward rate 232 – margin 135 – term structure 229 instantaneous forward rate interest – compounded 25, 32 – fixed 255 – floating 255 – simple 22 – variable 255 interest rate 22 interest rate option 254 interest rate swap 255 261 233 LIBID 232 LIBOR 232 line of best fit 120 liquidity 4, 74, 77, 87 log normal distribution 71, 186 logarithmic return 34, 52 long forward position 11, 125 maintenance margin 135 margin call 135 market portfolio 119 market price of risk 212 marking to market 134 Markowitz bullet 113 martingale 63, 83 Index 309 martingale probability 63, 250 maturity date 39 minimum variance – line 109 – portfolio 108 money market 43, 235 no-arbitrage principle 7, 79, 88 normal distribution 70, 186 option – American 183 – at the money 169 – call 13, 147, 181, 188 – European 173, 181 – in the money 169 – interest rate 254 – intrinsic value 169 – out of the money 169 – payoff 173 – put 18, 147, 181, 189 – time value 170 out of the money 169 par, bond trading at 42, 249 payoff 148, 173 periodic compounding 25 perpetuity 24, 30 portfolio 76, 87 – admissible 5 – attainable 107 – delta neutral 192 – delta-gamma neutral 198 – delta-vega neutral 198 – expected return 108 – market 119 – variance 108 – vega neutral 197 positive part 148 predictable strategy 77, 88 preferable compounding 36 present value 24, 27 principal 22 put option 18, 181 – American 147 – European 147, 189 put-call parity 150 – estimates 153 random interest rates random walk 67 rate – coupon 249 – effective 36 237 – forward 233 – – initial 232 – – instantaneous 233 – of interest 22 – of return 1, 49 – spot 229 regression line 120 residual random variable 121 residual variance 122 return 1, 49 – expected 53 – including dividends 50 – logarithmic 34, 52 reversed butterfly 209 rho 197 risk 10, 91 – diversifiable 122 – market price of 212 – systematic 122 – undiversifiable 122 risk premium 119, 123 risk-neutral – expectation 60, 83 – market 60 – probability 60, 83, 250 scenario 47 security market line 123 self-financing strategy 76, 88 short forward position 11, 125 short rate 235 short selling 5, 74, 77, 87 simple interest 22 spot rate 229 Standard and Poor Index 141 state 238 stochastic calculus 71, 185 stochastic differential equation 71 stock index 141 stock price 47 strategy 76, 87 – admissible 79, 88 – predictable 77, 88 – self-financing 76, 88 – value of 76, 87 strike price 13, 147 stripped bond 230 swap 256 swaption 258 systematic risk 122 term structure 229 theta 197 time value of money 21 310 trinomial tree model Mathematics for Finance 64 underlying 85, 147 undiversifiable risk 122 unit bond 39 value at risk 202 value of a portfolio 2 value of a strategy 76, 87 VaR 202 variable interest 255 Vasiček model 260 vega 197 vega neutral portfolio volatility 71 weights in a portfolio Wiener process 69 yield 216 yield to maturity 229 zero-coupon bond 39 197 94

Next, S(nτ + τ ) 1 ≈ 1 + mτ + σξ(n + 1) + σ 2 τ S(nτ ) 2 1 2 = 1 + m + σ τ + σξ(n + 1), 2 and so S(nτ + τ ) − S(nτ ) ≈ 1 m + σ 2 S(nτ )τ + σS(nτ )ξ(n + 1). 2 Since ξ(n + 1) = w(nτ + τ ) − w(nτ ), we obtain an approximate equation describing the dynamics of stock prices: 1 2 S(t + τ ) − S(t) ≈ m + σ S(t)τ + σS(t)(w(t + τ ) − w(t)), (3.8) 2 where t = nτ . The solution S(t) of this approximate equation is given by the same formula as in Proposition 3.7. For any N = 1, 2, . . . we consider a binomial tree model with time step of length τ = N1 . Let SN (t) be the corresponding stock prices and let wN (t) be the corresponding symmetric random walk with increments ξN (t) = wN (t) − n is the time after n steps. wN (t − N1 ), where t = N Exercise 3.25 Compute the expectation and variance of wN (t), where t = n N. 3. Risky Assets 69 We shall use the Central Limit Theorem2 to obtain the limit as N → ∞ of the random walk wN (t). To this end we put x(n) = k(n) − mτ √ σ τ for each n = 1, 2, . . . , which is a sequence of independent identically distributed random variables, each with expectation 0 and variance 1.

Risky Assets 67 Introducing a sequence of independent random variables ξ(n), each with two values √ + τ with probability 1/2, √ ξ(n) = − τ with probability 1/2, we can write the logarithmic return as k(n) = mτ + σξ(n). Exercise 3.23 Find the expectation and variance of ξ(n) and k(n). Exercise 3.24 Write S(1) and S(2) in terms of m, σ, τ , ξ(1) and ξ(2). Next, we introduce an important sequence of random variables w(n), called a symmetric random walk, such that w(n) = ξ(1) + ξ(2) + · · · + ξ(n), and w(0) = 0. Clearly, ξ(n) = w(n) − w(n − 1). Because of the last equality, the ξ(n) are referred to as the increments of w(n). From now on we shall often write S(t) and w(t) instead of S(n) and w(n) for t = τ n, where n = 1, 2, . . . . Proposition 3.7 The stock price at time t = τ n is given by S(t) = S(0) exp(mt + σw(t)). Proof By (3.2) S(t) = S(nτ ) = S(nτ − τ )ek(n) = S(nτ − 2τ )ek(n−1)+k(n) = · · · = S(0)ek(1)+···+k(n) = S(0)emnτ +σ(ξ(1)+···+ξ(n)) = S(0)emt+σw(t) , as required. 68 Mathematics for Finance In order to pass to the continuous-time limit we use the approximation 1 ex ≈ 1 + x + x2 , 2 accurate for small values of x, to obtain S(nτ + τ ) 1 = ek(n+1) ≈ 1 + k(n + 1) + k(n + 1)2 .

 

pages: 416 words: 39,022

Asset and Risk Management: Risk Oriented Finance by Louis Esch, Robert Kieffer, Thierry Lopez

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asset allocation, Brownian motion, business continuity plan, business process, capital asset pricing model, computer age, corporate governance, discrete time, diversified portfolio, implied volatility, index fund, interest rate derivative, iterative process, P = NP, p-value, random walk, risk/return, shareholder value, statistical model, stochastic process, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

INTERNET SITES http://www.aptltd.com http://www.bis.org/index.htm http://www.cga-canada.org/fr/magazine/nov-dec02/Cyberguide f.htm http://www.fasb.org http://www.iasc.org.uk/cmt/0001.asp http://www.ifac.org http://www.prim.lu Index absolute global risk 285 absolute risk aversion coefficient 88 accounting standards 9–10 accrued interest 118–19 actuarial output rate on issue 116–17 actuarial return rate at given moment 117 adjustment tests 361 Aitken extrapolation 376 Akaike’s information criterion (AIC) 319 allocation independent allocation 288 joint allocation 289 of performance level 289–90 of systematic risk 288–9 American option 149 American pull 158–9 arbitrage 31 arbitrage models 138–9 with state variable 139–42 arbitrage pricing theory (APT) 97–8, 99 absolute global risk 285 analysis of style 291–2 beta 290, 291 factor-sensitivity profile 285 model 256, 285–94 relative global risk/tracking error 285–7 ARCH 320 ARCH-GARCH models 373 arithmetical mean 36–7 ARMA models 318–20 asset allocation 104, 274 asset liability management replicating portfolios 311–21 repricing schedules 301–11 simulations 300–1 structural risk analysis in 295–9 VaR in 301 autocorrelation test 46 autoregressive integrated moving average 320 autoregressive moving average (ARMA) 318 average deviation 41 bank offered rate (BOR) 305 basis point 127 Basle Committee for Banking Controls 4 Basle Committee on Banking Supervision 3–9 Basle II 5–9 Bayesian information criterion (BIC) 319 bear money spread 177 benchmark abacus 287–8 Bernouilli scheme 350 Best Linear Unbiased Estimators (BLUE) 363 beta APT 290, 291 portfolio 92 bijection 335 binomial distribution 350–1 binomial formula (Newton’s) 111, 351 binomial law of probability 165 binomial trees 110, 174 binomial trellis for underlying equity 162 bisection method 380 Black and Scholes model 33, 155, 174, 226, 228, 239 for call option 169 dividends and 173 for options on equities 168–73 sensitivity parameters 172–3 BLUE (Best Linear Unbiased Estimators) 363 bond portfolio management strategies 135–8 active strategy 137–8 duration and convexity of portfolio 135–6 immunizing a portfolio 136–7 positive strategy: immunisation 135–7 bonds average instant return on 140 390 Index bonds (continued ) definition 115–16 financial risk and 120–9 price 115 price approximation 126 return on 116–19 sources of risk 119–21 valuing 119 bootstrap method 233 Brennan and Schwarz model 139 building approach 316 bull money spread 177 business continuity plan (BCP) 14 insurance and 15–16 operational risk and 16 origin, definition and objective 14 butterfly money spread 177 calendar spread 177 call-associated bonds 120 call option 149, 151, 152 intrinsic value 153 premium breakdown 154 call–put parity relation 166 for European options 157–8 canonical analysis 369 canonical correlation analysis 307–9, 369–70 capital asset pricing model (CAPM or MEDAF) 93–8 equation 95–7, 100, 107, 181 cash 18 catastrophe scenarios 20, 32, 184, 227 Cauchy’s law 367 central limit theorem (CLT) 41, 183, 223, 348–9 Charisma 224 Chase Manhattan 224, 228 Choleski decomposition method 239 Choleski factorisation 220, 222, 336–7 chooser option 176 chord method 377–8 classic chord method 378 clean price 118 collateral management 18–19 compliance 24 compliance tests 361 compound Poisson process 355 conditional normality 203 confidence coefficient 360 confidence interval 360–1 continuous models 30, 108–9, 111–13, 131–2, 134 continuous random variables 341–2 contract-by-contract 314–16 convergence 375–6 convertible bonds 116 convexity 33, 149, 181 of a bond 127–9 corner portfolio 64 correlation 41–2, 346–7 counterparty 23 coupon (nominal) rate 116 coupons 115 covariance 41–2, 346–7 cover law of probability 164 Cox, Ingersoll and Ross model 139, 145–7, 174 Cox, Ross and Rubinstein binomial model 162–8 dividends and 168 one period 163–4 T periods 165–6 two periods 164–5 credit risk 12, 259 critical line algorithm 68–9 debentures 18 decision channels 104, 105 default risk 120 deficit constraint 90 degenerate random variable 341 delta 156, 181, 183 delta hedging 157, 172 derivatives 325–7 calculations 325–6 definition 325 extrema 326–7 geometric interpretations 325 determinist models 108–9 generalisation 109 stochastic model and 134–5 deterministic structure of interest rates 129–35 development models 30 diagonal model 70 direct costs 26 dirty price 118 discrete models 30, 108, 109–11. 130, 132–4 discrete random variables 340–1 dispersion index 26 distortion models 138 dividend discount model 104, 107–8 duration 33, 122–7, 149 and characteristics of a bond 124 definition 121 extension of concept of 148 interpretations 121–3 of equity funds 299 of specific bonds 123–4 Index dynamic interest-rate structure 132–4 dynamic models 30 dynamic spread 303–4 efficiency, concept of 45 efficient frontier 27, 54, 59, 60 for model with risk-free security 78–9 for reformulated problem 62 for restricted Markowitz model 68 for Sharpe’s simple index model 73 unrestricted and restricted 68 efficient portfolio 53, 54 EGARCH models 320, 373 elasticity, concept of 123 Elton, Gruber and Padberg method 79–85, 265, 269–74 adapting to VaR 270–1 cf VaR 271–4 maximising risk premium 269–70 equities definition 35 market efficiency 44–8 market return 39–40 portfolio risk 42–3 return on 35–8 return on a portfolio 38–9 security risk within a portfolio 43–4 equity capital adequacy ratio 4 equity dynamic models 108–13 equity portfolio diversification 51–93 model with risk-free security 75–9 portfolio size and 55–6 principles 515 equity portfolio management strategies 103–8 equity portfolio theory 183 equity valuation models 48–51 equivalence, principle of 117 ergodic estimator 40, 42 estimated variance–covariance matrix method (VC) 201, 202–16, 275, 276, 278 breakdown of financial assets 203–5 calculating VaR 209–16 hypotheses and limitations 235–7 installation and use 239–41 mapping cashflows with standard maturity dates 205–9 valuation models 237–9 estimator for mean of the population 360 European call 158–9 European option 149 event-based risks 32, 184 ex ante rate 117 ex ante tracking error 285, 287 ex post return rate 121 exchange options 174–5 exchange positions 204 391 exchange risk 12 exercise price of option 149 expected return 40 expected return risk 41, 43 expected value 26 exponential smoothing 318 extrema 326–7, 329–31 extreme value theory 230–4, 365–7 asymptotic results 365–7 attraction domains 366–7 calculation of VaR 233–4 exact result 365 extreme value theorem 230–1 generalisation 367 parameter estimation by regression 231–2 parameter estimation using the semi-parametric method 233, 234 factor-8 mimicking portfolio 290 factor-mimicking portfolios 290 factorial analysis 98 fair value 10 fat tail distribution 231 festoon effect 118, 119 final prediction error (FPE) 319 Financial Accounting Standards Board (FASB) 9 financial asset evaluation line 107 first derivative 325 Fisher’s skewness coefficient 345–6 fixed-income securities 204 fixed-rate bonds 115 fixed rates 301 floating-rate contracts 301 floating-rate integration method 311 FRAs 276 Fréchet’s law 366, 367 frequency 253 fundamental analysis 45 gamma 156, 173, 181, 183 gap 296–7, 298 GARCH models 203, 320 Garman–Kohlhagen formula 175 Gauss-Seidel method, nonlinear 381 generalised error distribution 353 generalised Pareto distribution 231 geometric Brownian motion 112, 174, 218, 237, 356 geometric mean 36 geometric series 123, 210, 328–9 global portfolio optimisation via VaR 274–83 generalisation of asset model 275–7 construction of optimal global portfolio 277–8 method 278–83 392 Index good practices 6 Gordon – Shapiro formula 48–50, 107, 149 government bonds 18 Greeks 155–7, 172, 181 gross performance level and risk withdrawal 290–1 Gumbel’s law 366, 367 models for bonds 149 static structure of 130–2 internal audit vs. risk management 22–3 internal notation (IN) 4 intrinsic value of option 153 Itô formula (Ito lemma) 140, 169, 357 Itô process 112, 356 Heath, Jarrow and Morton model 138, 302 hedging formula 172 Hessian matrix 330 high leverage effect 257 Hill’s estimator 233 historical simulation 201, 224–34, 265 basic methodology 224–30 calculations 239 data 238–9 extreme value theory 230–4 hypotheses and limitations 235–7 installation and use 239–41 isolated asset case 224–5 portfolio case 225–6 risk factor case 224 synthesis 226–30 valuation models 237–8 historical volatility 155 histories 199 Ho and Lee model 138 homogeneity tests 361 Hull and White model 302, 303 hypothesis test 361–2 Jensen index 102–3 Johnson distributions 215 joint allocation 289 joint distribution function 342 IAS standards 10 IASB (International Accounting Standards Board) 9 IFAC (International Federation of Accountants) 9 immunisation of bonds 124–5 implied volatility 155 in the money 153, 154 independence tests 361 independent allocation 288 independent random variables 342–3 index funds 103 indifference curves 89 indifference, relation of 86 indirect costs 26 inequalities on calls and puts 159–60 inferential statistics 359–62 estimation 360–1 sampling 359–60 sampling distribution 359–60 instant term interest rate 131 integrated risk management 22, 24–5 interest rate curves 129 kappa see vega kurtosis coefficient 182, 189, 345–6 Lagrangian function 56, 57, 61, 63, 267, 331 for risk-free security model 76 for Sharpe’s simple index model 71 Lagrangian multipliers 57, 331 law of large numbers 223, 224, 344 law of probability 339 least square method 363 legal risk 11, 21, 23–4 Lego approach 316 leptokurtic distribution 41, 182, 183, 189, 218, 345 linear equation system 335–6 linear model 32, 33, 184 linearity condition 202, 203 Lipschitz’s condition 375–6 liquidity bed 316 liquidity crisis 17 liquidity preference 316 liquidity risk 12, 16, 18, 296–7 logarithmic return 37 logistic regression 309–10, 371 log-normal distribution 349–50 log-normal law with parameter 349 long (short) straddle 176 loss distribution approach 13 lottery bonds 116 MacLaurin development 275, 276 mapping cashflows 205–9 according to RiskMetricsT M 206–7 alternative 207–8 elementary 205–6 marginal utility 87 market efficiency 44–8 market model 91–3 market price of the risk 141 market risk 12 market straight line 94 Index market timing 104–7 Markowitz’s portfolio theory 30, 41, 43, 56–69, 93, 94, 182 first formulation 56–60 reformulating the problem 60–9 mathematic valuation models 199 matrix algebra 239 calculus 332–7 diagonal 333 n-order 332 operations 333–4 symmetrical 332–3, 334–5 maturity price of bond 115 maximum outflow 17–18 mean 343–4 mean variance 27, 265 for equities 149 measurement theory 344 media risk 12 Merton model 139, 141–2 minimum equity capital requirements 4 modern portfolio theory (MPT) 265 modified duration 121 money spread 177 monoperiodic models 30 Monte Carlo simulation 201, 216–23, 265, 303 calculations 239 data 238–9 estimation method 218–23 hypotheses and limitations 235–7 installation and use 239–41 probability theory and 216–18 synthesis 221–3 valuation models 237–8 multi-index models 221, 266 multi-normal distribution 349 multivariate random variables 342–3 mutual support 147–9 Nelson and Schaefer model 139 net present value (NPV) 298–9, 302–3 neutral risk 164, 174 New Agreement 4, 5 Newson–Raphson nonlinear iterative method 309, 379–80, 381 Newton’s binomial formula 111, 351 nominal rate of a bond 115, 116 nominal value of a bond 115 non-correlation 347 nonlinear equation systems 380–1 first-order methods 377–9 iterative methods 375–7 n-dimensional iteration 381 principal methods 381 393 solving 375–81 nonlinear Gauss-Seidel method 381 nonlinear models independent of time 33 nonlinear regression 234 non-quantifiable risks 12–13 normal distribution 41, 183, 188–90, 237, 254, 347–8 normal law 188 normal probability law 183 normality 202, 203, 252–4 observed distribution 254 operational risk 12–14 business continuity plan (BCP) and 16 definition 6 management 12–13 philosophy of 5–9 triptych 14 options complex 175–7 definition 149 on bonds 174 sensitivity parameters 155–7 simple 175 strategies on 175–7 uses 150–2 value of 153–60 order of convergence 376 Ornstein – Uhlenbeck process 142–5, 356 OTC derivatives market 18 out of the money 153, 154 outliers 241 Pareto distribution 189, 367 Parsen CAT 319 partial derivatives 329–31 payment and settlement systems 18 Pearson distribution system 183 perfect market 31, 44 performance evaluation 99–108 perpetual bond 123–4 Picard’s iteration 268, 271, 274, 280, 375, 376, 381 pip 247 pockets of inefficiency 47 Poisson distribution 350 Poisson process 354–5 Poisson’s law 351 portfolio beta 92 portfolio risk management investment strategy 258 method 257–64 risk framework 258–64 power of the test 362 precautionary surveillance 3, 4–5 preference, relation of 86 394 Index premium 149 price at issue 115 price-earning ratio 50–1 price of a bond 127 price variation risk 12 probability theory 216–18 process risk 24 product risk 23 pseudo-random numbers 217 put option 149, 152 quadratic form 334–7 qualitative approach 13 quantifiable risks 12, 13 quantile 188, 339–40 quantitative approach 13 Ramaswamy and Sundaresan model 139 random aspect of financial assets 30 random numbers 217 random variables 339–47 random walk 45, 111, 203, 355 statistical tests for 46 range forwards 177 rate fluctuation risk 120 rate mismatches 297–8 rate risk 12, 303–11 redemption price of bond 115 regression line 363 regressions 318, 362–4 multiple 363–4 nonlinear 364 simple 362–3 regular falsi method 378–9 relative fund risk 287–8 relative global risk 285–7 relative risks 43 replicating portfolios 302, 303, 311–21 with optimal value method 316–21 repos market 18 repricing schedules 301–11 residual risk 285 restricted Markowitz model 63–5 rho 157, 173, 183 Richard model 139 risk, attitude towards 87–9 risk aversion 87, 88 risk factors 31, 184 risk-free security 75–9 risk, generalising concept 184 risk indicators 8 risk management cost of 25–6 environment 7 function, purpose of 11 methodology 19–21 vs back office 22 risk mapping 8 risk measurement 8, 41 risk-neutral probability 162, 164 risk neutrality 87 risk of one equity 41 risk of realisation 120 risk of reinvestment 120 risk of reputation 21 risk per share 181–4 risk premium 88 risk return 26–7 risk transfer 14 risk typology 12–19 Risk$TM 224, 228 RiskMetricsTM 202, 203, 206–7, 235, 236, 238, 239–40 scenarios and stress testing 20 Schaefer and Schwartz model 139 Schwarz criterion 319 scope of competence 21 scorecards method 7, 13 security 63–5 security market line 107 self-assessment 7 semi-form of efficiency hypothesis 46 semi-parametric method 233 semi-variance 41 sensitivity coefficient 121 separation theorem 94–5, 106 series 328 Sharpe’s multi-index model 74–5 Sharpe’s simple index method 69–75, 100–1, 132, 191, 213, 265–9 adapting critical line algorithm to VaR 267–8 cf VaR 269 for equities 221 problem of minimisation 266–7 VaR in 266–9 short sale 59 short-term interest rate 130 sign test 46 simulation tests for technical analysis methods 46 simulations 300–1 skewed distribution 182 skewness coefficient 182, 345–6 specific risk 91, 285 speculation bubbles 47 spot 247 Index spot price 150 spot rate 129, 130 spreads 176–7 square root process 145 St Petersburg paradox 85 standard Brownian motion 33, 355 standard deviation 41, 344–5 standard maturity dates 205–9 standard normal law 348 static models 30 static spread 303–4 stationarity condition 202, 203, 236 stationary point 327, 330 stationary random model 33 stochastic bond dynamic models 138–48 stochastic differential 356–7 stochastic duration 121, 147–8 random evolution of rates 147 stochastic integral 356–7 stochastic models 109–13 stochastic process 33, 353–7 particular 354–6 path of 354 stock exchange indexes 39 stock picking 104, 275 stop criteria 376–7 stop loss 258–9 straddles 175, 176 strangles 175, 176 strategic risk 21 stress testing 20, 21, 223 strike 149 strike price 150 strong form of efficiency hypothesis 46–7 Student distribution 189, 235, 351–2 Student’s law 367 Supervisors, role of 8 survival period 17–18 systematic inefficiency 47 systematic risk 44, 91, 285 allocation of 288–9 tail parameter 231 taste for risk 87 Taylor development 33, 125, 214, 216, 275–6 Taylor formula 37, 126, 132, 327–8, 331 technical analysis 45 temporal aspect of financial assets 30 term interest rate 129, 130 theorem of expected utility 86 theoretical reasoning 218 theta 156, 173, 183 three-equity portfolio 54 395 time value of option 153, 154 total risk 43 tracking errors 103, 285–7 transaction risk 23–4 transition bonds 116 trend extrapolations 318 Treynor index 102 two-equity portfolio 51–4 unbiased estimator 360 underlying equity 149 uniform distribution 352 uniform random variable 217 utility function 85–7 utility of return 85 utility theory 85–90, 183 valuation models 30, 31–3, 160–75, 184 value at risk (VaR) 13, 20–1 based on density function 186 based on distribution function 185 bond portfolio case 250–2 breaking down 193–5 calculating 209–16 calculations 244–52 component 195 components of 195 definition 195–6 estimation 199–200 for a portfolio 190–7 for a portfolio of linear values 211–13 for a portfolio of nonlinear values 214–16 for an isolated asset 185–90 for equities 213–14 heading investment 196–7 incremental 195–7 individual 194 link to Sharp index 197 marginal 194–5 maximum, for portfolio 263–4 normal distribution 188–90 Treasury portfolio case 244–9 typology 200–2 value of basis point (VBP) 19–20, 21, 127, 245–7, 260–3 variable contracts 301 variable interest rates 300–1 variable rate bonds 115 variance 41, 344–5 variance of expected returns approach 183 variance – covariance matrix 336 Vasicek model 139, 142–4, 174 396 Index vega (kappa) 156, 173 volatility of option 154–5 yield curve 129 yield to maturity (YTM) 250 weak form of the efficiency hypothesis 46 Weibull’s law 366, 367 Wiener process 355 zero-coupon bond 115, 123, 129 zero-coupon rates, analysis of correlations on 305–7 Index compiled by Annette Musker

Bonds 141 By differentiating the value of the portfolio, we have: dVt = −Pt (s1 )(µt (s1 ) dt − σt (s1 ) dwt ) + X · Pt (s2 )(µt (s2 ) dt − σt (s2 ) dwt ) = [−Pt (s1 )µt (s1 ) + XPt (s2 )µt (s2 )] · dt + [Pt (s1 )σt (s1 ) − XPt (s2 )σt (s2 )] · dwt The arbitrage logic will therefore lead us to  −Pt (s1 )µt (s1 ) + XPt (s2 )µt (s2 )   = rt  −P (s ) + XP (s ) t t 1 2  P (s )σ (s ) − XPt (s2 )σt (s2 )   t 1 t 1 =0 −Pt (s1 ) + XPt (s2 ) In other words: XPt (s2 ) · (µt (s2 ) − rt ) = Pt (s1 ) · (µt (s1 ) − rt ) XPt (s2 ) · σt (s2 ) = Pt (s1 ) · σt (s1 ) We can eliminate X, for example by dividing the two equations member by member, which gives: µt (s1 ) − rt µt (s2 ) − rt = σt (s1 ) σt (s2 ) This shows that the expression λt (rt ) = µt (s) − rt is independent of s; this expression σt (s) is known as the market price of the risk. By replacing µt and σt with their value in the preceding relation, we arrive at Pt + (a + λb)Pr + b2 P − rP = 0 2 rr What we are looking at here is the partial derivatives equation of the second order, which together with the initial condition Ps (s, rt ) = l, defines the price process. This equation must be resolved for each specification of a(t, rt ), b(t, rt ) and λt (rt ). 4.5.1.2 The Merton model31 Because of its historical interest,32 we are showing the simplest model, the Merton model. This model assumes that the instant term rate follows a random walk model: drt = α · dt + σ · dwt with α and σ being constant and the market price of risk being zero (λ = 0). The partial derivatives equation for the prices takes the form: Pt + αPr + σ 2 P − rP = 0. 2 rr 31 Merton R., Theory of rational option pricing, Bell Journal of Economics and Management Science, Vol. 4, No. 1, 1973, pp. 141–83. 32 This is in fact the first model based on representation of changes in the spot rate using a stochastic differential equation. 142 Asset and Risk Management It is easy to verify that the solution to this equation (with the initial condition) is given by α σ2 Pt (s, rt ) = exp −(s − t)rt − (s − t)2 + (s − t)3 2 6 The average instant return rate is given by µt (s, rt ) = Pt + αPr + P σ 2 P 2 rr = rt · P = r t P which shows that in this case, the average return is independent of the maturity date.

This question is addressed in the following paragraphs, and the analysis is carried out at three levels according to the accessibility of information. The least that can be said is that the conclusions of the searches carried out in order to test efficiency are inconclusive and should not be used as a basis for forming clear and definitive ideas. 9 Fama E. F., Behaviour of Stock Market Prices, Journal of Business, Vol. 38, 1965, pp. 34–105. Fama E. F., Random Walks in Stock Market Prices, Financial Analysis Journal, 1965. Fama E. F., Efficient Capital Markets: A Review of Theory and Empirical Work, Journal of Finance, Vol. 25, 1970. 10 This approach is adopted in this work. 11 Refer for example to Bechu T. and Bertrand E., L’Analyse Technique, Economica, 1998. 46 Asset and Risk Management 3.1.2.2 Weak form The weak form of the efficiency hypothesis postulates that it is not possible to gain a particular advantage from the range of historical observations; the rates therefore purely and simply include the previous rate values.

 

pages: 263 words: 75,455

Quantitative Value: A Practitioner's Guide to Automating Intelligent Investment and Eliminating Behavioral Errors by Wesley R. Gray, Tobias E. Carlisle

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Albert Einstein, Andrei Shleifer, asset allocation, Atul Gawande, backtesting, Black Swan, capital asset pricing model, Checklist Manifesto, cognitive bias, compound rate of return, corporate governance, correlation coefficient, credit crunch, Daniel Kahneman / Amos Tversky, discounted cash flows, Eugene Fama: efficient market hypothesis, forensic accounting, hindsight bias, Louis Bachelier, p-value, passive investing, performance metric, quantitative hedge fund, random walk, Richard Thaler, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, statistical model, systematic trading, The Myth of the Rational Market, time value of money, transaction costs

In a collection of essays called The Random Character of Stock Market Prices (1964), Thorp read the English translation of a French dissertation written in 1900 by a student at the University of Paris, Louis Bachelier. Bachelier's dissertation unlocked the secret to valuing warrants: the so-called “random walk” theory. As the name suggests, the “random walk” holds that the movements made by security prices are random. While it might seem paradoxical, the random nature of the moves makes it possible to probabilistically determine the future price of the security. The implications of the random walk theory are profound, and they weren't lost on Thorp. He saw that he could apply the theory to handicap the value of the warrant. Where the warrant's price differed from Thorp's probabilistic valuation, Thorp recognized that an opportunity existed for him to trade the warrant and the underlying stock and to profit from the differential.

See Look-ahead bias Price ratios analysis of compound annual growth rates alpha and adjusted performance risk-adjusted performance and absolute measures of risk value premium and spread book-to-market composite formed from all metrics formed from the “best” price ratios top-performing earnings yield EBIT variation, outperformance by enterprise yield (EBITDA and EBIT variations) forward earnings estimate free cash flow yield gross profits yield long-term study methods of studying Princeton-Newport Partners PROBM model Procter & Gamble Profit margins growth maximum stability Pronovost, Peter Puthenpurackal, John Quality and Price, improving compared with Magic Formula finding Price finding Quality Quantitative value checklist Quantitative value strategy examining, results of analysis legend beating the market black box, looking inside man versus machine risk and return robustness Greenblatt's Magic Formula bargain price examination of findings good business Quality and Price, improving compared with Magic Formula finding Price finding Quality simplifying strategy implementation checklist tried-and-true value investing principles Quinn, Kevin The Random Character of Stock Market Prices (Bachelier) Random walk theory Regression analysis Representativeness heuristic “Returns to Trading Strategies Based on Price-to-Earnings and Price-to-Sales Ratios” (Nathan, Sivakumar, & Vijayakumar) Ridgeline Partners Risk-adjusted performance and absolute measures of risk R-squared Ruane, William Scaled net operating assets (SNOA) Scaled total accruals (STA) Schedule 13D Security Analysis (Graham & Dodd) See's Candies Self-attribution bias Sequoia Fund Sharpe, William Sharpe ratio Shiller, Robert Short selling Shumway, Tyler Simons, Jim Singleton, Henry Sloan, Richard Small sample bias “Some Insiders Are Indeed Smart Investors” (Giamouridis, Liodakis, & Moniz) Sortino ratio Stock buybacks, issuance, and announcements Stock market, predicting movements in sustainable alpha quantitative value strategy simplifying tried-and-true value investing principles model, testing benchmarking data errors historical data versus forward data size of portfolio and target stocks small sample bias transaction costs universe, parameters of Super Crunchers: Why Thinking-by-Numbers Is the New Way to Be Smart (Ayres) “The Superinvestors of Graham-and-Doddsville” (Buffett) Survivorship bias Sustainable alpha Taleb, Nassim Teledyne Tetlock, Philip Theory of Investment Value (Williams) Third Avenue Value Fund Thorp, Ed Total enterprise value (TEV) Transaction costs Tsai, Claire Tversky, Amos Value investors'errors Value portfolio Value premium and spread Wellman, Jay What Works on Wall Street (O'Shaughnessy) Whitman, Martin J.

They agreed, however, on one very important point: both believed it was possible to outperform the stock market, a belief that flew in the face of the efficient market hypothesis. While it is true that Thorp's strategy was grounded in the random walk, a key component of the efficient market hypothesis, he disagreed with the efficient market believers that it necessarily implied that markets were efficient. Indeed, Thorp went so as far as to call his book Beat the Market. Buffett also thought the efficient market hypothesis was nonsense, writing in his 1988 Shareholder Letter15: This doctrine [the efficient market hypothesis] became highly fashionable—indeed, almost holy scripture in academic circles during the 1970s. Essentially, it said that analyzing stocks was useless because all public information about them was appropriately reflected in their prices. In other words, the market always knew everything. As a corollary, the professors who taught EMT said that someone throwing darts at the stock tables could select a stock portfolio having prospects just as good as one selected by the brightest, most hard-working security analyst.

 

pages: 586 words: 159,901

Wall Street: How It Works And for Whom by Doug Henwood

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accounting loophole / creative accounting, affirmative action, Andrei Shleifer, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, borderless world, Bretton Woods, British Empire, capital asset pricing model, capital controls, central bank independence, corporate governance, correlation coefficient, correlation does not imply causation, credit crunch, currency manipulation / currency intervention, David Ricardo: comparative advantage, debt deflation, declining real wages, deindustrialization, dematerialisation, diversification, diversified portfolio, Donald Trump, equity premium, Eugene Fama: efficient market hypothesis, experimental subject, facts on the ground, financial deregulation, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, George Akerlof, George Gilder, hiring and firing, Hyman Minsky, implied volatility, index arbitrage, index fund, interest rate swap, Internet Archive, invisible hand, Isaac Newton, joint-stock company, Joseph Schumpeter, kremlinology, labor-force participation, late capitalism, law of one price, liquidationism / Banker’s doctrine / the Treasury view, London Interbank Offered Rate, Louis Bachelier, market bubble, Mexican peso crisis / tequila crisis, microcredit, minimum wage unemployment, moral hazard, mortgage debt, mortgage tax deduction, oil shock, payday loans, pension reform, Plutocrats, plutocrats, price mechanism, price stability, prisoner's dilemma, profit maximization, Ralph Nader, random walk, reserve currency, Richard Thaler, risk tolerance, Robert Gordon, Robert Shiller, Robert Shiller, shareholder value, short selling, Slavoj Žižek, South Sea Bubble, The Market for Lemons, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, transcontinental railway, women in the workforce, yield curve, zero-coupon bond

Fama, Eugene F. (1965a). "The Behavior of Stock Prices," Journal of Business 57, pp. 34-105. — (1965b). "Random Walks in Stock Market Prices," Financial Analysts JournaKSeptem- ber-October), pp. 55-59. — (1968). "What 'Random Walk' Really Means," Institutional Investor (April), pp. 38-40. — (1970). "Efficient Capital Markets: A Review of Theory and Empirical ^ork," Journal of Finance 25. pp. 383-423. — (1980). "Banking in the Theory of Finance,"/owmfl/ of Monetary Economics^, pp. 3S>-57. — (1981). "Stock Returns, Real Activity, Inflation, and Money," American Economic Re- view 71, pp. 545-565. — (1991). "Efficient Capital Markets: II," Journal of Finance 46, pp. 1575-1617. Fama, Eugene F., and Kenneth R. French (1988). "Permanent and Temporary Components of Stock Prices," Journal of Political Economy 96, pp. 246-273- — (1989) "Business Conditions and Expected Returns on Stocks and Bonds,"/owrna/ of Financial Economics 25, pp. 23^9

Work in the 1980s, using different — a skeptic on econometrics hesitates to use the phrase "more powerful" — statistical MARKET MODELS techniques, repeatedly found more patterns in prices than classic random walk theory allowed, especially if you examine portfolios consisting of a number of stocks. In other words, individual shares may follow more-or-less random patterns, but the market as a whole moves in trends (or, in statistical language, returns are autocorrelated), especially over the long term. "[Rjecent research," Fama concluded, "is able to show confidently that daily and weekly returns are predictable from past returns." Even more challenging to EMH orthodoxy is research that goes beyond price history. A number of studies during the 1970s and 1980s showed that stocks with low price/earnings ratios and/or high dividend yields — "cheap" stocks, in slang — would likely outperform stocks that were expensive by these measures, a sophisticated confirmation of old Wall Street wisdom.

Others, little better than haruspices, try to divine patterns in price graphs that supposedly portend dramatic upward or downward moves. Such "chartists" speak enthusiastically of pennants, rising wedges, head and shoulders, saucer bottoms. There is little evidence that chart-reading works at all; the patterns seen are probably little different from the butterflies and genitalia that one sees in a Rorschach test. The economist Burton Malkiel, author of the popular investment text A Random Walk Down Wall Street, had his students construct mythical stock price charts by flipping coins. When Malkiel showed these to practicing chartists, they discovered their favorite patterns lurking in the random squiggles (Malkiel 1990, pp. 135-136). Most market participants use some combination of technical and fundamental analysis, but that doesn't mean their performance is terribly successful. According to Norm Zadeh, who rates the performance of money managers, only about 1-2% of all money-slingers have a consistent and substantial record of good performance.

 

pages: 345 words: 87,745

The Power of Passive Investing: More Wealth With Less Work by Richard A. Ferri

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asset allocation, backtesting, Bernie Madoff, capital asset pricing model, cognitive dissonance, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, endowment effect, estate planning, Eugene Fama: efficient market hypothesis, fixed income, implied volatility, index fund, Long Term Capital Management, passive investing, Ponzi scheme, prediction markets, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, too big to fail, transaction costs, Vanguard fund, yield curve

Fama’s meticulously researched Ph.D. thesis was published in 1965 and titled “The Behavior of Stock Market Prices.” The purpose of the paper was to test the theory that stock market prices are random and follow what’s commonly referred to today as a random walk.8 Fama’s work led to the formation of the efficient market hypothesis (EMH), which is a theory of efficient security pricing in free and open markets. The theory states that all known and available information is already reflected in current securities prices. Thus, the price agreed to by a willing buyer and seller in the open market is the best estimate, good or bad, of the investment value of a security. Any new information is nearly instantaneously incorporated into market prices. This makes it almost impossible to capture excess returns without taking greater risk or having inside information about securities.

See Early performance studies Permanent loss Persistence of performance academic studies: bond funds Carhart’s work Fama and French “Hot Hands” study Personal trust(s): fiduciary investing and taxes and Pioneering Portfolio Management (Swensen) Plain vanilla index Policy changes Ponzi scheme Poor accounting Portfolio choices: bottom line and changing the model efficient portfolios fund selection strategies modeling the active bet modifications to model portfolios of active funds quantifying of random portfolio results real-world test relative performance model short-term/long-term Portfolio management: annual evaluation debate on facts about objective of options for Portfolio Selection: Efficient Diversification of Investments (Markowitz) Portfolio theory, modern Positive period weighting Predictors of top performance: fund expenses as qualitative factors as ratings as Pre-inflation return Price-earnings ratio (P/E): growth/value stocks portfolio returns and Price-to-book (P/B) Price-to-cash-flow Price Waterhouse Private trust management: categories of trusts restatement of trusts (third) taxes and UPIA and active management UPIA and passive investing Procrastinating non-index investors: changing/staying the course definition of endowment effect and land of the lost modern portfolio theory and veering off course Prospect theory Prudence, elements of Prudent Investor Act: A Guide to Understanding, The (Simon) Prudent Investor Rule Prudent Man Rule “Purity Hypothesis, The” Qualitative factors, performance and Random walk Random Walk Down Wall Street, A (Malkiel) Rating methods, performance and Real estate Real Estate Investment Trust Act Real Estate Investment Trusts (REITs) Real return Rebalancing portfolio Recovery, market Registered investment advisor (RIA) Reinganum, Marc REITs.

“Portfolio Selection,” The Journal of Finance 7, no. 1 (March 1952): 77–91. 8. Eugene Fama, “The Behavior of Stock Market Prices,” Journal of Business 38, no. 1 (January 1965): 34–105. 9. Ibid., 92. 10. William F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” The Journal of Finance 19, no. 3 (1964): 425–42. 11. Jack L. Treynor, “How to Rate Management of Investment Funds,” Harvard Business Review 43 (1965): 63–75. 12. William F. Sharpe, “Mutual Fund Performance,” Journal of Business 39 (1996): 119–138. 13. Michael C. Jensen, “The Performance of Mutual Funds in the Period 1945–1964,” The Journal of Finance 23, no. 2 (1967): 389–416. Chapter 3: The Birth of Index Funds 1. Burton Malkiel, A Random Walk Down Wall Street (New York: W.W. Norton, 1973). 2. Paul A. Samuelson, “Challenge to Judgment,” Journal of Portfolio Management 1, no. 1 (1974): 17–19. 3.

 

pages: 120 words: 39,637

The Little Book That Still Beats the Market by Joel Greenblatt

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backtesting, index fund, random walk, transaction costs

It is the same thing! You would be buying $10 worth of EBIT for $60, either way!43 Company A Company B Enterprise value (price + debt) 60 + 0 = $60 10 + 50 = $60 EBIT 10 10 A Random Walk Spoiled For many years, academics have debated whether it is possible to find bargain-priced stocks other than by chance. This notion, sometimes loosely referred to as the random walk or efficient market theory, suggests that for the most part, the stock market is very efficient at taking in all publicly available information and setting stock prices. That is, through the interaction of knowledgeable buyers and sellers, the market does a pretty good job of pricing stocks at “fair” value. This theory, along with the failure of most professional managers to beat the market averages over the long term,44 has understandably led to the movement toward indexing, a cost-effective strategy designed to merely match the market’s return.

The worst return during those 10+ years for following the Haugen strategy for 36 months straight (with annual turnover) was -43.1 percent. The worst 36-month period for the magic formula was +14.3 percent. Not only that, the magic formula used 69 fewer factors and a lot less math!52 So, here’s the point. The magic formula appears to perform very well. I think and hope it will continue to perform well in the future. I also hope that, just as Mark Twain aptly referred to golf as “a good walk spoiled,” perhaps someday the random walk will finally be considered spoiled as well.53 1 Bank deposits up to $100,000 are guaranteed by an agency of the U.S. government. You must hold your bank deposit or your bond until it matures (possibly 5 or 10 years, depending upon what you buy) to guarantee no loss of your original investment. 2 And yes, the dog was fine. 3 To find out what Jimbo should do, check out the box at the end of the chapter!

Each day he offers to buy your share of the business or sell you his share of the business at a particular price. Mr. Market always leaves the decision completely to you, and every day you have three choices. You can sell your shares to Mr. Market at his stated price, you can buy Mr. Market’s shares at that same price, or you can do nothing. Sometimes Mr. Market is in such a good mood that he names a price that is much higher than the true worth of the business. On those days, it would probably make sense for you to sell Mr. Market your share of the business. On other days, he is in such a poor mood that he names a very low price for the business. On those days, you might want to take advantage of Mr. Market’s crazy offer to sell you shares at such a low price and to buy Mr. Market’s share of the business. If the price named by Mr. Market is neither very high nor extraordinarily low relative to the value of the business, you might very logically choose to do nothing.

 

Data Mining: Concepts and Techniques: Concepts and Techniques by Jiawei Han, Micheline Kamber, Jian Pei

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bioinformatics, business intelligence, business process, Claude Shannon: information theory, cloud computing, computer vision, correlation coefficient, cyber-physical system, database schema, discrete time, distributed generation, finite state, information retrieval, iterative process, knowledge worker, linked data, natural language processing, Netflix Prize, Occam's razor, pattern recognition, performance metric, phenotype, random walk, recommendation engine, RFID, semantic web, sentiment analysis, speech recognition, statistical model, stochastic process, supply-chain management, text mining, thinkpad, web application

The eccentricity of a is 2, that is, , , and . Thus, the radius of G is 2, and the diameter is 3. Note that it is not necessary that . Vertices c, d, and e are peripheral vertices. Figure 11.13 A graph, G, where vertices c, d, and e are peripheral. SimRank: Similarity Based on Random Walk and Structural Context For some applications, geodesic distance may be inappropriate in measuring the similarity between vertices in a graph. Here we introduce SimRank, a similarity measure based on random walk and on the structural context of the graph. In mathematics, a random walk is a trajectory that consists of taking successive random steps. Similarity between people in a social network Let's consider measuring the similarity between two vertices in the AllElectronics customer social network of Example 11.18. Here, similarity can be explained as the closeness between two participants in the network, that is, how close two people are in terms of the relationship represented by the social network.

Ada and Bob may randomly forward such information to their friends (or neighbors ) in the network. The closeness between Ada and Bob can then be measured by the likelihood that other customers simultaneously receive the promotional information that was originally sent to Ada and Bob. This kind of similarity is based on the random walk reachability over the network, and thus is referred to as similarity based on random walk. Let's have a closer look at what is meant by similarity based on structural context, and similarity based on random walk. The intuition behind similarity based on structural context is that two vertices in a graph are similar if they are connected to similar vertices. To measure such similarity, we need to define the notion of individual neighborhood. In a directed graph , where V is the set of vertices and is the set of edges, for a vertex , the individual in-neighborhood of v is defined as(11.29) Symmetrically, we define the individual out-neighborhood of v as(11.30) Following the intuition illustrated in Example 11.20, we define SimRank, a structural-context similarity, with a value that is between 0 and 1 for any pair of vertices.

The probability of the tour is defined as(11.35) To measure the probability that a vertex w receives a message that originated simultaneously from u and v, we extend the expected distance to the notion of expected meeting distance, that is,(11.36) where is a pair of tours and of the same length. Using a constant C between 0 and 1, we define the expected meeting probability as(11.37) which is a similarity measure based on random walk. Here, the parameter C specifies the probability of continuing the walk at each step of the trajectory. It has been shown that for any two vertices, u and v. That is, SimRank is based on both structural context and random walk. 11.3.3. Graph Clustering Methods Let's consider how to conduct clustering on a graph. We first describe the intuition behind graph clustering. We then discuss two general categories of graph clustering methods. To find clusters in a graph, imagine cutting the graph into pieces, each piece being a cluster, such that the vertices within a cluster are well connected and the vertices in different clusters are connected in a much weaker way.

 

pages: 504 words: 139,137

Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined by Lasse Heje Pedersen

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algorithmic trading, Andrei Shleifer, asset allocation, backtesting, bank run, banking crisis, barriers to entry, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, commodity trading advisor, conceptual framework, corporate governance, credit crunch, Credit Default Swap, currency peg, David Ricardo: comparative advantage, declining real wages, discounted cash flows, diversification, diversified portfolio, Emanuel Derman, equity premium, Eugene Fama: efficient market hypothesis, fixed income, Flash crash, floating exchange rates, frictionless, frictionless market, Gordon Gekko, implied volatility, index arbitrage, index fund, interest rate swap, late capitalism, law of one price, Long Term Capital Management, margin call, market clearing, market design, market friction, merger arbitrage, mortgage debt, New Journalism, paper trading, passive investing, price discovery process, price stability, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, systematic trading, technology bubble, time value of money, total factor productivity, transaction costs, value at risk, Vanguard fund, yield curve, zero-coupon bond

To answer these questions, we first needed to know whether we were facing a liquidity spiral or an unlucky step in the random walk of an efficient market. The efficient market theory says that, going forward, prices should fluctuate randomly, whereas the liquidity spiral theory says that when prices are depressed by forced selling, prices will likely bounce back later. These theories clearly had different implications for how to position our portfolio. On Monday, we became completely convinced that we were facing a liquidity event. All market dynamics pointed clearly in the direction of liquidity and defied the random walk theory (which implies that losing every 10 minutes for several days in a row is next to impossible). Knowing that you are facing a liquidity event and that prices will eventually snap back is one thing; knowing when this will happen and what to do about it is another.

When the predictor is the dividend yield, we can also interpret the magnitude of the b coefficient. In particular, a naïve benchmark is that b = 1. This means that, if the dividend yield is one percentage point larger, then the stock return is also expected to be one percentage point larger. In other words, the dividend yield predicts the stock return because it is part of the stock return (as seen in equation 10.3), but it does not predict the price appreciation. In contrast, the random walk hypothesis b = 0 means that the price appreciation is expected to be low when the dividend yield is high, such that the overall expected equity return is independent of dividend yields. Perhaps the truth lies somewhere between these benchmarks? The data suggest otherwise. I run this regression from 1926 to 2013 with U.S. monthly data, where the monthly excess return is annualized by multiplying by 12 to make it comparable to annual dividends (the result is almost the same with 1-year forward returns, but the t-statistics must be estimated in a more complex way with overlapping data).2 The time series of the dividend yield is plotted in figure 10.1.

The losses came with remarkable consistency. Looking at the blinking screen with live P&L (profits and losses), I saw new million-dollar losses every 10 minutes for a couple of days—a clear pattern that defied the random walk theory of efficient markets and, ironically, showed remarkable likeness to my own theories. Let me explain, but let’s start from the beginning. My career as a finance guy started in 2001 when I graduated with a Ph.D. from Stanford Graduate School of Business and joined the finance faculty at the New York University Stern School of Business. My dissertation research studied how prices are determined in markets plagued by liquidity risk, and I hoped that being at a great university in the midst of things in New York City would help me find out what was going on both inside and outside the Ivory Tower.

 

Culture and Prosperity: The Truth About Markets - Why Some Nations Are Rich but Most Remain Poor by John Kay

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Albert Einstein, Asian financial crisis, Barry Marshall: ulcers, Berlin Wall, Big bang: deregulation of the City of London, California gold rush, complexity theory, computer age, constrained optimization, corporate governance, corporate social responsibility, correlation does not imply causation, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, Donald Trump, double entry bookkeeping, double helix, Edward Lloyd's coffeehouse, equity premium, Ernest Rutherford, European colonialism, experimental economics, Exxon Valdez, failed state, financial innovation, Francis Fukuyama: the end of history, George Akerlof, George Gilder, greed is good, haute couture, illegal immigration, income inequality, invention of the telephone, invention of the wheel, invisible hand, John Nash: game theory, John von Neumann, Kevin Kelly, knowledge economy, labour market flexibility, late capitalism, Long Term Capital Management, loss aversion, Mahatma Gandhi, market bubble, market clearing, market fundamentalism, means of production, Menlo Park, Mikhail Gorbachev, money: store of value / unit of account / medium of exchange, moral hazard, Naomi Klein, Nash equilibrium, new economy, oil shale / tar sands, oil shock, pets.com, popular electronics, price discrimination, price mechanism, prisoner's dilemma, profit maximization, purchasing power parity, QWERTY keyboard, Ralph Nader, RAND corporation, random walk, rent-seeking, risk tolerance, road to serfdom, Ronald Coase, Ronald Reagan, second-price auction, shareholder value, Silicon Valley, Simon Kuznets, South Sea Bubble, Steve Jobs, telemarketer, The Chicago School, The Death and Life of Great American Cities, The Market for Lemons, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, total factor productivity, transaction costs, tulip mania, urban decay, Washington Consensus, women in the workforce, yield curve, yield management

These observations are well-known, have influenced other people's assessments, and are "in the price." They are the reasons why the odds on Seabiscuit are short, the price of General Electric shares is high, mobile phone companies trade at large multiples of their current earnings, and the dollar is strong. There is powerful evidence to support the efficient market hypothesis. The theory predicts that the prices of risks will follow a "random walk." A random walk is a process in which the next step is equally likely to be in any direction. Many physical processes have these characteristics, such as the movement of particles in liquids. This is an area where models derived from statistical mechanics seem to work, and the Black-Scholes model described below is grounded in the analysis of physical systems. And numerous statistical analyses of prices in markets for securities and commodities have confirmed that they display the characteristics of a random walk.

And numerous statistical analyses of prices in markets for securities and commodities have confirmed that they display the characteristics of a random walk. In an early test of the theory, the statistician Maurice Kendall discovered that all but one of the series he studied fitted the random walk prediction. 5 It emerged that the one that did not was not in fact a series of actual market transactions but had been prepared as an average of estimated market prices. This is the kind of satisfYing confirmation of a theory that physicists often experience but is rarely available in the social sciences. The efficient market hypothesis invites a skeptical view of claims of the ability of experts to make money themselves-and even more, perhaps, of their ability to make money for other people-by trading risks. This skepticism is more readily applied to racing tipsters than to professional investment managers.

A characteristic of a market in which one side information asymmetry (buyer or seller) is better informed about the properties of the good or service than the other (seller or buyer). intellectual property Rights created by copyright, patent, or trademark legislation and associated regulations. market anomalies Observed deviations from the efficient market hypothesis. mercantilism A theory of international trade (widely held before Adam Smith and still adhered to by some devotees of DIY economics) that draws economies of scale { 364} noise trader Pareto efficiency Pareto improvement path dependency primary market productivity purchasing power parity put option random walk theory secondary market winner's curse Glossary an analogy between the exports and imports of states and the revenues and expenses of firms. A buyer or seller (especially in securities markets) whose behavior does not reflect views about the fundamental value (prospective earnings, etc.) of what he or she is buying. The property of an allocation of resources in which no one can be made better off without making someone else worse off A change that makes some people better off and no one worse off A dynamic process in which behavior is affected indefinitely by initial conditions.

 

pages: 437 words: 132,041

Alex's Adventures in Numberland by Alex Bellos

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Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Black Swan, Black-Scholes formula, Claude Shannon: information theory, computer age, Daniel Kahneman / Amos Tversky, family office, forensic accounting, game design, Georg Cantor, Henri Poincaré, Isaac Newton, pattern recognition, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, random walk, Richard Feynman, Richard Feynman, SETI@home, Steve Jobs, The Bell Curve by Richard Herrnstein and Charles Murray, traveling salesman

If the chances of losing are greater than the chances of winning, the map of the random walk drifts downward, rather than tracking the horizontal axis. In other words, bankruptcy looms quicker. Random walks explain why gambling favours the very rich. Not only will it take much longer to go bankrupt, but there is also more chance that your random walk will occasionally meander upward. The secret of winning, for the rich or the poor, however, is knowing when to stop. Inevitably, the mathematics of random walks contains some head-popping paradoxes. In the graphs chapter 9 where Coin Man moves up or down depending on the results of a coin toss, one would expect the graph of his random walk to regularly cross the horizontal axis. The coin gives a 50:50 chance of heads or tails, so perhaps we would expect him to spend an equal amount of time either side of his starting point. In fact, though, the opposite is true.

Instead of letting Coin Man’s random walk describe a physical journey, let it represent the value of his bank account. And let the coin flip be a gamble. Heads he wins £100, tails he loses £100. The value in his bank account will swing up and down in increasingly large waves. Let us say that the only barrier that will stop Coin Man playing is when the value of his account is £0. We know it is guaranteed he will get there. In other words, he will always go bankrupt. This phenomenon – that eventual impoverishment is a certainty – is known evocatively as gambler’s ruin. Of course, no casino bets are as generous as the flipping of a coin (which has a payback percentage of 100). If the chances of losing are greater than the chances of winning, the map of the random walk drifts downward, rather than tracking the horizontal axis.

Choose a number from 0 to 7 randomly. If the number comes up, trace a line in that direction. Do this repeatedly to create a path. Venn carried this out with the most unpredictable sequence of numbers he knew: the decimal expansion of pi (excluding 8s and 9s, and starting with 1415). The result, he wrote, was ‘a very fair graphical indication of randomness’. Venn’s sketch is thought to be the first-ever diagram of a ‘random walk’. It is often called the ‘drunkard’s walk’ because it is more colourful to imagine that the original dot is instead a lamp-post and the path traced is the random staggering of a drunk. One of the most obvious questions to ask is how far will the drunk wander from the point of origin before collapsing? On average, the longer he has been walking, the further away he will be. It turns out that his distance increases with the square root of the time spent walking.

 

pages: 440 words: 108,137

The Meritocracy Myth by Stephen J. McNamee

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affirmative action, Affordable Care Act / Obamacare, Bernie Madoff, British Empire, collective bargaining, computer age, conceptual framework, corporate governance, deindustrialization, delayed gratification, demographic transition, desegregation, deskilling, equal pay for equal work, estate planning, failed state, fixed income, gender pay gap, Gini coefficient, glass ceiling, helicopter parent, income inequality, informal economy, invisible hand, job automation, joint-stock company, labor-force participation, low-wage service sector, marginal employment, Mark Zuckerberg, mortgage debt, mortgage tax deduction, new economy, New Urbanism, obamacare, occupational segregation, pink-collar, Plutocrats, plutocrats, Ponzi scheme, post-industrial society, prediction markets, profit motive, race to the bottom, random walk, school choice, Scientific racism, Steve Jobs, The Bell Curve by Richard Herrnstein and Charles Murray, The Spirit Level, The Wealth of Nations by Adam Smith, too big to fail, trickle-down economics, upwardly mobile, We are the 99%, white flight, young professional

The best models account for only about half of the variance in income attainment and about two-thirds of the variance in occupational attainment. Some of the variance “unexplained” by these models could come from a combination of leaving out factors that matter and from less-than-perfect measures of the factors included. But some of the unexplained or residual variation is also likely due to simple random variation—or, in more everyday language, “luck.” The Random-Walk Hypothesis So far in this chapter, our discussion has revolved around education, jobs, and income. We have argued that the “going rate” of return for the jobs that people hold depends, at least in part, on factors that lie outside the control of individual workers themselves. Getting ahead in terms of the occupations people hold and the pay they receive involves an element of luck—being in the right place at the right time.

., cruise lines, medical and assisted-living services). Finally, developmental disequilibrium refers to unequal conditions of development in different countries that create opportunities to introduce products and services available in one place that are not yet available in another place. To some extent, those who are the most clever or most insightful might be better able to anticipate various market shakeups. However, the “random-walk hypothesis” developed by economists seems to account best for who ends up with the right idea, the right product, or the right service. The argument is simply that striking it rich tends to be like getting struck by lightning: many are walking around, but only a few get randomly struck. Large fortunes tend to be made quickly, taking early advantage of market shakeups. The window for striking it rich is very narrow since once it is open, others quickly rush in.

Clearly, some individual entrepreneurs who strike out on their own manage to defy the odds and do very well. Those who succeed do not necessarily work harder than those who fail; nor are they necessarily more inherently capable or meritorious. Having sufficient start-up capital to launch new enterprises (it takes money to make money) and being in the right place at the right time with the right idea (random-walk hypothesis) do, however, have a great deal to do with entrepreneurial success. The Case of Microsoft In rare circumstances, such individuals may take advantage of temporary market imbalances and launch new enterprises that start out small but evolve into corporate giants. One particularly prominent example is the establishment of the Microsoft Corporation in 1975, now the forty-second largest corporation in the world (Forbes 2012a).

 

pages: 464 words: 117,495

The New Trading for a Living: Psychology, Discipline, Trading Tools and Systems, Risk Control, Trade Management by Alexander Elder

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additive manufacturing, Atul Gawande, backtesting, Benoit Mandelbrot, buy low sell high, Checklist Manifesto, deliberate practice, diversification, Elliott wave, endowment effect, loss aversion, mandelbrot fractal, margin call, offshore financial centre, paper trading, Ponzi scheme, price stability, psychological pricing, quantitative easing, random walk, risk tolerance, short selling, South Sea Bubble, systematic trading, The Wisdom of Crowds, transaction costs, transfer pricing, traveling salesman, tulip mania

market data for profit targets in stops in Positive Directional line Positive mathematical expectation Power: of bears vs. bulls: A/D closing prices divergences Force Index MACD-Histogram MACD Line miscellaneous indicators and NH-NL zero line On-Balance Volume open interest volume profits and feeling of of trends Premiums: futures options Press, signals from Prechter, Robert Price(s). See also Closing prices; Opening prices on bar charts as consensus of value crowd behavior reflected in divergences from in Force Index indicators derived from as leader of market crowd long-term cycles in memories of of options in Random Walk theory short-term cycles in slippage support and resistance levels and understanding of volume value vs. Price risk, hedging and Price shocks Pring, Martin Private traders, see Individual traders Probabilities businessman's risk choices based on emotions vs.

People may have knowledge, but the emotional pull of the crowd often leads them to trade irrationally. A good analyst can detect repetitive patterns of crowd behavior on his charts and exploit them. Random Walk theorists claim that market prices change at random. Sure, there is a fair bit of randomness or “noise” in the markets, just as there is randomness in any crowd. Still, an intelligent observer can identify repetitive behavior patterns of a crowd and make sensible bets on their continuation or reversal. People have memories; they remember past prices, and their memories influence their decisions to buy or sell. Memories help create support under the market and resistance above it. Random Walkers deny that memories influence our behavior. As Milton Friedman pointed out, prices carry information about the availability of supply and the intensity of demand. Market participants use that information when deciding to buy or sell.

See also Japanese candlesticks Cash trades, futures compared to Catastrophic stops Ceilings, for commodities CFDs (contracts for difference) CFTC, see Commodity Futures Trading Commission Channels in A-trades Average True Range combining divergences and constructing in day-trading defined and moving averages in setting profit targets symmetrical Channel trading systems constructing channels and mass psychology standard deviation (Bollinger bands) symmetrical trading rules Chaos theory Chart analysis bar charts chaos theory detecting bias in diagonals in Efficient Market theory history of charting and insider trading Japanese candlesticks kangaroo tails “nature's law” Random Walk subjectiveness in support and resistance causes of strength of trading rules and true and false breakouts trends and trading ranges and conflicting timeframes of markets deciding to trade or wait hard right edge identifying and mass psychology as window into mass psychology Charting Commodity Market Price Behavior (L. Dee Belveal) Chart patterns: defined at right edge of charts RSI trendlines subjective interpretation of swings of mass psychology shown in Checklists Checklist Manifesto, The (Atul Gawande) Childhood, mental baggage from Churchill, Winston Classical chart analysis, see Chart analysis “Climax bottoms” Climax indicator Closing prices: Advance/Decline line on candlestick charts of daily and weekly bars of daily charts as most important consensus of value relationship of opening prices and for settlement of trading accounts Cohen, Abraham W.

 

pages: 500 words: 145,005

Misbehaving: The Making of Behavioral Economics by Richard H. Thaler

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Albert Einstein, Amazon Mechanical Turk, Andrei Shleifer, Apple's 1984 Super Bowl advert, Atul Gawande, Berlin Wall, Bernie Madoff, Black-Scholes formula, capital asset pricing model, Cass Sunstein, Checklist Manifesto, choice architecture, clean water, cognitive dissonance, conceptual framework, constrained optimization, Daniel Kahneman / Amos Tversky, delayed gratification, diversification, diversified portfolio, Edward Glaeser, endowment effect, equity premium, Eugene Fama: efficient market hypothesis, experimental economics, Fall of the Berlin Wall, George Akerlof, hindsight bias, Home mortgage interest deduction, impulse control, index fund, invisible hand, Jean Tirole, John Nash: game theory, John von Neumann, late fees, law of one price, libertarian paternalism, Long Term Capital Management, loss aversion, market clearing, Mason jar, mental accounting, meta analysis, meta-analysis, More Guns, Less Crime, mortgage debt, Nash equilibrium, Nate Silver, New Journalism, nudge unit, payday loans, Ponzi scheme, presumed consent, pre–internet, principal–agent problem, prisoner's dilemma, profit maximization, random walk, randomized controlled trial, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Coase, Silicon Valley, South Sea Bubble, statistical model, Steve Jobs, technology bubble, The Chicago School, The Myth of the Rational Market, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, transaction costs, ultimatum game, Walter Mischel

., 29 surveys used in experiments of, 38 psychological accounting, see mental accounting “Psychology and Economics Conference Handbook,” 163 “Psychology and Savings Policies” (Thaler), 310–13 Ptolemaic astronomy, 169–70 public goods, 144–45 Public Goods Game, 144–46 Punishment Game, 141–43, 146 Pythagorean theorem, 25–27 qualified default investment alternatives, 316 quantitative analysis, 293 Quarterly Journal of Economics, 197, 201 quasi-hyperbolic discounting, 91–92 quilt, 57, 59, 61, 65 Rabin, Matthew, 110, 181–83, 353 paternalism and, 323 racetracks, 80–81, 174–75 Radiolab, 305 randomized control trials (RCTs), 8, 338–43, 344, 371 in education, 353–54 Random Walk Down Walk Street, A (Malkiel), 242 rational expectations, 98, 191 in macroeconomics, 209 rational forecasts, 230–31 rationality: bounded, 23–24, 29, 162 Chicago debate on, 159–63, 167–68, 169, 170, 205 READY4K!, 343 real business cycle, 191 real estate speculation, 372 rebates, 121–22, 363 recessions, 131–32 fiscal policy in, 209 reciprocity, 182 Reder, Mel, 159 Reeves, Richard, 330, 332 reference price, 59, 61–62 regression toward the mean, 222–23 research and development, 189 reservation price, 150 retirement, savings for, see savings, for retirement return, risk vs., 225–29 returns, discounts and, 242 revealed preferences, 86 “right to carry” law, 265n risk: measurement of, 225–29 return vs., 225–29 “Risk and Uncertainty: A Fallacy of Large Numbers” (Samuelson), 194 risk aversion, 28–29, 33, 83, 84 crowds and, 301, 369 on Deal or No Deal, 298–99 equity premium and, 191–92 of managers, 190–91 moderate vs. extreme, 298–99 risk premium, 14–16, 226 irrationality of, 16–17 risk-seeking behavior, 81, 83 roadside stands, 146–47 Robie House, 270 Rochester, University of, 41, 51, 205, 216 Roger and Me (film), 122 rogue traders, 84 Roll, Richard, 167, 208 Romer, David, 292 Rosen, Sherwin, 12, 15, 17, 21, 35, 42, 321 at behavioral economics debate, 159 Rosett, Richard, 17, 34, 46, 68, 73 Ross, Lee, 181 Ross, Steve, 167 Roth, Alvin, 130, 148 Royal Dutch Shell, 248, 249, 251 rules (in self-control), 106–9, 111 Russell, Thomas, 18, 203 Russell Sage Foundation, 177–78, 179, 181, 185 Russell Sage summer camps, 181–84, 199 Russian roulette, 13–14 Russo, Jay, 122 S&P 500, 232, 233 Sadoff, Sally, 354 safety, paying for, 13–14 St.

Look around”: Quoted in Fox (2009), p. 199. 240 more rigorous, thorough, and polite version of the “idiots” paper: De Long et al. (1990). 241 “an expensive monument”: Graham ([1949] 1973), p. 242. 242 That is exactly what we found: Lee, Shleifer, and Thaler (1991). 242 thesis on closed-end funds: Thompson (1978). 242 A Random Walk Down Wall Street: Malkiel (1973). 243 “But they can’t”: Chen, Kan, and Miller (1993), p. 795. 243 the last set of stones: The five papers are: Lee, Shleifer, and Thaler (1991), Chen, Kan, and Miller (1993a), Chopra et al. (1993a), Chen, Kan, and Miller (1993b), and Chopra et al. (1993b). Chapter 26: Fruit Flies, Icebergs, and Negative Stock Prices 249 LTCM had collapsed: Lowenstein (2000). 249 in a paper they published on this topic: Shleifer and Vishny (1997). 250 an academic paper about the . . . episode: Lamont and Thaler (2003). 251 “we might define an efficient market”: Black (1986), p. 553. 252 “liar loans”: See Mian and Sufi (2014).

., Paul Andreassen, and Stanley Schachter. 1985. “II. Random and Non-Random Walks on the New York Stock Exchange.” Journal of Economic Behavior and Organization 6, no. 4: 331–8. Hsee, Christopher K., Yang Yang, Yangjie Gu, and Jie Chen. 2009. “Specification Seeking: How Product Specifications Influence Consumer Preference.” Journal of Consumer Research 35, no. 6: 952–66. Internal Revenue Service. 1998. “Revenue Ruling 98–30.” Internal Revenue Bulletin 25 (June 22): 8–9. Available at: http://www.irs.gov/pub/irs-irbs/irb98-25.pdf. Jackson, Eric. 2014. “The Case For Apple, Facebook, Microsoft Or Google Buying Yahoo Now.” Forbes.com, July 21. Available at: http://www.forbes .com/sites/ericjackson/2014/07/21/the-case-for-apple-facebook-micro soft-or-google-buying-yahoo-now. Jensen, Michael C. 1969. “Risk, The Pricing of Capital Assets, and the Evaluation of Investment Portfolios.”

 

pages: 584 words: 187,436

More Money Than God: Hedge Funds and the Making of a New Elite by Sebastian Mallaby

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Andrei Shleifer, Asian financial crisis, asset-backed security, automated trading system, bank run, barriers to entry, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bonfire of the Vanities, Bretton Woods, capital controls, Carmen Reinhart, collapse of Lehman Brothers, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, currency manipulation / currency intervention, currency peg, Elliott wave, Eugene Fama: efficient market hypothesis, failed state, Fall of the Berlin Wall, financial deregulation, financial innovation, financial intermediation, fixed income, full employment, German hyperinflation, High speed trading, index fund, Kenneth Rogoff, Long Term Capital Management, margin call, market bubble, market clearing, market fundamentalism, merger arbitrage, moral hazard, natural language processing, Network effects, new economy, Nikolai Kondratiev, pattern recognition, pre–internet, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, rolodex, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical arbitrage, statistical model, technology bubble, The Great Moderation, The Myth of the Rational Market, too big to fail, transaction costs

Of course, academia is a broad church, teaming with energetic skeptics. But from the mid 1960s to the mid 1980s, the prevailing view was that the market is efficient, prices follow a random walk, and hedge funds succeed mainly by being lucky. There is a powerful logic to this account. If it were possible to know with any confidence that the price of a particular bond or equity is likely to move up, smart investors would have pounced and it would have moved up already. Pouncing investors ensure that all relevant information is already in prices, though the next move of a stock will be determined by something unexpected. It follows that professional money managers who try to foresee price moves will generally fail in their mission. As this critique anticipates, plenty of hedge funds have no real “edge”—if you strip away the marketing hype and occasional flashes of dumb luck, there is no distinctive investment insight that allows them to beat the market consistently.

He was required to write a memo to the management explaining his miscalculations.23 The new risk-control system was connected to another rethink that followed the corn debacle: Weymar and his colleagues developed fresh respect for trends in prices. Of course, efficient-market theory holds that such trends do not exist: The random-walk consensus was so dominant that, through the 1970s and much of the 1980s, it was hard to get alternative views published in academic journals.24 But Frank Vannerson had gotten his hands on a trove of historical commodity price data that had been gathered and formatted by Dunn & Hargitt, a firm in Indiana. Before leaving Nabisco, Vannerson had spent a year working on the Dunn & Hargitt data, analyzing daily prices for fifteen commodities; and by the time Commodities Corporation opened its doors in March 1970, he had satisfied himself that price trends really did exist, no matter what academics might assert to the contrary.25 Moreover, Vannerson had devised a computer program that could trade on that finding.

Alfred Cowles, “A Revision of Previous Conclusions Regarding Stock Price Behavior,” Econometrica 28, no. 4 (October 1960). 45. By 1965, Jones’s earlier faith in charts was coming under attack even from the chartists themselves. In his 1949 essay in Fortune, Jones had singled out a Russian immigrant named Nicholas Molodovsky as “the most scientific and experimental of technical students,” reporting that with the exception of two episodes in which he had called the market wrong, “his predictions have been nearly perfect.” But in 1965 Molodovsky, by then the editor of the influential Financial Analysts Journal, commissioned a paper from a rising academic star named Eugene Fama, which appeared under the title “Random Walks in Stock Market Prices.” Fama compared chart following to astrology. By popularizing Fama’s random-walk theory, Molodovsky was burning the ground under Jones’s feet; the premise of Jones’s fund was under attack from one of its progenitors.

 

pages: 447 words: 104,258

Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues by Alain Ruttiens

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algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative finance, random walk, risk/return, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

MGARCH see multivariate GARCH process mixed data sampling (MIDAS) process mixed jump diffusion model model risk modified duration (MD) modified VaR (MVaR) moments CAPM money markets moneyness Monte Carlo simulation accuracy exotic options fractional Brownian motion jump processes sensitivities simulation examples VaR Moody’s rating agency mortgage-backed securities Morton see Heath, Jarrow and Morton model moving average (MA) process moving averages ARIMA process ARMA process MA process MSCI Barra MtM see marked to market multivariate GARCH (MGARCH) process MVaR see modified VaR NASDAQ index NDFs see non-deliverable forwards NDOs see non-delivery options neural networks (NNs) “no arbitrage” condition non-deliverable forwards (NDFs) non-delivery options (NDOs) non-financial commodity futures non-linear models non-path dependent options non-stationary processes normal distribution Norwegian krone (NOK) OECD see Organisation for Economic Co-operation and Development offer price Ohrstein–Uhlenbeck processes OIS see overnight index swaps Omega ratio “open” prices option pricing Black–Scholes formula CRR model exotic options finite difference methods implied volatility jump processes Merton model Monte Carlo simulations sensitivities valuation troubles volatility see also prices/pricing options bond duration credit derivative valuation option contract value pricing see also exotic options Organisation for Economic Co-operation and Development (OECD) out of the money (OTM) caps options outright forward operation overnight index swaps (OIS) parametric method, VaR Parkinson volatility participating forward contracts (PFCs) path-dependent options payer swaps percent per annum performance absolute measures attribution Calmar ratio contribution global example IR Jensen’s alpha market MDD non-normal returns Omega ratio relative measures risk measures Sharpe ratio Sortino ratio stocks portfolios swaps TE Treynor ratio Z-score PFCs see participating forward contracts platykurtic distributions POF see Proportion of failures test Poisson processes polynomial curve methods portfolios bond duration bond selection immunization performance attribution contribution Portfolio Theory risk management Portfolio Theory APT model CAPM equities hypotheses Markowitz model performance risk and return valuation troubles “position risk” concept present value (PV) bond duration CRSs IRSs short-term rates spot rates zero-coupon swaps price of risk, CAPM prices/pricing APT model bid/ask bonds CAPM caps CBs CDOs CRSs floors futures high/low IRSs “open”/“close” second-generation swaps spot instruments swaptions see also market prices; option pricing price of time, CAPM price-weighted indexes pricing sensitivities see sensitivities probability risk neutral see also stochastic processes Proportion of failures (POF) test putable bonds put options call-put parity see also options PV see present value quanto swaps randomness random numbers random walks RaV see Risk at Value realized volatility models real option method receiver swaps recovery rates reference currency (ref) regime-switching models regression, NNs relative VaR return measures expected return performance Portfolio Theory in practice risk vs return ratios several stock positions single stock positions time periods returns general Wiener process instantaneous measures “reverse cash and carry” operations rho risk see individual types Risk at Value (RaV) “risk-free” bonds risk-free yield curve risk management risk measures performance attribution contribution Portfolio Theory return measures risk vs return ratios several positions single position VaR risk neutral probability risk premium, CAPM “risky” bonds Rogers–Satchell volatility Roll, R.

This can be explained by economic factors: a company is supposed to re-invest all or part (in case of dividend distribution) of its profits, and thus grow over time, and stock prices must also follow inflation over the long run. Of course, on a shorter horizon of time, prices may decline, even during periods lasting several consecutive years. So that, equity and index options pricing models clearly fit with the random walk hypothesis (although not necessarily strictly Gaussian). Currency prices do not present any global trend over time: a currency is priced relatively to another currency, and economic as well as speculative hazards comfort the random walk hypothesis. But over time, interest rates show the peculiar behavior of successive rising and falling phases. Unfortunately, there is no hope for anticipating both the amplitude and the periodicity of such cycles. We may carefully bound these cycles by, upwards, the “abnormally” very high (more than, say, 15% p.a.) interest rates around the 1980s (that is, before central banks learned to actually control inflation) and by 0 downwards: since the 1990s, Japan has faced interest rates at 0% or very slightly higher, but actually no negative interest rates, including inflation.

The comparison between a (y + risk premium) and the yield of a risk-less bond of the same features is called yield spread analysis. Beyond its impact of a risky bond price, the credit default risk will be further developed in Chapter 13. Clean Price versus Dirty Price Bond prices are quoted by the market as shown above. But on the secondary market, in the case of a trade between two coupon dates, in addition to the market quoted price the buyer must pay to the seller the portion of the coupon pro rata temporis, called accrued interest. The same principle is also applied in accounting, between two coupon dates, according to the Mark-to-Market rules imposed by IFRS standards. The quoted price, ex coupon, is called the clean price, while the (full) price actually paid is the dirty price. Only the clean price is subject to price changes, due to Eq. 3.3, because of the effect of the discount rate y, subject to market rate changes.

 

pages: 471 words: 97,152

Animal Spirits: How Human Psychology Drives the Economy, and Why It Matters for Global Capitalism by George A. Akerlof, Robert J. Shiller

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affirmative action, Andrei Shleifer, asset-backed security, bank run, banking crisis, collateralized debt obligation, conceptual framework, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, Deng Xiaoping, Donald Trump, Edward Glaeser, en.wikipedia.org, experimental subject, financial innovation, full employment, George Akerlof, housing crisis, Hyman Minsky, income per capita, inflation targeting, invisible hand, Isaac Newton, Jane Jacobs, Jean Tirole, job satisfaction, Joseph Schumpeter, Long Term Capital Management, loss aversion, market bubble, market clearing, mental accounting, Mikhail Gorbachev, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, new economy, New Urbanism, Plutocrats, plutocrats, price stability, profit maximization, purchasing power parity, random walk, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, South Sea Bubble, The Chicago School, The Death and Life of Great American Cities, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, tulip mania, working-age population, Y2K, Yom Kippur War

., 178n6 Present value theory, 152–53 Price rigidity, 48 Prices: depression of the 1890s and, 59–60; fairness and, 6, 21, 22; Great Depression and, 68; money illusion and, 43–46, 48; variation in, 100. See also financial prices price-to-earnings-to-price feedback, 135 price-to-GDP-to-price feedback, 154 price-to-price feedback, 134–35, 154 Primary Credit Dealer Facility, 187n10 Princeton University, 19 prohibition (of alcohol), 39 Project Link, 16 Pullman Palace Car Company, 63 Purdue University, 128 Quetzalcóatl (López Portillo), 53–54 Quintini, Glenda, 183n14 quits, wages and, 103–4, 106 railroad strike of 1910 (Argentina), 139 Rainwater, Lee, 162, 196n14 Rajan, Raghuram G., 182n21 Randers, Jørgen, 194n29 randomness, 52 random-walk hypothesis, 103, 191n11 ratings of securities, 37, 91, 94, 170 rational expectations, xxiii, 5, 6, 168, 173, 178n4; bimetallism debate and, 60; in classical economics, 2, 3; confidence and, 12–13, 14; corruption and, 39; fairness and, 21, 22; feedback and, 140; financial prices and, 131, 132, 133, 136; money illusion and, 41, 42; real estate market and, 150, 153; saving and, 120, 122 Reagan, Ronald, xxv, 32, 36, 172, 175 real business cycle models, 178n6 real estate market, 4, 6, 135, 136, 149–56, 169–70, 172, 174, 195–96n1–15; baby boom and, 152; confidence and, 11, 13, 149, 156; confidence multiplier in, 153–55; naïve or intuitive beliefs about, 150–53; S&L crisis and, 32, 33.

Shefrin and Thaler assembled some of the evidence of anomalies and produced a behavioral life-cycle model that incorporates some of the best features of the life-cycle model of Ando and Modigliani (1963) and adjusts it for known facts about human behavior (Thaler 1994). For a broader discussion of these issues see Thaler (1994). 10. Keynes (1973 [1936], p. 96). 11. Hall (1978) found some apparently striking evidence in favor of this maximizing model in showing that a time series of aggregate U.S. consumption was approximately a random walk. However, subsequent evidence has generated other interpretations (Blinder et al. 1985; Hall 1988). Carroll and Summers (1991) found evidence against the random-walk hypothesis in that individual consumption tends to track predictable life-cycle changes in income, though Carroll (2001) backtracked a bit on their conclusions. Shea (1995a) found evidence that individual consumption changes can be forecast using data on future incomes implicit in union contracts. 12. Modigliani and Brumberg (1954) and Friedman (1957). 13.

If people tend to buy in reaction to stock price increases or sell in reaction to price decreases, then their reaction to past price changes has the potential to feed back into more price changes in the same direction, a phenomenon known as price-to-price feedback.10 A vicious circle can develop, causing a continuation of the cycle, at least for a while. Eventually an upward price movement, a bubble, must burst, since price is supported only by expectations of further price increases. They cannot go on forever. Price-to-price feedback itself may not be strong enough to create the major asset price bubbles we have seen. But, as we shall see, there are other forms of feedback besides that between prices. In particular there are feedbacks between the asset prices in the bubble and the real economy. This additional feedback increases the length of the cycle and amplifies the price-to-price effects.

 

pages: 261 words: 86,905

How to Speak Money: What the Money People Say--And What It Really Means by John Lanchester

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asset allocation, Basel III, Bernie Madoff, Big bang: deregulation of the City of London, bitcoin, Black Swan, blood diamonds, Bretton Woods, BRICs, Capital in the Twenty-First Century by Thomas Piketty, Celtic Tiger, central bank independence, collapse of Lehman Brothers, collective bargaining, credit crunch, Credit Default Swap, crony capitalism, Dava Sobel, David Graeber, disintermediation, double entry bookkeeping, en.wikipedia.org, estate planning, financial innovation, Flash crash, forward guidance, Gini coefficient, global reserve currency, high net worth, High speed trading, hindsight bias, income inequality, inflation targeting, interest rate swap, Isaac Newton, Jaron Lanier, joint-stock company, joint-stock limited liability company, Kodak vs Instagram, liquidity trap, London Interbank Offered Rate, London Whale, loss aversion, margin call, McJob, means of production, microcredit, money: store of value / unit of account / medium of exchange, moral hazard, neoliberal agenda, New Urbanism, Nick Leeson, Nikolai Kondratiev, Nixon shock, Northern Rock, offshore financial centre, oil shock, open economy, paradox of thrift, Plutocrats, plutocrats, Ponzi scheme, purchasing power parity, pushing on a string, quantitative easing, random walk, rent-seeking, reserve currency, Richard Feynman, Richard Feynman, road to serfdom, Ronald Reagan, Satoshi Nakamoto, security theater, shareholder value, Silicon Valley, six sigma, South Sea Bubble, sovereign wealth fund, Steve Jobs, The Chicago School, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, trickle-down economics, Washington Consensus, working poor, yield curve

If you look at the companies’ respective earnings, a share of Apple costs just over 11 times what the company earned last year, whereas a share of Amazon is valued at 3,500 times earnings. In other words, Amazon is 300 times more expensive than Apple. That might seem nuts, but the price is based on the idea that in the future, Amazon will earn huge amounts of money, so you buy the share now in order to get in early for the huge takeoff that is going to come. Apple on the other hand is more of a known quantity, so you are getting what you pay for. It’s very difficult to know what the realistic P/E ratio is for any stock: as Burton Malkiel put it in his efficient-market theory investment classic, A Random Walk Down Wall Street, “God Almighty does not know the proper price-earnings-multiple for a common stock.” 63 Historically, companies with low P/E ratios—what are known as “value stocks”—have tended to outperform those with high P/Es, in part because a high P/E implies high expectations that are easily disappointed.

Commenting on her in 1979, he said, “This election was about a woman who believes in inequality, passionately, who isn’t Keynesian, who is not worried about dole queues.” In his biography of Thatcher, Charles Moore says that in Walden’s view, “if interviewers had wanted to find the truth, they should have asked her, ‘Mrs Thatcher, do you believe in a more unequal society?’ ” # Book recommendation: Burton Malkiel’s classic A Random Walk Down Wall Street lays out a thoroughly convincing explication of the thesis, with lots of practical advice for private investors. Part II A LEXICON OF MONEY the aaaaa number A term I’ve just made up to denote 16,438, for the purpose of making sure it comes first in this lexicon. This number is, in the words of Melinda Gates, “the most important statistic in the world.” It’s the number of children under five who aren’t dying every day, compared with the number who were dying daily in 1990.

Alice Shroeder’s The Snowball, a biography of Warren Buffett, is very different in tone and texture, but it brings in a lot of stories and information from the world of finance, as does Sebastian Mallaby’s More Money Than God, a (suprisingly and convincingly positive) study of hedge funds. Some of you may well be thinking: but how is any of this going to help me become rich? If you are, here are two books for you: Burton Malkiel’s A Random Walk Down Wall Street, which explains efficient-market theory for the ordinary investor, and John Kay’s The Long and Short of It. Kay’s book is the best book ever written for the British individual investor, by a country mile. Ben Graham’s The Intelligent Investor, the first book written on the subject, remains one of the best. One of the liveliest areas of argument in this field concerns the poorest people in the world, and the question of how best to help them.

 

Think OCaml by Nicholas Monje, Allen Downey

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en.wikipedia.org, random walk

For example, reading your code might help if the problem is a typographical error, but not if the problem is a conceptual misunderstanding. If you don’t understand what your program does, you can read it 100 times and never see the error, because the error is in your head. Running experiments can help, especially if you run small, simple tests. But if you run experiments without thinking or reading your code, you might fall into a pattern I call “random walk programming,” which is the process of making random changes until the program does the right thing. Needless to say, random walk programming can take a long time. You have to take time to think. Debugging is like an experimental science. You should have at least one hypothesis about what the problem is. If there are two or more possibilities, try to think of a test that would eliminate one of them. Taking a break helps with the thinking. So does talking. If you explain the problem to someone else (or even yourself), you will sometimes find the answer before you finish asking the question.

Index abecedarian, 51 access, 56 accumulator histogram, 103 Ackerman function, 42 addition with carrying, 46 algorithm, 4, 9, 46, 107 Euclid, 43 RSA, 84 square root, 47 ambiguity, 6 anagram, 61 anagram set, 94 and operator, 32 Anonymous functions, 59 argument, 21, 23, 25, 29 arithmetic operator, 13 assignment, 18 tuple, 87–89, 94 assignment statement, 12 base case, 42 benchmarking, 109, 110 binary search, 61 bingo, 94 birthday paradox, 61 bisection search, 61 bisection, debugging by, 47 body, 23, 29, 35 boolean expression, 31, 35 borrowing, subtraction with, 46 bracket operator, 49 branch, 35 bug, 4, 9 calculator, 19 caml.inria.fr, 10 Car Talk, 85, 95 carrying, addition with, 46 case-sensitivity, variable names, 17 chained conditional, 33 char type, 11 character, 18, 49 comment, 17, 19 comparison string, 52 tuple, 89 compile, 1, 8 composition, 22, 25, 29 compound statement, 35 concatenation, 19, 26, 51 list, 56 condition, 35 conditional chained, 33 nested, 35 conditional execution, 32 conditional statement, 32, 35 cons operator, 55 consistency check, 84 counter, 53, 78 cummings, e. e., 4 Currying, 27 data structure, 94, 109 debugging, 4, 8, 9, 17, 28, 41, 53, 60, 84, 94, 109 by bisection, 47 emotional response, 8 experimental, 5 declaration, 85 default value, 106, 110 definition function, 22 recursive, 95 deterministic, 101, 110 development plan random walk programming, 110 diagram stack, 26 state, 12 dictionary lookup, 81 looping with, 80 reverse lookup, 81 Index Directive, 2 divisibility, 31 documentation, 10 dot notation, 29 Doyle, Arthur Conan, 5 Doyle, Sir Arthur Conan, 103 DSU pattern, 94 duplicate, 61, 85 element, 55, 60 emotional debugging, 8 empty list, 55 empty string, 53 encapsulation, 46 encryption, 84 epsilon, 46 error runtime, 4, 17, 39 semantic, 4, 12, 17 syntax, 4, 17 error message, 4, 8, 12, 17 escape character, 7 Euclid’s algorithm, 43 evaluate, 14 exception, 4, 9, 17 IndexError, 50 RuntimeError, 39 SyntaxError, 22 TypeError, 49 ValueError, 88 executable, 2, 9 experimental debugging, 5, 110 expression, 13, 14, 19 boolean, 31, 35 Fermat’s Last Theorem, 36 fibonacci function, 82 filter pattern, 60 find function, 51 flag, 85 float type, 11 floating-point, 18, 46 flow of execution, 24, 29 For loop, 70 for loop, 57 formal language, 5, 9 frame, 26 frequency, 79 letter, 94 word, 101, 111 function, 22, 28 113 ack, 42 fibonacci, 82 find, 51 log, 21 randint, 61 recursive, 37 sqrt, 22 String.length, 50 zip, 88 function argument, 25 function call, 21, 29 function definition, 22, 24, 29 function frame, 26 function parameter, 25 function, math, 21 function, reasons for, 28 function, trigonometric, 21 function, tuple as return value, 88 Functional Programming, 7 Functions Anonymous, 59 Currying, 27 gather, 94 GCD (greatest common divisor), 43 global variable, 85 greatest common divisor (GCD), 43 Guarded Patterns, 35 hash function, 85 hashtable, 77, 78, 84, 85 hashtbale subtraction, 106 header, 23, 29 Hello, World, 7 high-level language, 1, 8 Higher-Order Functions, 25 histogram, 79, 85 random choice, 102, 107 word frequencies, 102 HOF, 25 Holmes, Sherlock, 5 homophone, 86 if statement, 32 immutability, 53 implementation, 79, 85, 109 in, 15 index, 49, 53, 56, 77 starting at zero, 49 IndexError, 50 infinite recursion, 39, 42 114 int type, 11 integer, 18 long, 83 interactive mode, 2, 9 interlocking words, 61 interpret, 1, 8 invocation, 53 item, 53, 55 hashtable, 84 item update, 58 key, 77, 84 key-value pair, 77, 84 keyboard input, 33 keyword, 13, 19 labelled parameter, 104 language formal, 5 high-level, 1 low-level, 1 natural, 5 programming, 1 safe, 4 let, 15 letter frequency, 94 letter rotation, 53, 85 Linux, 5 list, 55, 60 concatenation, 56 element, 56 empty, 55 nested, 55 of tuples, 89 operation, 56 traversal, 57, 60 literalness, 6 local variable, 26, 29 log function, 21 logarithm, 111 logical operator, 31, 32 long integer, 83 lookup, 85 lookup, dictionary, 81 loop for, 57 Looping, 70 looping with dictionaries, 80 low-level language, 1, 8 map pattern, 60 Index mapping, 108 Markov analysis, 107 mash-up, 108 math function, 21 McCloskey, Robert, 51 membership binary search, 61 bisection search, 61 hashtable, 78 set, 78 memo, 82, 85 metathesis, 94 method, 53 string, 53 module, 7, 29 pprint, 84 random, 61, 102 string, 101 modulus operator, 31, 35 natural language, 5, 9 nested conditional, 33, 35 nested list, 55, 60 Newton’s method, 45 not operator, 32 number, random, 101 object code, 2, 9 operand, 13, 19 operator, 13, 19 and, 32 bracket, 49 cons, 55 logical, 31, 32 modulus, 31, 35 not, 32 or, 32 overloading, 16 relational, 32 string, 16 operator, arithmetic, 13 optional parameter, 104 or operator, 32 order of operations, 16, 18 override, 110 palindrome, 42 parameter, 25, 26, 29 labelled, 104 optional, 104 parentheses empty, 23 Index matching, 4 overriding precedence, 16 parameters in, 25 tuples in, 87 parse, 6, 9 Partial Application, 27 pattern filter, 60 map, 60 reduce, 60 search, 52, 53 swap, 87 Pattern Matching, 34 Pattern-Matching Guarded, 35 PEMDAS, 16 pi, 48 plain text, 101 poetry, 6 portability, 1, 8 pprint module, 84 precedence, 19 precondition, 61 prefix, 108 pretty print, 84 print statement, 7, 9 problem solving, 1, 8 program, 3, 9 Programming Functional, 7 programming language, 1 Programming Paradigms, 7 Functional, 7 Object-Oriented, 7 Project Gutenberg, 101 prompt, 2, 9, 34 prose, 6 pseudorandom, 101, 110 Puzzler, 85, 95 quotation mark, 7, 11 radian, 21 Ramanujan, Srinivasa, 48 randint function, 61 random function, 102 random module, 61, 102 random number, 101 random text, 108 random walk programming, 110 Read functions, 33 115 Recursion Tail-end, 40 recursion, 37, 42 infinite, 39 traversal, 50 recursive definition, 95 reduce pattern, 60 reducible word, 86, 95 redundancy, 6 References, 15, 69 relational operator, 32 return value, 21, 29 tuple, 88 reverse lookup, dictionary, 81 reverse lookup, hashtable, 85 reverse word pair, 61 rotation letters, 85 rotation, letter, 53 RSA algorithm, 84 rules of precedence, 16, 19 running pace, 19 runtime error, 4, 17, 39 RuntimeError, 39 safe language, 4 sanity check, 84 scaffolding, 84 scatter, 94 Scope, 15 scope, 15 Scrabble, 94 script, 2, 9 script mode, 2, 9 search pattern, 52, 53 search, binary, 61 search, bisection, 61 semantic error, 4, 9, 12, 17 semantics, 4, 9 sequence, 49, 53, 55, 87 set anagram, 94 set membership, 78 shape, 94 sine function, 21 slice, 53 source code, 2, 8 sqrt function, 22 square root, 45 stack diagram, 26 state diagram, 12, 18 116 statement, 18 assignment, 12 conditional, 32, 35 for, 57 if, 32 print, 7, 9 Strictly typed, 14 string, 11, 18 comparison, 52 operation, 16 string method, 53 String module, 50 string module, 101 string type, 11 String.length function, 50 structure, 6 subexpressions, 14 subtraction hashtable, 106 with borrowing, 46 suffix, 108 swap pattern, 87 syntax, 4, 9 syntax error, 4, 9, 17 SyntaxError, 22 Tail-end Recursion, 40 tail-end recursion, 42 testing interactive mode, 2 text plain, 101 random, 108 token, 6, 9 Toplevel, 2 toplevel, 9 traceback, 39, 41 traversal, 50, 52, 53, 80, 89, 103 list, 57 triangle, 36 trigonometric function, 21 tuple, 87, 88, 94 assignment, 87 comparison, 89 tuple assignment, 88, 89, 94 type, 11, 18 char, 11 float, 11 hashtable, 77 int, 11 list, 55 Index long, 83 str, 11 tuple, 87 unit, 12, 23 TypeError, 49 typographical error, 110 underscore character, 13 uniqueness, 61 unit type, 12, 18, 23 update histogram, 103 item, 58 use before def, 17 User input, 33 value, 11, 18, 85 default, 106 tuple, 88 ValueError, 88 variable, 12, 18 local, 26 Variables References, 15 While loop, 70 word frequency, 101, 111 word list, 78 word, reducible, 86, 95 words.txt, 78 zero, index starting at, 49 zip function, 88 Zipf’s law, 111

., 4 Currying, 27 data structure, 94, 109 debugging, 4, 8, 9, 17, 28, 41, 53, 60, 84, 94, 109 by bisection, 47 emotional response, 8 experimental, 5 declaration, 85 default value, 106, 110 definition function, 22 recursive, 95 deterministic, 101, 110 development plan random walk programming, 110 diagram stack, 26 state, 12 dictionary lookup, 81 looping with, 80 reverse lookup, 81 Index Directive, 2 divisibility, 31 documentation, 10 dot notation, 29 Doyle, Arthur Conan, 5 Doyle, Sir Arthur Conan, 103 DSU pattern, 94 duplicate, 61, 85 element, 55, 60 emotional debugging, 8 empty list, 55 empty string, 53 encapsulation, 46 encryption, 84 epsilon, 46 error runtime, 4, 17, 39 semantic, 4, 12, 17 syntax, 4, 17 error message, 4, 8, 12, 17 escape character, 7 Euclid’s algorithm, 43 evaluate, 14 exception, 4, 9, 17 IndexError, 50 RuntimeError, 39 SyntaxError, 22 TypeError, 49 ValueError, 88 executable, 2, 9 experimental debugging, 5, 110 expression, 13, 14, 19 boolean, 31, 35 Fermat’s Last Theorem, 36 fibonacci function, 82 filter pattern, 60 find function, 51 flag, 85 float type, 11 floating-point, 18, 46 flow of execution, 24, 29 For loop, 70 for loop, 57 formal language, 5, 9 frame, 26 frequency, 79 letter, 94 word, 101, 111 function, 22, 28 113 ack, 42 fibonacci, 82 find, 51 log, 21 randint, 61 recursive, 37 sqrt, 22 String.length, 50 zip, 88 function argument, 25 function call, 21, 29 function definition, 22, 24, 29 function frame, 26 function parameter, 25 function, math, 21 function, reasons for, 28 function, trigonometric, 21 function, tuple as return value, 88 Functional Programming, 7 Functions Anonymous, 59 Currying, 27 gather, 94 GCD (greatest common divisor), 43 global variable, 85 greatest common divisor (GCD), 43 Guarded Patterns, 35 hash function, 85 hashtable, 77, 78, 84, 85 hashtbale subtraction, 106 header, 23, 29 Hello, World, 7 high-level language, 1, 8 Higher-Order Functions, 25 histogram, 79, 85 random choice, 102, 107 word frequencies, 102 HOF, 25 Holmes, Sherlock, 5 homophone, 86 if statement, 32 immutability, 53 implementation, 79, 85, 109 in, 15 index, 49, 53, 56, 77 starting at zero, 49 IndexError, 50 infinite recursion, 39, 42 114 int type, 11 integer, 18 long, 83 interactive mode, 2, 9 interlocking words, 61 interpret, 1, 8 invocation, 53 item, 53, 55 hashtable, 84 item update, 58 key, 77, 84 key-value pair, 77, 84 keyboard input, 33 keyword, 13, 19 labelled parameter, 104 language formal, 5 high-level, 1 low-level, 1 natural, 5 programming, 1 safe, 4 let, 15 letter frequency, 94 letter rotation, 53, 85 Linux, 5 list, 55, 60 concatenation, 56 element, 56 empty, 55 nested, 55 of tuples, 89 operation, 56 traversal, 57, 60 literalness, 6 local variable, 26, 29 log function, 21 logarithm, 111 logical operator, 31, 32 long integer, 83 lookup, 85 lookup, dictionary, 81 loop for, 57 Looping, 70 looping with dictionaries, 80 low-level language, 1, 8 map pattern, 60 Index mapping, 108 Markov analysis, 107 mash-up, 108 math function, 21 McCloskey, Robert, 51 membership binary search, 61 bisection search, 61 hashtable, 78 set, 78 memo, 82, 85 metathesis, 94 method, 53 string, 53 module, 7, 29 pprint, 84 random, 61, 102 string, 101 modulus operator, 31, 35 natural language, 5, 9 nested conditional, 33, 35 nested list, 55, 60 Newton’s method, 45 not operator, 32 number, random, 101 object code, 2, 9 operand, 13, 19 operator, 13, 19 and, 32 bracket, 49 cons, 55 logical, 31, 32 modulus, 31, 35 not, 32 or, 32 overloading, 16 relational, 32 string, 16 operator, arithmetic, 13 optional parameter, 104 or operator, 32 order of operations, 16, 18 override, 110 palindrome, 42 parameter, 25, 26, 29 labelled, 104 optional, 104 parentheses empty, 23 Index matching, 4 overriding precedence, 16 parameters in, 25 tuples in, 87 parse, 6, 9 Partial Application, 27 pattern filter, 60 map, 60 reduce, 60 search, 52, 53 swap, 87 Pattern Matching, 34 Pattern-Matching Guarded, 35 PEMDAS, 16 pi, 48 plain text, 101 poetry, 6 portability, 1, 8 pprint module, 84 precedence, 19 precondition, 61 prefix, 108 pretty print, 84 print statement, 7, 9 problem solving, 1, 8 program, 3, 9 Programming Functional, 7 programming language, 1 Programming Paradigms, 7 Functional, 7 Object-Oriented, 7 Project Gutenberg, 101 prompt, 2, 9, 34 prose, 6 pseudorandom, 101, 110 Puzzler, 85, 95 quotation mark, 7, 11 radian, 21 Ramanujan, Srinivasa, 48 randint function, 61 random function, 102 random module, 61, 102 random number, 101 random text, 108 random walk programming, 110 Read functions, 33 115 Recursion Tail-end, 40 recursion, 37, 42 infinite, 39 traversal, 50 recursive definition, 95 reduce pattern, 60 reducible word, 86, 95 redundancy, 6 References, 15, 69 relational operator, 32 return value, 21, 29 tuple, 88 reverse lookup, dictionary, 81 reverse lookup, hashtable, 85 reverse word pair, 61 rotation letters, 85 rotation, letter, 53 RSA algorithm, 84 rules of precedence, 16, 19 running pace, 19 runtime error, 4, 17, 39 RuntimeError, 39 safe language, 4 sanity check, 84 scaffolding, 84 scatter, 94 Scope, 15 scope, 15 Scrabble, 94 script, 2, 9 script mode, 2, 9 search pattern, 52, 53 search, binary, 61 search, bisection, 61 semantic error, 4, 9, 12, 17 semantics, 4, 9 sequence, 49, 53, 55, 87 set anagram, 94 set membership, 78 shape, 94 sine function, 21 slice, 53 source code, 2, 8 sqrt function, 22 square root, 45 stack diagram, 26 state diagram, 12, 18 116 statement, 18 assignment, 12 conditional, 32, 35 for, 57 if, 32 print, 7, 9 Strictly typed, 14 string, 11, 18 comparison, 52 operation, 16 string method, 53 String module, 50 string module, 101 string type, 11 String.length function, 50 structure, 6 subexpressions, 14 subtraction hashtable, 106 with borrowing, 46 suffix, 108 swap pattern, 87 syntax, 4, 9 syntax error, 4, 9, 17 SyntaxError, 22 Tail-end Recursion, 40 tail-end recursion, 42 testing interactive mode, 2 text plain, 101 random, 108 token, 6, 9 Toplevel, 2 toplevel, 9 traceback, 39, 41 traversal, 50, 52, 53, 80, 89, 103 list, 57 triangle, 36 trigonometric function, 21 tuple, 87, 88, 94 assignment, 87 comparison, 89 tuple assignment, 88, 89, 94 type, 11, 18 char, 11 float, 11 hashtable, 77 int, 11 list, 55 Index long, 83 str, 11 tuple, 87 unit, 12, 23 TypeError, 49 typographical error, 110 underscore character, 13 uniqueness, 61 unit type, 12, 18, 23 update histogram, 103 item, 58 use before def, 17 User input, 33 value, 11, 18, 85 default, 106 tuple, 88 ValueError, 88 variable, 12, 18 local, 26 Variables References, 15 While loop, 70 word frequency, 101, 111 word list, 78 word, reducible, 86, 95 words.txt, 78 zero, index starting at, 49 zip function, 88 Zipf’s law, 111

 

pages: 483 words: 141,836

Red-Blooded Risk: The Secret History of Wall Street by Aaron Brown, Eric Kim

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Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Benoit Mandelbrot, Bernie Madoff, Black Swan, capital asset pricing model, central bank independence, Checklist Manifesto, corporate governance, credit crunch, Credit Default Swap, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, financial innovation, illegal immigration, implied volatility, index fund, Long Term Capital Management, loss aversion, margin call, market clearing, market fundamentalism, market microstructure, money: store of value / unit of account / medium of exchange, moral hazard, natural language processing, open economy, pre–internet, quantitative trading / quantitative finance, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, The Myth of the Rational Market, too big to fail, transaction costs, value at risk, yield curve

Its only risks now are that there might be some problem with the futures clearinghouse or some mismatch between the Treasuries it holds and the Treasuries deliverable under the futures contracts. Otherwise, it does not care if Treasury prices go up or down, or even if the U.S. government defaults. We always knew there were some risks to this kind of leverage, but they seemed much smaller than the risks you eliminated by hedging. We learned that was not necessarily true. In a severe credit crunch and liquidity crisis, even good leverage, the kind that offsets your risks, could kill. The next step is to think like a frequentist. What things did other people learn that were really just fluctuations in a random walk? U.S. Treasury bonds did great during the crisis, but that might not happen next time. A lot of people decided that illiquid investments were bad, without distinguishing carefully between the disaster of investments that were supposed to be liquid but weren’t versus investments everyone knew were illiquid all along.

To predict the future, you string together randomly selected days from the past—with replacement, meaning you can pick the same past day more than once. You do this many times to generate a distribution of possible future outcomes. Simple resampling works only when the data are independent—that is, when yesterday’s move doesn’t tell you anything about today’s. Another name for a series with independent changes is a random walk, which of course is one of the famous models in finance. I believed, however, that financial time series were typically not random walks. One kind of common deviation from a random walk is called autocorrelation. That means yesterday’s move tells you something about today’s move—up days are followed by other up days either more (positive autocorrelation) or less (negative autocorrelation) than half the time. Both kinds of autocorrelation are observed in financial time series, but back in 1980 I believed they had to be minor.

Suppose I study all the people making markets (that is, setting prices at which they will buy from or sell to anyone) in, say, oil futures. They set different prices, implying different betting odds on oil prices in the future. I’m only interested in the market makers generating consistent profits. But even within this group there is a variety of prices and also differences in the positions they have built up. You might argue that the differences in prices are going to be pretty small, and some kind of average or market-clearing price is the best estimate of probability. One issue with this is none of the prices directly measure probability; all of them blend in utility to some degree. A person who locks in a price for future oil may not believe the price of oil is going up. She may be unable to afford higher prices if that does happen, and is willing to take an expected loss in order to ensure survival of her business.

 

pages: 407 words: 114,478

The Four Pillars of Investing: Lessons for Building a Winning Portfolio by William J. Bernstein

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asset allocation, Bretton Woods, British Empire, buy low sell high, carried interest, corporate governance, cuban missile crisis, Daniel Kahneman / Amos Tversky, Dava Sobel, diversification, diversified portfolio, Edmond Halley, equity premium, estate planning, Eugene Fama: efficient market hypothesis, financial independence, financial innovation, fixed income, German hyperinflation, high net worth, hindsight bias, Hyman Minsky, index fund, invention of the telegraph, Isaac Newton, John Harrison: Longitude, Long Term Capital Management, loss aversion, market bubble, mental accounting, mortgage debt, new economy, pattern recognition, quantitative easing, railway mania, random walk, Richard Thaler, risk tolerance, risk/return, Robert Shiller, Robert Shiller, South Sea Bubble, transaction costs, Vanguard fund, yield curve

., 100 Precious metals stocks, 123–124, 155 Present value vs. discount rate, discounted dividend model (DDM), 46–48 Press coverage, 219–225 Prestiti, Venetian, 10–13 Price, annuity, 9–13 Price-to-earnings (P/E) ratio, 58, 68–69, 150, 174-175 Prices, stock (See Stock prices) Primerica, 83 Principal transaction, 196 Principia Pro software, Morningstar Inc., 98, 152, 205 Prudential-Bache, 200 Psychology of investing (Pillar 3) (See Behavioral economics) Purchase vs. investment, 45 Quinn, Jane Bryant, 220, 221 Radio Corporation of America, 132, 147 Railroad bubble, 143-145, 158, 159–160 “Railway time,” 144 “Random walk,” 25 A Random Walk Down Wall Street (Malkiel), 224 Randomness in market, 25, 175–177, 186 (See also Performance) Raskob, John J., 65, 147, 148 RCA, 132, 147 Real Estate Investment Trusts (REITs), 69, 72, 109, 123, 124, 250, 254, 263, 296 Real (inflation-adjusted) returns bonds, twentieth century, 19 discounted dividend model (DDM) for different instruments, 68–69 establishment of, 7 future outlook, 67–71 retirement investments, 230 retirement withdrawal strategies, 231–234 stock, 26 and young savers, 238–239 Realized returns, 71–73 Rebalancing, 286-292 Regan, Donald, 194 Regret avoidance, 177 Reinvesting income (benefits of), 61 REITs (Real Estate Investment Trusts), 69, 72, 109, 123, 124, 250, 254, 263, 296 Retained earnings and dividends paid, 59–60 Retirement planning, 229–241 end-period wealth, 26–27 immortality assumption, 229–235 impact of crash in stock market, 61-62 portfolio rebalancing, 276, 282, 285, 286-293 vs. young savers, 236–239 Returns in brokerage accounts, 198–199, 200 calculation of, 186–187n1 expected (See Expected returns) and market capitalization, 32–34 mutual funds, 203-208 rebalanced, 286-293 Risk bond prices, 11-20 company quality, 34–38 cyclical companies, 64 defined, 11 discounted dividend model (DDM), 41-42 historic record as gauge of, 32 interest rates, 13, 260 long-term, 22-29 and market capitalization, 34 and measurement, 22–29 Risk-return relationship diversification and rebalancing, 286-291 historical perspective, 6–13, 22-29, 38 retirement years, 231–236 short- vs. long-term risk and behavioral economics, 172–173, 184-185 summary, by investment type, 38–39 Risk premium, 184 Riskless assets, 110, 114, 260, 264 Rockefeller, Percy, 147 Rocket (Stephenson), 143 Roman Empire, interest rates in, 8–9 Russell 2000, 248 Russell 3000, 245, 246 Safety penalty, 184 Sales training for brokers, 200 Samuelson, Paul, 214 Sanborn, Robert, 84–85 Santayana, George, 6, 129 Sarnoff, Mrs.

If you do, then you’re also likely quite adept at seeing the George Washington Bridge or the face of Bruce Willis in the clouds scudding overhead. The pattern of annual stock returns is almost totally random and unpredictable. The return in the last year, or the past five years, gives you no hint of next year’s return—it is a “random walk.” As we’ll see later, no one—not the pundits from the big brokerage firms, not the newsletter writers, not the mutual fund managers, and certainly not your broker—can predict where the market will go tomorrow or next year. So the twentieth century has seen three severe drops in stock prices, one of them catastrophic. The message to the average investor is brutally clear: expect at least one, and perhaps two, very severe bear markets during your investing career. Long-term risk—the probability of running out of money over the decades—is an entirely different matter.

Bary, Andrew, “Vertigo: The New Math Behind Internet Capital’s Stock Price is Fearsome.” Barrons, January 10, 2000. Brooks, John, Once in Golconda. Wiley, 1999. Chamberlain, Lawrence, and Hay, William W., Investment and Speculation. New York, 1931. Chancellor, Edward, Devil Take the Hindmost. Penguin, 1999. Galbraith, John K., The Great Crash. Houghton Mifflin, 1988. Johnson, Paul M., The Birth of the Modern: World Society 1815–1830. Harper Collins, 1991. Kindleberger, Charles P., Manias, Panics, and Crashes. Wiley, 2000. Mackay, Charles, Extraordinary Popular Delusions and the Madness of Crowds. Harmony Books, 1980. Maddison, Angus, Monitoring the World Economy 1820-1992. OECD, 1995. Malkiel, Burton G., A Random Walk Down Wall Street. W. W. Norton, 1996. Nocera, Joseph, A Piece of the Action.

 

pages: 589 words: 69,193

Mastering Pandas by Femi Anthony

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Amazon Web Services, correlation coefficient, correlation does not imply causation, Debian, en.wikipedia.org, Internet of things, natural language processing, p-value, random walk, side project, statistical model

The exponential distribution can be described as the continuous limit of the Geometric distribution and is also Markovian (memoryless). A memoryless random variable exhibits the property whereby its future state depends only on relevant information about the current time and not the information from further in the past. An example of modeling a Markovian/memoryless random variable is modeling short-term stock price behavior and the idea that it follows a random walk. This leads to what is called the Efficient Market hypothesis in Finance. For more information, refer to http://en.wikipedia.org/wiki/Random_walk_hypothesis. The PDF of the exponential distribution is given by =. The expectation and variance are given by the following expression: For a reference, refer to the link at http://en.wikipedia.org/wiki/Exponential_distribution. The plot of the distribution and code is given as follows: In [15]: import scipy.stats clrs = colors.cnames x = np.linspace(0,4, 100) expo = scipy.stats.expon lambda_ = [0.5, 1, 2, 5] plt.figure(figsize=(12,4)) for l,c in zip(lambda_,clrs): plt.plot(x, expo.pdf(x, scale=1.

Other than appearing natively in the source dataset, missing values can be added to a dataset by an operation such as reindexing, or changing frequencies in the case of a time series: In [84]: import numpy as np import pandas as pd import matplotlib.pyplot as plt %matplotlib inline In [85]: date_stngs = ['2014-05-01','2014-05-02', '2014-05-05','2014-05-06','2014-05-07'] tradeDates = pd.to_datetime(pd.Series(date_stngs)) In [86]: closingPrices=[531.35,527.93,527.81,515.14,509.96] In [87]: googClosingPrices=pd.DataFrame(data=closingPrices, columns=['closingPrice'], index=tradeDates) googClosingPrices Out[87]: closingPrice tradeDates 2014-05-01 531.35 2014-05-02 527.93 2014-05-05 527.81 2014-05-06 515.14 2014-05-07 509.96 5 rows 1 columns The source of the preceding data can be found at http://yhoo.it/1dmJqW6. The pandas also provides an API to read stock data from various data providers, such as Yahoo: In [29]: import pandas.io.data as web In [32]: import datetime googPrices = web.get_data_yahoo("GOOG", start=datetime.datetime(2014, 5, 1), end=datetime.datetime(2014, 5, 7)) In [38]: googFinalPrices=pd.DataFrame(googPrices['Close'], index=tradeDates) In [39]: googFinalPrices Out[39]: Close 2014-05-01 531.34998 2014-05-02 527.92999 2014-05-05 527.81000 2014-05-06 515.14001 2014-05-07 509.95999 For more details, refer to http://pandas.pydata.org/pandas-docs/stable/remote_data.html.

probability density function (PDF) / Continuous probability distributions probability distributionsabout / Probability distributions probability mass function (pmf)about / Discrete probability distributions PYMC Pandas ExampleURL / IPython Notebook PyPI Readline packageURL / Windows Pythonabout / How Python and pandas fit into the data analytics mix features / How Python and pandas fit into the data analytics mix URL / How Python and pandas fit into the data analytics mix, Selecting a version of Python to use, Installing Python from compressed tarball libraries / How Python and pandas fit into the data analytics mix version, selecting / Selecting a version of Python to use installation, on Linux / Linux installation, on Windows / Core Python installation installation, on Mac OS/X / Mac OS X Anaconda package, URL / Installation of Python and pandas from a third-party vendor Python(x,y)URL / Other numeric or analytics-focused Python distributions Python 3.0URL / Selecting a version of Python to use references / Selecting a version of Python to use Python decoratorsreference link / pandas/util Python dictionary, DataFrame objectsDataFrame.to_panel method, using / Using the DataFrame.to_panel method DataFrame.to_panel method, references / Using the DataFrame.to_panel method other operations / Other operations Python extensionsused, for improving performance / Improving performance using Python extensions Python installation, on Linuxabout / Linux from compressed tarball / Installing Python from compressed tarball Python installation, on Mac OS/Xabout / Mac OS X URL / Mac OS X package manager, using / Installation using a package manager Python installation, on Windowsabout / Windows core Python installation / Core Python installation third-party software install / Third-party Python software installation URL / Third-party Python software installation Python Lexical AnalysisURL / Accessing attributes using dot operator Q quartileabout / Quartile reference link / Quartile R Rdata types / R data types column name, specifying in / Specifying column name in R multiple columns, selecting in / Multicolumn selection in R %in% operator / R %in% operator logical subsetting / Logical subsetting in R split-apply-combine, implementing in / Implementation in R melt() function / The R melt() function cut() method / An R example using cut() R, and pandasmatching operators, comparing in / Comparing matching operators in R and pandas R-matrixversus Numpy array / R-matrix and NumPy array compared random forest / Random forest random walk hypothesisreference link / The exponential distribution range / Range R DataFramesabout / R DataFrames versus pandas DataFrames / R's DataFrames versus pandas' DataFrames README file, scikit-learnreference link / Installing on Windows R listsabout / R lists versus pandas series / R lists and pandas series compared role of pandas, in machine learning / Role of pandas in machine learning S sample covariancereference link / The mean sample meanreference link / The mean scikit-learnabout / Role of pandas in machine learning installing / Installation of scikit-learn installing, via Anacondas / Installing via Anaconda installing, on Unix (Linux/Mac OSX) / Installing on Unix (Linux/Mac OS X) installing, on Windows / Installing on Windows reference link / Installing on Windows model. constructing for / Constructing a model using Patsy for scikit-learn scikit-learn ML/classifier interfaceabout / The scikit-learn ML/classifier interface reference link / The scikit-learn ML/classifier interface scipy.stats functionreference link / Quartile Scipy Lecture Notes, Interfacing with Creference link / Improving performance using Python extensions Seriescreating / Series creation creating, with numpy.ndarray / Using numpy.ndarray creating, with Python dictionary / Using Python dictionary creating, with scalar values / Using scalar values operations / Operations on Series Series operationsassignment / Assignment slicing / Slicing arithmetic and statistical operations / Other operations Setuptoolsabout / Third-party Python software installation URL / Third-party Python software installation shape manipulation, NumPy arrayabout / Array shape manipulation multi-dimensional array, flattening / Flattening a multi-dimensional array reshaping / Reshaping resizing / Resizing dimension, adding / Adding a dimension shifting / Shifting/lagging single rowappending, to DataFrame / Appending a single row to a DataFrame sortlevel() method / MultiIndexing sparse.pyreference link / pandas/core split-apply-combineabout / Split-apply-combine implementing, in R / Implementation in R implementing, in pandas / Implementation in pandas SQL-like merging/joining, of DataFrame objects / SQL-like merging/joining of DataFrame objects SQL joinsreference link / SQL-like merging/joining of DataFrame objects stack() functionabout / The stack() function stackingabout / Stacking and unstacking statistical hypothesis testsabout / Statistical hypothesis tests background / Background z-test / The z-test t-test / The t-test structured array, DataFrameURL / Using a structured array submodules, pandas/compatchainmap.py / pandas/compat chainmap_impl.py / pandas/compat pickle_compat.py / pandas/compat openpyxl_compat.py / pandas/compat submodules, pandas/computationapi.py / pandas/computation align.py / pandas/computation common.py / pandas/computation engines.py / pandas/computation eval.py / pandas/computation expressions.py / pandas/computation ops.py / pandas/computation pytables.py / pandas/computation scope.py / pandas/computation submodules, pandas/coreapi.py / pandas/core array.py / pandas/core base.py / pandas/core common.py / pandas/core config.py / pandas/core datetools.py / pandas/core frame.py / pandas/core generic.py / pandas/core categorical.py / pandas/core format.py / pandas/core groupby.py / pandas/core ops.py / pandas/core index.py / pandas/core internals.py / pandas/core matrix.py / pandas/core nanops.py / pandas/core panel.py / pandas/core panel4d.py / pandas/core panelnd.py / pandas/core series.py / pandas/core sparse.py / pandas/core strings.py / pandas/core submodules, pandas/ioapi.py / pandas/io auth.py / pandas/io common.py / pandas/io data.py / pandas/io date_converters.py / pandas/io excel.py / pandas/io ga.py / pandas/io gbq.py / pandas/io html.py / pandas/io json.py / pandas/io packer.py / pandas/io parsers.py / pandas/io pickle.py / pandas/io pytables.py / pandas/io sql.py / pandas/io to_sql(..) / pandas/io stata.py / pandas/io wb.py / pandas/io submodules, pandas/rpybase.py / pandas/rpy common.py / pandas/rpy mass.py / pandas/rpy var.py / pandas/rpy submodules, pandas/sparseapi.py / pandas/sparse array.py / pandas/sparse frame.py / pandas/sparse list.py / pandas/sparse panel.py / pandas/sparse series.py / pandas/sparse submodules, pandas/statsapi.py / pandas/stats common.py / pandas/stats fama_macbeth.py / pandas/stats interface.py / pandas/stats math.py / pandas/stats misc.py / pandas/stats moments.py / pandas/stats ols.py / pandas/stats plm.py / pandas/stats var.py / pandas/stats submodules, pandas/toolsutil.py / pandas/tools tile.py / pandas/tools rplot.py / pandas/tools plotting.py / pandas/tools pivot.py / pandas/tools merge.py / pandas/tools describe.py / pandas/tools submodules, pandas/tseriesapi.py / pandas/tseries converter.py / pandas/tseries frequencies.py / pandas/tseries holiday.py / pandas/tseries index.py / pandas/tseries interval.py / pandas/tseries offsets.py / pandas/tseries period.py / pandas/tseries plotting.py / pandas/tseries resample.py / pandas/tseries timedeltas.py / pandas/tseries tools.py / pandas/tseries util.py / pandas/tseries submodules, pandas/utilterminal.py / pandas/util print_versions.py / pandas/util misc.py / pandas/util decorators.py / pandas/util clipboard.py / pandas/util supervised learningversus unsupervised learning / Supervised versus unsupervised learning about / Supervised learning supervised learning algorithmsabout / Supervised learning algorithms model, constructing for scikit-learn with Patsy / Constructing a model using Patsy for scikit-learn general boilerplate code explanation / General boilerplate code explanation logistic regression / Logistic regression support vector machine (SVM) / Support vector machine decision trees / Decision trees random forest / Random forest supervised learning problemsclassification / Supervised versus unsupervised learning regression / Supervised versus unsupervised learning support vector machine (SVM) / Support vector machineURL / Support vector machine swaplevel function / Swapping and reordering levels SWIG Documentationreference link / Improving performance using Python extensions switchpoint detection, Bayesian analysis example / Bayesian analysis example – Switchpoint detection T t-distributionreference link / The t-test t-testabout / The t-test one sample independent t-test / Types of t-tests independent samples t-tests / Types of t-tests paired samples t-test / Types of t-tests reference link / Types of t-tests example / A t-test example tailed testreference link / Statistical hypothesis tests time-series-related instance methodsabout / Time series-related instance methods shifting/lagging / Shifting/lagging frequency conversion / Frequency conversion data, resampling / Resampling of data aliases, for Time Series frequencies / Aliases for Time Series frequencies Time-Series-related objectsdatetime.datetime / A summary of Time Series-related objects Timestamp / A summary of Time Series-related objects DatetimeIndex / A summary of Time Series-related objects Period / A summary of Time Series-related objects PeriodIndex / A summary of Time Series-related objects DateOffset / A summary of Time Series-related objects timedelta / A summary of Time Series-related objects TimeDelta object / DateOffset and TimeDelta objects time serieshandling / Handling time series TimeSeries.resample functionabout / Resampling of data Time series conceptsabout / Time series concepts and datatypes time series datareading in / Reading in time series data TimeDelta object / DateOffset and TimeDelta objects DateOffset object / DateOffset and TimeDelta objects Time series datatypesabout / Time series concepts and datatypes Period / Period and PeriodIndex PeriodIndex / PeriodIndex Time Series datatypesconversion between / Conversions between Time Series datatypes time series datatypesPeriodIndex / PeriodIndex Time Series frequenciesaliases / Aliases for Time Series frequencies Titanic problemnaïve approach / A naïve approach to Titanic problem transform() method / The transform() method Type I Error / Type I and Type II errors Type II Error / Type I and Type II errors U UEFA Champions LeagueURL / The groupby operation unbiased estimatorreference link / Deviation and variance Unix (Linux/Mac OSX)scikit-learn, installing on / Installing on Unix (Linux/Mac OS X) unstackingabout / Stacking and unstacking unsupervised learningversus supervised learning / Supervised versus unsupervised learning about / Unsupervised learning unsupervised learning algorithmsabout / Unsupervised learning algorithms dimensionality reduction / Dimensionality reduction K-means clustering / K-means clustering upsamplingabout / Resampling of data V 4V’s of big dataabout / 4 V's of big data, Veracity of big data volume / Volume of big data velocity / Velocity of big data variety / Variety of big data veracity / Veracity of big data varianceabout / Deviation and variance variety, big data / Variety of big data vector auto-regression classes, var.pyVAR / pandas/stats PanelVAR / pandas/stats vector autoregressionreference link / pandas/stats velocity, big data / Velocity of big data veracity, big data / Veracity of big data virtualenv toolabout / Virtualenv installing / Virtualenv installation and usage using / Virtualenv installation and usage URL / Virtualenv installation and usage volume, big data / Volume of big data W Wakariabout / Wakari by Continuum Analytics URL / Wakari by Continuum Analytics where() method / Using the where() method WindowsPython, installing / Windows, Core Python installation Anaconda installation / Windows panda installation / Windows IPython installation / Windows scikit-learn, installing on / Installing on Windows WinPythonURL / Other numeric or analytics-focused Python distributions World Bank Economic dataURL / Benefits of using pandas X xs method / Cross sections Z z-testabout / The z-test zettabytesURL / Volume of big data

 

pages: 999 words: 194,942

Clojure Programming by Chas Emerick, Brian Carper, Christophe Grand

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Amazon Web Services, Benoit Mandelbrot, cloud computing, continuous integration, database schema, domain-specific language, en.wikipedia.org, failed state, finite state, Firefox, game design, general-purpose programming language, mandelbrot fractal, Paul Graham, platform as a service, premature optimization, random walk, Schrödinger's Cat, semantic web, software as a service, sorting algorithm, Turing complete, type inference, web application

However, we can easily recreate index-step with stepper as well, assuming w and h are globally or locally bound to the width and height of the desired finite grid: (stepper #(filter (fn [[i j]] (and (< -1 i w) (< -1 j h))) (neighbours %)) #{2 3} #{3}) Maze generation Let’s study another example: Wilson’s maze generation algorithm.[112] Wilson’s algorithm is a carving algorithm; it takes a fully walled “maze” and carves an actual maze out of it by removing some walls. Its principle is: Randomly pick a location and mark it as visited. Randomly pick a location that isn’t visited yet—if there’s none, return the maze. Perform a random walk starting from the newly picked location until you stumble on a location that is visited—if you pass through a location more than once during the random walk, always remember the direction you take to leave it. Mark all the locations of the random walk as visited, and remove walls according to the last known “exit direction.” Repeat from 2. Generally, maze algorithms use a matrix to represent the maze, and each item of this matrix is a bitset indicating which walls are still up. The astute reader may twitch at the idea that in such a setup, as the state of a wall is stored twice: once in each location on each side of it.

(iterate (comp rand-nth paths) loc) generates an infinite random walk: it takes a location, applies paths on it to get the vector of adjacent locations and rand-nth to pick one. If paths had returned sets instead of a sequential type (like a vector), then (comp rand-nth seq paths) would have been necessary instead. (take-while unvisited walk) is the part of the random walk until (but not including) a visited location. (take-while unvisited walk) would be (take-while (complement visited) walk) if the code had been written with visited. (next walk) is infinite, but (take-while unvisited walk) is not, so zipmap only looks at the n first items of (next walk) (where n is (count (take-while unvisited walk))). The n first items of (next walk) is thus the random walk without the start location and including the first visited location.

"Maze") (.setContentPane (doto (proxy [javax.swing.JPanel] [] (paintComponent [^java.awt.Graphics g] (let [g (doto ^java.awt.Graphics2D (.create g) (.scale 10 10) (.translate 1.5 1.5) (.setStroke (java.awt.BasicStroke. 0.4)))] (.drawRect g -1 -1 w h) (doseq [[[xa ya] [xb yb]] (map sort maze)] (let [[xc yc] (if (= xa xb) [(dec xa) ya] [xa (dec ya)])] (.drawLine g xa ya xc yc)))))) (.setPreferredSize (java.awt.Dimension. (* 10 (inc w)) (* 10 (inc h)))))) .pack (.setVisible true))) (draw 40 40 (maze (grid 40 40))) The True Wilson’s Algorithm Actually, we fibbed: maze is not exactly an implementation of Wilson’s algorithm. In our code, when the random walk reaches a location already in the graph (maze), we add a whole tree constituted by all the locations visited during the random walk instead of just the branch of this tree going from the starting point to the end location. Obviously, our algorithm is faster since it adds more locations to the maze at once. However, the selling point of Wilson’s algorithm is that each maze has the same probability to be generated. Empirical measures (looking at the maze distribution over samples generated by both Wilson’s and our algorithms) hint that this property still holds in our variant, but we haven’t proved it formally and we haven’t computed its time complexity.

 

pages: 460 words: 107,712

A Devil's Chaplain: Selected Writings by Richard Dawkins

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Albert Einstein, Alfred Russel Wallace, Buckminster Fuller, butterfly effect, Claude Shannon: information theory, complexity theory, Desert Island Discs, double helix, Douglas Hofstadter, epigenetics, experimental subject, Fellow of the Royal Society, gravity well, Necker cube, out of africa, phenotype, placebo effect, random walk, Richard Feynman, Richard Feynman, Silicon Valley, stem cell, Stephen Hawking, Steven Pinker, the scientific method

A belief in the ubiquity of gradualistic evolution does not necessarily commit us to Darwinian natural selection as the steering mechanism guiding the search through genetic space. It is highly probable that Motoo Kimura is right to insist that most of the evolutionary steps taken through genetic space are unsteered steps. To a large extent the trajectory of small, gradualistic steps actually taken may constitute a random walk rather than a walk guided by selection. But this is irrelevant if – for the reasons given above – our concern is with adaptive evolution as opposed to evolutionary change per se. Kimura himself rightly insists9 that his ‘neutral theory is not antagonistic to the cherished view that evolution of form and function is guided by Darwinian selection’. Further, the theory does not deny the role of natural selection in determining the course of adaptive evolution, but it assumes that only a minute fraction of DNA changes in evolution are adaptive in nature, while the great majority of phenotypically silent molecular substitutions exert no significant influence on survival and reproduction and drift randomly through the species.

Further, the theory does not deny the role of natural selection in determining the course of adaptive evolution, but it assumes that only a minute fraction of DNA changes in evolution are adaptive in nature, while the great majority of phenotypically silent molecular substitutions exert no significant influence on survival and reproduction and drift randomly through the species. The facts of adaptation compel us to the conclusion that evolutionary trajectories are not all random. There has to be some nonrandom guidance towards adaptive solutions because nonrandom is what adaptive solutions precisely are. Neither random walk nor random saltation can do the trick on its own. But does the guiding mechanism necessarily have to be the Darwinian one of nonrandom survival of random spontaneous variation? The obvious alternative class of theory postulates some form of nonrandom, i.e. directed, variation. Nonrandom, in this context, means directed towards adaptation. It does not mean causeless. Mutations are, of course, caused by physical events, for instance, cosmic ray bombardment.

Whereas I would do so on logical grounds, Gould prefers an empirical assault. He looks at the actual course of evolution and argues that such apparent progress as can in general be detected is artefactual (like the baseball statistic). Cope’s rule of increased body size, for example, follows from a simple ‘drunkard’s walk’ model. The distribution of possible sizes is confined by a left wall, a minimal size. A random walk from a beginning near the left wall has nowhere to go but up the size distribution. The mean size has pretty well got to increase, and it doesn’t imply a driven evolutionary trend towards larger size. As Gould convincingly argues, the effect is compounded by a human tendency to give undue weight to new arrivals on the geological scene. Textbook biological histories emphasize a progression of grades of organization.

 

pages: 443 words: 51,804

Handbook of Modeling High-Frequency Data in Finance by Frederi G. Viens, Maria C. Mariani, Ionut Florescu

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algorithmic trading, asset allocation, automated trading system, backtesting, Black-Scholes formula, Brownian motion, business process, continuous integration, corporate governance, discrete time, distributed generation, fixed income, Flash crash, housing crisis, implied volatility, incomplete markets, linear programming, mandelbrot fractal, market friction, market microstructure, martingale, Menlo Park, p-value, pattern recognition, performance metric, principal–agent problem, random walk, risk tolerance, risk/return, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process

See also Volatility index (VIX) pVIX cVIX spread, 106 Qiu, Hongwei, xiv, 97 Q-learning algorithm, 65 Quadratic covariation formula, 244 Quadratic covariation-realized covariance estimator, 266 Quadratic utility function, 286 Quadratic variation, estimate of, 224 Quadrinomial tree method, 99–100 volatility index convergence and, 105 vs. CBOE procedure, 100–101 Quantile–quantile (QQ) plots, 80 of empirical CDF, 136 of high-frequency tranche prices, 92, 94 of tranche prices, 83–84 ‘‘Quantile type’’ rule, 30 Quantum mechanics, 385 Quote-to-quote returns, 258, 260 Random variables, 334–336 Random walk, 126 Rare-event analysis, 32–33 Rare-event detection, 28, 30–32 Rare events detecting and evaluating, 29–35 equity price and, 44 trades profile and, 42, 43 Rare-events distribution, 41–44 peaks in, 42 Real daily integrated covariance, regressing, 281 Real integrated covariance regressions, results of, 282–285 Realized covariance (RC), 269 estimator for, 280 measures of, 272 Realized covariance plus leads and lags (RCLL), 266 estimator for, 280, 290 Realized covariance–quadratic variation estimator, 244 Realized variance, 12 Realized volatility, microstructure noise and, 274 Index Realized volatility estimator, 253–254, 256 results of, 276–279 Realized volatility estimator performance, ranking, 279 Realized-volatility-type measures, 275 Real-valued functions, 350, 351, 388–389 Refresh time, 267 Refresh time procedure, 244 Refresh time synchronization method, 268 Regime-switching default correlation, 81–84 Regime-switching default correlation model, 76 Regime-switching model, drawback of, 84–85 ‘‘Regret-free’’ prices, 238 Regular asynchronous trading, 264 Regular nonsynchronous trading, 268 Regular synchronous trading, 268 Relative risk process, 296 Rellich’s theorem, 398 Representative ADT algorithm, 52–53, 54.

Additionally, the combination of Adaboost and the BSC can be used as a semiautomated strategic planning system that continuously updates itself for board-level decisions of directors or for investment decisions of portfolio managers. REFERENCES Acharya VV, John K, Sundaram RK. On the optimality of resetting executive stock options. J Financ Econ 2000;57:65–101. Alexander S. Price movements in speculative markets: trends or random walks. Ind Manag Rev 1961;2:7–26. Algoet PH, Cover TM. Asymptotic optimality and asymptotic equipartition properties of log-optimum investment. Ann Probab 1988;16:876–898. Allen F, Karjalainen R. Using genetic algorithms to find technical trading rules. J Financ Econ 1999;51:245–271. Altman EI. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy.

See also Constant rebalanced portfolio technical analysis 436 Portfolios (continued ) (CRP-TA) trading algorithm; Multiagent portfolio management system; Subprime MBS portfolios MBS, 77 tranches of, 77 vintage of, 77 Portfolios value, expected change in, 385 Portfolio utility, 286 Position strategy, 33 Positive process, 310 Powell’s method, 6, 14, 19 Power-type utility functions, 305 Preaveraging technique, 267 Prediction nodes, 50, 51 Prediction rule, 48, 49 Prespecified terminal time, 295 Price behavior, analyzing after rare events, 28 Price change distributions, 31 Price distribution distortion, 91 Price evolution in time, 30 Price movement(s) corresponding to small volume, 30 detecting and evaluating, 44 persistence of, 27–46 Price movement methodology, results of, 35–41 Price process, 121 Price recovery probability of, 44 after rare events, 45 Price volatility, UHFT and, 241 Price–volume relationship, 27–28 outlying observations of, 28 Principal–agent conflict, 53 Principal–agent problem, 60 Probability of favorable price movement, 35–36 Poisson, 240 Probability density, 13–14 Probability density function (pdf), 119, 120, 163, 171, 335. See also Forecast pdfs; pdf forecasting; Sample pdfs Probability distributions, 165 Probability mass function (pmf), 171 Probability surfaces, 35, 37 Proportionality constant, 402 Pure optimal stopping problems, 311 Put options, demand for, 106 Index Put options chains, constructed VIX using, 105–106 p-values, 138–139, 204–205 pVIX-b, 102–103, 105.

 

Stock Market Wizards: Interviews With America's Top Stock Traders by Jack D. Schwager

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Asian financial crisis, banking crisis, barriers to entry, Black-Scholes formula, commodity trading advisor, computer vision, East Village, financial independence, fixed income, implied volatility, index fund, Jeff Bezos, John von Neumann, locking in a profit, Long Term Capital Management, margin call, paper trading, passive investing, pattern recognition, random walk, risk tolerance, risk-adjusted returns, short selling, Silicon Valley, statistical arbitrage, the scientific method, transaction costs, Y2K

JOHN BENDER tion in the formula is that the probabilities of prices being at different levels at the time of the option expiration can be described by a normal curve*—the highest probabilities being for prices that are close to the current level and the probabilities for any price decreasing the further above or below the market it is.] A normal distribution would be appropriate if stock price movements were analogous to what is commonly called "the drunkard's walk." If you have a drunkard in a narrow corridor, and all he can do is lurch forward or backward, in order for his movements to be considered a random walk, the following criteria would have to be met: 1. He has to be equally likely to lurch forward as backward. 2. He has to lurch forward by exactly the same distance he lurches backward. 3. He has to lurch once every constant time interval. Those are pretty strict requirements. Not many variables meet these conditions. Stock prices, I would argue, don't even come close [substituting daily price changes for the drunkard's steps], I don't mean to suggest that Black and Scholes made stupid assumptions; they made the only legitimate assumptions possible, not being traders themselves.

For example, if people expect a stock to find support at 65, lo and behold, they're willing to buy it at 66. That is not a random walk statement. *See note in final section of this chapter. Q U E S T I O N I N G THE OBVIOUS I'll give you another example. Assume people get excited about tech stocks for whatever reason and start buying them. Which funds are going to have the best performance next quarter when mom-andpop public decide where to invest their money?—the tech funds. Which funds are going to have the best inflows during the next quarter?—the tech funds. What stocks are they going to buy?—not airlines, they're tech funds. So the tech funds will go up even more. Therefore they're going to have better performance and get the next allocation, and so on. You have all the ingredients for a trend. Again, this is not price behavior that is consistent with a random walk assumption. You've seen this pattern increasingly in the recent run-up in the U.S. stock market.

Stock prices, I would argue, don't even come close [substituting daily price changes for the drunkard's steps], I don't mean to suggest that Black and Scholes made stupid assumptions; they made the only legitimate assumptions possible, not being traders themselves. In fact, they won the Nobel Prize for it. Although, to be honest, that always seemed a bit strange to me because all they used was high school mathematics. All my trading operates on the premise that the most important part is the part that Black-Scholes left out—the assumption of the probability distribution. Why do you say with such assurance that stock prices don't even come close to a random walk? As one example, whether you believe in it or not, there is such a thing as technical analysis, which tries to define support and resistance levels and trends. Regardless of whether technical analysis has any validity, enough people believe in it to impact the market.

 

pages: 402 words: 110,972

Nerds on Wall Street: Math, Machines and Wired Markets by David J. Leinweber

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AI winter, algorithmic trading, asset allocation, banking crisis, barriers to entry, Big bang: deregulation of the City of London, butterfly effect, buttonwood tree, buy low sell high, capital asset pricing model, citizen journalism, collateralized debt obligation, corporate governance, Craig Reynolds: boids flock, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Danny Hillis, demand response, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman, en.wikipedia.org, experimental economics, financial innovation, Gordon Gekko, implied volatility, index arbitrage, index fund, information retrieval, Internet Archive, John Nash: game theory, Khan Academy, load shedding, Long Term Capital Management, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, market fragmentation, market microstructure, Mars Rover, moral hazard, mutually assured destruction, natural language processing, Network effects, optical character recognition, paper trading, passive investing, pez dispenser, phenotype, prediction markets, quantitative hedge fund, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Renaissance Technologies, Richard Stallman, risk tolerance, risk-adjusted returns, risk/return, Ronald Reagan, semantic web, Sharpe ratio, short selling, Silicon Valley, Small Order Execution System, smart grid, smart meter, social web, South Sea Bubble, statistical arbitrage, statistical model, Steve Jobs, Steven Levy, Tacoma Narrows Bridge, the scientific method, The Wisdom of Crowds, time value of money, too big to fail, transaction costs, Turing machine, Upton Sinclair, value at risk, Vernor Vinge, yield curve, Yogi Berra

The retranslation of the Russian back to English this time was “The spirit is of willing of but of the flesh is of weak.” 31. The CIA In-Q-Tel venture capitalists are found here: www.inqtel.org/. Part Two Alpha as Life 90 Nerds on Wall Str eet I ndex funds are passive investments; their goal is to deliver a return that matches a benchmark index. The Old Testament of indexing is Burton Malkiel’s classic A Random Walk Down Wall Street, first published in 1973 by W.W. Norton and now in its ninth edition. For typical individual investors, without special access to information, it offers what is likely the best financial advice they will ever get: It is hard to consistently beat the market, especially after fees. A passive strategy will do better in the long run. Of course, no one thinks of oneself as a typical individual investor.

.” — HACKER PROVERB T he beginning of index investing in the 1970s was the result of a convergence of events, one of those ripe apple moments. Institutional investors began to use firms like A.G. Becker to actually compare the total performance of their hired managers with index benchmarks, and found that many of them fell short, especially after the substantial fees the investors were paying. Yale professor Burton Malkiel popularized the academic efficient market arguments in A Random Walk Down Wall Street, writing in 1973, “[We need] a new investment instrument: a no-load, minimummanagement-fee mutual fund that simply buys the hundreds of stocks making up the market averages and does no trading [of securities]. . . . Fund spokesmen are quick to point out, ‘you can’t buy the averages.’ It’s about time the public could.” Computers had gotten to the point where one could be put in an office setting without having to tear out walls and bring in industrialstrength air-conditioning, raised floors for the cables, and special power systems.

Dave Goldberg’s opening address to the conference included an insightful assessment of the state of evolutionary computing, in theory and in practice. Somehow, he managed to work in a story involving his Perils and Pr omise of Evolutionary Computation on Wall Str eet 187 Lithuanian grandmother’s recipe for chicken soup, which began, “First, steal a chicken.” There was no Lithuanian chicken soup at that GECCO, but there were some amazing demonstrations of learning programs. Robot control strategies started out as random walks, and after a few hundred simulated generations, they were moving like R2D2 on a good day. There were novel circuit, network, and even protein designs produced by artificial genetic methods.2 The financial guys, many of whom I recognized from more Wall Street–oriented events, and I were trolling for ideas, people to hire, and software to take home. I found all three, and so, several years later, when the GECCO crowd came to New York to focus on financial applications (and maybe get some of these guys hired), I was invited to give one of the keynote talks on what we had been up to.

 

pages: 478 words: 126,416

Other People's Money: Masters of the Universe or Servants of the People? by John Kay

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Affordable Care Act / Obamacare, asset-backed security, bank run, banking crisis, Basel III, Bernie Madoff, Big bang: deregulation of the City of London, bitcoin, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, call centre, capital asset pricing model, Capital in the Twenty-First Century by Thomas Piketty, cognitive dissonance, corporate governance, Credit Default Swap, cross-subsidies, dematerialisation, diversification, diversified portfolio, Edward Lloyd's coffeehouse, Elon Musk, Eugene Fama: efficient market hypothesis, eurozone crisis, financial innovation, financial intermediation, fixed income, Flash crash, forward guidance, Fractional reserve banking, full employment, George Akerlof, German hyperinflation, Goldman Sachs: Vampire Squid, Growth in a Time of Debt, income inequality, index fund, inflation targeting, interest rate derivative, interest rate swap, invention of the wheel, Irish property bubble, Isaac Newton, London Whale, Long Term Capital Management, loose coupling, low cost carrier, M-Pesa, market design, millennium bug, mittelstand, moral hazard, mortgage debt, new economy, Nick Leeson, Northern Rock, obamacare, Occupy movement, offshore financial centre, oil shock, passive investing, peer-to-peer lending, performance metric, Peter Thiel, Piper Alpha, Ponzi scheme, price mechanism, purchasing power parity, quantitative easing, quantitative trading / quantitative finance, railway mania, Ralph Waldo Emerson, random walk, regulatory arbitrage, Renaissance Technologies, rent control, Richard Feynman, risk tolerance, road to serfdom, Robert Shiller, Robert Shiller, Ronald Reagan, Schrödinger's Cat, shareholder value, Silicon Valley, Simon Kuznets, South Sea Bubble, sovereign wealth fund, Spread Networks laid a new fibre optics cable between New York and Chicago, Steve Jobs, Steve Wozniak, The Great Moderation, The Market for Lemons, the market place, The Myth of the Rational Market, the payments system, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Tobin tax, too big to fail, transaction costs, tulip mania, Upton Sinclair, Vanguard fund, Washington Consensus, We are the 99%, Yom Kippur War

Interest rates are expected to rise, Procter and Gamble owns many powerful brands, the Chinese economy is growing rapidly: these factors are fully reflected in the current level of long-term interest rates, the Procter & Gamble stock price and the exchange rate between the dollar and the renminbi. Since everything that is already known is ‘in the price’, only things that are not already known can influence the price. In an efficient market prices will therefore follow what is picturesquely described as a ‘random walk’ – the next move is as likely to be up as down. And since everything that is known is in the price, that price will represent the best available estimate of the underlying value of a security. A small further step of analogous reasoning leads to the ‘no arbitrage’ condition: each security is appropriately priced in relation to all other securities, so that it is never possible to make money by selling one and buying another.

., 2011, Money and Power: How Goldman Sachs Came to Rule the World, New York, Random House, p. 515. 17. Ceresney, A., 2013, ‘Statement on the Tourre Verdict’, US Securities and Exchange Commission Public Statement, 1 August. 18. Loewenstein, G., 1987, ‘Anticipation and the Value of Delayed Consumption’, Economic Journal, 97 (387), September, pp. 666–84. 19. There are many studies of this. See, for example, Malkiel, B. G., 2012, A Random Walk down Wall Street, 10th edn, New York and London, W.W. Norton. pp. 177–83. Porter, G.E., and Trifts, J.W., 2014, ‘The Career Paths of Mutual Fund Managers: The Role of Merit’, Financial Analysts Journal, 70 (4), July/August, pp. 55–71. Philips, C.B., Kinniry Jr, F.M., Schlanger, T., and Hirt, J.M., 2014, ‘The Case for Index-Fund Investing’, Vanguard Research, April, https://advisors.vanguard.com/VGApp/iip/site/advisor/researchcommentary/article/IWE_InvComCase4Index. 20.

, Proceedings, Federal Reserve Bank of Chicago, pp. 639–45. Loewenstein, G., 1987, ‘Anticipation and the Value of Delayed Consumption’, Economic Journal, 97 (387), September. Lucas Jr, R.E., 2003, ‘Macroeconomic Priorities’, The American Economic Review, 93 (1), March, pp. 1–14. Macmillan, H., 1957, ‘Leader’s Speech’, remarks at Conservative Party rally, Bedford, 20 July. Malkiel, B.G., 2012, A Random Walk down Wall Street, 10th edn, New York and London, W.W. Norton. Manne, H.G., 1965, ‘Mergers and the Market for Corporate Control’, The Journal of Political Economy, 73 (2), April, pp. 110–20. Markopolos, H., 2010, No One Would Listen: A True Financial Thriller, Hoboken, NJ, Wiley. Martin, F., 2013, Money: The Unauthorised Biography, London, Bodley Head. McArdle, M., 2009, ‘Why Goldman Always Wins’, The Atlantic, 1 October.

 

pages: 543 words: 147,357

Them And Us: Politics, Greed And Inequality - Why We Need A Fair Society by Will Hutton

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Andrei Shleifer, asset-backed security, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bretton Woods, capital controls, carbon footprint, Carmen Reinhart, Cass Sunstein, centre right, choice architecture, cloud computing, collective bargaining, conceptual framework, Corn Laws, corporate governance, credit crunch, Credit Default Swap, debt deflation, decarbonisation, Deng Xiaoping, discovery of DNA, discovery of the americas, discrete time, diversification, double helix, Edward Glaeser, financial deregulation, financial innovation, financial intermediation, first-past-the-post, floating exchange rates, Francis Fukuyama: the end of history, Frank Levy and Richard Murnane: The New Division of Labor, full employment, George Akerlof, Gini coefficient, global supply chain, Growth in a Time of Debt, Hyman Minsky, I think there is a world market for maybe five computers, income inequality, inflation targeting, interest rate swap, invisible hand, Isaac Newton, James Dyson, James Watt: steam engine, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, knowledge worker, labour market flexibility, Long Term Capital Management, Louis Pasteur, low-wage service sector, mandelbrot fractal, margin call, market fundamentalism, Martin Wolf, means of production, Mikhail Gorbachev, millennium bug, moral hazard, mortgage debt, new economy, Northern Rock, offshore financial centre, open economy, Plutocrats, plutocrats, price discrimination, private sector deleveraging, purchasing power parity, quantitative easing, race to the bottom, railway mania, random walk, rent-seeking, reserve currency, Richard Thaler, rising living standards, Robert Shiller, Robert Shiller, Ronald Reagan, Rory Sutherland, shareholder value, short selling, Silicon Valley, Skype, South Sea Bubble, Steve Jobs, The Market for Lemons, the market place, The Myth of the Rational Market, the payments system, the scientific method, The Wealth of Nations by Adam Smith, too big to fail, unpaid internship, value at risk, Washington Consensus, working poor, éminence grise

Happily ignoring the accumulated wisdom of Russell, Knight, Keynes and Newton, from the 1960s onwards, a group of mathematical economists hypothesised that the financial markets were different. There is abundant data about the movement of the prices of financial assets, although actually defining the universe of data proved much more problematic in practice. If you make the assumptions that financial markets are efficient containing all the information that they can, and that consequently all price movements are independent of each other and cannot be related to each other or the past, then important conclusions follow. Financial prices will move wholly randomly, as likely to go up as down – the ‘random walk’. If this is true then, as mentioned earlier, financial data will correspond to the law of large numbers and follow the same rules that dictate the distribution of, say, tall, average and short people, dice rolls and flips of a coin.

It could only be a legitimate question if the markets were not efficient, prices were not randomly distributed and events were not distributed on Gaussian principles, but nobody who wanted to stay in the mainstream could suggest such things. There is an enormous intellectual and financial investment in the status quo. Academics have built careers, reputations and tenure on a particular view of the world being right. Only an earthquake can persuade them to put up their hands and acknowledge they were wrong. When the mathematician Benoit Mandelbrot began developing his so-called fractal mathematics and power laws in the early 1960s, arguing that the big events outside the normal distribution are the ones that need explaining and assaulting the whole edifice of mathematical theory and the random walk, MIT’s Professor Paul Cootner (the great random walk theorist) exclaimed: ‘surely, before consigning centuries of work to the ash pile, we should like some assurance that all our work is truly useless’.

What Weatherstone wanted to know was how much money the bank would lose if it were hit by a big event outside the normal distribution of events. Such events are statistically improbable but still possible. But would they present too much risk, and bring down the whole bank? This led to the development of mathematically computed value at risk (VaR), which was based on the same assumptions about random walks, efficient markets and bell curves that had been used when pricing derivatives. The VaR figure is the maximum amount a financial institution might lose on any given day with a probability of 95 per cent or higher. Dick Fuld, the CEO of Lehman Brothers, could comfort himself throughout 2007 and even the first half of 2008 that his bank was exposed to less than $100 million of VaR on any given day (between 95 and 99 per cent confidence level).

 

pages: 162 words: 50,108

The Little Book of Hedge Funds by Anthony Scaramucci

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Andrei Shleifer, asset allocation, Bernie Madoff, business process, carried interest, Credit Default Swap, diversification, diversified portfolio, Donald Trump, Eugene Fama: efficient market hypothesis, fear of failure, fixed income, follow your passion, Gordon Gekko, high net worth, index fund, Long Term Capital Management, mail merge, margin call, merger arbitrage, NetJets, Ponzi scheme, profit motive, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk-adjusted returns, risk/return, Ronald Reagan, Saturday Night Live, Sharpe ratio, short selling, Silicon Valley, too big to fail, transaction costs, Vanguard fund, Y2K, Yogi Berra

Sure, I had heard the term in a Corporate Finance class at Tufts University—my undergraduate alma mater—but the concept barely registered. In plain prose, Professor Malkiel explained that due to perfect information being priced immediately into the markets, the stock prices moved in a random walk. There was no discernible way to predict future prices. Nope. Sorry. No technical analysis, no fundamental analysis, nothing. See, current stock prices were nothing more than a representation of the net present value of the future cash flow streams of each respective company. They were perfectly priced by the market and therefore no one had an edge. If something exogenous happened, well, that would be immediately reflected in price. If you just happened to be on the right side of it, you were the lucky one. You were the monkey on the end of a row of countless monkeys that was flipping a coin and despite the odds it kept coming up heads.

The world of finance was operating under Eugene Fama’s efficient market theory, which was developed in the 1960s at the University of Chicago. Here is the gist of it. If markets were rendered efficient, it followed that prices would move in a random pattern, and consequently those who achieved high levels of success would be investors who most quickly acted upon the fundamental news that was available to everybody. In other words, the only thing that moved a stock price was new information; any other changes were random and not predictable. As such, hedge fund managers did not have an edge . . . or did they? It was April of 1987. I was a first-year law student at Harvard, and desperately wanted to be a summer associate at Goldman Sachs. As I sat in Baker Library, anxiously waiting for my first interview with Goldman Sachs, I picked up A Random Walk on Wall Street by Burton Malkiel. It was then that I got my first exposure to the efficient market theory.

Arbitrage Before we delve into the individual relative value strategies, we must first define arbitrage. Arbitrage is a financial transaction that involves two similar items that are priced differently in different markets. In practice, the trader simultaneously purchases a position in one market and sells the similar position in a different market at a different price. In other words, he is exploiting the price differences of identical positions by buying the same security at a lower price and selling it right away at a higher price. In a perfect scenario, the arbitrageur profits from a difference in the price between the two and earns an immediate profit with no market risk. For example, an announced deal might provide an opportunity for risk arbitrage, or the issuance of a convertible bond by a publicly traded company may signal an opportunity for convertible arbitrage.

 

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Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb

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Antoine Gombaud: Chevalier de Méré, availability heuristic, backtesting, Benoit Mandelbrot, Black Swan, complexity theory, corporate governance, currency peg, Daniel Kahneman / Amos Tversky, discounted cash flows, diversified portfolio, endowment effect, equity premium, global village, hindsight bias, Long Term Capital Management, loss aversion, mandelbrot fractal, mental accounting, meta analysis, meta-analysis, quantitative trading / quantitative finance, QWERTY keyboard, random walk, Richard Feynman, Richard Feynman, road to serfdom, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, Steven Pinker, stochastic process, too big to fail, Turing test, Yogi Berra

With no mathematical literacy we can launch a Monte Carlo simulation of an eighteen-year-old Christian Lebanese successively playing Russian roulette for a given sum, and see how many of these attempts result in enrichment, or how long it takes on average before he hits the obituary. We can change the barrel to contain 500 holes, a matter that would decrease the probability of death, and see the results. Monte Carlo simulation methods were pioneered in martial physics in the Los Alamos laboratory during the A-bomb preparation. They became popular in financial mathematics in the 1980s, particularly in the theories of the random walk of asset prices. Clearly, we have to say that the example of Russian roulette does not need such apparatus, but many problems, particularly those resembling real-life situations, require the potency of a Monte Carlo simulator. Monte Carlo Mathematics It is a fact that “true” mathematicians do not like Monte Carlo methods. They believe that they rob us of the finesse and elegance of mathematics. They call it “brute force.”

Literally every great thinker has dabbled with it, most of them obsessively. The two greatest minds to me, Einstein and Keynes, both started their intellectual journeys with it. Einstein wrote a major paper in 1905, in which he was almost the first to examine in probabilistic terms the succession of random events, namely the evolution of suspended particles in a stationary liquid. His article on the theory of the Brownian movement can be used as the backbone of the random walk approach used in financial modeling. As for Keynes, to the literate person he is not the political economist that tweed-clad leftists love to quote, but the author of the magisterial, introspective, and potent Treatise on Probability. For before his venturing into the murky field of political economy, Keynes was a probabilist. He also had other interesting attributes (he blew up trading his account after experiencing excessive opulence—people’s understanding of probability does not translate into their behavior).

While early economic models excluded randomness, Arthur explained how “unexpected orders, chance meetings with lawyers, managerial whims . . . would help determine which ones achieved early sales and, over time, which firms dominated.” MATHEMATICS INSIDE AND OUTSIDE THE REAL WORLD A mathematical approach to the problem is in order. While in conventional models (such as the well-known Brownian random walk used in finance) the probability of success does not change with every incremental step, only the accumulated wealth, Arthur suggests models such as the Polya process, which is mathematically very difficult to work with, but can be easily understood with the aid of a Monte Carlo simulator. The Polya process can be presented as follows: Assume an urn initially containing equal quantities of black and red balls.

 

Data Mining the Web: Uncovering Patterns in Web Content, Structure, and Usage by Zdravko Markov, Daniel T. Larose

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Firefox, information retrieval, Internet Archive, iterative process, natural language processing, pattern recognition, random walk, recommendation engine, semantic web, speech recognition, statistical model, William of Occam

c 0.726 b 0.413 50 CHAPTER 2 HYPERLINK-BASED RANKING PAGERANK The hyperlinks are not only ways to propagate the prestige score of a page to pages to which it links, they are also paths along which web users travel from one web page to another. In this respect, the popularity (or prestige) of a web page can be measured in terms of how often an average web user visits it. To estimate this we may use the metaphor of the “random web surfer,” who clicks on hyperlinks at random with uniform probability and thus implements the random walk on the web graph. Assume that page u links to Nu web pages and page v is one of them. Then once the web surfer is at page u, the probability of visiting page v will be 1/Nu . This intuition suggests a more sophisticated scheme of propagation of prestige through the web links also involving the out-degree of the nodes. The idea is that the amount of prestige that page v receives from page u is 1/Nu of the prestige of u.

The simplified PageRank algorithm generally works with loops; however, there is a special configuration of nodes that the algorithm cannot deal with properly. Consider, for example, two pages that point to each other but do not point to other pages. Such an isolated loop is called a rank sink. If pointed to from an outside page, it accumulates rank but never distributes it to other nodes. To deal with the rank sink situation, we return to the random surfer model. As we have already noted, computing page rank is based on the idea of a random walk on the web graph, but the random surfer may get trapped into a rank sink. To avoid this situation we try to model the behavior of a real web surfer who gets bored running into a loop and jumps to some other web page outside the rank sink. For this purpose we introduce a rank source E, a vector over all web pages, which defines the probability distribution of jumping to a web page at random. Thus, the modified PageRank equation becomes A(v, u)R(v) R(u) = λ + E(u) Nv v The PageRank equation can be solved by using the eigenvector approach.

Below we present an iterative algorithm, which basically implements the power iteration 52 CHAPTER 2 HYPERLINK-BASED RANKING method for computing the dominant eigenvector with a small modification of the way the normalization is done. r R ← R0 r loop: ◦ Q←R R ← A TQ ◦ d ← Q1 − R1 ◦ ◦ R ← R + dE r while R − Q > ε 1 The initial rank vector R0 can be any vector over the web pages, A T is the transpose of the adjacency matrix with weights 1/Nu , and E is the rank source vector. The parameter d implements the normalization step and also affects the rate of convergence positively. The alternative approach would be just to add E to R and then normalize (R ← R/R1 ). As defined, the PageRank algorithm implements the random surfer model, where: r The rank vector R defines the probability distribution of a random walk on the graph of the Web. r With some low probability the surfer jumps to a random page chosen according to the distribution E. The source of rank E is usually chosen as a uniform vector with a small norm (e.g., E1 = 0.15). The way it affects the model of the random surfer is that the jumps to a random page happen more often if the norm of E is larger. In terms of PageRank score, a larger E means less contribution of the link structure to the final score (i.e., the rank distribution in R gets closer to E).

 

pages: 312 words: 35,664

The Mathematics of Banking and Finance by Dennis W. Cox, Michael A. A. Cox

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barriers to entry, Brownian motion, call centre, correlation coefficient, inventory management, iterative process, linear programming, meta analysis, meta-analysis, P = NP, pattern recognition, random walk, traveling salesman, value at risk

Further, a 2 is equally likely to appear on any subsequent roll of the dice. 4.3 ESTIMATION OF PROBABILITIES There are a number of ways in which you can arrive at an estimate of Prob(A) for the event A. Three possible approaches are: r A subjective approach, or ‘guess work’, which is used when an experiment cannot be easily r repeated, even conceptually. Typical examples of this include horse racing and Brownian motion. Brownian motion represents the random motion of small particles suspended in a gas or liquid and is seen, for example, in the random walk pattern of a drunken man. The classical approach, which is usually adopted if all sample points are equally likely (as is the case in the rolling of a dice as discussed above). The probability may be measured with certainty by analysing the event. Using the same mathematical notation, a mathematical definition of this is: Prob(A) = Number of events classifiable as A Total number of possible events A typical example of such a probability is a lottery.

Index a notation 103–4, 107–20, 135–47 linear regression 103–4, 107–20 slope significance test 112–20 variance 112 abscissa see horizontal axis absolute value, notation 282–4 accuracy and reliability, data 17, 47 adaptive resonance theory 275 addition, mathematical notation 279 addition of normal variables, normal distribution 70 addition rule, probability theory 24–5 additional variables, linear programming 167–70 adjusted cash flows, concepts 228–9 adjusted discount rates, concepts 228–9 Advanced Measurement Approach (AMA) 271 advertising allocation, linear programming 154–7 air-conditioning units 182–5 algorithms, neural networks 275–6 alternatives, decisions 191–4 AMA see Advanced Measurement Approach analysis data 47–52, 129–47, 271–4 Latin squares 131–2, 143–7 linear regression 110–20 projects 190–2, 219–25, 228–34 randomised block design 129–35 sampling 47–52, 129–47 scenario analysis 40, 193–4, 271–4 trends 235–47 two-way classification 135–47 variance 110–20, 121–7 anonimised databases, scenario analysis 273–4 ANOVA (analysis of variance) concepts 110–20, 121–7, 134–47 examples 110–11, 123–7, 134–40 formal background 121–2 linear regression 110–20 randomised block design 134–5, 141–3 tables 110–11, 121–3, 134–47 two-way classification 136–7 appendix 279–84 arithmetic mean, concepts 37–45, 59–60, 65–6, 67–74, 75–81 assets classes 149–57 reliability 17, 47, 215–18, 249–60 replacement of assets 215–18, 249–60 asymptotic distributions 262 ATMs 60 averages see also mean; median; mode concepts 37–9 b notation 103–4, 107–20, 132–5 linear regression 103–4, 107–20 variance 112 back propagation, neural networks 275–7 backwards recursion 179–87 balance sheets, stock 195 bank cashier problem, Monte Carlo simulation 209–12 Bank for International Settlements (BIS) 267–9, 271 banks Basel Accord 262, 267–9, 271 failures 58 loss data 267–9, 271–4 modelling 75–81, 85, 97, 267–9, 271–4 profitable loans 159–66 bar charts comparative data 10–12 concepts 7–12, 54, 56, 59, 205–6, 232–3 discrete data 7–12 examples 9–12, 205–6, 232–3 286 Index bar charts (cont.) narrative explanations 10 relative frequencies 8–12 rules 8–9 uses 7–12, 205–6, 232–3 base rates, trends 240 Basel Accord 262, 267–9, 271 bathtub curves, reliability concepts 249–51 Bayes’theorem, probability theory 27–30, 31 bell-shaped normal distribution see normal distribution bi-directional associative memory 275 bias 1, 17, 47–50, 51–2, 97, 129–35 randomised block design 129–35 sampling 17, 47–50, 51–2, 97, 129–35 skewness 41–5 binomial distribution concepts 55–8, 61–5, 71–2, 98–9, 231–2 examples 56–8, 61–5, 71–2, 98–9 net present value (NPV) 231–2 normal distribution 71–2 Pascal’s triangle 56–7 uses 55, 57, 61–5, 71–2, 98–9, 231–2 BIS see Bank for International Settlements boards of directors 240–1 break-even analysis, concepts 229–30 Brownian motion 22 see also random walks budgets 149–57 calculators, log functions 20, 61 capital Basel Accord 262, 267–9, 271 cost of capital 219–25, 229–30 cash flows adjusted cash flows 228–9 future cash flows 219–25, 227–34, 240–1 net present value (NPV) 219–22, 228–9, 231–2 standard deviation 232–4 central limit theorem concepts 70, 75 examples 70 chi-squared test concepts 83–4, 85, 89, 91–5 contingency tables 92–5 examples 83–4, 85, 89, 91–2 goodness of fit test 91–5 multi-way tables 94–5 tables 84, 91 Chu Shi-Chieh’s Ssu Yuan Y Chien 56 circles, tree diagrams 30–5 class intervals concepts 13–20, 44–5, 63–4, 241–7 histograms 13–20, 44–5 mean calculations 44–5 mid-points 44–5, 241–7 notation 13–14, 20 Sturges’s formula 20 variance calculations 44–5 classical approach, probability theory 22, 27 cluster sampling 50 coin-tossing examples, probability theory 21–3, 53–4 collection techniques, data 17, 47–52, 129–47 colours, graphical presentational approaches 9 combination, probability distribution (density) functions 54–8 common logarithm (base 10) 20 communications, decisions 189–90 comparative data, bar charts 10–12 comparative histograms see also histograms examples 14–19 completed goods 195 see also stock . . . conditional probability, concepts 25–7, 35 confidence intervals, concepts 71, 75–81, 105, 109, 116–20, 190, 262–5 constraining equations, linear programming 159–70 contingency tables, concepts 92–5 continuous approximation, stock control 200–1 continuous case, failures 251 continuous data concepts 7, 13–14, 44–5, 65–6, 251 histograms 7, 13–14 continuous uniform distribution, concepts 64–6 correlation coefficient concepts 104–20, 261–5, 268–9 critical value 105–6, 113–20 equations 104–5 examples 105–8, 115–20 costs capital 219–25, 229–30 dynamic programming 180–82 ghost costs 172–7 holding costs 182–5, 197–201, 204–8 linear programming 167–70, 171–7 sampling 47 stock control 182–5, 195–201 transport problems 171–7 trend analysis 236–47 types 167–8, 182 counting techniques, probability distribution (density) functions 54 covariance see also correlation coefficient concepts 104–20, 263–5 credit cards 159–66, 267–9 credit derivatives 97 see also derivatives Index credit risk, modelling 75, 149, 261–5 critical value, correlation coefficient 105–6, 113–20 cumulative frequency polygons concepts 13–20, 39–40, 203 examples 14–20 uses 13–14 current costs, linear programming 167–70 cyclical variations, trends 238–47 data analysis methods 47–52, 129–47, 271–4 collection techniques 17, 47–52, 129–47 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 design/approach to analysis 129–47 errors 129–47 graphical presentational approaches 1–20, 149–57 identification 2–5, 261–5 Latin squares 131–2, 143–7 loss data 267–9, 271–4 neural networks 275–7 qualities 17, 47 randomised block design 129–35 reliability and accuracy 17, 47 sampling 17, 47–52 time series 235–47 trends 5, 10, 235–47 two-way classification analysis 135–47 data points, scatter plots 2–5 databases, loss databases 272–4 debentures 149–57 decisions alternatives 191–4 Bayes’theorem 27–30, 31 communications 189–90 concepts 21–35, 189–94, 215–25, 228–34, 249–60 courses of action 191–2 definition 21 delegation 189–90 empowerment 189–90 guesswork 191 lethargy pitfalls 189 minimax regret rule 192–4 modelling problems 189–91 Monty Hall problem 34–5, 212–13 pitfalls 189–94 probability theory 21–35, 53–66, 189–94, 215–18 problem definition 129, 190–2 project analysis guidelines 190–2, 219–25, 228–34 replacement of assets 215–18, 249–60 staff 189–90 287 steps 21 stock control 195–201, 203–8 theory 189–94 degrees of freedom 70–1, 75–89, 91–5, 110–20, 136–7 ANOVA (analysis of variance) 110–20, 121–7, 136–7 concepts 70–1, 75–89, 91–5, 110–20, 136–7 delegation, decisions 189–90 density functions see also probability distribution (density) functions concepts 65–6, 67, 83–4 dependent variables, concepts 2–5, 103–20, 235 derivatives 58, 97–8, 272 see also credit . . . ; options design/approach to analysis, data 129–47 dice-rolling examples, probability theory 21–3, 53–5 differentiation 251 discount factors adjusted discount rates 228–9 net present value (NPV) 220–1, 228–9, 231–2 discrete data bar charts 7–12, 13 concepts 7–12, 13, 44–5, 53–5, 72 discrete uniform distribution, concepts 53–5 displays see also presentational approaches data 1–5 Disraeli, Benjamin 1 division notation 280, 282 dynamic programming complex examples 184–7 concepts 179–87 costs 180–82 examples 180–87 principle of optimality 179–87 returns 179–80 schematic 179–80 ‘travelling salesman’ problem 185–7 e-mail surveys 50–1 economic order quantity see also stock control concepts 195–201 examples 196–9 empowerment, staff 189–90 error sum of the squares (SSE), concepts 122–5, 133–47 errors, data analysis 129–47 estimates mean 76–81 probability theory 22, 25–6, 31–5, 75–81 Euler, L. 131 288 Index events independent events 22–4, 35, 58, 60, 92–5 mutually exclusive events 22–4, 58 probability theory 21–35, 58–66, 92–5 scenario analysis 40, 193–4, 271–4 tree diagrams 30–5 Excel 68, 206–7 exclusive events see mutually exclusive events expected errors, sensitivity analysis 268–9 expected value, net present value (NPV) 231–2 expert systems 275 exponent notation 282–4 exponential distribution, concepts 65–6, 209–10, 252–5 external fraud 272–4 extrapolation 119 extreme value distributions, VaR 262–4 F distribution ANOVA (analysis of variance) 110–20, 127, 134–7 concepts 85–9, 110–20, 127, 134–7 examples 85–9, 110–20, 127, 137 tables 85–8 f notation 8–9, 13–20, 26, 38–9, 44–5, 65–6, 85 factorial notation 53–5, 283–4 failure probabilities see also reliability replacement of assets 215–18, 249–60 feasibility polygons 152–7, 163–4 finance selection, linear programming 164–6 fire extinguishers, ANOVA (analysis of variance) 123–7 focus groups 51 forward recursion 179–87 four by four tables 94–5 fraud 272–4, 276 Fréchet distribution 262 frequency concepts 8–9, 13–20, 37–45 cumulative frequency polygons 13–20, 39–40, 203 graphical presentational approaches 8–9, 13–20 frequentist approach, probability theory 22, 25–6 future cash flows 219–25, 227–34, 240–1 fuzzy logic 276 Garbage In, Garbage Out (GIGO) 261–2 general rules, linear programming 167–70 genetic algorithms 276 ghost costs, transport problems 172–7 goodness of fit test, chi-squared test 91–5 gradient (a notation), linear regression 103–4, 107–20 graphical method, linear programming 149–57, 163–4 graphical presentational approaches concepts 1–20, 149–57, 235–47 rules 8–9 greater-than notation 280–4 Greek alphabet 283 guesswork, modelling 191 histograms 2, 7, 13–20, 41, 73 class intervals 13–20, 44–5 comparative histograms 14–19 concepts 7, 13–20, 41, 73 continuous data 7, 13–14 examples 13–20, 73 skewness 41 uses 7, 13–20 holding costs 182–5, 197–201, 204–8 home insurance 10–12 Hopfield 275 horizontal axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 hypothesis testing concepts 77–81, 85–95, 110–27 examples 78–80, 85 type I and type II errors 80–1 i notation 8–9, 13–20, 28–30, 37–8, 103–20 identification data 2–5, 261–5 trends 241–7 identity rule 282 impact assessments 21, 271–4 independent events, probability theory 22–4, 35, 58, 60, 92–5 independent variables, concepts 2–5, 70, 103–20, 235 infinity, normal distribution 67–72 information, quality needs 190–4 initial solution, linear programming 167–70 insurance industry 10–12, 29–30 integers 280–4 integration 65–6, 251 intercept (b notation), linear regression 103–4, 107–20 interest rates base rates 240 daily movements 40, 261 project evaluation 219–25, 228–9 internal rate of return (IRR) concepts 220–2, 223–5 examples 220–2 interpolation, IRR 221–2 interviews, uses 48, 51–2 inventory control see stock control Index investment strategies 149–57, 164–6, 262–5 IRR see internal rate of return iterative processes, linear programming 170 j notation 28–30, 37, 104–20, 121–2 JP Morgan 263 k notation 20, 121–7 ‘know your customer’ 272 Kohonen self-organising maps 275 Latin squares concepts 131–2, 143–7 examples 143–7 lead times, stock control 195–201 learning strategies, neural networks 275–6 less-than notation 281–4 lethargy pitfalls, decisions 189 likelihood considerations, scenario analysis 272–3 linear programming additional variables 167–70 concepts 149–70 concerns 170 constraining equations 159–70 costs 167–70, 171–7 critique 170 examples 149–57, 159–70 finance selection 164–6 general rules 167–70 graphical method 149–57, 163–4 initial solution 167–70 iterative processes 170 manual preparation 170 most profitable loans 159–66 optimal advertising allocation 154–7 optimal investment strategies 149–57, 164–6 returns 149–57, 164–6 simplex method 159–70, 171–2 standardisation 167–70 time constraints 167–70 transport problems 171–7 linear regression analysis 110–20 ANOVA (analysis of variance) 110–20 concepts 3, 103–20 equation 103–4 examples 107–20 gradient (a notation) 103–4, 107–20 intercept (b notation) 103–4, 107–20 interpretation 110–20 notation 103–4 residual sum of the squares 109–20 slope significance test 112–20 uncertainties 108–20 literature searches, surveys 48 289 loans finance selection 164–6 linear programming 159–66 risk assessments 159–60 log-normal distribution, concepts 257–8 logarithms (logs), types 20, 61 losses, banks 267–9, 271–4 lotteries 22 lower/upper quartiles, concepts 39–41 m notation 55–8 mail surveys 48, 50–1 management information, graphical presentational approaches 1–20 Mann–Whitney test see U test manual preparation, linear programming 170 margin of error, project evaluation 229–30 market prices, VaR 264–5 marketing brochures 184–7 mathematics 1, 7–8, 196–9, 219–20, 222–5, 234, 240–1, 251, 279–84 matrix plots, concepts 2, 4–5 matrix-based approach, transport problems 171–7 maximum and minimum, concepts 37–9, 40, 254–5 mean comparison of two sample means 79–81 comparisons 75–81 concepts 37–45, 59–60, 65–6, 67–74, 75–81, 97–8, 100–2, 104–27, 134–5 confidence intervals 71, 75–81, 105, 109, 116–20, 190, 262–5 continuous data 44–5, 65–6 estimates 76–81 hypothesis testing 77–81 linear regression 104–20 normal distribution 67–74, 75–81, 97–8 sampling 75–81 mean square causes (MSC), concepts 122–7, 134–47 mean square errors (MSE), ANOVA (analysis of variance) 110–20, 121–7, 134–7 median, concepts 37, 38–42, 83, 98–9 mid-points class intervals 44–5, 241–7 moving averages 241–7 minimax regret rule, concepts 192–4 minimum and maximum, concepts 37–9, 40 mode, concepts 37, 39, 41 modelling banks 75–81, 85, 97, 267–9, 271–4 concepts 75–81, 83, 91–2, 189–90, 195–201, 215–18, 261–5 decision-making pitfalls 189–91 economic order quantity 195–201 290 Index modelling (cont.) guesswork 191 neural networks 275–7 operational risk 75, 262–5, 267–9, 271–4 output reviews 191–2 replacement of assets 215–18, 249–60 VaR 261–5 moments, density functions 65–6, 83–4 money laundering 272–4 Monte Carlo simulation bank cashier problem 209–12 concepts 203–14, 234 examples 203–8 Monty Hall problem 212–13 queuing problems 208–10 random numbers 207–8 stock control 203–8 uses 203, 234 Monty Hall problem 34–5, 212–13 moving averages concepts 241–7 even numbers/observations 244–5 moving totals 245–7 MQMQM plot, concepts 40 MSC see mean square causes MSE see mean square errors multi-way tables, concepts 94–5 multiplication notation 279–80, 282 multiplication rule, probability theory 26–7 multistage sampling 50 mutually exclusive events, probability theory 22–4, 58 n notation 7, 20, 28–30, 37–45, 54–8, 103–20, 121–7, 132–47, 232–4 n!

Pascal’s triangle, concepts 56–7 payback period, concepts 219, 222–5 PCs see personal computers people costs 167–70 perception 275 permutation, probability distribution (density) functions 55 personal computers (PCs) 7–9, 58–60, 130–1, 198–9, 208–10, 215–18, 253–5 pictures, words 1 pie charts concepts 7, 12 critique 12 examples 12 planning, data collection techniques 47, 51–2 plot, concepts 1, 10 plus or minus sign notation 279 Poisson distribution concepts 58–66, 72–3, 91–2, 200–1, 231–2 examples 58–65, 72–3, 91–2, 200–1 net present value (NPV) 231–2 normal distribution 72–3 stock control 200–1 suicide attempts 62–5 uses 57, 60–5, 72–3, 91–2, 200–1, 231–2 291 population considerations, sampling 47, 49–50, 75–95, 109, 121–7 portfolio investments, VaR 262–5 power notation 282–4 predictions, neural networks 276–7 presentational approaches concepts 1–20 good presentation 1–2 management information 1–20 rules 8–9 trends 5, 10, 235–47 price/earnings ratio (P/E ratio), concepts 222 principle of optimality, concepts 179–87 priors, concepts 28–30 Prob notation 21–35, 68–70, 254–5 probability distribution (density) functions see also normal distribution binomial distribution 55–8, 61–5, 71–2, 98–9, 231–2 combination 54–8 concepts 53–95, 203, 205, 231–2, 257–60 continuous uniform distribution 64–6 counting techniques 54 discrete uniform distribution 53–5, 72 examples 53–5 exponential distribution 65–6, 209–10, 252–5 log-normal distribution 257–8 net present value (NPV) 231–2 permutation 55 Poisson distribution 58–66, 72–3, 91–2, 200–1, 231–2 probability theory addition rule 24–5 Bayes’theorem 27–30, 31 classical approach 22, 27 coin-tossing examples 21–3, 53–4 concepts 21–35, 53–66, 200–1, 203, 215–18, 231–2 conditional probability 25–7, 35 decisions 21–35, 53–66, 189–94, 215–18 definitions 22 dice-rolling examples 21–3, 53–5 estimates 22, 25–6, 32–5, 75–81 event types 22–4 examples 25–35, 53–5 frequentist approach 22, 25–6 independent events 22–4, 35, 58, 60, 92–5 Monty Hall problem 34–5, 212–13 multiplication rule 26–7 mutually exclusive events 22–4, 58 notation 21–2, 24–30, 54–5, 68–9, 75–6, 79–81, 83–5, 99–104, 121–2, 131–5, 185–7, 254–5 overlapping probabilities 25 simple examples 21–2 subjective approach 22 292 Index probability theory (cont.) tree diagrams 30–5 Venn diagrams 23–4, 28 problems, definition importance 129, 190–2 process costs 167–70 production runs 184–7 products awaiting shipment 195 see also stock . . . profit and loss accounts, stock 195 profitable loans, linear programming 159–66 projects see also decisions alternatives 191–4, 219–25 analysis guidelines 190–2, 219–25, 228–34 break-even analysis 229–30 courses of action 191–2 evaluation methods 219–25, 227, 228–34 finance issues 164–6 guesswork 191 IRR 220–2, 223–5 margin of error 229–30 net present value (NPV) 219–22, 228–9, 231–2 P/E ratio 222 payback period 219, 222–5 returns 164–6, 219–25, 227–34 sponsors 190–2 quality control 61–4 quality needs, information 190–4 quartiles, concepts 39–41 questionnaires, surveys 48, 50–1 questions, surveys 48, 51–2, 97 queuing problems, Monte Carlo simulation 208–10 quota sampling 50 r! notation 54–5 r notation 104–20, 135–47 random numbers, Monte Carlo simulation 207–8 random samples 49–50 random walks see also Brownian motion concepts 22 randomised block design ANOVA (analysis of variance) 134–5, 141–3 concepts 129–35 examples 130–1, 140–3 parameters 132–5 range, histograms 13–20 ranks, U test 99–102 raw materials 195 see also stock . . . reciprocals, numbers 280–4 recursive calculations 56–8, 61–2, 179–87 regrets, minimax regret rule 192–4 relative frequencies, concepts 8–12, 14–20 relevance issues, scenario analysis 272, 273–4 reliability bathtub curves 249–51 concepts 17, 47, 215–18, 249–60 continuous case 251 data 17, 47 definition 251 examples 249 exponential distribution 252–5 obsolescence 215–18 systems/components 215–18, 249–60 Weibull distribution 255–7, 262 reorder levels, stock control 195–201 replacement of assets 215–18, 249–60 reports, formats 1 residual sum of the squares, concepts 109–20, 121–7, 132–47 returns dynamic programming 179–80 IRR 220–2, 223–5 linear programming 149–57, 164–6 net present value (NPV) 219–22, 228–9, 231–2 optimal investment strategies 149–57, 164–6 P/E ratio 222 payback period 219, 222–5 projects 164–6, 219–25, 227–34 risk/uncertainty 227–34 risk adjusted cash flows 228–9 adjusted discount rates 228–9 Basel Accord 262, 267–9, 271 concepts 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 definition 227 loan assessments 159–60 management 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 measures 232–4, 271–4 net present value (NPV) 228–9, 231–2 operational risk 27–8, 75, 262–5, 267–9, 271–4 profiles 268–9 scenario analysis 40, 193–4, 271–4 sensitivity analysis 40, 264–5, 267–9 uncertainty 227–34 VaR 261–5 RiskMetrics 263 rounding 281–4 sample space, Venn diagrams 23–4, 28 sampling see also surveys analysis methods 47–52, 129–47 bad examples 50–1 bias 17, 47–50, 51–2, 97, 129–35 cautionary notes 50–2 Index central limit theorem 70, 75 cluster sampling 50 comparison of two sample means 79–81 concepts 17, 47–52, 70, 75–95, 109, 121–7, 129–47 costs 47 hypothesis testing 77–81, 85–95 mean 75–81 multistage sampling 50 normal distribution 70–1, 75–89 planning 47, 51–2 population considerations 47, 49–50, 75–95, 109, 121–7 problems 50–2 questionnaires 48, 50–1 quota sampling 50 random samples 49–50 selection methods 49–50, 77 size considerations 49, 77–8, 129 stratified sampling 49–50 systematic samples 49–50 units of measurement 47 variables 47 variance 75–81, 83–9, 91–5 scaling, scenario analysis 272 scatter plots concepts 1–5, 103–4 examples 2–3 uses 3–5, 103–4 scenario analysis anonimised databases 273–4 concepts 40, 193–4, 271–4 likelihood considerations 272–3 relevance issues 272, 273–4 scaling 272 seasonal variations, trends 236–40, 242–7 security costs 167–70 selection methods, sampling 49–50, 77 semantics 33–4 sensitivity analysis, concepts 40, 264–5, 267–9 sets, Venn diagrams 23–4, 28 sign test, concepts 98–9 significant digits 281–4 simplex method, linear programming 159–70, 171–2 simulation, Monte Carlo simulation 203–14, 234 size considerations, sampling 49, 77–8, 129 skewness, concepts 41–5 slope significance test see also a notation (gradient) linear regression 112–20 software packages reports 1 stock control 198–9 293 sponsors, projects 190–2 spread, standard deviation 41–5 square root 282–4 SS see sum of the squares SSC see sum of the squares for the causes SST see sum of the squares of the deviations Ssu Yuan Y Chien (Chu Shi-Chieh) 56 staff decision-making processes 189–90 training needs 189 standard deviation see also variance cash flows 232–4 concepts 41–5, 67–81, 83, 97–8, 102, 104–20, 232–4 correlation coefficient 104–20 examples 42–5, 232–4 normal distribution 67–81, 83, 97–8, 102, 232–4 uses 41–5, 104–20, 232–4 standard terms, statistics 37–45 standardisation, linear programming 167–70 statistical terms 1, 37–45 concepts 1, 37–45 maximum and minimum 37–9, 40, 254–5 mean 37–45 median 37, 38–42 mode 37, 39, 41 MQMQM plot 40 skewness 41–5 standard deviation 41–5 standard terms 37–45 upper/lower quartiles 39–41 variance 41–5 statistics, concepts 1, 37–45 std(x) notation (standard deviation) 42–5 stock control concepts 195–201, 203–8 continuous approximation 200–1 costs 182–5, 195–201 economic order quantity 195–201 holding costs 182–5, 197–201, 204–8 lead times 195–201 Monte Carlo simulation 203–8 non-zero lead times 199–201 order costs 197–201 Poisson distribution 200–1 variable costs 197–201 volume discounts 199–201 stock types 195 stratified sampling 49–50 Sturges’s formula 20 subjective approach, probability theory 22 subtraction notation 279 successful products, tree diagrams 30–3 suicide attempts, Poisson distribution 62–5 294 Index sum of the squares for the causes (SSC), concepts 122–5, 133–47 sum of the squares of the deviations (SST), concepts 122–5 sum of the squares (SS) ANOVA (analysis of variance) 110–20, 121–7, 134–5 concepts 109–20, 121–7, 132, 133–47 supply/demand matrix 171–7 surveys see also sampling bad examples 50–1 cautionary notes 50–2 concepts 48–52, 97 interviews 48, 51–2 literature searches 48 previous surveys 48 problems 50–2 questionnaires 48, 50–1 questions 48, 51–2, 97 symmetry, skewness 41–5, 67–9, 75–6, 98–9 systematic errors 130 systematic samples 49–50 systems costs 167–70 t statistic concepts 75–81, 97–8, 114–20, 121, 123, 125, 127 tables 75, 81 tables ANOVA (analysis of variance) 110–11, 121–3, 134–47 chi-squared test 84, 91 contingency tables 92–5 F distribution 85–8 normal distribution 67, 74 t statistic 75, 81 tabular formats, reports 1 telephone surveys 50–2 text surveys 50–1 three-dimensional graphical representations 9 time constraints, linear programming 167–70 time series concepts 235–47 cyclical variations 238–47 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 trade finance 164–6 training needs, communications 189 transport problems concepts 171–7 ghost costs 172–7 ‘travelling salesman’ problem, dynamic programming 185–7 tree diagrams examples 30–4 Monty Hall problem 34–5 probability theory 30–5 trends analysis 235–47 concepts 235–47 cyclical variations 238–47 graphical presentational approaches 5, 10, 235–47 identification 241–7 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 true rank, U test 99–102 truncated normal distribution, concepts 259, 260 truncation concepts, scatter plots 2–3 Twain, Mark 1 two-tail test, hypothesis testing 77–81, 109 two-way classification analysis 135–47 examples 137–40 type I and type II errors examples 80–1 hypothesis testing 80–1 U test, concepts 99–102 uncertainty concepts 108–20, 227–34 definition 227 linear regression 108–20 net present value (NPV) 228–9, 231–2 risk 227–34 upper/lower quartiles, concepts 39–41 valuations, options 58, 97–8 value at risk (VaR) calculation 264–5 concepts 261–5 examples 262–3 extreme value distributions 262–4 importance 261 variable costs, stock control 197–201 variables bar charts 7–8 concepts 2–3, 7–12, 13–14, 27–35, 70, 103–20, 121–7 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 correlation coefficient 104–20 data collection techniques 47 dependent/independent variables 2–5, 70, 103–20, 235 histograms 13–20 Index linear programming 149–70 linear regression 3, 103–20 scatter plots 2–5 sensitivity analysis 40, 264–5, 267–9 variance see also standard deviation ANOVA (analysis of variance) 110–20, 121–7, 134–47 chi-squared test 83–4, 85, 89, 91–5 comparisons 83–9 concepts 41–5, 65–6, 67, 75–81, 83–9, 91–5, 102, 104, 107, 110–20, 233–4, 263–5 continuous data 44–5 covariance 104–20, 263–5 examples 42–5 F distribution 85–9, 110–20, 127, 134–7 linear regression 104, 107, 110–20 var(x) notation (variance) 42–5, 233–4 VC see venture capital 295 Venn diagrams, concepts 23–4, 28 venture capital (VC) 149–57 vertical axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 volume discounts, stock control 199–201 Weibull distribution concepts 255–7, 262 examples 256–7 ‘what/if’ analysis 33 Wilcoxon test see U test words, pictures 1 work in progress 195 Z charts, concepts 245–7 z notation 67–74, 102, 105, 234 zero factorial 54–5 Index compiled by Terry Halliday

 

pages: 326 words: 97,089

Five Billion Years of Solitude: The Search for Life Among the Stars by Lee Billings

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Albert Einstein, Arthur Eddington, California gold rush, Colonization of Mars, cosmological principle, cuban missile crisis, dark matter, Dava Sobel, double helix, Edmond Halley, full employment, hydraulic fracturing, index card, Isaac Newton, Kuiper Belt, Magellanic Cloud, music of the spheres, out of africa, Peter H. Diamandis: Planetary Resources, planetary scale, profit motive, quantitative trading / quantitative finance, Ralph Waldo Emerson, RAND corporation, random walk, Search for Extraterrestrial Intelligence, Searching for Interstellar Communications, Silicon Valley, Solar eclipse in 1919, technological singularity, the scientific method, transcontinental railway

Instead of a noose, the scaffold held a thin steel pendulum, loosely suspended above a steel square by a tiny embedded magnet. He would place magnets of various strengths and shapes strategically upon the square and give the pendulum a gentle bump; it would swing to and fro for long periods, kicking between magnetic fields with sufficient force to overcome the frictional loss of momentum from moving through the air. Its motions followed a chaotic random walk, never exactly repeating any given path. Laughlin savored the toy for how its complex behavior could unfold solely from the simple initial conditions of each magnet’s position and the strength and trajectory of an initiatory nudge. It reminded him of his struggles to predict the typical outcomes that emerged from the chaotic gravitational interactions of black holes, stars, and planets, and his efforts to squeeze faint signals from backgrounds of meaningless noise.

The clouds had cleared. He sighed, cursed, produced a turkey sandwich from his bag, and ate it with resignation. “This seems excessive, even for the associate director,” Wiktorowicz said between bites. “It’s like the telescope just lost its mind. Maybe the ghost of that French guy with dysentery is trying to stick it to us.” “I think it just drifted into a rough mood and needed to cool off with a random walk,” Zachary said. “Cheer up, Sloane. We’re gonna help it find itself.” Laughlin and I excused ourselves to go watch the transit from the parking lot beneath the suddenly clear sky. As we left I glanced again at the netbook’s video feed from Mauna Kea. Wiktorowicz was staring dejectedly at the screen, slowly chewing another turkey sandwich. The worm-bite arc had become a perfectly circular bullet hole in the Sun—Venus had slid well within the disk, and its ingress had passed.

He said, ‘You have these natural skills, but you need to be able to support yourself and not rely on any man!’ He wanted me to be independent, and just didn’t think it was a good career choice.” Seager’s father valued practicality, but time and time again, he told her she must think big, set goals, and visualize herself reaching them. Otherwise, she should not expect success. Despite that advice, Seager often described her early path toward astronomy as an unfocused “random walk,” like that of a photon bouncing chaotically around the seething heart of a star. She appeased her father by first concentrating on physics, reasoning that would boost her chances of employment both within and outside of academia, but the more she learned, the less interest she could muster. “I believed you could perfectly describe everything with equations,” she said. “Then I learned that approximations were rampant.

 

pages: 741 words: 179,454

Extreme Money: Masters of the Universe and the Cult of Risk by Satyajit Das

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affirmative action, Albert Einstein, algorithmic trading, Andy Kessler, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, BRICs, British Empire, capital asset pricing model, Carmen Reinhart, carried interest, Celtic Tiger, clean water, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Fall of the Berlin Wall, financial independence, financial innovation, fixed income, full employment, global reserve currency, Goldman Sachs: Vampire Squid, Gordon Gekko, greed is good, happiness index / gross national happiness, haute cuisine, high net worth, Hyman Minsky, index fund, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, job automation, Johann Wolfgang von Goethe, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, Kevin Kelly, labour market flexibility, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Martin Wolf, merger arbitrage, Mikhail Gorbachev, Milgram experiment, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Naomi Klein, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, pets.com, Plutocrats, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, quantitative easing, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Feynman, Richard Thaler, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, Rod Stewart played at Stephen Schwarzman birthday party, rolodex, Ronald Reagan, Ronald Reagan: Tear down this wall, savings glut, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, The Chicago School, The Great Moderation, the market place, the medium is the message, The Myth of the Rational Market, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond

Random movements in prices, devoid of any trend or cycle, were a depressing prospect for economists. Maurice Kendall, a British statistician, described it as the work of “the Demon of Chance,” randomly drawing a number from a distribution of possible price changes, which, when added to today’s price, determined the next price. While working for a stock market newsletter, Eugene Fama noticed patterns in stock prices that would appear and disappear rapidly. In his doctoral dissertation, he laid out the argument that stock prices were random, reflecting all available information relevant to its value. Prices followed a random walk and market participants could not systematically profit from market inefficiencies. The EMH does not require market price to be always accurate. Investors force the price to fluctuate randomly around its real value.

If you own shares over a year, then most of the time the share price moves up or down a small amount. On some days you may get a large or very large price change. VAR ranks the price changes from largest fall to largest rise. Assuming that prices follow a random walk and price changes fit a normal distribution, you can calculate the probability of a particular size price change. You can answer questions like what is the likely maximum price change and loss on your holding at a specific probability level, say 99 percent, which equates to 1 day out of 100 days. A VAR figure of $50 million at 99 percent over a 10-day holding period means that the bank has a 99 percent probability that it will not suffer a loss of more than $50 million over a 10-day period. VAR became accepted best practice, enshrined in bank regulations. Risk, the unknown unknown, was now a known unknown or even a known known.

On average, investors buying all the stocks in the market would earn higher returns with lower risk. Fund managers with high returns simply took higher risk rather than possessing supernatural skill. Demon of Chance The efficient market hypothesis (EMH) stated that the stock prices followed a random walk, a formal mathematical statement of a trajectory consisting of successive random steps. Pioneers Jules Regnault (in the nineteenth century) and Louis Bachelier (early twentieth century) had discovered that short-term price changes were random—a coin toss could predict up or down moves. Bachelier’s Sorbonne thesis established that the probability of a given change in price was consistent with the Gaussian or bell-shaped normal distribution, well-known in statistical theory. Aware of the importance of his insights, Bachelier claimed: “the present theory resolves the majority of problems in the study of speculation.”5 His examiners disagreed.

 

pages: 662 words: 180,546

Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown by Philip Mirowski

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Andrei Shleifer, asset-backed security, bank run, barriers to entry, Basel III, Berlin Wall, Bernie Madoff, Bernie Sanders, Black Swan, blue-collar work, Bretton Woods, Brownian motion, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, constrained optimization, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, dark matter, David Brooks, David Graeber, debt deflation, deindustrialization, Edward Glaeser, Eugene Fama: efficient market hypothesis, experimental economics, facts on the ground, Fall of the Berlin Wall, financial deregulation, financial innovation, Flash crash, full employment, George Akerlof, Goldman Sachs: Vampire Squid, Hernando de Soto, housing crisis, Hyman Minsky, illegal immigration, income inequality, incomplete markets, invisible hand, Jean Tirole, joint-stock company, Kenneth Rogoff, knowledge economy, l'esprit de l'escalier, labor-force participation, liquidity trap, loose coupling, manufacturing employment, market clearing, market design, market fundamentalism, Martin Wolf, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Nash equilibrium, night-watchman state, Northern Rock, Occupy movement, offshore financial centre, oil shock, payday loans, Ponzi scheme, precariat, prediction markets, price mechanism, profit motive, quantitative easing, race to the bottom, random walk, rent-seeking, Richard Thaler, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, savings glut, school choice, sealed-bid auction, Silicon Valley, South Sea Bubble, Steven Levy, technoutopianism, The Chicago School, The Great Moderation, the map is not the territory, The Myth of the Rational Market, the scientific method, The Wisdom of Crowds, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thorstein Veblen, Tobin tax, too big to fail, transaction costs, War on Poverty, Washington Consensus, We are the 99%, working poor

,” on Hyman Minsky influence of on “informational efficacy” and “allocative efficiency,” on Keynesian Theory in New York Review of Books orthodox economics profession on reason for becoming an economist “The Return of Depression Economics,” Kydland–Prescott notion L La Bute, Neil Laibson, David Laissez-faire Lal, Deepak LAMP (Liberal Archief, Ghent) Lanchester, John Landsbanki Lange, Oskar Lasn, Kalle Late Neoliberalism Lehman Brothers Leoni, Bruno Les Mots et les Choses Levin, Richard Levine, David Levitt, Steven Levy, David Lewis, Michael, The Big Short Liberatarianism Liberty Institute Liberty International Liberty League LIBOR scandal Lilly Endowment LinkedIn L’Institut Universitaire des Hautes Etudes Internationales at Geneva Litan, Robert Competitive Equity The Derivatives Dealer’s Club “In Defense of Much, But Not All, Financial Innovation,” writings of Lloyd’s Bank Lo, Andrew on economic crisis Harris & Harris Group Professor of Finance A Non-Random Walk Down Wall Street “Reading About the Financial Crisis,” Lohmann, Larry “Looting: The Economic Underworld of Bankruptcy for Profit” (Romer) Lowenstein, Roger LSE (London School of Economics) Lucas, Robert E. as Bank of Sweden Prize winner on corruption on economic crisis followers of on Keynes neoclassical economists on rational-expectations macroeconomics movement Luntz, Frank M Mack, Christy MacKenzie, Donald MacKinley, A. Craig, A Non-Random Walk Down Wall Street MacroMarkets LLC Madoff, Bernie Make Markets Be Markets (Roosevelt Institute) Mallaby, Sebastian Mankiw, Gregory Marcet, Albert Market Design, Inc.

The journalist Roger Lowenstein declared, “The upside of the current Great Recession is that it could drive a stake through the heart of the academic nostrum known as the efficient-market hypothesis.”57 There was more than sufficient ammunition to choose from to rain fire down on the EMH, not least because it had been the subject of repeated criticism from within the economics profession since the 1980s. But what the journalists like Cassidy, Fox, and Lowenstein and commentators like Krugman neglected to inform their readers was that the back and forth, the intellectual thrust and empirical parry, had ground to a standoff more than a decade before the crisis, as admirably explained in Lo and MacKinlay, A Non-Random Walk Down Wall Street: There is an old joke, widely told among economists, about an economist strolling down the street with a companion when they come upon a $100 bill lying on the ground. As the companion reaches down to pick it up, the economist says, “Don’t bother—if it were a real $100 bill, someone would have already picked it up.” This humorous example of economic logic gone awry strikes dangerously close to home for students of the Efficient Markets Hypothesis, one of the most important controversial and well-studied propositions in all the social sciences.

Competitive Equity: A Better Way to Organize Mutual Funds (Washington: American Enterprise Institute, 2007). Lo, Andrew. “Reading About the Financial Crisis,” Journal of Economic Literature, 50 (2012): 151-178. Lo, Andrew. “Reconciling Efficient Markets with Behavioral Finance: The Adaptive Markets Hypothesis,” Journal of Investment Consulting 7 (2005): 21–44. Lo, Andrew, and Craig MacKinlay. A Non-Random Walk Down Wall Street (Princeton: Princeton University Press, 1999). Loewenstein, George, and Peter Ubel. “Economics Behaving Badly,” New York Times, July 14, 2010. Lofgren, Mike. “Revolt of the Rich,” American Conservative, September 2012. Lohmann, Larry. “Carbon Trading: A Critical Dialogue,” Development Dialogue no. 48, September 2006. Lohmann, Larry. “Carbon Trading, Climate Justice, and the Production of Ignorance,” Development 51 (2008): 359–65.

 

pages: 224 words: 13,238

Electronic and Algorithmic Trading Technology: The Complete Guide by Kendall Kim

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algorithmic trading, automated trading system, backtesting, corporate governance, Credit Default Swap, diversification, en.wikipedia.org, family office, financial innovation, fixed income, index arbitrage, index fund, interest rate swap, linked data, market fragmentation, natural language processing, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, short selling, statistical arbitrage, Steven Levy, transaction costs, yield curve

The options include: 3 4 Sang Lee, ‘‘Algorithmic Trading: Hype or Reality?’’ Aite Group Report 20050328, March 2005: 16–17. Lori Master, White Paper: ‘‘ECN Aggregators—Increasing Transparency and Liquidity in Equity Markets,’’ Random Walk Computing, Fall 2004: 6–8. Automating Trade and Order Flow 25 . Send blocks of 50,000 shares through a broker dealer to satisfy soft dollar agreements such as sell-side research, etc. . Utilize an algorithm such as Volume-Weighted Average Price (VWAP) and let the algorithm judge the patterns, and smart routing features will search for the best firm price available at the time of each order. 5. The executing trading desks would send back the execution information to the trader’s OMS. The OMS can then submit the fill data to a system such as AccessPlexus for execution quality evaluation. 2.7 Order Routing Order routing is the domain of direct market access (DMA) technology providers.

H high-touch trading trades in which prices are quoted over the phone. I implementation shortfall André Perold defines implementation shortfall as the difference in return between a theoretical portfolio and the implemented portfolio.3 In a paper portfolio, a portfolio manager looks at prevailing prices, in relation to execution prices in an actual portfolio. Implementation shortfall measures the price distance between the final, realized trade price, and a pre-trade decision price. implicit cost the price at which an investor or money manager can purchase an asset (the dealer’s asking price) and the price at which you can sell the same asset at the same point in time (the dealer’s bid price). The price impact this usually creates by trading an asset pushes up the price when buying an asset and pushes it down while selling. indicative prices confirmation, trades in which prices are published but require manual interdealer systems allow dealers to execute transactions electronically with other dealers through the fully anonymous services of interdealer brokers.

Under NYSE Rule 80A, if the DJIA moves up or down 2% from the previous closing value, program trading orders to buy or sell the Standard & Poor’s 500 stocks as part of index arbitrage strategies must be entered with directions to have the order executions effected in a manner that stabilizes share prices. The collar restrictions are lifted if the DJIA returns to or within 1% of its previous closing value. The futures exchanges set the price limits that aim to lessen sharp price swings in contracts, such as stock index futures. A price limit does not stop trading in the futures, but prohibits trading at prices below the preset limit during a price decline. Intraday price limits are removed when preset times during the trading session, such as 10 minutes after the threshold, are reached. Daily price limits remain in effect for the entire trading session. Specific price limits are set by the exchanges for each stock index futures contract. There are no price limits for U.S. stock index options, equity options, or stocks.8 Circuit breakers were put into place in 1988 in order to keep any future markets from dropping relentlessly in a market downturn.

 

pages: 263 words: 20,730

Exploring Python by Timothy Budd

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c2.com, centre right, general-purpose programming language, index card, random walk, sorting algorithm, web application

The function random.randint(0,1) will produce the values 0 and 1 with equal probability. Maintain a value that indicates the current location of the drunk, and at each step of the simulation move either right or left. Display the value of the array after each step. 17. The two dimensional variation on the random walk starts in the middle of a grid, such as an 11 by 11 array. At each step the drunk has four choices: up, down, left or right. Earlier in the chapter we described how to create a two-dimensional array of numbers. Using this data type, write a simulation of the two-dimensional random walk. 18. One list is equal (==) to another if they have the same length and the corresponding elements are equal. It is perhaps surprising that lists can also be compared with the relational operators, such as <. Experiment with this operator, and see if you can develop a general rule to explain when one list is less than another. >>> [1, 2] < [1, 2, 3] True >>> [4, 5] < [1, 2, 3] False >>> Exploring Python – Chapter 4 - Strings, Lists and Tuples 21 14.

On each iteration it makes two calls on randint to simulate rolling a pair of dice. Compute the sum of the two dice, and record the number of times each value appears. After the loop, print the array of sums. You can initialize the array using the idiom shown earlier in this chapter: times = [0] * 12 # make an array of 12 elements, initially zero 16. A classic problem that can be solved using an array is the random walk. Imagine a drunken man standing on the center square of a sidewalk consisting of 11 squares. At each step the drunk can elect to go either right or left. How long will it be until he reaches the end of the sidewalk, and how many times will he have stood on each square? To solve the problem, represent the number of times the drunk has stood on a square as an array. This can be created and initialized to zero with the following statement: times = [0] * 11 Use the function random.randint from the random module to compute random numbers.

One way might be to simply represent the information on each product in three successive lines of text, such as the following: Toast O’Matic 42 12.95 Kitchen Chef Blender 193 47.43 Did you immediately understand that there are currently 42 Toast O’Matics in the inventory and that they cost $12.95 each? Compare the description just given to the following XML encoding of the same data: <inventory> <product> <name>Toast O’Matic</name> <onHand>42</onHand> <price>12.95</price> </product> <product> <name>Kitchen Chef Blender</name> <onHand>193</onHand> <price>47.43</price> </produce> </inventory> This example illustrates both the advantages and the disadvantages of the XML format. The advantage is that the information is more self-documenting. It is clear what each field represents. You can read the information and immediately know what it means. Since the information is ordinary text, it can be read by both humans and computers.

 

pages: 289 words: 113,211

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

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affirmative action, Albert Einstein, asset allocation, backtesting, Black Swan, Black-Scholes formula, Bonfire of the Vanities, butterfly effect, commodity trading advisor, computer age, disintermediation, diversification, double entry bookkeeping, Edward Lorenz: Chaos theory, family office, financial innovation, fixed income, frictionless, frictionless market, George Akerlof, implied volatility, index arbitrage, Jeff Bezos, London Interbank Offered Rate, Long Term Capital Management, loose coupling, margin call, market bubble, market design, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, new economy, Nick Leeson, oil shock, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk tolerance, risk/return, Robert Shiller, Robert Shiller, rolodex, Saturday Night Live, shareholder value, short selling, Silicon Valley, statistical arbitrage, The Market for Lemons, time value of money, too big to fail, transaction costs, tulip mania, uranium enrichment, yield curve, zero-coupon bond

Because information is by definition random, the future course of the stock would also be random. It might continue to rise, or it might turn the other way. Each stock was paired with another stock, so only company-specific information would affect the relative pricing of the pair. Any broader information would make both stocks move, and the relative value of the pair would remain unchanged. The company-specific effects could be diversified away by holding many pairs since they would be independent from one company to another. In this way Bamberger’s trading strategy gave obeisance to efficient markets. He assumed information would move prices as a random walk, but he constructed the portfolio in a way that negated the impact of that information, at least in a statistical sense. That 186 ccc_demon_165-206_ch09.qxd 7/13/07 2:44 PM Page 187 T H E B R AV E N E W W O R L D OF HEDGE FUNDS left the portfolio solely exposed to liquidity demand.

In an age in which people are willing to invest money in virtual stocks, where by definition there are no prospects of earnings and where price appreciation is obtained through nothing short of an unsustainable bubble, it is not too hard to see how a real dot-com, with real prospects, no matter how dim, could attract investors. Market bubbles have been explained by the tendency of investors to follow trends and by the dynamics of crowd psychology—the need for people to be part of a successful herd. But neither trend-following strategies nor irrational crowd behavior is necessary to create market bubbles. Even if we assume as a starting point that the stock market is a random walk and 168 ccc_demon_165-206_ch09.qxd 7/13/07 2:44 PM Page 169 T H E B R AV E N E W W O R L D OF HEDGE FUNDS is governed by rational behavior, and even if we assert at the outset that all trades reflect the full consideration of the most up-to-date information, merely the fact that there are winners and losers will lead to booms and busts that have little to do with the rational application of information.1 The simplest market cycle is based on two psychological characteristics of investors.

Markets are efficient, which is to say that they react immediately and appropriately to 210 ccc_demon_207-242_ch10.qxd 2/13/07 1:47 PM COCKROACHES AND Page 211 HEDGE FUNDS all relevant information; when the news comes out, they adjust instantly. Since information coming into a market is by definition unknown and random, and since the market reacts fully and immediately to this new information, market prices move about randomly. From this comes the assertion that the market is a random walk. Full adherence to the efficient markets hypothesis leaves much of the financial industry in a paradoxical position. It is precisely the activity of the many people trying to track down information to make profitable trades that leads the markets to be efficient. But in the aggregate this leaves investors and traders unable to extract profits for all their trouble.

 

How I Became a Quant: Insights From 25 of Wall Street's Elite by Richard R. Lindsey, Barry Schachter

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Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business process, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Nick Leeson, P = NP, pattern recognition, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative finance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional

The academic scene exploded in the 1960s with seminal ideas like the capital asset pricing model, and in the 1970s with arbitrage pricing theory and the Black-Scholes-Merton option pricing formula. In 1965, the University of Chicago’s Eugene Fama published “The Behavior of Stock Prices,” which laid the foundation of the efficient market hypothesis. Fama theorized that stock prices fully and instantaneously reflect all available information. In the same year, Paul Samuelson at MIT published his “Proof that Properly Anticipated Prices Fluctuate Randomly,” which showed that, in an efficient market, price changes are random and thus inherently unpredictable. Burton Malkiel at Princeton later popularized these views in A Random Walk Down Wall Street, published in 1973. Academic analyses of the burgeoning amount of available data seemed to support market efficiency.

Academic analyses of the burgeoning amount of available data seemed to support market efficiency. Computer-enabled dissections of actual market prices suggested that price changes followed a random walk. Furthermore, Michael Jensen, one of Fama’s doctoral students, analyzed mutual fund performance from 1945 to 1964 and found that professional managers had not outperformed the market. If one could not predict security prices, active management was futile. The solution seemed to be to shift the emphasis from security selection to constructing portfolios that offered the market’s return with the market’s risk. Requiring no security research and little trading, these portfolios could capture the long-term upward trend in overall stock prices. Low-cost, passive index funds were born. The efficient market hypothesis prevailed in academia during the 1970s, and Wharton was no exception.

For those who argue that it is the particular securities, not the factor exposure that generates the sought-for returns, I suggest ranking three or more securities as investment candidates in each investment sector considered. Wait a couple of months and correlate those rankings against the performance observed over those months. Do this for a number of sectors for a number of time periods and you will develop both a sense of humility and an appreciation of the random walk hypotheses. Articles During my travels, I have coauthored three articles, the essence of which is not included in the stories above. In 1998, Andre Perold and I coauthored “The Free Lunch in Currency Hedging: Implications for Investment Policy and Performance Standards.”11 We argued that, because currency boasts a long-term expected return that is close to zero, the sizable effects of currency risk can be removed with minimal transaction costs without the portfolio suffering much of a reduction in long-term return.

 

pages: 386 words: 122,595

Naked Economics: Undressing the Dismal Science (Fully Revised and Updated) by Charles Wheelan

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affirmative action, Albert Einstein, Andrei Shleifer, barriers to entry, Berlin Wall, Bernie Madoff, Bretton Woods, capital controls, Cass Sunstein, central bank independence, clean water, collapse of Lehman Brothers, congestion charging, Credit Default Swap, crony capitalism, currency manipulation / currency intervention, Daniel Kahneman / Amos Tversky, David Brooks, demographic transition, diversified portfolio, Doha Development Round, Exxon Valdez, financial innovation, floating exchange rates, George Akerlof, Gini coefficient, Gordon Gekko, greed is good, happiness index / gross national happiness, Hernando de Soto, income inequality, index fund, interest rate swap, invisible hand, job automation, Joseph Schumpeter, Kenneth Rogoff, libertarian paternalism, low skilled workers, lump of labour, Malacca Straits, market bubble, microcredit, money: store of value / unit of account / medium of exchange, Network effects, new economy, open economy, presumed consent, price discrimination, price stability, principal–agent problem, profit maximization, profit motive, purchasing power parity, race to the bottom, RAND corporation, random walk, rent control, Richard Thaler, rising living standards, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, school vouchers, Silicon Valley, Silicon Valley startup, South China Sea, Steve Jobs, The Market for Lemons, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, transaction costs, transcontinental railway, trickle-down economics, urban sprawl, Washington Consensus, Yogi Berra, young professional

So even if you believe that there will be an occasional $100 bill lying on the ground, you should also recognize that it won’t be lying there for long. Second, the most effective critics of the efficient markets theory think the average investor probably can’t beat the market and shouldn’t try. Andrew Lo of MIT and A. Craig MacKinlay of the Wharton School are the authors of a book entitled A Non-Random Walk Down Wall Street in which they assert that financial experts with extraordinary resources, such as supercomputers, can beat the market by finding and exploiting pricing anomalies. A BusinessWeek review of the book noted, “Surprisingly, perhaps, Lo and MacKinlay actually agree with Malkiel’s advice to the average investor. If you don’t have any special expertise or the time and money to find expert help, they say, go ahead and purchase index funds.”8 Warren Buffett, arguably the best stock picker of all time, says the same thing.9 Even Richard Thaler, the guy beating the market with his behavioral growth fund, told the Wall Street Journal that he puts most of his retirement savings in index funds.10 Indexing is to investing what regular exercise and a low-fat diet are to losing weight: a very good starting point.

So, faced with the prospect of giving up consumption in the present for plodding success in the future, we eagerly embrace faster, easier methods—and are then shocked when they don’t work. This chapter is not a primer on personal finance. There are some excellent books on investment strategies. Burton Malkiel, who was kind enough to write the foreword for this book, has written one of the best: A Random Walk Down Wall Street. Rather, this chapter is about what a basic understanding of markets—the ideas covered in the first two chapters—can tell us about personal investing. Any investment strategy must obey the basic laws of economics, just as any diet is constrained by the realities of chemistry, biology, and physics. To borrow the title of Wally Lamb’s best-selling novel: I know this much is true.

But look what happens as the time frame gets longer: Only 45 percent of actively managed funds beat the S&P over a twenty-year stretch, which is the most relevant time frame for people saving for retirement or college. In other words, 55 percent of the mutual funds that claim to have some special stock-picking ability did worse over two decades than a simple index fund, our modern equivalent of a monkey throwing a towel at the stock pages. If you had invested $10,000 in the average actively managed equity fund in 1973, when Malkiel’s heretical book A Random Walk Down Wall Street first came out, it would be worth $355,091 today (many editions later). If you had invested the same amount of money in an S&P 500 index fund, it would now be worth $364,066. Data notwithstanding, the efficient markets theory is obviously not the most popular idea on Wall Street. There is an old joke about two economists walking down the street. One of them sees a $100 bill lying in the street and points it out to his friend.

 

Investment: A History by Norton Reamer, Jesse Downing

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Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, Brownian motion, buttonwood tree, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, moral hazard, mortgage debt, Network effects, new economy, Nick Leeson, Own Your Own Home, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

The size of the equity premium, then, is really due to loss aversion experienced by investors whose frequency of evaluations is too great; if investors looked at their equities portfolios over longer time frames, they would demand lower premiums and this puzzle would be resolved.49 Other explanations that have been offered by behavioral economists focus on earnings uncertainty and how that influences investors’ willingness to bear risk, and yet others develop a dynamic loss aversion model where investors react differently to stocks that fall after a run-up compared to those that fall directly after purchase. Another place where this behavioral lens has been applied to financial markets beyond the equity premium puzzle is momentum. Recent work has looked at momentum in the markets by analyzing serial correlations through time. The idea is that a perfectly efficient market that incorporates all information in prices instantaneously should be a statistical random walk, and a random walk should not exhibit consistent correlations with itself, or “autocorrelations,” through time. Thus, detecting serial autocorrelations may undermine the notion of efficient markets. The behavioral school has proposed two explanations for these results. First, it could be that there are feedback effects whereby market participants see the market rising and decide to buy in; or equivalently, participants could see it falling and then sell their own positions, a reaction also known as the bandwagon effect.

So, they worked together to get to the bottom of it, only to find that much of the earlier work was rife with inconsistencies and ambiguity.12 They determined that new work was required, and that was precisely what they produced, publishing their results in the American Economic Review in 1958 with a paper entitled “The Cost of Capital, Corporation Finance and the Theory of Investment.”13 The result was the Modigliani-Miller theorem, which was among the work for which Merton Miller would win the Nobel Prize in Economics in 1990 and would help Modigliani win the 1985 prize (along with his work on the life-cycle hypothesis).14 The Modigliani-Miller theorem first established several conditions under which their results would hold: no taxes or bankruptcy costs, no asymmetric information, a random walk pricing process, and an efficient market. If these conditions hold, the value of a firm should be unaffected by the capital structure it adopts. In other words, the sum of the value of the debt and the value of the equity should remain constant regardless of how 234 Investment: A History that sum is distributed across debt and equity individually. Given that these assumptions do not hold perfectly in the real world, there have been reformulations of the theorem to account for taxes. This was not an obvious result before its publication, and it ultimately generated a flurry of literature in the field of corporate finance on the role of capital structure and its interaction with asset pricing. Paul Samuelson and Bridging the Gap in Derivatives Theory We now come full circle within the discussion of the evolution of asset pricing theory and return to the pricing of derivatives.

The theory of derivatives pricing is largely resolved and can tell us quite successfully what the price of an option on a particular stock should be, given the stock’s price. It is not to say that there is nothing left to do, but rather that we now more or less know what a solution “should look like.” Typically, the modifications for derivatives pricing involve either alterations of some now well-known differential equations or, in the case where there is no explicit mathematical solution, the use of computer simulations. Of course, upon reflection, it is no real wonder that the theory of derivatives pricing is in a much more advanced state than other theories of pricing of financial assets; it has the benefit of taking the price of the underlying asset as an input, whereas the nonderivative field of asset pricing faces the greater problem of asking what that very stock price should be.

 

pages: 484 words: 136,735

Capitalism 4.0: The Birth of a New Economy in the Aftermath of Crisis by Anatole Kaletsky

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bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Black Swan, bonus culture, Bretton Woods, BRICs, Carmen Reinhart, cognitive dissonance, collapse of Lehman Brothers, Corn Laws, correlation does not imply causation, credit crunch, currency manipulation / currency intervention, David Ricardo: comparative advantage, deglobalization, Deng Xiaoping, Edward Glaeser, Eugene Fama: efficient market hypothesis, eurozone crisis, experimental economics, F. W. de Klerk, failed state, Fall of the Berlin Wall, financial deregulation, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, George Akerlof, global rebalancing, Hyman Minsky, income inequality, invisible hand, Isaac Newton, Joseph Schumpeter, Kenneth Rogoff, laissez-faire capitalism, Long Term Capital Management, mandelbrot fractal, market design, market fundamentalism, Martin Wolf, moral hazard, mortgage debt, new economy, Northern Rock, offshore financial centre, oil shock, paradox of thrift, peak oil, pets.com, Ponzi scheme, post-industrial society, price stability, profit maximization, profit motive, quantitative easing, Ralph Waldo Emerson, random walk, rent-seeking, reserve currency, rising living standards, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, statistical model, The Chicago School, The Great Moderation, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, too big to fail, Washington Consensus

The assumptions made by the Efficient Market Hypothesis thus allowed very precise formulas to be developed for pricing options and complex financial instruments of all kinds. And these formulas, because of their mathematical precision, appeared to justify the enormous increases in leverage and reliance on risk-management systems that so spectacularly failed. In this sense, the 2007-09 crisis could fairly be described as a failure of mathematical economics and nothing more. If the Efficient Market Hypothesis had been valid, fairly simple and logically irrefutable mathematical calculations could have been used to show that most of the financial crises of the past twenty years were literally impossible. For example, if the daily fluctuations on Wall Street had really followed a random walk, the odds of a one-day movement greater than 25 percent would be about one in three trillion.

The assumption that financial markets were “efficient” also meant that, in the absence of new and genuinely unpredictable information, financial market movements would be meaningless random fluctuations, equivalent to tossing a coin or a drunken sailor’s random walk. This chaotic-sounding view was actually reassuring to investors and bankers. For if market movements were really just random coin tosses, they would be highly predictable over longer periods, in the same way that the profits of a lottery or the takings of a casino can be reliably predicted. Specifically, the coin tossing or random walk analogies could be shown by simple mathematics to imply what statisticians call a Normal, or Gaussian, probability distribution over any reasonable period of time. This may sound obscure and academic, but like the methodology of rational expectations, the near-universal use of the Normal distribution in finance was a very important issue that led directly to the financial collapse in 2007-08.

Labor’s weak bargaining power in the postcrisis environment also means that stagflation is unlikely to occur in the long run from oil and other commodities physically running out. Even if the exhaustion of global oil supplies happens sooner than expected and sends energy prices sharply higher, this will not produce inflation unless wages rise in tandem. If labor’s bargaining power remains weak, rising oil prices will simply reduce the amount of money people have to spend on other goods and services. Thus, dwindling oil supplies will lead to big shifts in relative prices between oil and other goods but not to an increase in the average price level of all goods. The same will be true if energy prices rise substantially, as they probably will, to promote investment in more secure and less polluting energy sources. On balance, oil and commodities seem unlikely to return as major risk factors for stagflation in the next decade.

 

pages: 519 words: 104,396

Priceless: The Myth of Fair Value (And How to Take Advantage of It) by William Poundstone

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availability heuristic, Cass Sunstein, collective bargaining, Daniel Kahneman / Amos Tversky, delayed gratification, Donald Trump, East Village, en.wikipedia.org, endowment effect, equal pay for equal work, experimental economics, experimental subject, feminist movement, game design, German hyperinflation, Henri Poincaré, high net worth, index card, invisible hand, John von Neumann, laissez-faire capitalism, loss aversion, market bubble, mental accounting, meta analysis, meta-analysis, Nash equilibrium, new economy, payday loans, Potemkin village, price anchoring, price discrimination, psychological pricing, Ralph Waldo Emerson, RAND corporation, random walk, RFID, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, rolodex, Steve Jobs, The Chicago School, The Wealth of Nations by Adam Smith, ultimatum game, working poor

Market shows up every day quoting sky-high prices that only seem to go up. Most investors find it impossible to ignore the siren song. How could Mr. Market be so very wrong, day after day? As early as 1982, Stanford economist Kenneth Arrow identified Tversky and Kahneman’s work as a plausible explanation for stock market bubbles. Lawrence Summers took up this theme in a 1986 paper, “Does the Stock Market Rationally Reflect Fundamental Values?” Summers (now head of the National Economic Council for the Obama administration) was the first to make an extended case for what might now be called the coherent arbitrariness of stock prices. From day to day the market reacts promptly to the latest economic news. The resulting “random walk” of prices has been cited as proof that the market knows true values. Because stock prices already reflect everything known about a company’s future earnings, only the unpredictable stream of financial news, good and bad, can change prices.

Because stock prices already reflect everything known about a company’s future earnings, only the unpredictable stream of financial news, good and bad, can change prices. Summers astutely pointed out that this “proof” doesn’t hold water. The random walk is a prediction of the efficient market model, just as missing your train is a prediction of the Friday-the-13th-is-unlucky theory. You can’t prove anything from that, as there could be other causes producing the same effect. Summers sketched one, a model in which stock prices have a strong arbitrary component yet adjust coherently to the day’s financial news. Summers’s idea is a scary one. It proposes that stock prices could be a collective hallucination. Once investors stop believing, it all comes tumbling down. “Who would know what the value of the Dow Jones Industrial Average should be?”

As you’d expect, they saw higher sales when the sale prices were highlighted as such. Buyers didn’t know that $Y was a bargain price unless the catalog told them it was. Sale price markers were more powerful motivators than charm prices. Consumers were more likely to buy an item marked with the sale price on the left than with the charm price on the right. Anderson and Simester tried both gimmicks together, using sale-marked charm prices like “Reg $48 SALE $39.” This had the strongest effect of all. The effect was not additive, though. It boosted sales only a little more than the sale price alone did. This could mean that sale prices and charm prices exploit the same mental principle. Standing on its own, a charm price implies a discount that’s not there. It’s like a mime faking a glass wall. The price’s audience reacts to the virtual discount in much the way they react to an actual one.

 

pages: 297 words: 91,141

Market Sense and Nonsense by Jack D. Schwager

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asset allocation, Bernie Madoff, Brownian motion, collateralized debt obligation, commodity trading advisor, conceptual framework, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, fixed income, high net worth, implied volatility, index arbitrage, index fund, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, pattern recognition, performance metric, pets.com, Ponzi scheme, quantitative trading / quantitative finance, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, statistical arbitrage, statistical model, transaction costs, two-sided market, value at risk, yield curve

Both of these explanations, however, are inconsistent with the efficient market hypothesis. In the first instance, according to the efficient market hypothesis, price declines are responses to negative changes in fundamentals rather than selling begetting more selling, as was the case in portfolio insurance. In the second, the efficient market hypothesis asserts that the overall market price is always correct—a contention that makes an adjustment from a price overvaluation a self-contradiction. The efficient market hypothesis is inextricably linked to an underlying assumption that market price changes follow a random walk process (that is, price changes are normally distributed7). The assumption of a normal distribution allows one to calculate the probability of different-size price moves. Mark Rubinstein, an economist, colorfully described the improbability of the October 1987 stock market crash: Adherents of geometric Brownian motion or lognormally distributed stock returns (one of the foundation blocks of modern finance) must ever after face a disturbing fact: assuming the hypothesis that stock index returns are lognormally distributed with about a 20% annualized volatility (the historical average since 1928), the probability that the stock market could fall 29% in a single day is 10−160.

See Minimum acceptable return (MAR) ratio Marcus, Michael Margin Margin calls Marginal production loss Market bubbles Market direction Market neutral fund Market overvaluation Market panics Market price delays and inventory model of Market price response Market pricing theory Market psychology Market risk Market sector convertible arbitrage hedge funds and CTA funds hidden risk long-only funds market dependency past and future correlation performance impact by strategy Market timing skill Market-based risk Maximum drawdown (MDD) Mean reversion Mean-reversion strategy Merger arbitrage funds Mergers, cyclical tendency Metrics Minimum acceptable return (MAR) ratio and Calmar ratio Mispricing Mocking Monetary policy Mortgage standards Mortgage-backed securities (MBSs) Mortgages Multifund portfolio, diversified Mutual fund managers, vs. hedge fund managers Mutual funds National Futures Association (NFA) Negative returns Negative Sharpe ratio, and volatility Net asset valuation (NAV) Net exposure New York Stock Exchange (NYSE) Newsletter recommendation NINJA loans Normal distribution Normally distributed returns Notional funding October 1987 market crash Offsetting positions Option ARM Option delta Option premium Option price, underlying market price Option timing Optionality Out-of-the-money options Outperformance Pairs trading Palm Palm IPO Palm/3 Com Past high-return strategies Past performance back-adjusted return measures evaluation of going forward with incomplete information visual performance evaluation Past returns about and causes of future performance hedge funds high and low return periods implications of investment insights market sector past highest return strategy relevance of sector selection select funds and sources of Past track records Performance-based fees Portfolio construction principles Portfolio fund risk Portfolio insurance Portfolio optimization past returns volatility as risk measure Portfolio optimization software Portfolio rebalancing about clarification effect of reason for test for Portfolio risks Portfolio volatility Price aberrations Price adjustment timing Price bubble Price change distribution The price in not always right dot-com mania Pets.com subprime investment Pricing models Prime broker Producer short covering Professional management Profit incentives Pro-forma statistics Pro-forma vs. actual results Program sales Prospect theory Puts Quantitative measures beta correlation monthly average return Ramp-up period underperformance Random selection Random trading Random walk process Randomness risk Rare events Rating agencies Rational behavior Redemption frequency notice penalties Redemption liquidity Relative velocity Renaissance Medallion fund Return periods, high and low long term investment S&P performance Return retracement ratio (RRR) Return/risk performance Return/risk ratios vs. return Returns comparison measures relative vs. absolute objective Reverse merger arbitrage Risk assessment of for best strategy and leverage measurement vs. failure to measure measures of perception of vs. volatility Risk assessment Risk aversion Risk evaluation Risk management Risk management discipline Risk measurement vs. no risk measurement Risk mismeasurement asset risk vs. failure to measure hidden risk hidden risk evaluation investment insights problem source value at risk (VaR) volatility as risk measure volatility vs. risk Risk reduction Risk types Risk-adjusted allocation Risk-adjusted return Risk/return metrics Risk/return ratios Rolling window return charts Rubin, Paul Rubinstein, Mark Rukeyser, Louis S&P 500, vs. financial newsletters S&P 500 index S&P returns study of Sasseville, Caroline Schwager Analytics Module SDR Sharpe ratio Sector approach Sector funds Sector past performance Securities and Exchange Commission (SEC) Select funds, past returns and Selection bias Semistrong efficiency Shakespearian monkey argument Sharpe ratio back-adjusted return measures vs.

This maximum loss (the premium paid) would occur on an option held until expiration if the strike price was above the prevailing market price. For example, if IBM was trading at $205 when the 210 option expired, the option would expire worthless. If at expiration, however, the price of the underlying market was above the strike price, the option would have some value and would hence be exercised. However, if the difference between the market price and the strike price was less than the premium paid for the option, the net result of the trade would still be a loss. In order for a call buyer to realize a net profit, the difference between the market price and the strike price would have to exceed the premium paid when the call was purchased (after adjusting for commission cost). The higher the market price, the greater the resulting profit. The buyer of a put seeks to profit from an anticipated price decline by locking in a sales price.

 

pages: 263 words: 84,410

Tulipomania: The Story of the World's Most Coveted Flower & the Extraordinary Passions It Aroused by Mike Dash

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Ponzi scheme, random walk, South Sea Bubble, spice trade, trade route, tulip mania

A $4,000 bottle of Coca-Cola Pendergrast, For God, Country, p. 211. The history of the tulip to the present day Krelage, Drie Eeuwen Bloembollen-export, pp. 15–18. Craze for dahlias Bulgatz, Ponzi Schemes, pp. 108–09. During this episode there was even talk of the propagation of blue dahlias—as much a botanical impossibility as the black tulip. Craze for gladioli Posthumus, “Tulip Mania in Holland,” p. 148. Chinese spider lily mania Malkiel, Random Walk down Wall Street, pp. 82–83. Florida land boom Bulgatz, Ponzi Schemes, pp. 46–75. BIBLIOGRAPHY Unpublished Material Municipal Archives, Haarlem Notarial registers, vols. 120–50 Burial registers, vols. 70–76 Index to Heerenboek Manuscript entitled Aanteekeningen van C. J. Gonnet Betreffende de Dovestalmanege in de Grote Houstraat, de Schouwburg op het Houtplein, het Stadhuis in de Frase Tijd, Haarlemse Plateelbakkers en Plateelbakkerijen en de Tulpomanie van 1637–1912 Stadsbibliotheek, Haarlem Chrispijn van de Passe, Een Cort Verhael van den Tulipanen ende haere Oefeninghe… (contemporary pamphlet, n.p., n.d., c. 1620?)

Amsterdam: Meulenhoff, 1979. Lesger, C., and L. Noordegraaf, eds. Entrepreneurs and Entrepreneurship in Modern Times: Merchants and Industrialists Within the Orbit of the DutchStaple Market. The Hague, 1995. Mackay, Charles. Memoirs of Extraordinary Popular Delusions and the Madness of Crowds. Ware: Wordsworth Editions, 1995. Malcolm, Noel. Kosovo: A Short History. London: Macmillan, 1998. Malkiel, Burton. A Random Walk down Wall Street. New York: W.W. Norton,1996. Mansel, Philip. Constantinople: City of the World’s Desire, 1453–1924. London: John Murray, 1995. Martels, Z. R. M. W. von. Augerius Gislenius Busbequius: Leven en Werk van de Keizerlijke Gezant aan het hof van Süleyman de Grote. Unpublished Ph.D. diss., University of Groningen, 1989. Mather, John. Economic Production of Tulips and Daffodils. London: Colling-ridge, 1961.

Wood-backed slates were given to both the buyer and the seller, and the florist who wished to buy would jot down the price he was prepared to pay on his slate; but he would choose a sum well below the actual value of the bulbs he wanted. The seller would name his own price on another slate, and naturally that would be exorbitantly high. The two bids would then be passed to intermediaries nominated by the principals, and they would mutually agree on what they considered a fair price. This sum would fall somewhere between the two prices written on the slates, but certainly not necessarily in the middle. The compromise price would then be scrawled on the slates, and the boards would be passed back to the florists. At this point bulb buyer and bulb seller had the option of either accepting or rejecting the arbitration. They accepted by letting the revised price stand; at that point the transaction was concluded, and the purchase price would be noted in the college register.

 

pages: 339 words: 109,331

The Clash of the Cultures by John C. Bogle

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asset allocation, collateralized debt obligation, corporate governance, corporate social responsibility, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, diversified portfolio, estate planning, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, Flash crash, Hyman Minsky, income inequality, index fund, interest rate swap, invention of the wheel, market bubble, market clearing, mortgage debt, new economy, Occupy movement, passive investing, Ponzi scheme, principal–agent problem, profit motive, random walk, rent-seeking, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, statistical arbitrage, The Wealth of Nations by Adam Smith, transaction costs, Vanguard fund, William of Occam

See Defined benefit (DB) pension plans; Defined contribution (DC) pension plans; Retirement system “People-who-live-in-glass-houses” syndrome PIMCO (Pacific Investment Management Company) Pioneer Fund Politics Portfolio managers, experience and stability of Portfolio turnover: actively managed equity funds exchange traded funds index funds mutual funds Stewardship Quotient and Positive Alpha Press, financial Pricing strategy PRIMECAP Management Company Principals Product, as term Product proliferation, in mutual fund industry Product strategy Profit strategy Proxy statement access by institutional investors, proposed Proxy vote disclosure by mutual funds Prudent Man Rule Public accountants Putnam, Samuel Putnam Management Company Quantitative techniques Random Walk Down Wall Street, A (Malkiel) Rappaport, Alfred Rating agencies Real market Redemptions, shareholder Regulatory issues REIT index fund Retirement accumulation, inadequate Retirement system: about Ambachtsheer, Keith, on asset allocation and investment selection components conflicts of interest costs, excessive current flaws in flexibility, excessive 401(k) retirement plans ideal investor education, lack of longevity risk, failure to deal with mutual funds in New Pension Plan, The pensions, underfunded recommendations retirement accumulation, inadequate savings, inadequacy of “Seven Deadly Sins,” speculation and stock market collapse and value extracted by financial sector Returns: asset allocation and balanced funds defined benefit pension plans projections of equity mutual funds exchange traded funds investment large-cap funds market mutual fund industry speculative Wellington Fund Reversion to the mean (RTM) Riepe, James S.

In very different degrees and in very different ways, speculation plays a major role in the operation of our nation’s retirement plan system, creating challenges and risks that we must work to resolve in the interests of our citizen/investors. I’ll discuss that subject in depth in Chapter 7. 1 A year later, another article, “The Loser’s Game,” by investment professional Charles D. Ellis, published in the Financial Analysts Journal, also gave me encouragement. Even earlier, in the first edition of his remarkable book A Random Walk Down Wall Street (1973), Princeton professor Burton G. Malkiel also issued a challenge for someone to start “a mutual fund that simply buys the hundreds of stocks making up the market averages.” Alas, I didn’t read his book until the early 1980s. 2 My thinking has long been informed by a fifteenth-century maxim known as Occam’s Razor (after English philosopher Sir William of Occam): When there are multiple solutions to a problem, pick the simplest one. 3 That high cost was justified by a Wells Fargo spokesperson because “we (the manager) can make a lot of money.

Leave aside for the moment that such steps are designed to increase corporate earnings, to meet Wall Street’s expectations, and to increase the firm’s stock price. And usually downsizing does just that, at least in the short run. But the jury is still out as to whether these near-term efficiencies and these failures to invest adequately for the future eventually erode the company’s prospects for long-term growth. Once again, the central issue posed is a manifestation of the basic issue of this book—the harm done when a culture of short-term speculation focused on the price of a stock overwhelms a culture of long-term investment focused on the intrinsic value of a corporation. Further, the enormous existing structure of corporate stock option plans for senior management is almost all about evanescent prices, with little relevance to durable intrinsic values. This dichotomy can easily persist in the short run. But in the long run, price and value must be virtually identical.

 

pages: 266 words: 86,324

The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow

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Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, V2 rocket, Watson beat the top human players on Jeopardy!

The molecules fly first this way, then that, moving in a straight line only until deflected by an encounter with one of their sisters. As mentioned in the Prologue, this type of path—in which at various points the direction changes randomly—is often called a drunkard’s walk, for reasons obvious to anyone who has ever enjoyed a few too many martinis (more sober mathematicians and scientists sometimes call it a random walk). If particles that float in a liquid are, as atomic theory predicts, constantly and randomly bombarded by the molecules of the liquid, one might expect them to jiggle this way and that owing to the collisions. But there are two problems with that picture of Brownian motion: first, the molecules are far too light to budge the visible floating particles; second, molecular collisions occur far more frequently than the observed jiggles.

George Spencer-Brown, Probability and Scientific Inference (London: Longmans, Green, 1957), pp. 55–56. Actually, 10 is a gross underestimate. 12. Janet Maslin, “His Heart Belongs to (Adorable) iPod,” New York Times, October 19, 2006. 13. Hans Reichenbach, The Theory of Probability, trans. E. Hutton and M. Reichenbach (Berkeley: University of California Press, 1934). 14. The classic text expounding this point of view is Burton G. Malkiel, A Random Walk Down Wall Street, now completely revised in an updated 8th ed. (New York: W. W. Norton, 2003). 15. John R. Nofsinger, Investment Blunders of the Rich and Famous—and What You Can Learn from Them (Upper Saddle River, N.J.: Prentice Hall, Financial Times, 2002), p. 62. 16. Hemang Desai and Prem C. Jain, “An Analysis of the Recommendations of the ‘Superstar’ Money Managers at Barron’s Annual Roundtable,” Journal of Finance 50, no. 4 (September 1995): 1257–73. 17.

Finally, Bernoulli’s theorem concerns how many heads to expect if, say, you plan to conduct many tosses of a balanced coin, whereas Bayes investigated Bernoulli’s original goal, the issue of how certain you can be that a coin is balanced if you observe a certain number of heads. The theory for which Bayes is known today came to light on December 23, 1763, when another chaplain and mathematician, Richard Price, read a paper to the Royal Society, Britain’s national academy of science. The paper, by Bayes, was titled “An Essay toward Solving a Problem in the Doctrine of Chances” and was published in the Royal Society’s Philosophical Transactions in 1764. Bayes had left Price the article in his will, along with £100. Referring to Price as “I suppose a preacher at Newington Green,” Bayes died four months after writing his will.3 Despite Bayes’s casual reference, Richard Price was not just another obscure preacher. He was a well-known advocate of freedom of religion, a friend of Benjamin Franklin’s, a man entrusted by Adam Smith to critique parts of a draft of The Wealth of Nations, and a well-known mathematician.

 

pages: 819 words: 181,185

Derivatives Markets by David Goldenberg

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Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Norbert Wiener, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, Y2K, yield curve, zero-coupon bond

71; calculation of equilibrium forward prices 78; solution 86; pricing zero-coupon bond with face value equal to current forward price of underlying commodity 73; solution to 86; pricing zero-coupon bonds 72; solution to 86; settling a forward commitment 72; zero-coupon bond, pricing on basis of forward contract at compounded riskfree rate 73 consensus in risk-neutral valuation 598–9; with consensus 599; without consensus 599–601 consumption capital asset pricing model (CCAPM) 605 contango and backwardation 198–9 context in study of options markets 326–7 contingent claim pricing 514–17 continuation region 385 641 continuous compounding and discounting 69–71 continuous dividends from stocks, modeling yields from 93–4 continuous yields, modeling of 90–4 contract life, payments over 88 contract month listings 214, 215, 228 contract offerings 227–8 contract size 19, 214, 215, 227, 228 contract specifications 17, 18–19 contracts offered 257–8 convenience, risk-neutral valuation by 631–2 convenience yield 89 convergence of futures to cash price at expiration 189 convexity of option price 406 correlation effect 165–6 cost-of-carry 89; model of, spread and price of storage for 195 counterparty risk 11, 12–13, 140 covered call hedging strategy 419–27; economic interpretation of 426–7; protective put strategies, covered calls and 419; writes, types of 420–6 credit spreads 298–9 cumulative distribution function 544 currency futures 213–17; contract specifications 213–15; forward positions vs. futures positions 220; pricing vs. currency forward pricing 225; quote mechanism, future price quotes 216–17; risk management strategies using 217–24 currency spot and currency forwards 103–9 currency swaps, notional value of 274 current costs: of generating alternative payoffs 78; payoffs and 66; related strategies and, technique of going back and forth between 393 current price as predictor of future stock prices 531 daily price limits 228, 229 daily settlement process 144–51, 153; financial futures contracts and 216, 260 642 INDEX dealer intermediated plain vanilla swaps 284–93; arbitraging swaps market 292–3; asked side in 286; bid side in 285; dealer’s spread 286; example of 284–6; hedging strategy: implications of 291–2; outline of 288–90; plain vanilla swaps as hedge vehicles 286–92 dealer’s problem, finding other side to swap 294–8; asked side in 295; bid side in 295; credit spreads in spot market (AA-type firms) 296; dealer swap schedule (AA-type firms) 295; selling a swap 296; swap cash flows 298; synthetic floating-rate financing (AA-type firms) 297; transformation from fixed-rate to floating rate borrowing 297–8 decision-making: option concept in 324; process of, protection of potential value in 36–7 default in forward market contracting 11–12 deferred spot transactions 78–9 delayed exercise premium 331, 337 delivery dates 19 demutualization 139–40 derivative prices: co-movements between spot prices and 26; underlying securities and 66 directional trades 371–2 discounted option prices 527–8 discounted stock price process 524–5, 527–8, 530 discrete-time martingale, definition of 521 diversifiable risk 225 diversification, maximum effect of 419–20 dividend-adjusted geometric mean (for S&P 500) 227 dividend payments, effect on stock prices 94–8 dividend payout process 97, 111; connection between capital gains process and 111–13 dollar equivalency 227, 234, 239–40 dollar returns, percentage rates of 366 domestic economy (DE) 103–4, 105 dominance principle 372, 373; implications of 374–88 double expectations (DE) 534–5 duration for interest-rate swaps 300 dynamic hedging 473–506; BOPM as riskneutral valuation relationship (RNVR) formula (N > 1) 490–3; hedging a European call option (N=2) 477–85; implementation of binomial option pricing model for (N=2) 485–90; multiperiod BOPM model (N=3) 494; multiperiod BOPM model (N > 1), path integral approach 493–500; numerical example of binomial option pricing model (N=2) 487–90; option price behavior (N=2) 476; path structure for multi-period BOPM model (N=3) 497; stock price behavior (N=2) 475–6; stock price evolution (N-period binomial process), summary of 499; value contributions for multi-period BOPM model (N=3) 498; see also binomial option pricing model (BOPM) economy-wide factors, risk and 225–6 effective date 293 effective payoff 220, 233 effective price, invoice price on delivery and 153–6 efficient market hypotheses (EMH) 517; features of 532; guide to modeling prices 529–33; option pricing in continuous time 558, 560, 561; semi-strong form of 531; strong form of 531, 532; weak form of 531 EFP eligibility 214 embedded leverage 79–80 endogenous variables 614–15 equilibrium forward prices 402; comparison with equilibrium futures prices 193–5; valuation of forward contracts (assets without dividend yield) 78 equilibrium (no-arbitrage) in full carrying charge market 190–3; classical short selling a commodity 192; Exchange Traded Funds (ETF) 191–2; formal arbitrage opportunity 192; non-interest carrying changes, arb without 192–3; setting up arb 190; unwinding arb 190–2 INDEX equity in customer’s account 145, 148 equivalent annual rate (EAR) 70 equivalent martingale measures (EMMs) 507–38; arithmetic Brownian motion (ABM) model of prices 530–1; computation of EMMs 529; concept checks: contingent claim pricing, working with 514; martingale condition, calculation of 525; option pricing, working with 514; two period investment strategy under EMM, proof for (t=0) 521; solution to 538; contingent claim pricing 514–17; concept check: interpretation of pricing a European call option 514; pricing a European call option 514–15; pricing any contingent claim 515–17; current price as predictor of future stock prices 531; discounted option prices 527–8; discounted stock price process 524–5, 527–8, 530; discrete-time martingale, definition of 521; double expectations (DE) 534–5; efficient market hypotheses (EMH) basis for modeling 517; features of 532; guide to modeling prices 529–33; semi-strong form of 531; strong form of 531, 532; weak form of 531; equivalent martingale representation of stock prices 524–6; examples of EMMs 517–21; exercises for learning development of 537; fair game, notion of 518–19; fundamental theorem of asset pricing (FTAP_1) 509, 511–12, 517, 528–9, 530, 532, 533; ‘independence,’ degrees of 536; investment strategy under, twoperiod example 519–21; key concepts 537; martingale properties 533–6; nonconstructive existence theorem for 529; numeraire, concept of 524; option prices, equivalent martingale representation of 526–8; option pricing in continuous time 540; option price representation 543; physical probability measure, martingale hypothesis for 530; pricing states 509; primitive ArrowDebreu (AD) securities, option pricing and 508–14; concept check: pricing 643 ADu() and ADd() 514; exercise 1, pricing B(0,1) 510; exercise 2, pricing ADu() and ADd() 511–14; random variables 536; random walk model of prices 530–1; risk-averse investment 522; risk-neutral investment 521–2, 523; riskneutral valuation 596–7; construction of 601–3; risk premiums in stock prices and 532–3; riskless bonds 509; Sharpe ratio 526; state-contingent financial securities 508; ‘state prices’ 509; stock prices and martingales 521–6; sub (super) martingale, definition of 524; summary of EMM approach 528–9; tower property (TP) 533–4; uncorrelated martingale increments (UCMI) 531, 535–6; wealth change, fair game expectation 520 Eurodollar (ED) deposit creation 253 Eurodollar (ED) futures 220–1, 245, 246, 249, 250, 252–64; ‘buying’ and ‘selling’ futures 256; cash settlement, forced convergence and 258–61; contract specifications for 254–5; forced conversion of 260; interest-rate swaps 278; strips of 280–1; lending (offering) 249–50; liabilities and 246; open positions, calculation of profits and losses on 262–4; placing 248–9; quote mechanism 256–8; spot Eurodollar market 245–54; taking 249; timing in 257 European call options: synthesis of: modelbased option pricing (MBOP) 453–64; hedge ratio and dollar bond position, definition of (step 2) 455; implications of replication (step 4) 462–4; parameterization (step 1) 454; replicating portfolio, construction of 456–62; replication, pricing by 463; valuation at expiration 446; see also hedging a European call option in BOPM (N=2) European options 328, 333, 342, 357, 375, 398, 445, 553 European Put-Call Parity 416, 417, 418, 419, 426, 429; financial innovation with 401–5; implications of 394–400; 644 INDEX American option pricing model, analogue for European options 396–8; European call option 394–6; European option pricing model, interpretation of 397–8; European put option 398–9; synthesis of forward contracts from puts and calls 399–400 exchange membership 139–40 exchange rate risks and currency futures positions 217–20; Lufthansa example 217–20 exchange rates, New York closing snapshot (April 7, 2014) 104 exchange rule in financial futures contracts 214, 228 exchange-traded funds (ETFs) 191–2, 226 exercise of options 328 exercise price 328, 336 exercises for learning development: binomial option pricing model (BOPM) 501–5; equivalent martingale measures (EMMs) 537; financial futures contracts 266–8; hedging with forward contracts 56–61; hedging with futures contracts 205–7; interest-rate swaps 315–16; market organization for futures contracts 158–9; model-based option pricing (MBOP) 469–71; option pricing in continuous time 590–3; option trading strategies 364–6, 431–3; options markets 341–2; rational option pricing (ROP) 409–12; risk-neutral valuation 634–5; spot, forward, and futures contracting 27–9; valuation of forward contracts (assets with dividend yield) 116–17; valuation of forward contracts (assets without dividend yield) 83–5 exit mechanism in forward market contracting 15–16 exogenous variables in risk-neutral valuation 614–15 expiration date in options markets 336 expiration month code 336 fair game, notion of 518–19 fancy forward prices 19, 25 Fed Funds Rate (FFR) 251 Federal Funds (FF) 249–50, 251, 252 Federal Reserve system (US) 249 financial engineering techniques 337–8 financial futures contracts 211–70; all-orNone (AON) orders 215; Bank of International Settlements (BIS) 246; basis risk 223, 237, 238; cross hedging and 244; block trade eligibility 214, 228; block trade minimum 214, 228; commentary 216–17; concept checks: backwardation and contango, markets in?

increment of ABM process 555; shifted arithmetic Brownian motion 655 (ABM) model of prices 541–2; reduced process 570; stochastic differential equations (SDEs) 553, 559, 562–3, 564, 566, 567–8, 570, 571, 583; stochastic integral equations (SIEs) 559, 560, 561, 564, 565–6, 567; stochastic processes 540–1, 543, 562, 587, 588; transition density function for shifted arithmetic Brownian motion 545–6; Wiener measure (and process) 540–1 option sellers 328 option trading strategies 345–67, 415–34; basic (naked) strategies 347–63; ‘calling away’ of stock 422; concept checks: covered call strategies, choice of 426; solution to 434; covered call write, upside potential of 422; solution to 433; cushioning calls 422; In-the-Money covered call writes 421; solution to 433; market for call options, dealing with profit potential and 354; solution to 367; payout present value on longing zerocoupon riskless bond 362; solution to 367; positions taken, definition of risk relative to 427; profit diagram for long call option, working on 418; rationalization of profits, short call positions 357; stock price fluctuations, dealing with 353; solution to 366–7; upside volatility in short positions, dealing with 359; covered call hedging strategy 419–27; economic interpretation of 426–7; covered call writes, types of 420–6; covered calls and protective put strategies 419; diversification, maximum effect of 419–20; Dollar Returns, percentage rates of 366; economic characteristics 358; European Put-Call Parity 416, 417, 418, 419, 426, 429; exercises for learning development of 364–6, 431–3; finite-maturity financial instruments, options as 354; generation of synthetic option strategies from European Put-Call Parity 416–18; Inthe-Money covered call writes 421–4; key concepts 364, 431; long a European call option on the underlying 351–5; 656 INDEX economic characteristics 353; long a European put option on the underlying 348, 357–9; economic characteristics 358; long a zero-coupon riskless bond and hold to maturity 348, 360–2; economic characteristic 361; long call positions, difference between long underlying positions and 354; long the underlying 347–9; economic characteristics 349; Merck stock price fluctuations 346–7; natural and synthetic strategies 416; natural stock, economic equivalence with synthetic stock 418; Out-of-the-Money covered call writes 424–6; potential price paths 346–7; profit diagrams 346–7; protective put hedging strategy 427–30; economic interpretation of 429–30; insurance, puts as 427–9; puts as insurance 427–9; short a European call option on the underlying 348, 355–7; economic characteristics 357; short a European put option on the underlying 348, 359–60; economic characteristics 360; short a zero-coupon riskless bond and hold to maturity 348, 362–3; economic characteristic 363; short the underlying 348, 349–51; economic characteristics 351; synthetic equivalents on basic (naked) strategies 416–18; synthetic strategies, natural strategies and 416 option valuation: binomial option pricing model (BOPM) 445–8; risk-neutral valuation 624–33; direct valuation by risk-averse investor 626–31; manipulations 624–6; for risk-neutral investors 631–3 options and options scenarios 323–6 Options Clearing Corporation (OCC) 328 options markets 323–44; American options 328; anticipation of selling 339; anticipatory buying 339–40; basic American call (put) option pricing model 332–4; buying back stock 339; CBOE (Chicago Board Options Exchange) 324–5, 334; asked price entries 335, 336; bid entries 335, 336; equity option specifications 343; exchange-traded option contracts 325; last sale entries 335, 336; Merck call options and price quotes 334–7; mini equity option specifications 344; net entries 335, 336; open interest entries 335, 336; volume entries 335, 336; concept checks: individual equity options, product specifications for 326; solution to 342; mini equity options, product specifications for 326; solution to 342; MRK OV-E price quote 337; option positions 331; option sales 332; solution to 342; option’s rights 331; payoff diagram construction 338; put option positions 332; context in study of 326–7; decision-making, option concept in 324; delayed exercise premium 331, 337; European options 328; exercise price 328, 336; exercises for learning development of 341–2; exercising options 328; expiration date 336; expiration month code 336; financial engineering techniques 337–8; immediate exercise value 330; implicit short positions 340; importance of options 323–4; In-the-Money calls 337; insurance features, options and 327; intrinsic value 326, 330, 333, 337; key concepts 341; learning options, framework for 326–7; leverage, options and 327; liquidity option 333; long and short positions, identification of 339–40; long positions 339–40; long vs. short positions 339–40; maturity dates 328; moneyness 329; naked (unhedged) positions 327; non-simultaneous price quote problem 334–6; option buyers 328; option market premiums 328; option sellers 328; options and options scenarios 323–6; Options Clearing Corporation (OCC) 328; options embedded in ordinary securities 324; options in corporate finance 324; payoff and profit diagrams 326, 338; plain vanilla put and call options, definitions and terminology for 327–32; put and call INDEX options 323–5, 327, 328, 329, 338; puts and calls, infrastructure for understanding about 337–8; reading option price quotes 334–7; real asset options 324; short positions 339–40; short sales, covering of 339; speculation on option prices 327; standard equity option 336; standard stock option 334; strategic, option-like scenarios 324; strike price 328; strike price code 336; time premium 326, 330–1, 333, 337; underlying assets or scenarios 327, 334; identification of long and short positions in 339–40; see also binomial option pricing model (BOPM); equivalent martingale measures (EMMs); model-based option pricing (MBOP) in real time; rational option pricing (ROP) order execution 125–6; futures contract definition and 126 order submission 125–6 orders, types of 127–34 Out-of-the-Money covered call writes 424–6 over the counter (OTC): markets 12–13, 14, 17 over-the-counter (OTC): bilateral agreements 278 overall profits (and losses) 144, 150, 151, 153, 156, 157 overnight averages 11 par swap rate 294, 301 parameterization 454, 477–8, 502 partial equilibrium (PE) 453; models of, risk-neutral valuation and 614 participants in futures market 122–5 path structures: in binomial process 440–2, 442–4; multi-period BOPM model (N=3) 497; thinking of BOPM in terms of paths 493–9 paying fixed 293; in interest rate derivatives (IRDs) 278–9; and receiving floating in commodity forward contracts 276 payoff and profit: diagrams of 326, 338; difference between 66 payoff position with forward contracts 37 payoff to long forward position in IBM 40 657 payoff to short forward position in IBM 43 payoffs per share: to naked long forward contract 68–9; to naked long spot position 67, 68–9 perfect negative correlation 166 perfect positive correlation 609–11 performance bonds (margins) 144–5, 148 physical probability: measure of, martingale hypothesis for 530; risk-neutralization of 604 pit trading, order flow process and 136–9 plain vanilla interest-rate swaps 274; dealer intermediated swaps 284–93; non-dealer intermediated swaps 281–4 plain vanilla put and call options, definitions and terminology for 327–32 portfolio price dynamics, replication of 457 portfolio theory, hedging as 165–8 portfolio variance, calculation of 179–81 position accountability 214, 215, 228, 229 preference-free risk-neutral valuation 598, 600 present and future spot prices 20–3 present value (PV): valuation of forward contracts (assets with dividend yield) 94; valuation of forward contracts (assets without dividend yield) 69, 75 price contingent claims with unhedgeable risks 599–601 price paths: ending at specific terminal price, numbers of 442–4; numbers of 440–2 price quotes: in forward markets 9–11; in futures markets 17–19; in spot markets 6–7 pricing a swap 294 pricing by arbitrage and FTAP2 597–8 pricing currency forwards 105 pricing European options under shifted arithmetic Brownian motion (ABM) with no drift 542–51; Bachelier option pricing formula, derivation of 547–51; fundamental theorems of asset pricing (FTAP) 542–3; transition density functions 543–7 658 INDEX pricing foreign exchange forward contracts using no-arbitrage 106–7 pricing mechanism, risk-neutral valuation and 596 pricing options: at expiration (BOPM) 445–6; at time t=0 (BOPM) 446–8; tools for (MBOP) 448–53; relationships between tools 450–3 pricing states 509 pricing zero-coupon, unit discount bonds in continuous time 69–73 primitive Arrow-Debreu (AD) securities, option pricing and 508–14; concept check, pricing ADu() and ADd() 514; exercise 1, pricing B(0,1) 510; exercise 2, pricing ADu() and ADd() 511–14 probability density function 544 profit diagrams 346–7 protection, market orders with 127–9 protective put hedging strategy 427–30; economic interpretation of 429–30; insurance, puts as 427–9 put and call options 323–5, 327, 328, 329, 338; infrastructure for understanding about 337–8 puts as insurance 427–9 quality spreads 299 random variables 536 random walk model of prices 530–1 randomness, state of nature and 23 rate of return of risky asset over small time interval, components of 555–6 rational option pricing (ROP) 369–414; adjusted intrinsic value (AIV) for a European call, definition of 375–6; adjusted time premium (ATP) 397; basic European option pricing model, interpretation of 397–8; certainty equivalent (CE) cash flow 397; concept checks: adjusted intrinsic value (AIV) for calls, calculation of 413; solution to 413; adjusted intrinsic value (AIV) for puts, calculation of 381; solution to 413; directional trades and relative trades, difference between 372; dominance principle and value of European call option 376; solution to 413; exercise price of options, working with 391; forward contracts, overpaying on 403; generalized forward contracts, current value on 404; rational option pricing (ROP) or model-based option pricing (MBOP) 407; short stock position, risk management of 399; solution to 413–14; working from strategies to current costs and back 393; solution to 413; continuation region 385; convexity of option price 406; current costs and related strategies, technique of going back and forth between 393; directional trades 371–2; dominance principle 372, 373; implications of 374–88; equilibrium forward price 402; European Put-Call Parity, financial innovation with 401–5; European Put-Call Parity, implications of 394–400; American option pricing model, analogue for European options 396–8; European call option 394–6; European option pricing model, interpretation of 397–8; European put option 398–9; synthesis of forward contracts from puts and calls 399–400; exercises for learning development of 409–12; financial innovation using European Put-Call Parity 401–5; American Put-Call Parity (no dividends) 403–5; generalized forward contracts 401–3; full replication of European call option (embedded insurance contract) 391–2; generalized forward price 402; key concepts 408–9; LBAC (lower bound for American call option on underlying, no dividends) 374–5; LBACD (lower bound for American call option on underlying, continuous dividends) 383–5; call on underlier with continuous, proportional dividends over life of option 384–5; call on underlier with no dividends over life of option 384; LBAP (lower bound for American put option on underlying, INDEX no dividends) 378–80; intrinsic value lower bound for American put, example of 379–80; LBAPD (lower bound for American put option on underlying, continuous dividends) 387–8; LBEC (lower bound for European call option on underlying, no dividends) 375–8; implications of 377–8; LBECD (lower bound for European call option on underlying, continuous dividends) 382–3; LBEP (lower bound for European put option on underlying, no dividends) 380–1; adjusted intrinsic value (AIV) for European put, definition of 380–1; LBEPD (lower bound for European put option on underlying, continuous dividends) 386–7; model-based option pricing (MBOP) 371, 398; model-independent vs. model-based option pricing 370–1; model risk 372; No-Arbitrage in Equilibrium (NAIE) 372, 405–6; partial replication of European call option (embedded forward contract) 388–91; postscript on 405–7; relative pricing trades vs. directional trades 371–2; risk-free arbitrage 373; static replication, principle of 393–4; static replication and European Put-Call Parity (no dividends) 388–94; current costs and related strategies, technique of going back and forth between 393; fully replicating European call option (embedded insurance contract) 391–2; partially replicating European call option (embedded forward contract) 388–91; working backwards from payoffs to costs to derive European Put-Call Parity 393–4; sub-replication 404; super-replication 404; working backwards from payoffs to costs to derive European Put-Call Parity 393–4 raw price change, present value of 243 reading option price quotes 334–7 real asset options 324 realization of daily value 149 659 realized daily cash flows, creation of 243 receiving floating 293 receiving variable in interest rate derivatives (IRDs) 279–80 recontracting future positions 149, 151 Registered Commodity Representatives (RCRs) 122–3 relative pricing 65–6 relative pricing trades vs. directional trades 371–2 relative risks of hedge portfolio’s return, analysis of 618–24; risk-averse investor in hedge portfolio, role of risk premia for 620–4; risk neutrality in hedge portfolio, initial look at 618–20 replicability: option pricing in continuous time 588; risk-neutral valuation 597–8, 600, 601, 603, 605, 606, 614, 615, 631, 633 replicating portfolio, construction of 478–84; concept check, interpretation of hedge ratio 482; down state, replication in 481; hedge ratio, interpretation of 482–3; replication over period 2 (under scenario 1) 479–82; replication under scenario 2 (over period 2) 484; scenarios 478–9; solving equations for ?

This suggested that empirical stock price processes meet the condition of ‘independent increments’. The first model of prices consistent with the empirical findings was the random walk model or what we will call, in continuous time, the arithmetic EQUIVALENT MARTINGALE MEASURES 531 Brownian motion model (ABM). We will be discussing this model in detail in Chapter 16. Later, it was found that independence was too strong a condition, because the results of the empirical tests seemed only to establish the weaker uncorrelated increments property (see the Appendix, section 15.7, for this distinction). This is when martingales entered the picture, because Samuelson (1965) produced his theoretical paper explaining the empirical findings that many researchers had observed up to that time. As established in the Appendix, section 15.7, if the underlying martingale process has finite first and second moments, then martingales will have uncorrelated increments.

 

pages: 823 words: 220,581

Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned? by Steve Keen

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accounting loophole / creative accounting, banking crisis, banks create money, barriers to entry, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, butterfly effect, capital asset pricing model, cellular automata, central bank independence, citizen journalism, clockwork universe, collective bargaining, complexity theory, correlation coefficient, credit crunch, David Ricardo: comparative advantage, debt deflation, diversification, double entry bookkeeping, en.wikipedia.org, Eugene Fama: efficient market hypothesis, experimental subject, Financial Instability Hypothesis, Fractional reserve banking, full employment, Henri Poincaré, housing crisis, Hyman Minsky, income inequality, invisible hand, iterative process, John von Neumann, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market clearing, market microstructure, means of production, minimum wage unemployment, open economy, place-making, Ponzi scheme, profit maximization, quantitative easing, RAND corporation, random walk, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Schrödinger's Cat, scientific mainstream, seigniorage, six sigma, South Sea Bubble, stochastic process, The Great Moderation, The Wealth of Nations by Adam Smith, Thorstein Veblen, time value of money, total factor productivity, tulip mania, wage slave

In the case of the stock market, it means at least four things: that the collective expectations of stock market investors are accurate predictions of the future prospects of companies; that share prices fully reflect all information pertinent to the future prospects of traded companies; that changes in share prices are entirely due to changes in information relevant to future prospects, where that information arrives in an unpredictable and random fashion; and that therefore stock prices ‘follow a random walk,’ so that past movements in prices give no information about what future movements will be – just as past rolls of dice can’t be used to predict what the next roll will be. These propositions are a collage of the assumptions and conclusions of the ‘efficient markets hypothesis’ (EMH) and the ‘capital assets pricing model’ (CAPM), which were formal extensions to Fisher’s (pre-Depression) time value of money theories.

Others added ancillary elements – such as the argument that how a firm is internally financed has no impact on its value, that dividends are irrelevant to a share’s value, and so on. If this set of theories were correct, then the propositions cited earlier would be true: the collective expectations of investors will be an accurate prediction of the future prospects of companies; share prices will fully reflect all information pertinent to the future prospects of traded companies.14 Changes in share prices will be entirely due to changes in information relevant to future prospects; and prices will ‘follow a random walk,’ so that past movements in prices give no information about what future movements will be. Reservations The outline above covers the theory as it is usually presented to undergraduates (and victims of MBA programs), and as it was believed by its adherents among stockbrokers and speculators (of whom there are now almost none).

But it also inspired other researchers to develop alternative theories of stock market movements. The Fractal Markets Hypothesis The Fractal Markets Hypothesis is primarily a statistical interpretation of stock market prices, rather than a model of how the stock market, or investors in it, actually behave. Its main point is that stock market prices do not follow the random walk predicted by the EMH,5 but conform to a much more complex pattern called a fractal. As a result, the statistical tools used by the EMH, which were designed to model random processes, will give systematically misleading predictions about stock market prices. The archetypal set of random numbers is known as the ‘normal’ distribution, and its mathematical properties are very well known. A normal distribution with an average value of zero and a standard deviation of 1 will throw up a number greater than 1 15 percent of the time, a number greater than 2 just over 2 percent of the time, and a number greater than 3 only once every 750 times, and so on.

 

pages: 467 words: 154,960

Trend Following: How Great Traders Make Millions in Up or Down Markets by Michael W. Covel

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Albert Einstein, asset allocation, Atul Gawande, backtesting, Bernie Madoff, Black Swan, buy low sell high, capital asset pricing model, Clayton Christensen, commodity trading advisor, correlation coefficient, Daniel Kahneman / Amos Tversky, delayed gratification, deliberate practice, diversification, diversified portfolio, Elliott wave, Emanuel Derman, Eugene Fama: efficient market hypothesis, fiat currency, fixed income, game design, hindsight bias, housing crisis, index fund, Isaac Newton, John Nash: game theory, linear programming, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market fundamentalism, market microstructure, mental accounting, Nash equilibrium, new economy, Nick Leeson, Ponzi scheme, prediction markets, random walk, Renaissance Technologies, Richard Feynman, Richard Feynman, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, systematic trading, the scientific method, Thomas L Friedman, too big to fail, transaction costs, upwardly mobile, value at risk, Vanguard fund, volatility arbitrage, William of Occam

We are influenced heavily by standard finance theory that revolves almost entirely around normal distribution worship. Michael Mauboussin and Kristen Bartholdson see clearly the state of affairs: “Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk, and Black-Scholes models. Value-at-risk (VaR) models, for example, attempt to quantify how much loss a portfolio may suffer with a given probability. While there are various forms of VaR models, a basic version relies on standard deviation as a measure of risk. Given a normal distribution, it is relatively straightforward to measure standard deviation, and hence risk. However, if price changes are not normally distributed, standard deviation can be a very misleading proxy for risk.”14 Chapter 8 • Science of Trading The problem with using standard deviation as a risk measurement can be seen with the example where two traders have similar standard deviations, but might show entirely different distribution of returns.

Ultimately, it is the dollar-weighted collective opinion of all market participants that determines whether a stock goes up or down. This consensus is revealed by analyzing price. Mark Abraham Quantitative Capital Management, L.P. 10 Trend Following (Updated Edition): Learn to Make Millions in Up or Down Markets “I often hear people swear they make money with technical analysis. Do they really? The answer, of course, is that they do. People make money using all sorts of strategies, including some involving tea leaves and sunspots. The real question is: Do they make more money than they would investing in a blind index fund that mimics the performance of the market as a whole? Most academic financial experts believe in some form of the random-walk theory and consider technical analysis almost indistinguishable from a pseudoscience whose predictions are either worthless or, at best, so barely discernibly better than chance as to be unexploitable because of transaction costs.”12 Markets aren’t chaotic, just as the seasons follow a series of predictable trends, so does price action.

The catallactic concept of exchange ratios and prices precludes anything that is the effect of actions of a central authority, of people resorting to violence and threats in the name of society or the state or of an armed pressure group. In declaring that it is not the business of the government to determine prices, we do not step beyond the borders of logical thinking. A government can no more determine prices than a goose can lay hen’s eggs.”3 Although government can’t determine prices in the long run, in the short term as we have all seen with the popping of the credit bubble, the government can greatly affect the market system. However, at the end of the day, all we have are prices and speculation. Because that is the case, finding out how to best “speculate” using market prices is a worthy endeavor. The joy of winning and the pain of losing are right up there with the pain of winning and the joy of losing.

 

pages: 537 words: 144,318

The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money by Steven Drobny

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Albert Einstein, Asian financial crisis, asset allocation, asset-backed security, backtesting, banking crisis, Bernie Madoff, Black Swan, Bretton Woods, BRICs, British Empire, business process, capital asset pricing model, capital controls, central bank independence, collateralized debt obligation, Commodity Super-Cycle, commodity trading advisor, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, debt deflation, diversification, diversified portfolio, equity premium, family office, fiat currency, fixed income, follow your passion, full employment, Hyman Minsky, implied volatility, index fund, inflation targeting, interest rate swap, inventory management, invisible hand, London Interbank Offered Rate, Long Term Capital Management, market bubble, market fundamentalism, market microstructure, moral hazard, North Sea oil, open economy, peak oil, pension reform, Ponzi scheme, prediction markets, price discovery process, price stability, private sector deleveraging, profit motive, purchasing power parity, quantitative easing, random walk, reserve currency, risk tolerance, risk-adjusted returns, risk/return, savings glut, Sharpe ratio, short selling, sovereign wealth fund, special drawing rights, statistical arbitrage, stochastic volatility, The Great Moderation, time value of money, too big to fail, transaction costs, unbiased observer, value at risk, Vanguard fund, yield curve

As equity and equity-like assets get to be more and more expensive, you want to have more and more cash and cash-like assets in your portfolio because the volatility on the downside can increase. If we think of valuations as departures from long-term fair value, then many approaches have been shown to allow better forecasting of returns in equities—at least better than a random walk. For judging valuation levels, I would start with price-to-earnings multiples, price-to-book multiples, or whatever kind of fundamental earnings model you want to use. Tobin’s Q ratio, as demonstrated by Andrew Smithers’ work, has correctly identified over- and undervalued episodes in the U.S. equity market, and the use of cyclically adjusted price to earnings ratios has worked in a similar manner. Everybody on the Street generates these kinds of numbers, and you can take an average of them or develop your own metric. I am not that smart, so I just try to talk to enough people to get a sense of what fundamental value might be.

See Risk premia payment Price/earnings (P/E) multiples, exchange rate valuation (relationship) Primary Dealer Credit Facility, placement Prime broker risk Princeton University (endowment) Private equity cash flow production tax shield/operational efficiency arguments Private sector debt, presence Private-to-public sector risk Probability, Bayesian interpretation Professor, The bubble predication capital loss, avoidance capital management cataclysms, analysis crowding factor process diversification efficient markets, disbelief fiat money, cessation global macro fund manager hedge fund space historical events, examination idea generation inflation/deflation debate interview investment process lessons LIBOR futures ownership liquidity conditions, change importance market entry money management, quality opportunities personal background, importance portfolio construction management positioning process real macro success, personality traits/characteristics (usage) returns, generation risk aversion rules risk management process setback stocks, purchase stop losses time horizon Titanic scenario threshold trades attractiveness, measurement process expression, options (usage) personal capital, usage quality unlevered portfolio Property/asset boom Prop shop trading, preference Prop trader, hedge fund manager (contrast) Protectionism danger hedge process Public college football coach salary, public pension manager salary (contrast) Public debt, problems Public pensions average wages to returns endowments impact Q ratio (Tobin) Qualitative screening, importance Quantitative easing (QE) impact usage Quantitative filtering Random walk, investment Real annual return Real assets Commodity Hedger perspective equity-like exposure Real estate, spread trade Real interest rates, increase (1931) Real macro involvement success, personality traits/characteristics (usage) Real money beta-plus domination denotation evolution flaws hedge funds, differentiation impacts, protection importance investors commodity exposure diversification, impact macro principles management, change weaknesses Real money accounts importance long-only investment focus losses (2008) Real money funds Commodity Hedger operation Equity Trader management flexibility frontier, efficiency illiquid asset avoidance importance leverage example usage management managerial reserve optimal portfolio construction failure portfolio management problems size Real money managers Commodity Investor scenario liquidity, importance long-term investor misguidance poor performance, usage (excuse) portfolio construction valuation approach, usage Real money portfolios downside volatility, mitigation leverage, amount management flaws Rear view mirror investment process Redemptions absence problems Reflexivity Rehypothecation Reichsmarks, foreign holders (1922-1923) Relative performance, inadequacy Reminiscences of a Stock Operator (Lefèvre) Renminbi (2005-2009) Repossession property levels Republic of Turkey examination investment rates+equities (1999-2000) Reserve currency, question Resource nationalism Returns forecast generation maximization momentum models targets, replacement Return-to-worst-drawdown, ratios (improvement) Reward-to-variability ratio Riksbank (Sweden) Risk amount, decision aversion rules capital, reduction collars function positive convexity framework, transition function global macro manager approach increase, leverage (usage) measurement techniques, importance parameters Pensioner management pricing reduction system, necessity Risk-adjusted return targets, usage Risk assets, decrease Risk-free arbitrage opportunities Risk management Commodity Hedger process example game importance learning lessons portfolio level process P&L, impact tactic techniques, importance Risk premia annualization earning level, decrease specification Risk/reward trades Risk-versus-return, Pensioner approach Risk-versus-reward characteristics opportunities Roll yield R-squared (correlation) Russia crisis Russia Index (RTSI$) (1995-2002) Russia problems Savings ratio, increase Scholes, Myron Sector risk, limits Securities, legal lists Self-reinforcing cycles (Soros) Sentiment prediction swings Seven Sisters Sharpe ratio increase return/risk Short-dated assets Short selling, ban Siegel’s Paradox example Single point volatility 60-40 equity-bond policy portfolio 60-40 model 60-40 portfolio standardization Smither, Andrew Socialism, Equity Trader concern Society, functioning public funds, impact real money funds, impact Softbank (2006) Soros, George self-reinforcing cycles success Sovereign wealth fund Equity Trader operation operation Soybeans (1970-2009) Special drawing rights (SDR) Spot price, forward price (contrast) Spot shortages/outages, impact Standard deviation (volatility) Standard & Poor’s 500 (S&P500) (2009) decrease Index (1986-1995) Index (2000-2009) Index (2008) shorting U.S. government bonds, performance (contrast) Standard & Poor’s (S&P) shorts, coverage Stanford University (endowment) State pension fund Equity Trader operation operation Stochastic volatility Stock index total returns (1974-2009) Stock market increase, Predator nervousness Stocks hedge funds, contrast holders, understanding pickers, equity index futures usage shorting/ownership, contrast Stops, setting Stress tests, conducting Subprime Index (2007-2009) Sunnies, bidding Super Major Survivorship bias Sweden AP pension funds government bond market Swensen, David equity-centric portfolio Swiss National Bank (SNB) independence Systemic banking crisis Tactical asset allocation function models, usage Tactical expertise Tail hedging, impact Tail risk Take-private LBO Taleb, Nassim Tax cut sunset provisions Taxes, hedge Ten-year U.S. government bonds (2008-2009) Theta, limits Thundering Herd (Merrill Lynch) Time horizons decrease defining determination shortening Titanic funnel, usage Titanic loss number Titanic scenario threshold Topix Index (1969-2000) Top-line inflation Total credit market, GDP percentage Total dependency ratio Trade ideas experience/awareness, impact generation process importance origination Traders ability Bond Trader hiring characteristics success, personality characteristics Trades attractiveness, measurement process hurdle money makers, percentage one-year time horizon selection, Commodity Super Cycle (impact) time horizon, defining Trading decisions, policy makers (impact) floor knowledge noise level ideas, origination Tragedy of the commons Transparency International, Corruption Perceptions Index Treasury Inflation-Protected Securities (TIPS) trade Triangulated conviction Troubled Asset Relief Program (TARP) Turkey economy inflation/equities (1990-2009) investment rates+equities (1999-2000) stock market index (ISE 100) Unconventional Success (Swensen) Underperformance, impact Undervaluation zones, examination United Kingdom (UK), two-year UK swap rates (2008) United States bonds pricing debt (1991-2008) debt (2000-2008) home prices (2000-2009) hyperinflation listed equities, asset investment long bonds, market pricing savings, increase stocks tax policy (1922-1936) trade deficit, narrowing yield curves (2004-2006) University endowments losses impact unlevered portfolio U.S.

Roll Yield, Backwardation and Contango Roll Yield—The amount of return generated in a backwardated futures market that is achieved by rolling a futures contract into the higher-priced spot market. As time passes and the futures contract appreciates, traders will take profits in the near-dated positions and purchase less-expensive futures contracts. Backwardation allows the trader to consistently profit from the rise in a futures’ price as it nears expiration or the spot price. The biggest risk to this strategy is that the market will shift, resulting in a futures price above the spot price, a condition is known as contango. Backwardation—The market condition in which the spot price is above the futures price. This is also known an inverted sloping forward curve. This is said to occur due to the convenience yield being higher than the prevailing risk-free rate.

 

pages: 471 words: 124,585

The Ascent of Money: A Financial History of the World by Niall Ferguson

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Admiral Zheng, Andrei Shleifer, Asian financial crisis, asset allocation, asset-backed security, Atahualpa, bank run, banking crisis, banks create money, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, BRICs, British Empire, capital asset pricing model, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, collateralized debt obligation, colonial exploitation, Corn Laws, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, deglobalization, diversification, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Glaeser, Edward Lloyd's coffeehouse, financial innovation, financial intermediation, fixed income, floating exchange rates, Fractional reserve banking, Francisco Pizarro, full employment, German hyperinflation, Hernando de Soto, high net worth, hindsight bias, Home mortgage interest deduction, Hyman Minsky, income inequality, interest rate swap, Isaac Newton, iterative process, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, labour mobility, London Interbank Offered Rate, Long Term Capital Management, market bubble, market fundamentalism, means of production, Mikhail Gorbachev, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, mortgage tax deduction, Naomi Klein, Nick Leeson, Northern Rock, pension reform, price anchoring, price stability, principal–agent problem, probability theory / Blaise Pascal / Pierre de Fermat, profit motive, quantitative hedge fund, RAND corporation, random walk, rent control, rent-seeking, reserve currency, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, savings glut, seigniorage, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spice trade, structural adjustment programs, technology bubble, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, too big to fail, transaction costs, value at risk, Washington Consensus, Yom Kippur War

Short-Term Capital Mismanagement Imagine another planet - a planet without all the complicating frictions caused by subjective, sometimes irrational human beings. One where the inhabitants were omniscient and perfectly rational; where they instantly absorbed all new information and used it to maximize profits; where they never stopped trading; where markets were continuous, frictionless and completely liquid. Financial markets on this planet would follow a ‘random walk’, meaning that each day’s prices would be quite unrelated to the previous day’s but would reflect all the relevant information available. The returns on the planet’s stock market would be normally distributed along the bell curve (see Chapter 3), with most years clustered closely around the mean, and two thirds of them within one standard deviation of the mean. In such a world, a ‘six standard deviation’ sell-off would be about as common as a person shorter than one and a half feet in our world.

unsafe investment bet 229 protectionism 159. see also free trade Prussian government bonds 86 public housing 246-7 publicly owned firms 353 Public Works Administration 246-7 Pückler-Muskau, Prince 90 Putin, Vladimir 276 put options 12 ‘quants’ 321-7 Quantum Fund 319 Quilmes 274 race divisions 243-6 . see also anti-Semitism; ethnic minorities Rachman, Peter 252 railways 226 Rand Corporation 323 random drift 350 randomness 342 ‘random walk’ 320 Ranieri, Lewis 259 rating agencies 268 raw materials see resources RCA 160 Reagan, Ronald 252 and capital account liberalization 312 and S&Ls 254 welfare reforms 219 real estate see property recessions 103-4 prospects of 8 recourse 270n. recovery, economic 274 red-lining (credit rating) 250 re-emerging markets 288 Rees-Mogg, Lord 166 reflation 142 reflexivity 316 Reform Bills see electoral reform Regulation Q 249 regulation/regulators 54 and change 356-7 deregulation 170 Reichsmark, collapse of 101-5 religious minorities 2 Renaissance 3 Renaissance (company) 330 Renda, Mario 255 renminbi 333 rented accommodation: private 230 public see council housing; landlords; public housing rentes/rentiers 73-4 reparations see Germany reporting, pressures of 354 representative governments 26 repression (political) 214 Republican Party 170 reserve ratio 48-9 residential mortgage-backed collateralized debt obligations (RMBS CDOs) 272 residential mortgage-backed securities (RMBS) 260n.

Pinochet, Augusto 213 Pisa 32-3 Pius II, Pope 45-6 Pizarro, Francisco 19-21 plagues 182 Poland 107 political reform see electoral reform politicians 12 Pope, Alexander 156 Popper, Karl 316 population issues 192n.. see also pensions, ageing populations Portinari, Tommaso 46-7 Portugal 81 exploration and East Indies trade 127-8 and Jews 36 ‘post-American’ era 3 Potosí 22-3 pound sterling 55. see also gold standard poverty and poor countries: causes of 2 incomes 2 and international investment 286-7 lack of financial institutions and credit 13 loan sharks and 13 and microfinance 280-81 and property ownership 267-8 real estate occupied by 274 see also aid; emerging markets; incomes; workhouses pre-modern societies 184 Preobrazhensky, Yevgeni 107 prestanze and prestiti 71-2 price controls 338 price-earnings ratios 123-4 ‘price revolution’ 26 price rises 26 Princip, Gavrilo 298 private equity partnerships/firms 5 privatization 116 probability 188-90 Proctor & Gamble 160 productivity 210 promissory notes 27. see also paper money Pro Mujer 278-80 property-owning democracies 233 property/real estate: access to ownership 230n. compared with stock market 261-3 developers 277 English-speaking world’s passion for 4 establishing ownership/title 274-6 home ownership: Britain 230n. ; USA 241-2 illiquidity 273 investment in 123 law 274-7 and political power 234 price indexes 261-3 price rises and downturns 8 regional variations in prices 233n. unsafe investment bet 229 protectionism 159. see also free trade Prussian government bonds 86 public housing 246-7 publicly owned firms 353 Public Works Administration 246-7 Pückler-Muskau, Prince 90 Putin, Vladimir 276 put options 12 ‘quants’ 321-7 Quantum Fund 319 Quilmes 274 race divisions 243-6 . see also anti-Semitism; ethnic minorities Rachman, Peter 252 railways 226 Rand Corporation 323 random drift 350 randomness 342 ‘random walk’ 320 Ranieri, Lewis 259 rating agencies 268 raw materials see resources RCA 160 Reagan, Ronald 252 and capital account liberalization 312 and S&Ls 254 welfare reforms 219 real estate see property recessions 103-4 prospects of 8 recourse 270n.

 

pages: 288 words: 16,556

Finance and the Good Society by Robert J. Shiller

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bank run, banking crisis, barriers to entry, Bernie Madoff, capital asset pricing model, capital controls, Carmen Reinhart, Cass Sunstein, cognitive dissonance, collateralized debt obligation, collective bargaining, computer age, corporate governance, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Donald Trump, Edward Glaeser, eurozone crisis, experimental economics, financial innovation, full employment, fundamental attribution error, George Akerlof, income inequality, invisible hand, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, land reform, loss aversion, Louis Bachelier, Mahatma Gandhi, Mark Zuckerberg, market bubble, market design, means of production, microcredit, moral hazard, mortgage debt, Occupy movement, passive investing, Ponzi scheme, prediction markets, profit maximization, quantitative easing, random walk, regulatory arbitrage, Richard Thaler, road to serfdom, Robert Shiller, Robert Shiller, Ronald Reagan, self-driving car, shareholder value, Sharpe ratio, short selling, Simon Kuznets, Skype, Steven Pinker, telemarketer, The Market for Lemons, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, Vanguard fund, young professional, Zipcar

Moreover, statistical research—as in the work of Holbrook Working in 1934 and Maurice Kendall in 1953—had already found evidence, years before Fama, that short-run changes in prices in speculative markets are hard to forecast.5 But Fama raised this theory to the status of a broad new scienti c paradigm and likened to astrologers the old-fashioned analysts who looked to patterns in stock market data for trading opportunities. Fama believed that market prices were too perfect to be predictable, to show any pattern other than a random walk. Fama used a data set that had recently been compiled by the Center for Research in Security Prices (CRSP) at the University of Chicago, founded in 1960 with a $50,000 grant from Merrill Lynch. The center’s initial purpose was to put a huge set of monthly (later daily) stock prices, and associated information about capital changes and dividends that would allow accurate computation of returns, on magnetic tape so that the data could be analyzed with a univac computer.

“Hedging Real-Estate Risk.” Journal of Portfolio Management, Special Real Estate Issue 35(5):92–103. Fair, Ray C., and Robert J. Shiller. 1990. “Comparing Information in Forecasts from Econometric Models.” American Economic Review 80(3):375–89. Falke, Armin. 2004. “Charitable Giving as a Gift Exchange: Evidence from a Field Experiment.” IZA Discussion Paper 1148. University of Bonn. Fama, Eugene F. 1965. “Random Walks in Stock Market Prices.” Financial Analysts Journal 21(5):55–59. Fama, Eugene F., and Kenneth French. 2005. “Financing Decisions: Who Issues Stock?” Journal of Financial Economics 76(3):549–74. Fehr, Ernst. 2009. “Social Preferences and the Brain.” In Paul Glimcher, Colin Camerer, Ernst Fehr, and Russell Poldrack, eds., Neuroeconomics: Decision Making and the Brain, 215–30. Amsterdam: Elsevier. Festinger, Leon. 1954.

JOE SALESMAN: First, you could collect a lot of dollars—maybe hundreds, sometimes thousands—for simply agreeing to sell your just-bought stock at a higher price than you paid. This agreement money is paid to you right away, on the very next business day—money that’s yours to keep forever. Your second source of pro t could be the cash dividends due you as the owner of the stock. The third source of pro t would be in the increase in price of the shares from what you paid, to the agreed selling price.7 The argument is apparently e ective but ultimately deceptive, for it emphasizes only the number of income sources, but does not suggest a comparison of the price received for the option with the expected loss in those cases when the stock price exceeds the agreement price. If the customer’s attention is diverted from consideration of this price, or if the customer has no idea how to price options and thus cannot estimate whether the o ered options price is a good one, then the customer could be lured into a bad deal.

 

pages: 519 words: 118,095

Your Money: The Missing Manual by J.D. Roth

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Airbnb, asset allocation, bank run, buy low sell high, car-free, Community Supported Agriculture, delayed gratification, diversification, diversified portfolio, estate planning, Firefox, fixed income, full employment, Home mortgage interest deduction, index card, index fund, late fees, mortgage tax deduction, Own Your Own Home, passive investing, Paul Graham, random walk, Richard Bolles, risk tolerance, Robert Shiller, Robert Shiller, speech recognition, traveling salesman, Vanguard fund, web application, Zipcar

Compare unit pricing. An item's unit price tells you the cost for each unit of measurement. For example, the unit price of a box of cereal tells you how much you're paying for each ounce. If you're lucky, your grocery store already posts unit pricing for most items, which makes comparing them easy. If not, carry a calculator. Note The biggest package isn't always the most cost-effective. Stores know that people want to buy in bulk, so sometimes they actually make the larger package's unit price higher than the smaller package's. Choose a store and learn its prices. Because supermarkets monkey with prices, you can't be sure a deal is really a deal unless you know what the store usually charges. Use a price book (see the box on the next page) to uncover regular and sale prices. Once you know one store's prices, you can save even more by learning another store's prices and comparing them to the first store's.

In general, the movements of stocks, bonds, commodities (The Tools of Investing), and real estate aren't strongly correlated; for example, just because the stock market is down doesn't mean the real estate market will be down, too. The same is generally true of the returns on these asset classes—they're normally independent of each other. (But sometimes, as in the recent financial crisis, there's a whole lot of correlation going on!) Over time. "Risk is also reduced for investors who build up a retirement nest egg by putting their money in the market regularly over time," writes Burton Malkiel in The Random Walk Guide to Investing. By using techniques like dollar-cost averaging (see All-in-one funds), you ensure that you're not investing all your money when the market is high. There are other types of diversification, too. For example, when you buy foreign stocks, you're diversifying by geography. How much should you diversify and how should you do it? There's no one right answer—it depends on you and your financial goals.

According to the 2009 National Retirement Risk Index from the Center for Retirement Research, 51% of Americans are "at risk of being unable to maintain their pre-retirement standard of living in retirement" (http://tinyurl.com/CRR-nrri). Part of the reason is that these folks didn't plan ahead and set aside enough when they were young. "The amount of capital you start with is not nearly as important as getting started early," writes Burton Malkiel in The Random Walk Guide to Investing. "Procrastination is the natural assassin of opportunity. Every year you put off investing makes your ultimate retirement goals more difficult to achieve." An article about retirement in the February 2010 issue of Consumer Reports featured a survey of more than 24,000 of the magazine's readers. The findings won't surprise you: "Satisfied retirees planned early and lived within their means," the article noted.

 

pages: 559 words: 155,372

Chaos Monkeys: Obscene Fortune and Random Failure in Silicon Valley by Antonio Garcia Martinez

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Airbnb, airport security, Amazon Web Services, Burning Man, Celtic Tiger, centralized clearinghouse, cognitive dissonance, collective bargaining, corporate governance, Credit Default Swap, crowdsourcing, death of newspapers, El Camino Real, Elon Musk, Emanuel Derman, financial independence, global supply chain, Goldman Sachs: Vampire Squid, hive mind, income inequality, interest rate swap, intermodal, Jeff Bezos, Malcom McLean invented shipping containers, Mark Zuckerberg, Maui Hawaii, means of production, Menlo Park, minimum viable product, move fast and break things, Network effects, Paul Graham, performance metric, Peter Thiel, Ponzi scheme, pre–internet, Ralph Waldo Emerson, random walk, Sand Hill Road, Scientific racism, second-price auction, self-driving car, Silicon Valley, Silicon Valley startup, Skype, Snapchat, social graph, social web, Socratic dialogue, Steve Jobs, telemarketer, urban renewal, Y Combinator, éminence grise

I saw relatively little of my ersatz AdGrok proceeds in the form of Facebook stock. All of that three-year struggle of endless sixteen-hour days, whether for AdGrok or for Facebook (and hating most of it, as if you couldn’t tell), was mostly for nothing. So you see, the boys and I have very different financial futures awaiting us. Some of it was due to the detailed vagaries of tech compensation and the random walks of public stock prices. Mostly, though, it was due to my getting chewed up and spit out by the Facebook machine within two years, while the boys gamboled in the bucolic hipster pastures of Twitter for four years and counting—the very pastures I struggled and plotted mightily to avoid, and which I traded for the horror show that would thanklessly reject me despite the moneymaker I built them. Who says karma doesn’t exist?

The crowd went wild as the hour expired, and just as quickly the entire riot disbursed as everyone hurried back to phones and risk reports. The trading floor smelled like the inside of a deep fryer for the whole day. Capitalism marched inexorably onward.* Of course, the betting didn’t stop at burgers. Analysts would be pressed into push-up contests, with over/under bets on the total. And so, on a random walk across the floor, busily engaged with the important work of capitalism, one could trip on a trading analyst and a particularly fit sales VP, faces red with exertion, sweating through their pressed shirts and pumping out their 237th push-up in an hour, with shouted bets raging all around. On Friday afternoons, to shatter the preweekend slump, the entire desk would play an interesting game. Everybody chucked his or her corporate ID into a sack, and anted up something like twenty to one hundred dollars (higher ranks paid more).

Large investment banks (such as my former employer Goldman Sachs) form what’s called a “syndicate” (“mafia” might be a better term) wherein they offer to effectively buy those shares from Facebook, and then sell them into the capital markets, usually by pushing it via their sales force onto wealthy clients or institutional investors. That syndicate either guarantees a price (“firm commitment”) or promises to get the best price it can (“best effort”). In the former case, the bank is taking real execution risk, and stands to lose money if it doesn’t engineer a “pop” in the stock on opening day. To mitigate the risk, the bank convinces the offering company to expect a lower price, while simultaneously jacking up what real price the market will bear with a zealous sales pitch to the market’s deepest pockets. Thus, it is absolutely jejune to think that a stock’s rise on opening day is due to clamoring and unexpected interest. Similar to Captain Renault in Casablanca, Wall Street bankers are shocked—shocked!—that there should be such a large and positive price dislocation in the market they just rigged. As proof of the complete charlatanism at work in most IPOs, let’s ask ourselves a question: Are there other situations in the financial world in which the banks are responsible for setting, ab initio so to speak, a fair market price, and in which that routinely works out?

 

Trend Commandments: Trading for Exceptional Returns by Michael W. Covel

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Albert Einstein, Bernie Madoff, Black Swan, commodity trading advisor, correlation coefficient, delayed gratification, diversified portfolio, en.wikipedia.org, Eugene Fama: efficient market hypothesis, family office, full employment, Lao Tzu, Long Term Capital Management, market bubble, market microstructure, Mikhail Gorbachev, moral hazard, Nick Leeson, oil shock, Ponzi scheme, prediction markets, quantitative trading / quantitative finance, random walk, Sharpe ratio, systematic trading, the scientific method, transaction costs, tulip mania, upwardly mobile, Y2K

Coyle, Daniel. The Talent Code: Greatness Isn’t Born. It’s Grown. Here’s How. New York: Bantam Books, 2009. Crabel, Toby. Day Trading with Short Term Price Patterns and Opening Range Breakout. Jupiter: Rahfelt and Associates, 1990. Douglas, Mark. The Disciplined Trader: Developing Winning Attitudes. New York: New York Institute of Finance, 1990. Dubner, Stephen, and Steven D. Levitt. Freakonomics: A Rogue Economist Explores the Hidden Side of Everything. New York: Harper Collins, 2005. Eng, William. Trading Rules: Strategies for Success. Chicago: Dearborn Financial Publishing, Inc., 1990. Bibliography 243 Fabricand, Burton. The Science of Winning: A Random Walk Along the Road to Investment Riches. London: High Stakes Publishing, 2002. Farleigh, Richard. Taming the Lion: 100 Secret Strategies for Investing.

For a good return, you gotta go bettin’ on chance and then you’re back with anarchy, right back in the jungle.1 Price Action Tell me something the “market” does not know. The idea that you can know enough about Apple, oil, GE, and gold to trade them all the same way may seem preposterous, but think about what they all have in common: Price. Market price is objective data. You can look at individual price histories, without knowing which market is which, and still trade all successfully. That is not what they teach at Harvard, Wharton, Kellogg, Stern, Darden, or pick your favorite business school du jour. Don’t guess how far a trend will go. You cannot. Price makes the news, not the other way around. A market is going to go where a market is going to go.2 However, the concept of price as the critical trading cue may be too simple for mass acceptance.

. • A loss never bothers me after I take it. But being wrong, not taking the loss, that is what does the damage to the pocketbook and to the soul. • The trend is evident to a man who has an open mind and reasonably clear sight. • In a narrow market, when price moves within a narrow range, the thing to do is to watch the market, read the tape to determine the limits of prices, and make up your mind that you will not take an interest until the price breaks through the limit in either direction. • Watch the market with one objective: to determine the direction of price tendency. • Prices, like everything else, move along the line of least resistance. 240 Tre n d C o m m a n d m e n t s • It cost me a million dollars to learn that the dangerous enemy to a trader is the susceptibility to the urging of magnetic personality combined with a brilliant mind. • Have a profit?

 

pages: 204 words: 58,565

Keeping Up With the Quants: Your Guide to Understanding and Using Analytics by Thomas H. Davenport, Jinho Kim

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Black-Scholes formula, business intelligence, business process, call centre, computer age, correlation coefficient, correlation does not imply causation, Credit Default Swap, en.wikipedia.org, feminist movement, Florence Nightingale: pie chart, forensic accounting, global supply chain, Hans Rosling, hypertext link, invention of the telescope, inventory management, Jeff Bezos, margin call, Moneyball by Michael Lewis explains big data, Netflix Prize, p-value, performance metric, publish or perish, quantitative hedge fund, random walk, Renaissance Technologies, Robert Shiller, Robert Shiller, self-driving car, sentiment analysis, six sigma, Skype, statistical model, supply-chain management, text mining, the scientific method

“What are the chances?” they might comment. It turns out that the chances are pretty good—just over 50 percent, in fact (see http://keepingupwiththequants.weebly.com). An understanding of probability is extremely useful not only for understanding birthday parties, but also a variety of human endeavors. If you don’t understand probability, you won’t understand that the stock market is a random walk (that is, changes in stock prices involve no discernable pattern or trend) and that some stock pickers are likely to do better than average for a number of years in a row, but then inevitably crash to earth. You won’t understand the regression to the mean phenomenon; if your income is well above average, for example, your child’s income is likely to be less than yours. You will probably lose a lot of money if you don’t understand probability and you frequent the casinos in Las Vegas.

The simplest kind of option, which is often referred to as a call option, is one that gives the right to buy a single share of common stock. A risk premium is the amount an investor pays for a stock or other asset over the price of a risk-free investment. In general, the higher the price of the stock, the greater the value of the option. When the stock price is much greater than the exercise price, the option is almost sure to be exercised. On the other hand, if the price of the stock is much less than the exercise price, the option is almost sure to expire without being exercised, so its value will be near zero. If the expiration date of the option is very far in the future, the value of the option will be approximately equal to the price of the stock. Normally, the value of an option declines as its maturity date approaches, as long as the value of the stock does not change.

The solution to this equation was the Black-Scholes formula, which suggested how the price of a call option might be calculated as a function of a risk-free interest rate, the price variance of the asset on which the option was written, and the parameters of the option (strike price, term, and the market price of the underlying asset). The formula introduces the concept that, the higher the share price today, the higher the volatility of the share price, the higher the risk-free interest rate, the longer the time to maturity, and the lower the exercise price, then the higher the option value. The valuation of other derivative securities proceeds along similar lines. RESULTS PRESENTATION AND ACTION. Black and Scholes tried to publish their paper first by submitting it to the Journal of Political Economy, but it was promptly rejected. Still convinced that their paper had merit, they submitted it to the Review of Economics and Statistics,