compound rate of return

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

algorithmic trading, asset allocation, automated trading system, backtesting, Bear Stearns, Black Swan, Brownian motion, business continuity plan, buy and hold, compound rate of return, Edward Thorp, Elliott wave, endowment effect, fixed income, general-purpose programming language, index fund, John Markoff, 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 free rate, risk-adjusted returns, Sharpe ratio, short selling, statistical arbitrage, statistical model, survivorship bias, systematic trading, transaction costs

This is also consistent with P1: JYS c06 JWBK321-Chan September 24, 2008 13:57 98 Printer: Yet to come QUANTITATIVE TRADING the fact that the geometric mean of a set of numbers is always smaller than the arithmetic mean (unless the numbers are identical, in which case the two means are the same). When we assume, as I did, that the arithmetic mean of the returns is zero, the geometric mean, which gives the average compounded rate of return, must be negative. The take-away lesson here is that risk always decreases long-term growth rate—hence the importance of risk management! *This example was reproduced with corrections from my blog article “Maximizing Compounded Rate of Return,” which you can find at epchan.blogspot.com/2006/ 10/maximizing-compounded-rate-of-return.html. Often, because of uncertainties in parameter estimations, and also because return distributions are not really Gaussian, traders prefer to cut this recommended leverage in half for safety.

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. This is also consistent with P1: JYS c06 JWBK321-Chan September 24, 2008 13:57 98 Printer: Yet to come QUANTITATIVE TRADING the fact that the geometric mean of a set of numbers is always smaller than the arithmetic mean (unless the numbers are identical, in which case the two means are the same).


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

activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, asset allocation, Atul Gawande, backtesting, beat the dealer, Black Swan, business cycle, butter production in bangladesh, buy and hold, 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, Edward Thorp, Eugene Fama: efficient market hypothesis, forensic accounting, hindsight bias, intangible asset, Louis Bachelier, p-value, passive investing, performance metric, quantitative hedge fund, random walk, Richard Thaler, risk free rate, risk-adjusted returns, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, statistical model, survivorship bias, systematic trading, The Myth of the Rational Market, time value of money, transaction costs

FIGURE 1.2 Graham Simple Value Strategy Performance Chart (1976 to 2011) Table 1.2 presents the results from our study of the simple Graham value strategy. Graham's strategy turns $100 invested on January 1, 1976, into $36,354 by December 31, 2011, which represents an average yearly compound rate of return of 17.80 percent—outperforming even Graham's estimate of approximately 15 percent per year. This compares favorably with the performance of the S&P 500 over the same period, which would have turned $100 invested on January 1, 1976, into $4,351 by December 31, 2011, an average yearly compound rate of return of 11.05 percent. The performance of the Graham strategy is attended by very high volatility, 23.92 percent versus 15.40 percent for the total return on the S&P 500.

We also weight the stocks in the portfolio by market capitalization to make the returns comparable to the market capitalization–weighted S&P 500, while Greenblatt equally weights the stocks in his portfolios (we discuss our back-test procedures in detail in Chapter 11). Importantly, the Magic Formula's performance does compare favorably with the performance of the S&P 500 over the same period, which would have turned $100 invested on January 1, 1964, into $7,871 by December 31, 2011, an average yearly compound rate of return of 9.52 percent. Table 2.1 confirms that Greenblatt's Magic Formula was a better risk-adjusted bet: Sharpe, Sortino, and drawdowns are all better than the S&P 500. TABLE 2.1 Performance Statistics for the Magic Formula Strategy (1964 to 2011) Figures 2.2(a) and 2.2(b) show the rolling 1-year and 10-year returns for the Magic Formula for the period 1964 to 2011.

FIGURE 2.5 Magic Formula and Quality and Price Strategies Comparative Performance Chart (1964 to 2011) Table 2.4 sets out the summary annual performance statistics for Quality and Price. Quality and Price handily outpaces the Magic Formula, turning $100 invested on January 1, 1964, into $93,135 by December 31, 2011, which represents an average yearly compound rate of return of 15.31 percent. Recall that the Magic Formula turned $100 invested on January 1, 1964, into $32,313 by December 31, 2011, which represents a CAGR of 12.79 percent. As you can see in Table 2.4, while much improved, Quality and Price is not a perfect strategy: the better returns are attended by higher volatility and worse drawdowns.


Analysis of Financial Time Series by Ruey S. Tsay

Asian financial crisis, asset allocation, backpropagation, Bayesian statistics, Black-Scholes formula, Brownian motion, business cycle, 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 free rate, risk tolerance, short selling, statistical model, stochastic process, stochastic volatility, telemarketer, transaction costs, value at risk, volatility smile, Wiener process, yield curve

. √ The standard deviation of the price 6 months from now is 241.92 = 15.55. Next, let r be the continuously compounded rate of return per annum from time t to T . Then we have PT = Pt exp[r (T − t)], where T and t are measured in years. Therefore, PT 1 r= ln T −t Pt . By Eq. (6.9), we have ln PT Pt ∼N σ2 µ− 2 (T − t), σ 2 (T − t) . Consequently, the distribution of the continuously compounded rate of return per annum is σ2 σ2 r ∼ N µ− , . 2 T −t The continuously compounded rate of return √ is, therefore, normally distributed with mean µ − σ 2 /2 and standard deviation σ/ T − t. Consider a stock with an expected rate of return of 15% per annum and a volatility of 10% per annum.

Consider a stock with an expected rate of return of 15% per annum and a volatility of 10% per annum. The distribution of the continuously compounded rate of return of the stock over two years is normal√with mean 0.15 − 0.01/2 = 0.145 or 14.5% per annum and standard deviation 0.1/ 2 = 0.071 or 7.1% per annum. These results allow us to construct confidence intervals (C.I.) for r . For instance, a 95% C.I. for r is 0.145±1.96 × 0.071 per annum (i.e., 0.6%, 28.4%). 6.5 DERIVATION OF BLACK–SCHOLES DIFFERENTIAL EQUATION In this section, we use Ito’s lemma and assume no arbitrage to derive the Black– Scholes differential equation for the price of a derivative contingent to a stock valued at Pt .

Obtain the mean and standard deviation of the distribution and construct a 95% confidence interval for the stock price. 7. A stock price is currently $60 per share and follows the geometric Brownian motion d Pt = µPt dt +σ Pt dt. Assume that the expected return µ from the stock is 20% per annum and its volatility is 40% per annum. What is the probability distribution for the continuously compounded rate of return of the stock over 2 years? Obtain the mean and standard deviation of the distribution. 8. Suppose that the current price of Stock A is $70 per share and the price follows the jump diffusion model in Eq. (6.26). Assume that the risk-free interest rate is 8% per annum and the stock volatility is 30% per annum.


pages: 330 words: 59,335

The Outsiders: Eight Unconventional CEOs and Their Radically Rational Blueprint for Success by William Thorndike

Albert Einstein, Atul Gawande, Berlin Wall, Checklist Manifesto, choice architecture, Claude Shannon: information theory, collapse of Lehman Brothers, compound rate of return, corporate governance, discounted cash flows, diversified portfolio, Donald Trump, Fall of the Berlin Wall, Gordon Gekko, impact investing, intangible asset, Isaac Newton, Louis Pasteur, Mark Zuckerberg, NetJets, Norman Mailer, oil shock, pattern recognition, Ralph Waldo Emerson, Richard Feynman, shared worldview, shareholder value, six sigma, Steve Jobs, Thomas Kuhn: the structure of scientific revolutions

Under the leadership of Jim Hale and Phil Meek, Capital Cities evolved an approach to the newspaper business that grew out of its experience in operating TV stations, with an emphasis on careful cost control and maximizing advertising market share. What is remarkable in looking at the company’s four major newspaper operations is the consistent year-after-year-after-year growth in revenues and operating cash flow. Amazingly, these properties, which were sold to Knight Ridder in 1997, collectively produced a 25 percent compound rate of return over an average twenty-year holding period. According to the Kansas City Star’s publisher Bob Woodworth (subsequently the CEO of Pulitzer Inc.), the operating margin at the Star, the company’s largest paper, expanded from the single digits in the mid-1970s to a high of 35 percent in 1996, while cash flow grew from $12.5 million to $68 million.

In 1993, Chabraja joined the company as general counsel and senior vice president, with the implicit understanding that he would become Mellor’s successor. Chabraja set ambitious goals for himself when he became CEO. Specifically, he wanted to quadruple the company’s stock price over his first ten years as CEO (a 15 percent compound rate of return). He looked back into S&P records and found that this was an appropriately difficult target: fewer than 5 percent of all Fortune 500 companies had achieved that benchmark in the prior ten-year period. Chabraja looked coolly at the company’s prospects for the next ten years and concluded that he could get about two-thirds of the way there through market growth and improved operating margins.


pages: 153 words: 12,501

Mathematics for Economics and Finance by Michael Harrison, Patrick Waldron

Brownian motion, buy low sell high, capital asset pricing model, compound rate of return, discrete time, incomplete markets, law of one price, market clearing, Myron Scholes, Pareto efficiency, risk tolerance, riskless arbitrage, short selling, stochastic process

Conditions have been derived under which there is only one meaningful real root to this polynomial equation, in other words one corresponding to a positive IRR.1 Consider a quadratic example. Simple rates of return are additive across portfolios, so we use them in one period cross sectional studies, in particular in this chapter. Continuously compounded rates of return are additive across time, so we use them in multi-period single variable studies, such as in Chapter 7. Consider as an example the problem of calculating mortgage repayments. 6.2.2 Notation The investment opportunity set for the portfolio choice problem will generally consist of N risky assets.


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

addicted to oil, asset allocation, backtesting, Black-Scholes formula, Bretton Woods, business cycle, buy and hold, 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, dogs of the Dow, equity premium, Eugene Fama: efficient market hypothesis, Everybody Ought to Be Rich, 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, Money creation, Myron Scholes, new economy, oil shock, passive investing, Paul Samuelson, popular capitalism, prediction markets, price anchoring, price stability, purchasing power parity, random walk, Richard Thaler, risk free rate, risk tolerance, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, South Sea Bubble, stocks for the long run, survivorship bias, technology bubble, The Great Moderation, The Wisdom of Crowds, transaction costs, tulip mania, Vanguard fund

This time the returns were even higher despite the fact that they made no adjustment for any of the new firms or new industries that had surfaced in the interim. They wrote: If a portfolio of common stocks selected by such obviously foolish methods as were employed in this study will show an annual compound rate of return as high as 14.2 percent, then a small investor with limited knowledge of market conditions can place his savings in a diversified list of common stocks with some assurance that, given time, his holding will provide him with safety of principal and an adequate annual yield.21 Many dismissed the Eiteman and Smith study because it did not include the Great Crash of 1929 to 1932.

See Chapter 20. 130 PART 2 Valuation, Style Investing, and Global Markets discount to such safe and liquid assets as government bonds. As stocks become more liquid, their valuation relative to earnings and dividends should rise.12 The Equity Risk Premium Over the past 200 years the average compound rate of return on stocks in comparison to safe long-term government bonds—the equity premium—has been between 3 and 31⁄2 percent.13 In 1985, economists Rajnish Mehra and Edward Prescott published a paper entitled “The Equity Premium: A Puzzle.”14 In their work they showed that given the standard models of risk and return that economists had developed over the years, one could not explain the large gap between the returns on equities and fixed-income assets found in the historical data.


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

Asian financial crisis, asset allocation, backtesting, buy and hold, 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, Pareto efficiency, Performance of Mutual Funds in the Period, Ponzi scheme, quantitative trading / quantitative finance, random walk, risk free rate, risk-adjusted returns, risk/return, selection bias, Sharpe ratio, short selling, stochastic process, survivorship bias, systematic trading, tail risk, technology bubble, transaction costs, value at risk, zero-sum game

Finally, the average assets under management in this study were $34.68 million compared to $5.01 million in TABLE 13.3 Summary of CTA Average Attributes, February 1974–February 1998, 974 CTA Programs Attribute Mean Std. Error Min Max Months listed Average monthly return (%) Margin to equity ratio (%) Annual compounded rate of return (%) Annual standard deviation (%) Maximum drawdown Management fee (%) Incentive fee (%) Assets (Millions $) 65.14 1.31 19.40 45.91 1.34 10.58 5.00 −3.14 1.03 278.00 13.47 100.00 12.75 26.24 −0.27 2.46 20.27 34.68 15.14 18.41 0.18 1.31 4.45 186.95 −47.51 0.79 −0.99 0.00 0.00 0.10 139.00 142.89 0.10 6.00 50.00 2,954.00 253 The Effect of Management and Incentive Fees on the Performance of CTAs Golec’s sample.

We examined the issue by fitting two ordinary least squares (OLS) cross-sectional regressions on the means and standard deviations of returns of the CTAs on their fee parameters as follows: ARORj = b0 + b1km + b2ki + b3ln(At − 1) + ej (13.3) sj = a0 + a1km + a2ki + a3ln(At − 1) + uj (13.4) where ARORj = annual compounded rate of return for CTAj sj = annual standard deviation of CTAj returns ej, uj = error terms. Because the distribution of assets under management is clearly skewed, we use the natural logarithm of assets under management as the “size” variable. Significance tests use White’s (see Greene 2000) heteroskedasticity consistent standard errors.


Beat the Market by Edward Thorp

beat the dealer, buy and hold, compound rate of return, Edward Thorp, margin call, Paul Samuelson, RAND corporation, short selling, transaction costs

This is not as revealing as Figure 7.2, which contains this information on a semi-log grid. There, equal vertical distances represent equal percentage changes and a straight line represents a constant percentage increase, compounded annually. The greater the slope of the line, the greater the compound rate of increase. Since we are interested in compound rate of return, a *This is the arithmetic average. For investors interested mainly in long-term growth, the equivalent annual compounding rate, which is 26% before taxes, is a more important figure. Elsewhere in the book we have referred to these figures of 26% and 30% by citing “more than 25% for seventeen years.”


pages: 194 words: 59,336

The Simple Path to Wealth: Your Road Map to Financial Independence and a Rich, Free Life by J L Collins

"side hustle", asset allocation, Bernie Madoff, buy and hold, compound rate of return, diversification, financial independence, full employment, German hyperinflation, index fund, money market fund, nuclear winter, passive income, payday loans, risk tolerance, Vanguard fund, yield curve

The magazine interviewer then points out, and good for him, that even during the “lost decade” of the 2000s, the buy and hold strategy of stock investing would have returned 4%. The professor responds: “Think about how that person earned 4%. He lost 30%, saw a big bounce back, and so on, and the compound rate of return….was 4%. But most investors did not wait for the dust to settle. After the first 25% loss, they probably reduced their holdings, and only got part way back in after the market somewhat recovered. It’s human behavior.” Hold the bloody phone! Correct premise, wrong conclusion. We’ll come back to this in a moment.


pages: 232 words: 71,024

The Decline and Fall of IBM: End of an American Icon? by Robert X. Cringely

AltaVista, Bernie Madoff, business cycle, business process, cloud computing, commoditize, compound rate of return, corporate raider, full employment, if you build it, they will come, immigration reform, interchangeable parts, invention of the telephone, Khan Academy, knowledge worker, low skilled workers, Paul Graham, platform as a service, race to the bottom, remote working, Robert Metcalfe, Robert X Cringely, shareholder value, Silicon Valley, six sigma, software as a service, Steve Jobs, Toyota Production System, Watson beat the top human players on Jeopardy!, web application

Sure, productivity has gone up, but that can be done through automation or by beating more work out of employees (more on that later). Jensen and Meckling created the very problem they purported to solve—a problem that really hadn’t existed in the first place. Maximizing shareholder return dropped the compounded rate of return on the S&P 500 from 7.5 percent annually from 1933-76, to 6.5 percent annually from 1977 to today. That one percent may not look like much, but from the point of view of the lady at the bank the loss of so much compound interest may well have led to our corporate malaise of today. Profits are high—but are they real?


pages: 819 words: 181,185

Derivatives Markets by David Goldenberg

Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, correlation coefficient, 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, Myron Scholes, Norbert Wiener, Paul Samuelson, price mechanism, random walk, reserve currency, risk free rate, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, yield curve, zero-coupon bond, zero-sum game

The only difference between these two results is the compounding method for interest and the time interval. Suppose that [0,1] corresponds to one year and therefore τ=1.0. Then, under simple interest compounding, $1 grows to $1*(1+rA) where rA is the annual interest rate under simple compounding. On the other hand, $1 invested in an account that grows continuously at a continuously compounded rate of return rc for one year is . If we equate these two terminal amounts, we get the continuously compounded rate rc that is equivalent to the simple interest rate rA. It is that rate that gives the same terminal amount as the simple rate, . We can carry out the exact same procedure when time to maturity is τ.

The first method will be called the historical volatility estimator method. It is described below, A. The Historical Volatility Estimator Method 1. Collect historical data, say daily closing prices, for a given stock over a given historical period. 2. Calculate the log price relatives which are defined as ln(Si/Si–1). This represents the continuously compounded rate of return of the stock over the period [i–1,i]. 3. Calculate the mean of these log price relatives in the ordinary manner as the sum of the log price relatives divided by the number of log price relatives. Call this quantity E{ln(Si/Si–1)}. 4. The next step is to calculate the standard deviation of these log price relatives over the entire period, .


pages: 249 words: 77,342

The Behavioral Investor by Daniel Crosby

affirmative action, Asian financial crisis, asset allocation, availability heuristic, backtesting, bank run, Black Swan, buy and hold, cognitive dissonance, colonial rule, compound rate of return, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, disinformation, diversification, diversified portfolio, Donald Trump, endowment effect, feminist movement, Flash crash, haute cuisine, hedonic treadmill, housing crisis, IKEA effect, impact investing, impulse control, index fund, Isaac Newton, job automation, longitudinal study, loss aversion, market bubble, market fundamentalism, mental accounting, meta-analysis, Milgram experiment, moral panic, Murray Gell-Mann, Nate Silver, neurotypical, passive investing, pattern recognition, Ponzi scheme, prediction markets, random walk, Richard Feynman, Richard Thaler, risk tolerance, Robert Shiller, Robert Shiller, science of happiness, Shai Danziger, short selling, South Sea Bubble, Stanford prison experiment, Stephen Hawking, Steve Jobs, stocks for the long run, sunk-cost fallacy, Thales of Miletus, The Signal and the Noise by Nate Silver, Tragedy of the Commons, tulip mania, Vanguard fund, When a measure becomes a target

O’Shaughnessy used the now-familiar methodology of dividing stocks into deciles and observing returns from 1963 to the end of 2009. His results highlight the efficacy of value investing and the power of slightly improved annualized returns to greatly compound wealth. Looking at price-to-earnings (P/E) ratios, he found that the cheapest decile of stocks with respect to P/E ratios turned $10,000 into $10,202,345 for a compound rate of return of 16.25% per year. Compare that to the index return of 11.22% that would have turned that same $10,000 into a mere $1,329,513. Buying cheap stocks would have made you $9,000,000 dollars more and done so with less volatility, defying the efficient market notion that more risk is required for great returns.117 But what of the most expensive decile of stocks, the glamour names?


pages: 300 words: 77,787

Investing Demystified: How to Invest Without Speculation and Sleepless Nights by Lars Kroijer

Andrei Shleifer, asset allocation, asset-backed security, Bernie Madoff, bitcoin, Black Swan, BRICs, Carmen Reinhart, cleantech, compound rate of return, credit crunch, diversification, diversified portfolio, equity premium, estate planning, fixed income, high net worth, implied volatility, index fund, intangible asset, invisible hand, Kenneth Rogoff, market bubble, money market fund, passive investing, pattern recognition, prediction markets, risk tolerance, risk/return, Robert Shiller, Robert Shiller, selection bias, sovereign wealth fund, too big to fail, transaction costs, Vanguard fund, yield curve, zero-coupon bond

We also assume that investors expect to be paid a similar premium for investing in equities over safe government bonds in future as they have historically. The size of the equity risk premium is subject to much debate, but numbers in the order of 4–5% are often quoted. If you study the returns of the world equity markets over the past 100 years (see Table 5.1) the annual compounding rate of return for this period is close to this range. Of course it is impossible to know if the markets over that period have been particularly attractive or poor for equityholders compared to what the future has in store. The equity risk premium is not a law of nature, but simply an expectation of future returns, in this case based on what those markets achieved in the past, including the significant drawdowns that occurred.


The Simple Living Guide by Janet Luhrs

air freight, Albert Einstein, car-free, cognitive dissonance, Community Supported Agriculture, compound rate of return, financial independence, follow your passion, Golden Gate Park, job satisfaction, late fees, money market fund, music of the spheres, passive income, Ralph Waldo Emerson, risk tolerance, telemarketer, the rule of 72, urban decay, urban renewal, Whole Earth Review

Either way, she was going to be 44 years old. This got her very excited. How $100 Invested Monthly Will Grow at Various Annual Compound Rates of Return YEARS 5% 7% 9% 5 $6,801 $7,159 $7,542 10 15,528 17,308 19,351 15 26,729 31,696 37,841 20 41,103 52,093 66,789 25 59,551 81,007 112,112 30 83,226 121,997 183,074 35 113,609 180,105 294,178 40 152,602 262,481 468,132 For all of you who never saw a compound interest chart, please refer to the box entitled: How $100 Invested Monthly Will Grow at Various Annual Compound Rates of Return. Make a copy and put it on your wall in a prominent place if that will help you to stick with your pay-yourself goal.


pages: 219 words: 15,438

The Essays of Warren Buffett: Lessons for Corporate America by Warren E. Buffett, Lawrence A. Cunningham

buy and hold, compensation consultant, compound rate of return, corporate governance, Dissolution of the Soviet Union, diversified portfolio, dividend-yielding stocks, fixed income, George Santayana, index fund, intangible asset, invisible hand, large denomination, low cost airline, low cost carrier, oil shock, passive investing, price stability, Ronald Reagan, Tax Reform Act of 1986, the market place, transaction costs, Yogi Berra, zero-coupon bond

Further illuminating the folly of junk bonds is an essay in this collection by Charlie Munger that discusses Michael Milken's approach to finance. Wall Street tends to embrace ideas based on revenue-generating power, rather than on financial sense, a tendency that often perverts good ideas to bad ones. In a history of zero-coupon bonds, for example, Buffett shows that they can enable a purchaser to lock in a compound rate of return equal to a coupon rate that a normal bond paying periodic interest would not provide. Using zero-coupons thus for a time enabled a borrower to borrow more without need of additional free cash flow to pay the interest expense. Problems arose, however, when zero-coupon bonds started to be issued by weaker and weaker credits whose free cash flow could not sustain increasing debt obligations.


Monte Carlo Simulation and Finance by Don L. McLeish

algorithmic bias, 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, risk free rate, Sharpe ratio, short selling, stochastic process, stochastic volatility, survivorship bias, the market place, transaction costs, value at risk, Wiener process, zero-coupon bond, zero-sum game

However, for the moment let us assume that the upper barrier is so high that its influence can be neglected, so that the only absorbtion with any substantial probability is at the lower barrier. We interested in the estimate of return from the two portfolios, and a preliminary estimate indicates a continuously compounded rate of return from portfolio 1 of R1 = ln(56.625/40) = 35% and from portfolio two of R2 = ln(56.25/40) = 34%. Is this difference significant and are these returns reasonably accurate in view of the survivorship bias? We assume a geometric Brownian motion for both portfolios, (5.34) dSt = µSt dt + σSt dWt , and define O = S(0), C = S(T ), H = max S(t), 0 t T L = min S(t) 0 t T with parameters µ, σ possibly different.


pages: 294 words: 89,406

Lying for Money: How Fraud Makes the World Go Round by Daniel Davies

bank run, banking crisis, Bernie Madoff, bitcoin, Black Swan, Bretton Woods, business cycle, business process, collapse of Lehman Brothers, compound rate of return, cryptocurrency, financial deregulation, fixed income, Frederick Winslow Taylor, Gordon Gekko, high net worth, illegal immigration, index arbitrage, Nick Leeson, offshore financial centre, Peter Thiel, Ponzi scheme, price mechanism, principal–agent problem, railway mania, Ronald Coase, Ronald Reagan, Savings and loan crisis, short selling, social web, South Sea Bubble, tail risk, The Great Moderation, the payments system, The Wealth of Nations by Adam Smith, time value of money, web of trust

If you want to steal a lot of money, you have to keep the fraud going. You also have to keep the fraud going if you haven’t figured out your escape route yet, or if you just blundered into it and don’t have a plan at all. But while the fraud is going, it has to be growing; the returns and repayments you owe to other people are growing at a compound rate of return, so you have to commit ever-increasing amounts of new fraud to stand still. This snowball property is the main challenge in managing an ongoing fraud. The Pigeon King Modern versions of Ponzi’s scheme tend to follow him in trying to avoid dealing with even lightly regulated markets. One of Ponzi’s highest priorities from the start of the scheme was to be sure that his dealings in postal reply coupons were not covered by the Commonwealth of Massachussetts’ ‘blue-sky laws’, which had been enacted to regulate the activities of stock promoters who would ‘sell shares in the blue sky’ unless prevented from doing so.


pages: 416 words: 118,592

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

accounting loophole / creative accounting, Albert Einstein, asset allocation, asset-backed security, backtesting, Bear Stearns, beat the dealer, Bernie Madoff, BRICs, butter production in bangladesh, buy and hold, capital asset pricing model, compound rate of return, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, dogs of the Dow, Edward Thorp, 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, money market fund, mortgage tax deduction, new economy, Own Your Own Home, passive investing, Paul Samuelson, pets.com, Ponzi scheme, price stability, profit maximization, publish or perish, purchasing power parity, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, short selling, Silicon Valley, South Sea Bubble, stocks for the long run, survivorship bias, The Myth of the Rational Market, the rule of 72, The Wisdom of Crowds, transaction costs, Vanguard fund, zero-coupon bond

Treasury bills 3.7 3.1 Common stocks have clearly provided very generous long-run rates of return. It has been estimated that if George Washington had put just one dollar aside from his first presidential salary and invested it in common stocks, his heirs would have been millionaires more than ten times over by 2010. Roger Ibbotson estimates that stocks have provided a compounded rate of return of more than 8 percent per year since 1790. (As the table above shows, returns have been even more generous since 1926, when common stocks of large companies earned almost 10 percent.) But this return came only at substantial risk to investors. Total returns were negative in about three years out of ten.


pages: 403 words: 119,206

Toward Rational Exuberance: The Evolution of the Modern Stock Market by B. Mark Smith

bank run, banking crisis, business climate, business cycle, buy and hold, capital asset pricing model, compound rate of return, computerized trading, credit crunch, cuban missile crisis, discounted cash flows, diversified portfolio, Donald Trump, Eugene Fama: efficient market hypothesis, financial independence, financial innovation, fixed income, full employment, income inequality, index arbitrage, index fund, joint-stock company, locking in a profit, Long Term Capital Management, Louis Bachelier, margin call, market clearing, merger arbitrage, money market fund, Myron Scholes, Paul Samuelson, price stability, random walk, Richard Thaler, risk free rate, risk tolerance, Robert Bork, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, short selling, stocks for the long run, the market place, transaction costs

The Dow Jones Industrials broke through the December 1961 high in 1963, and eventually established a new high slightly over 1,000 in early 1966. Thus an investor who bought the Dow Industrial stocks at the “overpriced” high of 734.51 in December 1961 would, over the next four years, achieve a compounded rate of return (including dividends) of approximately 11%, roughly the historic average rate of return for stocks over the century. Had he simply ignored the unpleasant volatility of 1962, the long-term investor would have made out just fine. Perhaps even more surprisingly, the investor who owned the highmultiple “glamour” stocks before the 1962 break also did quite well over the long term, if he had the stomach to ride out the severe downdrafts of 1962.


pages: 400 words: 124,678

The Investment Checklist: The Art of In-Depth Research by Michael Shearn

Asian financial crisis, barriers to entry, Bear Stearns, business cycle, call centre, Clayton Christensen, collective bargaining, commoditize, compensation consultant, compound rate of return, Credit Default Swap, estate planning, intangible asset, Jeff Bezos, London Interbank Offered Rate, margin call, Mark Zuckerberg, money market fund, Network effects, pink-collar, risk tolerance, shareholder value, six sigma, Skype, Steve Jobs, supply-chain management, technology bubble, time value of money, transaction costs, urban planning, women in the workforce, young professional

This was during the days of a serious amount of LBO activity, and the comment signaled to Green that the CEO had the right attitude regarding the alignment of shareholders and management interests. Green purchased the stock on April 26, 1991 at $3.07 per share and sold it on June 8, 1998 at $9.99 per share, a compound rate of return of more than 18 percent.5 Buying Shares to Track a Business You can buy a few shares in a stock that meets your criteria to force yourself to follow the business. By purchasing a very small piece of a business, you’ve guaranteed that you will not forget the business, and that you’ll have consistent reminders about that business.


pages: 482 words: 121,672

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

accounting loophole / creative accounting, Albert Einstein, asset allocation, asset-backed security, beat the dealer, Bernie Madoff, bitcoin, butter production in bangladesh, buttonwood tree, buy and hold, capital asset pricing model, compound rate of return, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, Detroit bankruptcy, diversification, diversified portfolio, dogs of the Dow, Edward Thorp, Elliott wave, Eugene Fama: efficient market hypothesis, experimental subject, feminist movement, financial innovation, financial repression, fixed income, framing effect, George Santayana, hindsight bias, Home mortgage interest deduction, index fund, invisible hand, Isaac Newton, Long Term Capital Management, loss aversion, margin call, market bubble, money market fund, mortgage tax deduction, new economy, Own Your Own Home, passive investing, Paul Samuelson, pets.com, Ponzi scheme, price stability, profit maximization, publish or perish, purchasing power parity, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, short selling, Silicon Valley, South Sea Bubble, stocks for the long run, survivorship bias, the rule of 72, The Wisdom of Crowds, transaction costs, Vanguard fund, zero-coupon bond, zero-sum game

Common stocks have clearly provided very generous long-run rates of return. It has been estimated that if George Washington had put just one dollar aside from his first presidential salary and invested it in common stocks, his heirs would have been millionaires more than ten times over by 2014. Roger Ibbotson estimates that stocks have provided a compounded rate of return of more than 8 percent per year since 1790. (As the table above shows, returns have been even more generous since 1926, when common stocks of large companies earned about 10 percent.) But this return came only at substantial risk to investors. Total returns were negative in about three years out of ten.


pages: 517 words: 139,477

Stocks for the Long Run 5/E: the Definitive Guide to Financial Market Returns & Long-Term Investment Strategies by Jeremy Siegel

Asian financial crisis, asset allocation, backtesting, banking crisis, Bear Stearns, Black-Scholes formula, break the buck, Bretton Woods, business cycle, buy and hold, buy low sell high, California gold rush, capital asset pricing model, carried interest, central bank independence, cognitive dissonance, compound rate of return, computer age, computerized trading, corporate governance, correlation coefficient, Credit Default Swap, Daniel Kahneman / Amos Tversky, Deng Xiaoping, discounted cash flows, diversification, diversified portfolio, dividend-yielding stocks, dogs of the Dow, equity premium, Eugene Fama: efficient market hypothesis, eurozone crisis, Everybody Ought to Be Rich, Financial Instability Hypothesis, fixed income, Flash crash, forward guidance, fundamental attribution error, housing crisis, Hyman Minsky, implied volatility, income inequality, index arbitrage, index fund, indoor plumbing, inflation targeting, invention of the printing press, Isaac Newton, joint-stock company, London Interbank Offered Rate, Long Term Capital Management, loss aversion, market bubble, mental accounting, Money creation, money market fund, mortgage debt, Myron Scholes, new economy, Northern Rock, oil shock, passive investing, Paul Samuelson, Peter Thiel, Ponzi scheme, prediction markets, price anchoring, price stability, purchasing power parity, quantitative easing, random walk, Richard Thaler, risk free rate, risk tolerance, risk/return, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, selling pickaxes during a gold rush, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, stocks for the long run, survivorship bias, technology bubble, The Great Moderation, the payments system, The Wisdom of Crowds, transaction costs, tulip mania, Tyler Cowen: Great Stagnation, Vanguard fund

This time the returns were even higher despite the fact that they made no adjustment for any of the new firms or new industries that had surfaced in the interim. They wrote: If a portfolio of common stocks selected by such obviously foolish methods as were employed in this study will show an annual compound rate of return as high as 14.2 percent, then a small investor with limited knowledge of market conditions can place his savings in a diversified list of common stocks with some assurance that, given time, his holding will provide him with safety of principal and an adequate annual yield.22 Many dismissed the Eiteman and Smith study because the period studied did not include the Great Crash of 1929 to 1932.


pages: 582 words: 160,693

The Sovereign Individual: How to Survive and Thrive During the Collapse of the Welfare State by James Dale Davidson, William Rees-Mogg

affirmative action, agricultural Revolution, bank run, barriers to entry, Berlin Wall, borderless world, British Empire, California gold rush, clean water, colonial rule, Columbine, compound rate of return, creative destruction, Danny Hillis, debt deflation, ending welfare as we know it, epigenetics, Fall of the Berlin Wall, falling living standards, feminist movement, financial independence, Francis Fukuyama: the end of history, full employment, George Gilder, Hernando de Soto, illegal immigration, income inequality, independent contractor, informal economy, information retrieval, Isaac Newton, Kevin Kelly, market clearing, Martin Wolf, Menlo Park, money: store of value / unit of account / medium of exchange, new economy, New Urbanism, Norman Macrae, offshore financial centre, Parkinson's law, pattern recognition, phenotype, price mechanism, profit maximization, rent-seeking, reserve currency, road to serfdom, Ronald Coase, Sam Peltzman, school vouchers, seigniorage, Silicon Valley, spice trade, statistical model, telepresence, The Nature of the Firm, the scientific method, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade route, transaction costs, Turing machine, union organizing, very high income, Vilfredo Pareto

But remember, that assumes an annual tax payment of $45,000. 156 Compared to a tax haven like Bermuda, where the income tax is zero, the lifetime loss for paying taxes at American rates would be about $1.1 billion. You may object that an annual return of 20 percent is a high rate of return. No doubt you would be right. But given the startling growth in Asia in recent decades, many investors in the world have achieved that and better. The compound rate of return in Hong Kong real estate since 1950 has been more than 20 percent per annum. Even some economies that are less widely known for growth have afforded easy opportunities for high profits. You could have pocketed an average real return of more than 30 percent annually in U.S. dollar deposits in Paraguayan banks over the last three decades.


pages: 542 words: 145,022

In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest by Andrew W. Lo, Stephen R. Foerster

"Robert Solow", Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, Charles Lindbergh, compound rate of return, corporate governance, Covid-19, COVID-19, credit crunch, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, Edward Glaeser, equity premium, estate planning, Eugene Fama: efficient market hypothesis, family office, fiat currency, financial innovation, financial intermediation, fixed income, hiring and firing, Hyman Minsky, implied volatility, index fund, interest rate swap, Internet Archive, invention of the wheel, Isaac Newton, John Meriwether, John von Neumann, joint-stock company, Kenneth Arrow, linear programming, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, money market fund, money: store of value / unit of account / medium of exchange, Myron Scholes, new economy, New Journalism, Own Your Own Home, passive investing, Paul Samuelson, Performance of Mutual Funds in the Period, prediction markets, price stability, profit maximization, quantitative trading / quantitative finance, RAND corporation, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, Savings and loan crisis, selection bias, shareholder value, Sharpe ratio, short selling, South Sea Bubble, stochastic process, stocks for the long run, survivorship bias, tail risk, Thales and the olive presses, Thales of Miletus, The Myth of the Rational Market, The Wisdom of Crowds, Thomas Bayes, time value of money, transaction costs, transfer pricing, tulip mania, Vanguard fund, yield curve, zero-coupon bond, zero-sum game

He managed the endowment of his alma mater, Cambridge University, from 1921 until his death in 1946, and a recent study by David Chambers, Elroy Dimson, and Justin Foo has painstakingly reconstructed the investment returns of Keynes’s portfolio.37 From the end of August 1921 to the end of August 1946, the annual compound return on his discretionary portfolio was 14.41 percent, versus 8.96 percent for the equally weighted UK equity market index during the same period. But Chambers and Dimson discovered a fact far more remarkable than Keynes’s overall performance: Keynes made a sharp improvement in his investment approach in 1932. From 1921 to 1931 he generated a compound rate of return of only 8.06 percent, only marginally better than the equally weighted UK equity market index return of 6.67 percent. But from 1931 to 1946 Keynes produced a compound return of 18.84 percent, far outstripping the equally weighted UK index return of 10.52 percent during this fifteen-year interval.


Trade Your Way to Financial Freedom by van K. Tharp

asset allocation, backtesting, Bretton Woods, buy and hold, buy the rumour, sell the news, capital asset pricing model, commodity trading advisor, compound rate of return, computer age, distributed generation, diversification, dogs of the Dow, Elliott wave, high net worth, index fund, locking in a profit, margin call, market fundamentalism, passive income, prediction markets, price stability, random walk, reserve currency, risk tolerance, Ronald Reagan, Savings and loan crisis, Sharpe ratio, short selling, Tax Reform Act of 1986, transaction costs

Futures Market Models Kaufman Adaptive Moving-Average Approach Kaufman doesn’t really discuss position sizing in his book Smarter Trading. He does discuss some of the results of position sizing such as risk and reward, using the academic definitions of the terms. By risk he means the annualized standard deviation of the equity changes, and by reward he means the annualized compounded rate of return. He suggests that when two systems have the same returns, the rational investor will choose the system with the lower risk. Kaufman also brings up another interesting point in his discussion—the 50-year rule. He says that levees were built along the Mississippi River to protect them from the largest flood that has occurred in the last 50 years.


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

Albert Einstein, Andrew Wiles, asset allocation, availability heuristic, backtesting, Black Swan, butter production in bangladesh, buy and hold, capital asset pricing model, cognitive dissonance, compound rate of return, computerized trading, 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, p-value, pattern recognition, Paul Samuelson, Ponzi scheme, price anchoring, price stability, quantitative trading / quantitative finance, Ralph Nelson Elliott, random walk, retrograde motion, revision control, risk free rate, risk tolerance, risk-adjusted returns, riskless arbitrage, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, source of truth, statistical model, stocks for the long run, systematic trading, the scientific method, transfer pricing, unbiased observer, yield curve, Yogi Berra

The same conclusion can be found in the statistics provided by Hulbert’s financial digest, which currently follows the performance of over 500 investment portfolios recommended by newsletters. In one Hulbert study, 57 newsletters were tracked for the 10year period from August 1987 through August 1998. During that time, less than 10 percent of the newsletters beat the Wilshire 5000 Index’s compound rate of return. Armstrong also contends that expertise, beyond a minimal level, adds little in the way of predictive accuracy. Thus, consumers would be better off buying the least expensive predictions, which are likely to be as accurate as the most expensive, or investing the modest effort required to achieve a level of accuracy that would be comparable to the most expensive experts.


pages: 695 words: 194,693

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

Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, 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 market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, 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, tulip mania, wage slave

That fund is actually alive today, and you can trace its daily fluctuations from 1932 to the present. The sponsoring company, American Funds, still maintains the daily record of prices and dividends. Reinvesting dividends (and not having to pay taxes), each dollar invested in the fund in 1932 would have grown to $2,747 by 2010; an annual, compound rate of return of about 10.7%. This is just about what an investment in a broad index of large US stocks would have earned—10.9%. You might not have beaten the market, but you would have made a great return over nearly eighty years, just as Edgar Lawrence Smith predicted. Those eight decades included four major US wars (Second World War, Korean War, Vietnam War, and the Gulf Wars), and they included most of the Great Depression and the Great Recession.


Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen

3Com Palm IPO, accounting loophole / creative accounting, Airbus A320, Asian financial crisis, asset allocation, asset-backed security, banking crisis, Bear Stearns, Bernie Madoff, big-box store, Black-Scholes formula, break the buck, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, carried interest, collateralized debt obligation, compound rate of return, computerized trading, conceptual framework, corporate governance, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-subsidies, discounted cash flows, disintermediation, diversified portfolio, equity premium, eurozone crisis, financial innovation, financial intermediation, fixed income, frictionless, fudge factor, German hyperinflation, implied volatility, index fund, information asymmetry, intangible asset, interest rate swap, inventory management, Iridium satellite, Kenneth Rogoff, law of one price, linear programming, Livingstone, I presume, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, market bubble, market friction, money market fund, moral hazard, Myron Scholes, new economy, Nick Leeson, Northern Rock, offshore financial centre, Ponzi scheme, prediction markets, price discrimination, principal–agent problem, profit maximization, purchasing power parity, QR code, quantitative trading / quantitative finance, random walk, Real Time Gross Settlement, risk free rate, risk tolerance, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, Silicon Valley, Skype, Steve Jobs, sunk-cost fallacy, Tax Reform Act of 1986, The Nature of the Firm, the payments system, the rule of 72, time value of money, too big to fail, transaction costs, University of East Anglia, urban renewal, VA Linux, value at risk, Vanguard fund, yield curve, zero-coupon bond, zero-sum game, Zipcar

Our only hope of gaining insights from historical rates of return is to look at a very long period.5 Arithmetic Averages and Compound Annual Returns Notice that the average returns shown in Table 7.1 are arithmetic averages. In other words, we simply added the 112 annual returns and divided by 112. The arithmetic average is higher than the compound annual return over the period. The 112-year compound annual return for common stocks was 9.3%.6 The proper uses of arithmetic and compound rates of return from past investments are often misunderstood. Therefore, we call a brief time-out for a clarifying example. Suppose that the price of Big Oil’s common stock is $100. There is an equal chance that at the end of the year the stock will be worth $90, $110, or $130. Therefore, the return could be –10%, +10%, or +30% (we assume that Big Oil does not pay a dividend).

This bias would be small in most corporate-finance applications, however. 10Some of the disagreements simply reflect the fact that the risk premium is sometimes defined in different ways. Some measure the average difference between stock returns and the returns (or yields) on long-term bonds. Others measure the difference between the compound rate of return on stocks and the interest rate. As we explained above, this is not an appropriate measure of the cost of capital. 11There is some theory behind this instinct. The high risk premium earned in the market seems to imply that investors are extremely risk-averse. If that is true, investors ought to cut back their consumption when stock prices fall and wealth decreases.


pages: 1,164 words: 309,327

Trading and Exchanges: Market Microstructure for Practitioners by Larry Harris

active measures, Andrei Shleifer, asset allocation, automated trading system, barriers to entry, Bernie Madoff, business cycle, buttonwood tree, buy and hold, compound rate of return, computerized trading, corporate governance, correlation coefficient, data acquisition, diversified portfolio, fault tolerance, financial innovation, financial intermediation, fixed income, floating exchange rates, High speed trading, index arbitrage, index fund, information asymmetry, information retrieval, interest rate swap, invention of the telegraph, job automation, law of one price, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, market clearing, market design, market fragmentation, market friction, market microstructure, money market fund, Myron Scholes, Nick Leeson, open economy, passive investing, pattern recognition, Ponzi scheme, post-materialism, price discovery process, price discrimination, principal–agent problem, profit motive, race to the bottom, random walk, rent-seeking, risk free rate, risk tolerance, risk-adjusted returns, selection bias, shareholder value, short selling, Small Order Execution System, speech recognition, statistical arbitrage, statistical model, survivorship bias, the market place, transaction costs, two-sided market, winner-take-all economy, yield curve, zero-coupon bond, zero-sum game

Capital additions would inflate the performance and capital distributions would deflate it. Analysts use two approaches to address the problem of capital additions and distributions. The most common approach is to compute the internal rate of return for the portfolio. The internal rate of return (IRR) is the compounded rate of return that a savings account would have to earn to exactly replicate the capital flows into and out of the portfolio. The IRR calculation assumes that beginning and ending savings account balances are equal to the beginning and ending portfolio values. The IRR is approximately a time- and value-weighted geometric average of the total returns measured between each capital addition and distribution.


pages: 892 words: 91,000

Valuation: Measuring and Managing the Value of Companies by Tim Koller, McKinsey, Company Inc., Marc Goedhart, David Wessels, Barbara Schwimmer, Franziska Manoury

activist fund / activist shareholder / activist investor, air freight, ASML, barriers to entry, Basel III, BRICs, business climate, business cycle, business process, capital asset pricing model, capital controls, Chuck Templeton: OpenTable:, cloud computing, commoditize, compound rate of return, conceptual framework, corporate governance, corporate social responsibility, creative destruction, credit crunch, Credit Default Swap, discounted cash flows, distributed generation, diversified portfolio, energy security, equity premium, fixed income, index fund, intangible asset, iterative process, Long Term Capital Management, market bubble, market friction, Myron Scholes, negative equity, new economy, p-value, performance metric, Ponzi scheme, price anchoring, purchasing power parity, quantitative easing, risk free rate, risk/return, Robert Shiller, Robert Shiller, Savings and loan crisis, shareholder value, six sigma, sovereign wealth fund, speech recognition, stocks for the long run, survivorship bias, technology bubble, time value of money, too big to fail, transaction costs, transfer pricing, two and twenty, value at risk, yield curve, zero-coupon bond

Therefore, to determine a security’s expected return for one period, the best unbiased predictor is the arithmetic average of many one-period returns. A one-period risk premium, however, can’t value a company with many years of cash flow. Instead, long-dated cash flows must be discounted using a compounded rate of return. But when compounded, the arithmetic average will generate a discount factor that is biased upward (too high). APPENDIX F 853 The cause of the bias is quite technical, so we provide only a summary here. There are two reasons why compounding the historical arithmetic average leads to a biased discount factor.