Louis Bachelier

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pages: 206 words: 70,924

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

Abraham Wald, Albert Einstein, Bayesian statistics, Bear Stearns, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, 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 engineering, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John Meriwether, John von Neumann, Joseph Schumpeter, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, Myron Scholes, Paul Samuelson, price stability, principal–agent problem, quantitative trading / quantitative finance, RAND corporation, random walk, risk free rate, risk tolerance, risk/return, Robert Solow, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, Thales and the olive presses, Thales of Miletus, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

Baggs (1774), London; reprinted by Gregg International Publishers (1969). 6. Robert J. Leonard, “Creating a Context for Game Theory,” History of Political Economy, 24 (Supplement) (1992), 29–76, at p. 39. 7. http://en.wikipedia.org/wiki/Louis_Bachelier, date accessed January 23, 2012. 8. Alfred Cowles and H. Jones, “Some A Posteriori Probabilities in Stock Market Action,” Econometrica, 5(3) (1937), 280–94. 9. Louis Bachelier, “Theorie de la speculation,” Annales scientifiques de l’Ecole Normale Superieure, 3rd series, 17 (1900), 21–86. 10. C.M. Sprenkle, “Warrant Prices as Indications of Expectations and Preferences,” Yale Economic Essays, 1(22) (1961), 178–231. 16 Applications 1.

The modern quants, and trillions 6 The Rise of the Quants of dollars of financial investment each year, now rely on the pricing tools provided by William Sharpe, Fischer Black and Myron Scholes, and Robert Merton, based on the earlier foundational work of Jacob Marschak and a then obscure but brilliant French PhD student at the turn of the twentieth century named Louis Bachelier. In our future, we shall inevitably rely even more on the products of these great minds. We will now turn to how the concepts came about and now affect us all so profoundly. Part I Jacob Marschak We can often discover the formative roots of one or two great insights that eventually culminated in a Nobel Prize for many of the great minds described in this series.

The scientific analysis of securities pricing By 1950, Marschak had introduced to finance theory a method to price risk, through his mean-variance approach. Much later, however, we discovered that he was not the first to offer a measure of the cost of volatility of financial instruments. At the turn of the twentieth century, the French mathematician Louis Bachelier (1870–1946) produced a PhD thesis with the title “The Theory of Speculation.” In this revolutionary thesis, Bachelier was the first to apply the mathematical model of Brownian motion to the movement of security prices. He did so five years before Albert Einstein applied the same model to the movement of small particles.


pages: 338 words: 106,936

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

Alan Greenspan, Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Apollo 11, Asian financial crisis, bank run, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, Bonfire of the Vanities, book value, Bretton Woods, Brownian motion, business cycle, butterfly effect, buy and hold, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, coastline paradox / Richardson effect, collateralized debt obligation, collective bargaining, currency risk, dark matter, Edward Lorenz: Chaos theory, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, Financial Modelers Manifesto, fixed income, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, Jim Simons, John Nash: game theory, junk bonds, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, Market Wizards by Jack D. Schwager, martingale, Michael Milken, military-industrial complex, Myron Scholes, Neil Armstrong, new economy, Nixon triggered the end of the Bretton Woods system, Paul Lévy, Paul Samuelson, power law, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk free rate, risk-adjusted returns, Robert Gordon, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, Stuart Kauffman, The Chicago School, The Myth of the Rational Market, tulip mania, Vilfredo Pareto, volatility smile

Courtault, Jean-Michel, and Youri Kabanov. 2002. Louis Bachelier: Aux origines de la finance mathématique. Paris: Presses Universitaires Franc-Comtoises. Cox, John C., and Mark Rubinstein. 1985. Options Markets. Englewood Cliffs, NJ: Prentice Hall. Dash, Mike. 1999. Tulipomania: The Story of the World’s Most Coveted Flower and the Extraordinary Passions It Aroused. New York: Three Rivers Press. David, F. N. 1962. Games, Gods & Gambling: A History of Probability and Statistical Ideas. New York: Simon & Schuster. Davis, Mark, and Alison Etheridge. 2006. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance.

For an hour each day they met beneath ornately carved reliefs and a massive skylight to trade the permanent government bonds, called rentes, that had funded France’s global ambitions for a century. Imperial and imposing, it was the center of the city at the center of the world. Or so it would have seemed to Louis Bachelier as he approached it for the first time, in 1892. He was in his early twenties, an orphan from the provinces. He had just arrived in Paris, fresh from his mandatory military service, to resume his education at the University of Paris. He was determined to be a mathematician or a physicist, whatever the odds — and yet, he had a sister and a baby brother to support back home.

He was sitting in his office, in the economics department at MIT. The year was 1955, or thereabouts. Laid out in front of him was a half-century-old PhD dissertation, written by a Frenchman whom Samuelson was quite sure he had never heard of. Bachelor, Bacheler. Something like that. He looked at the front of the document again. Louis Bachelier. It didn’t ring any bells. Its author’s anonymity notwithstanding, the document open on Samuelson’s desk was astounding. Here, fifty-five years previously, Bachelier had laid out the mathematics of financial markets. Samuelson’s first thought was that his own work on the subject over the past several years — the work that was supposed to form one of his students’ dissertation — had lost its claim to originality.


pages: 461 words: 128,421

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

"Friedman doctrine" OR "shareholder theory", Abraham Wald, activist fund / activist shareholder / activist investor, Alan Greenspan, Albert Einstein, Andrei Shleifer, AOL-Time Warner, asset allocation, asset-backed security, bank run, beat the dealer, behavioural economics, Benoit Mandelbrot, Big Tech, Black Monday: stock market crash in 1987, Black-Scholes formula, book value, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, card file, Carl Icahn, Cass Sunstein, collateralized debt obligation, compensation consultant, complexity theory, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, democratizing finance, Dennis Tito, discovery of the americas, diversification, diversified portfolio, Dr. Strangelove, Edward Glaeser, Edward Thorp, endowment effect, equity risk premium, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, fixed income, floating exchange rates, George Akerlof, Glass-Steagall Act, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, information asymmetry, invisible hand, Isaac Newton, John Bogle, John Meriwether, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, junk bonds, Kenneth Arrow, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, market bubble, market design, Michael Milken, Myron Scholes, New Journalism, Nikolai Kondratiev, Paul Lévy, Paul Samuelson, pension reform, performance metric, Ponzi scheme, power law, prediction markets, proprietary trading, prudent man rule, pushing on a string, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Bork, Robert Shiller, rolodex, Ronald Reagan, seminal paper, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, Skinner box, Social Responsibility of Business Is to Increase Its Profits, South Sea Bubble, statistical model, stocks for the long run, tech worker, 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, Two Sigma, Tyler Cowen, value at risk, Vanguard fund, Vilfredo Pareto, volatility smile, Yogi Berra

Henri Poincaré, The Value of Science: Essential Writings of Henri Poincaré (New York: The Modern Library, 2001), 402. 4. Louis Bachelier, “Theory of Speculation,” in The Random Character of Stock Prices, trans. A. James Boness, ed. Paul Cootner (Cambridge, Mass.: MIT Press, 1969), 28. 5. Bachelier, “Theory of Speculation,” 17. 6. Poincaré, Value of Science, 419. 7. Bachelier, “Theory of Speculation,” 25–26. 8. This and all other biographical information on Bachelier is from Jean-Michel Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” Mathematical Finance (July 2000): 341–53. Poincaré’s report on Bachelier’s thesis, translated by Selime Baftiri-Balazoski and Ulrich Haussman, is also included in the article. 9.

Fisher was just the first in a line of distinguished scholars who saw reason and scientific order in the market and made fools of themselves on the basis of this conviction. Most of the others came along much later, though. Irving Fisher was ahead of his time. HE WAS NOT, HOWEVER, ALONE in his advanced thoughts about financial markets. In Paris, mathematics student Louis Bachelier studied the price fluctuations on the Paris Bourse (exchange) in a similar spirit. The result was a doctoral thesis that, when unearthed more than half a century after its completion in 1900, would help to relaunch the study of financial markets. Bachelier undertook his investigation at a time when scientists had begun to embrace the idea that while there could be no absolute certainty about anything, uncertainty itself could be a powerful tool.

To get it to that point, he had to face head-on some knotty questions that he had ignored in his original paper. The biggest conundrum was how a person was supposed to go about being a statistical man not in a game with clearly defined rules but in a messy, uncertain world. How was one to assign numerical probabilities to uncertain future events? The answer—as Louis Bachelier had concluded back in 1900—is that there is no one way. Everyone’s assessments of the future are of necessity personal and subjective. But rules could be devised for how to adjust those assessments in the face of new evidence, and the man who set them down in the early 1950s was Jimmie Savage, Markowitz’s statistics professor.


pages: 364 words: 101,286

The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson

Alan Greenspan, Albert Einstein, asset allocation, Augustin-Louis Cauchy, behavioural economics, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black Monday: stock market crash in 1987, Black-Scholes formula, British Empire, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, electricity market, Elliott wave, equity premium, equity risk premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, financial engineering, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John Meriwether, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, Myron Scholes, new economy, paper trading, passive investing, Paul Lévy, Paul Samuelson, plutocrats, power law, price mechanism, quantitative trading / quantitative finance, Ralph Nelson Elliott, RAND corporation, random walk, risk free rate, risk tolerance, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, Vilfredo Pareto, volatility smile

Futures Commission Merchant Reports for 2003. On the Web at http://www.cftc.gov/tm/tmfcm.htm. Cootner, Paul H, ed. 1964. The Random Character of Stock Market Prices. Cambridge, MA.: MIT Press. Courtault, Jean-Michel. 2000. Louis Bachelier: On the centenary of Théorie de la Spéculation. Mathematical Finance 10 (3) July: 339-353. Courtault, Jean-Michel et al. 2000. Louis Bachelier: Fondateur de la finance mathématique. A Web site, sponsored by the Université de Franche-Comté, publishing primary manuscripts and photographs of Bachelier’s life and times, for the centenary of his doctoral thesis: http://sjepg.univfcomte.fr/La_recherche/Libre/bachelier/page01/page01.htm.

The fundamental concept: Prices are not predictable, but their fluctuations can be described by the mathematical laws of chance. Therefore, their risk is measurable, and manageable. This is now orthodoxy to which I subscribe—up to a point. Work in this field began in 1900, when a youngish French mathematician, Louis Bachelier, had the temerity to study financial markets at a time “real” mathematicians did not touch money. In the very different world of the seventeenth century, Pascal and Fermat (he of the famous “last theorem” that took 350 years to be proved) invented probability theory to assist some gambling aristocrats.

He had a keen sense of the beautiful in mathematics. He once said: “A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.” Before Poincaré on that day in 1900 was one of his doctoral students, Louis Bachelier.1 Jobs for Ph.D.’s were scarce; and so the award of a doctorate in France was a formal, trying process. The young mathematician’s schooling had been mediocre, at best. Now he had to pass two final tests before Poincaré and the doctoral “jury.” The lesser one was an oral examination on a standard topic, chosen and approved beforehand.


pages: 425 words: 122,223

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

Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, corporate raider, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, Glass-Steagall Act, Great Leap Forward, guns versus butter model, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, junk bonds, Kenneth Arrow, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, Michael Milken, money market fund, Myron Scholes, new economy, New Journalism, Paul Samuelson, Performance of Mutual Funds in the Period, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk free rate, risk/return, Robert Shiller, Robert Solow, Ronald Reagan, stochastic process, Thales and the olive presses, 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, zero-sum game

While no one goes so far as to say that it is impossible to make good predictions or that all predictions are destined to be wrong, the abundant evidence and the robust character of the theories that explain the evidence confirm that the task of predicting stock prices is formidable by any measure. The exploration into whether investors can successfully forecast stock prices has roots that reach all the way back to 1900, when Louis Bachelier, a young French mathematician, completed his dissertation for the degree of Doctor of Mathematical Sciences at the Sorbonne. The title of the dissertation was “The Theory of Speculation.” This extraordinary piece of work, some seventy pages long, was the first effort ever to employ theory, including mathematical techniques, to explain why the stock market behaves as it does.

Sharpe’s work was not all they were unaware of. An impressive body of research on the predictability of stock prices was readily available to anyone who wanted to look at it—but few people did. The researchers who carried out this research and the theorists who explained its findings built a powerful structure on the foundations that Louis Bachelier and Alfred Cowles had prepared for them. They include a famous columnist on Newsweek magazine, a college football star who majored in French and never took a course in math, a compulsive marathon-runner, and an economist at MIT whose gloomy conclusions led him to observe, “I must confess that the fun has gone out of it somehow.”

A 1688 treatise on the workings of the Amsterdam stock exchange by Joseph de la Vega reveals that options and similar types of securities in common use today were already dominating trading activities at the time. This is significant, as Amsterdam was the most sophisticated and important financial center of the seventeenth century, even more important than London. And we have seen that Louis Bachelier, in the course of writing his thesis in Paris in 1900, was attracted to the problem of valuing options. Options are everywhere around us. The father who tells his little boy to stop watching television and go to bed “or else” is giving his son an interesting option. The boy has no obligation to turn off the TV and go to bed, but his father has given him the right to take up the option of keeping the set on and accepting his punishment.


pages: 432 words: 106,612

Trillions: How a Band of Wall Street Renegades Invented the Index Fund and Changed Finance Forever by Robin Wigglesworth

Albert Einstein, algorithmic trading, asset allocation, Bear Stearns, behavioural economics, Benoit Mandelbrot, Big Tech, Black Monday: stock market crash in 1987, Blitzscaling, Brownian motion, buy and hold, California gold rush, capital asset pricing model, Carl Icahn, cloud computing, commoditize, coronavirus, corporate governance, corporate raider, COVID-19, data science, diversification, diversified portfolio, Donald Trump, Elon Musk, Eugene Fama: efficient market hypothesis, fear index, financial engineering, fixed income, Glass-Steagall Act, Henri Poincaré, index fund, industrial robot, invention of the wheel, Japanese asset price bubble, Jeff Bezos, Johannes Kepler, John Bogle, John von Neumann, Kenneth Arrow, lockdown, Louis Bachelier, machine readable, money market fund, Myron Scholes, New Journalism, passive investing, Paul Samuelson, Paul Volcker talking about ATMs, Performance of Mutual Funds in the Period, Peter Thiel, pre–internet, RAND corporation, random walk, risk-adjusted returns, road to serfdom, Robert Shiller, rolodex, seminal paper, Sharpe ratio, short selling, Silicon Valley, sovereign wealth fund, subprime mortgage crisis, the scientific method, transaction costs, uptick rule, Upton Sinclair, Vanguard fund

Peter Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (New York: Wiley, 1992), 23. 2. Bernstein, Capital Ideas, 23. 3. Mark Davis, “Louis Bachelier’s Theory of Speculation,” talk, Imperial College, https://f-origin.hypotheses.org/wp-content/blogs.dir/1596/files/2014/12/Mark-Davis-Talk.pdf. 4. L. Carraro and P. Crépel, “Louis Bachelier,” Encyclopedia of Math, www.encyclopediaofmath.org/images/f/f1/LouisBACHELIER.pdf. 5. Carraro and Crépel, “Louis Bachelier.” 6. Colin Read, The Efficient Market Hypothesists: Bachelier, Samuelson, Fama, Ross, Tobin, and Shiller (Basingstoke, UK: Palgrave Macmillan, 2013), 48. 7.

The cofounder of Protégé Partners, a hedge fund investment firm, who took Buffett up on his bet that an index fund could beat the finest money managers in the world over a decade. JACK BOGLE. The founder of Vanguard, one of the biggest index fund managers in the world, and often dubbed “Saint Jack” due to his exhortation for the investment industry to give more people a “fair shake” through cheap passive investment vehicles. LOUIS BACHELIER. An early-twentieth-century French mathematician who died in obscurity, but whose work on the “random walk” of stocks would make him the intellectual godfather of passive investing. ALFRED COWLES III. The wealthy tuberculosis-plagued heir of a newspaper fortune who undertook one of the first rigorous studies of how well investment professionals actually performed versus the broader stock market.

Chapter 2 THE GODFATHER LEONARD “JIMMIE” SAVAGE, a University of Chicago statistics professor with Coke-bottle glasses and an eclectic, brilliant mind, was rummaging through the university library in 1954 when he made a discovery: a book by a little-known turn-of-the-twentieth-century French mathematician named Louis Bachelier with ideas astonishingly far ahead of their time. Savage sent postcards lauding the work to some of his friends and asked if they had “ever heard of this guy?”1 One of the recipients was Paul Samuelson, a rock-star economist who would go on to become the first American to win a Nobel Prize in the field.


pages: 239 words: 69,496

The Wisdom of Finance: Discovering Humanity in the World of Risk and Return by Mihir Desai

activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, AOL-Time Warner, assortative mating, Benoit Mandelbrot, book value, Brownian motion, capital asset pricing model, Carl Icahn, carried interest, Charles Lindbergh, collective bargaining, corporate governance, corporate raider, discounted cash flows, diversified portfolio, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, follow your passion, George Akerlof, Gordon Gekko, greed is good, housing crisis, income inequality, information asymmetry, Isaac Newton, Jony Ive, Kenneth Rogoff, longitudinal study, Louis Bachelier, low interest rates, Monty Hall problem, moral hazard, Myron Scholes, new economy, out of africa, Paul Samuelson, Pierre-Simon Laplace, principal–agent problem, Ralph Waldo Emerson, random walk, risk/return, Robert Shiller, Ronald Coase, short squeeze, Silicon Valley, Steve Jobs, Thales and the olive presses, Thales of Miletus, The Market for Lemons, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tim Cook: Apple, tontine, transaction costs, vertical integration, zero-sum game

Putnam’s Magazine 2, no. 11 (November 1853): 546–57; and Bellow, Saul. Seize the Day. New York: Viking Press, 1956. For more on the role of government securities in English literature, see “Percents and Sensibility; Personal Finance in Jane Austen’s Time.” Economist, December 24, 2005. On the contributions of Louis Bachelier, see Bachelier, Louis. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Translated and with an introduction by Mark Davis and Alison Etheridge. Princeton, NJ: Princeton University Press, 2006; Bernstein, Jeremy. “Bachelier.” American Journal of Physics 73, no. 5 (2005): 395; Pearle, Philip, Brian Collett, Kenneth Bart, David Bilderback, Dara Newman, and Scott Samuels.

This narrative concludes that finance lost its way by promoting precision and models over human reality by trying to describe inherently social phenomena with physics and quantum mechanics. This is a convenient narrative that suits those who are dissatisfied with the rise of finance—but it is shoddy intellectual history. In fact, the person who beat Albert Einstein to the punch by five years was Louis Bachelier, a doctoral student in Paris. Rather than studying the movement of particles, he studied the movement of stocks and derived the mathematics to describe all kinds of motion, including the motion of pollen particles observed by Robert Brown. How did he do it? He realized that he could employ and generalize the magical distribution created by the quincunx into settings where outcomes weren’t the locations of falling balls, but rather processes of motion that were the result of lots of molecules behaving as if they were going through a quincunx.


pages: 403 words: 119,206

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

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

The force which moves them checks the inflow gradually and time elapses before it can be told with certainty whether the tide has been seen or not. Coincidentally, as Charles Dow was propounding his theory of stock price movements, a young French mathematician, starting with a similar conception of the market, reached profoundly different conclusions. Louis Bachelier completed his doctoral dissertation at the Sorbonne in Paris in 1900. Entitled “The Theory of Speculation,” it was the first work to employ mathematical techniques to explain stock market behavior. Bachelier, like Dow, believed that the stock market at all times accurately represented the collective wisdom of all participants.

Bachelier has evidenced an original and precise mind,” but also commented, “The topic is somewhat remote from those our candidates are in the habit of treating.”13 Over fifty years were to pass before anyone took the slightest interest in his work. J. P. Morgan and his associates undoubtedly never heard of Louis Bachelier and were probably quite unfamiliar with the Dow theory. The problem they faced as they attempted to bring U.S. Steel to market was much more immediate: how to ensure that the market could absorb the heavy weight of the new securities to be issued. Fortunately, the tone of the market in 1901 was good, even exuberant.

While this concept may seem unremarkable, it was to be at the root of a raging debate at the end of the decade between a new generation of impertinent academic researchers on one side and high-profile portfolio managers on the other. For the first time, formerly ignored voices of scholars like Louis Bachelier and Harry Markowitz would finally make themselves heard on Wall Street. An SEC investigation of the 1962 market “crash” concluded that “neither this study nor that of the New York Stock Exchange was able to isolate and identify the cause of the market events [of late May 1962].” The SEC noted that “there was some speculation at the time that these events might be the result of some conspiracy or deliberate misconduct.


pages: 415 words: 125,089

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

Alan Greenspan, Albert Einstein, Alvin Roth, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Bayesian statistics, behavioural economics, Big bang: deregulation of the City of London, Bretton Woods, business cycle, buttonwood tree, buy and hold, capital asset pricing model, cognitive dissonance, computerized trading, 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 engineering, financial innovation, full employment, Great Leap Forward, index fund, invention of movable type, Isaac Newton, John Nash: game theory, John von Neumann, Kenneth Arrow, linear programming, loss aversion, Louis Bachelier, mental accounting, moral hazard, Myron Scholes, Nash equilibrium, Norman Macrae, Paul Samuelson, Philip Mirowski, Post-Keynesian economics, probability theory / Blaise Pascal / Pierre de Fermat, prudent man rule, random walk, Richard Thaler, Robert Shiller, Robert Solow, spectrum auction, statistical model, stocks for the long run, The Bell Curve by Richard Herrnstein and Charles Murray, The Wealth of Nations by Adam Smith, Thomas Bayes, trade route, transaction costs, tulip mania, Vanguard fund, zero-sum game

He was short and plump, carried an enormous head set off by a thick spade beard and splendid mustache, was myopic, stooped, distraught in speech, absent-minded and wore pince-nez glasses attached to a black silk ribbon.5 Poincare was another mathematician in the long line of child prodigies that we have met along the way. He grew up to be the leading French mathematician of his time. Nevertheless, Poincare made the great mistake of underestimating the accomplishments of a student named Louis Bachelier, who earned a degree in 1900 at the Sorbonne with a dissertation titled "The Theory of Speculation."6 Poincare, in his review of the thesis, observed that "M. Bachelier has evidenced an original and precise mind [but] the subject is somewhat remote from those our other candidates are in the habit of treating."

[I]t is meaningless and fatally misleading to speak of the probability, in an objective sense, that a judgment is correct."12 Knight, like Arrow, had no liking for clouds of vagueness. Knight's ideas are particularly relevant to financial markets, where all decisions reflect a forecast of the future and where surprise occurs regularly. Louis Bachelier long ago remarked, "Clearly the price considered most likely by the market is the true current price: if the market judged otherwise, it would quote not this price, but another price higher or lower." The consensus forecasts embedded in security prices mean that those prices will not change if the expected happens.

Perhaps they ignored the challenge of valuing an option because the key to the puzzle is in the price of uncertainty, a concept that seems more appropriate to our own times than it may have seemed to theirs. The first effort to use mathematics rather than intuition in valuing an option was made by Louis Bachelier back in 1900. In the 1950s and 1960s, a few more people tried their hands at it, including Paul Samuelson. The puzzle was finally solved in the late 1960s by an odd threesome, none of whom was yet thirty years old when their collaboration began.' Fischer Black was a physicist-mathematician with a doctorate from Harvard who had never taken a course in economics or finance.


Investment: A History by Norton Reamer, Jesse Downing

activist fund / activist shareholder / activist investor, Alan Greenspan, Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Bear Stearns, behavioural economics, Berlin Wall, Bernie Madoff, book value, break the buck, Brownian motion, business cycle, buttonwood tree, buy and hold, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, Cornelius Vanderbilt, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, dogs of the Dow, 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, flying shuttle, Glass-Steagall Act, Gordon Gekko, Henri Poincaré, Henry Singleton, high net worth, impact investing, index fund, information asymmetry, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, John Bogle, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, managed futures, margin call, means of production, Menlo Park, merger arbitrage, Michael Milken, money market fund, moral hazard, mortgage debt, Myron Scholes, negative equity, Network effects, new economy, Nick Leeson, Own Your Own Home, Paul Samuelson, pension reform, Performance of Mutual Funds in the Period, Ponzi scheme, Post-Keynesian economics, price mechanism, principal–agent problem, profit maximization, proprietary trading, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Sand Hill Road, Savings and loan crisis, seminal paper, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, survivorship bias, tail risk, technology bubble, Teledyne, The Wealth of Nations by Adam Smith, time value of money, tontine, too big to fail, transaction costs, two and twenty, underbanked, Vanguard fund, working poor, yield curve

Indeed, the demand curve for a financial asset is far more complicated and subject to much greater change than it is, for example, for consumer goods, in which case it emerges out of simple human desires to consume certain quantities of the good at particular prices. What, then, is the appropriate way to think about pricing financial assets? The Father of Mathematical Finance It has been said that mathematical finance emerged largely out of Louis Bachelier’s work on the theory of derivatives pricing at the turn of the twentieth century. Bachelier’s father was a vendor of wine who also dabbled in science as a hobby. When Louis’s parents died abruptly after he achieved his bachelor’s degree, he found himself thrust into the position of steward of his family’s business.

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 man who, in a sense, connected the earlier work of Louis Bachelier to that of Black and Scholes, described later, was Paul Samuelson. Samuelson made a stunning breadth of contributions to economics until the end of his life at the age of ninety-four. Hailing from Gary, Indiana, he studied at the University of Chicago in the early 1930s, taking several classes alongside such distinguished classmates as Milton Friedman.

.; Dan Kedmey, “2 Years and 900 Pages Later, the Volcker Rule Gets the Green Light,” TIME.com, December 11, 2013, http://business.time .com/2013/12/11/2-years-and-900-pages-later-the-volcker-rule-gets -the-green-light. Carmen M. Reinhart and Kenneth S. Rogoff, This Time Is Different: Eight Centuries of Financial Folly (Princeton, NJ: Princeton University Press, 2011), xliv–xlv and 238–239. 7. THE EMERGENCE OF INVESTMENT THEORY 1. Jean-Michel Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” Mathematical Finance 10, no. 3 (July 2000): 342–343. 370 7. The Emergence of Investment Theory 2. Ibid., 341–344. 3. Ibid., 346–347. 4. “Fisher, Irving” in Concise Encyclopedia of Economics, ed. David R. Henderson, Library of Economics and Liberty, 2008, http://www .econlib.org/library/Enc/bios/Fisher.html. 5.


pages: 665 words: 159,350

Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else by Jordan Ellenberg

Albert Einstein, AlphaGo, Andrew Wiles, autonomous vehicles, British Empire, Brownian motion, Charles Babbage, Claude Shannon: information theory, computer age, coronavirus, COVID-19, deep learning, DeepMind, Donald Knuth, Donald Trump, double entry bookkeeping, East Village, Edmond Halley, Edward Jenner, Elliott wave, Erdős number, facts on the ground, Fellow of the Royal Society, Geoffrey Hinton, germ theory of disease, global pandemic, government statistician, GPT-3, greed is good, Henri Poincaré, index card, index fund, Isaac Newton, Johannes Kepler, John Conway, John Nash: game theory, John Snow's cholera map, Louis Bachelier, machine translation, Mercator projection, Mercator projection distort size, especially Greenland and Africa, Milgram experiment, multi-armed bandit, Nate Silver, OpenAI, Paul Erdős, pets.com, pez dispenser, probability theory / Blaise Pascal / Pierre de Fermat, Ralph Nelson Elliott, random walk, Rubik’s Cube, self-driving car, side hustle, Snapchat, social distancing, social graph, transcontinental railway, urban renewal

Taqqu, “Bachelier and His Times: A Conversation with Bernard Bru,” Finance and Stochastics 5, no. 1 (2001): 5, from which most of this account is drawn. Jean-Michel Courtault et al., in “Louis Bachelier on the Centenary of Theorie de la Speculation,” Mathematical Finance 10, no. 3 (July 2000): 341–53, says on p. 343 that Bachelier’s grades were quite good. Dreyfus was convicted: All material on Poincaré and the Dreyfus affair is from Gray, Henri Poincaré, 166–69. “[O]ne might fear”: Courtault et al., “Louis Bachelier on the Centenary of Théorie de la Spéculation,” 348. Bachelier did end up: The story of Bachelier is drawn from Taqqu, “Bachelier and His Times,” 3–32.

It was once often called a “drunkard’s walk,” though in the kinder present era most people no longer think of a life-ruining addiction as an amusing peg to hang a mathematical concept on. A RANDOM WALK TO THE BOURSE Ross and Pearson weren’t the only people thinking about random walks as the new century rolled in. In Paris, Louis Bachelier, a young man from Normandy, was working at the Bourse, the great stock exchange at the financial center of France. He began studying mathematics at the Sorbonne in the 1890s, taking great interest in the probability courses, which were taught by Henri Poincaré. Bachelier was not a typical student; an orphan, he had to work for his living, and hadn’t received the lycée training that had molded most of his peers in the styles and mores of French mathematics.

In 1926 he fell ill from a nasty infestation of parasitic amoebas, and he had to move back to the United States. A few years afterward, the stock market went haywire and threw the world into depression, so Elliott had a lot of free time, and a lot of motivation to restore some order to a financial world that no longer fit into neat double-entry bookkeeping. Elliott surely didn’t know about Louis Bachelier’s work on stock prices as a random walk, but if he had, he wouldn’t have given it a minute. He didn’t want to believe stock prices were randomly jittering like dust suspended in fluid. He wanted something more like the comforting physical laws that kept the planets safely in their orbits. Elliott compared himself to Edmond Halley, who figured out in the seventeenth century that the apparently random comings and goings of comets actually obeyed a rigid timetable.


pages: 374 words: 114,600

The Quants by Scott Patterson

Alan Greenspan, Albert Einstein, AOL-Time Warner, asset allocation, automated trading system, Bear Stearns, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, Blythe Masters, Bonfire of the Vanities, book value, Brownian motion, buttonwood tree, buy and hold, buy low sell high, capital asset pricing model, Carl Icahn, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, commoditize, computerized trading, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Dr. Strangelove, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, Financial Modelers Manifesto, fixed income, Glass-Steagall Act, global macro, Gordon Gekko, greed is good, Haight Ashbury, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, index fund, invention of the telegraph, invisible hand, Isaac Newton, Jim Simons, job automation, John Meriwether, John Nash: game theory, junk bonds, Kickstarter, law of one price, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, margin call, Mark Spitznagel, merger arbitrage, Michael Milken, military-industrial complex, money market fund, Myron Scholes, NetJets, new economy, offshore financial centre, old-boy network, Paul Lévy, Paul Samuelson, Ponzi scheme, proprietary trading, quantitative hedge fund, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Robert Mercer, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Savings and loan crisis, Sergey Aleynikov, short selling, short squeeze, 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

(The mystery remained unsolved for decades, until Albert Einstein, in 1905, discovered that the strange movement, by then known as Brownian motion, was the result of millions of microscopic particles buzzing around in a frantic dance of energy.) The connection between Brownian motion and market prices was made in 1900 by a student at the University of Paris named Louis Bachelier. That year, he’d written a dissertation called “The Theory of Speculation,” an attempt to create a formula that would capture the movement of bonds on the Paris stock exchange. The first English translation of the essay, which had lapsed into obscurity until it resurfaced again in the 1950s, had been included in the book about the market’s randomness that Thorp had read in New Mexico.

Everywhere he looked he saw the same thing: huge leaps where they didn’t belong—on the outer edges of the bell curve. After combing through the data, Mandelbrot wrote a paper detailing his findings, “The Variation of Certain Speculative Prices.” Published as an internal research report at IBM, it was a direct attack on the normal distributions used to model the market. While praising Louis Bachelier, a personal hero of Mandelbrot’s, the mathematician asserted that “the empirical distributions of price changes are usually too ‘peaked’ relative to samples” from standard distributions. The reason: “Large price changes are much more frequent than predicted.” Mandelbrot proposed an alternative method to measure the erratic behavior of prices, one that borrows a mathematical technique devised by the French mathematician Paul Lévy, whom he’d studied under in Paris.

The future, therefore, is random, a Brownian motion coin flip, a drunkard’s walk through the Parisian night. The groundwork for the efficient-market hypothesis had begun in the 1950s with the work of Markowitz and Sharpe, who eventually won the Nobel Prize for economics (together with Merton Miller) in 1990 for their work. Another key player was Louis Bachelier, the obscure French mathematician who argued that bond prices move according to a random walk. In 1954, MIT economist Paul Samuelson—another future Nobel laureate—received a postcard from Leonard “Jimmie” Savage, a statistician at Chicago. Savage had been searching through stacks at a library and stumbled across the work of Bachelier, which had largely been forgotten in the half century since it had been written.


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A Mathematician Plays the Stock Market by John Allen Paulos

Alan Greenspan, AOL-Time Warner, Benoit Mandelbrot, Black-Scholes formula, book value, Brownian motion, business climate, business cycle, butter production in bangladesh, butterfly effect, capital asset pricing model, confounding variable, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, dogs of the Dow, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, equity risk premium, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, intangible asset, invisible hand, Isaac Newton, it's over 9,000, John Bogle, John Nash: game theory, Larry Ellison, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Myron Scholes, Nash equilibrium, Network effects, passive investing, Paul Erdős, Paul Samuelson, Plato's cave, Ponzi scheme, power law, price anchoring, Ralph Nelson Elliott, random walk, Reminiscences of a Stock Operator, Richard Thaler, risk free rate, Robert Shiller, short selling, six sigma, Stephen Hawking, stocks for the long run, survivorship bias, transaction costs, two and twenty, ultimatum game, UUNET, Vanguard fund, Yogi Berra

This may be why market pundits seem so much more certain than, say, sports commentators, who are comparatively frank in acknowledging the huge role of chance. Efficiency and Random Walks The Efficient Market Hypothesis formally dates from the 1964 dissertation of Eugene Fama, the work of Nobel prize-winning economist Paul Samuelson, and others in the 1960s. Its pedigree, however, goes back much earlier, to a dissertation in 1900 by Louis Bachelier, a student of the great French mathematician Henri Poincare. The hypothesis maintains that at any given time, stock prices reflect all relevant information about the stock. In Fama’s words: “In an efficient market, competition among the many intelligent participants leads to a situation where, at any point in time, actual prices of individual securities already reflect the effects of information based both on events that have already occurred and on events which, as of now, the market expects to take place in the future.”

Although the practice and theory of insurance have a long history (Lloyd’s of London dates from the late seventeenth century), it wasn’t until 1973 that a way was found to rationally assign costs to options. In that year Fischer Black and Myron Scholes published a formula that, although much refined since, is still the basic valuation tool for options of all sorts. Their work and that of Robert Merton won the Nobel prize for economics in 1997. Louis Bachelier, whom I mentioned in chapter 4, also devised a formula for options more than one hundred years ago. Bachelier’s formula was developed in connection with his famous 1900 doctoral dissertation in which he was the first to conceive of the stock market as a chance process in which price movements up and down were normally distributed.


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

Abraham Wald, Alan Greenspan, Albert Einstein, An Inconvenient Truth, Andrei Shleifer, anti-communist, AOL-Time Warner, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black Monday: stock market crash in 1987, Black-Scholes formula, Blythe Masters, book value, Bretton Woods, British Empire, business cycle, capital asset pricing model, carbon tax, Carl Icahn, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, corporate raider, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, different worldview, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial engineering, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, Garrett Hardin, George Akerlof, Glass-Steagall Act, global supply chain, Gunnar Myrdal, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, information asymmetry, Intergovernmental Panel on Climate Change (IPCC), invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kickstarter, laissez-faire capitalism, Landlord’s Game, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, low interest rates, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, military-industrial complex, Minsky moment, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, Myron Scholes, Naomi Klein, negative equity, Network effects, Nick Leeson, Nixon triggered the end of the Bretton Woods system, Northern Rock, paradox of thrift, Pareto efficiency, Paul Samuelson, Phillips curve, Ponzi scheme, precautionary principle, price discrimination, price stability, principal–agent problem, profit maximization, proprietary trading, 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 Solow, Ronald Coase, Ronald Reagan, Savings and loan crisis, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, subprime mortgage crisis, tail risk, Tax Reform Act of 1986, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, Tragedy of the Commons, transaction costs, Two Sigma, unorthodox policies, value at risk, Vanguard fund, Vilfredo Pareto, wealth creators, zero-sum game

Before too long, other investors will hear about the geniuses’ methods and copy them. When this happens, the market will incorporate the new information, and the juicy returns that the geniuses were making will be arbitraged away. Prediction will no longer work, and the market will return to a state of being unfathomable. The first person to develop this type of logic was Louis Bachelier, a French mathematician who, way back in 1900, wrote a doctoral dissertation entitled “The Theory of Speculation.” Take an individual stock. At any moment in time, Bachelier observed, some optimists think it will go up; some pessimists think it will go down. If there are more of the former than the latter, their purchases will bid the price up.

Mutual funds were able to insure themselves against the risk of corporations defaulting on their bonds, banks could insure themselves against some of their lenders defaulting, and insurance companies could insure against the chances of a freak hurricane leaving them with enormous claims from their policyholders. In each of these areas, the key was the development of mathematical methods to price risk. Almost all of these methods relied, to some extent, on the Black-Scholes formula and the bell curve. Simply by invoking the ghost of Louis Bachelier, it was possible to take much of the danger out of finance. Or was it? As far back as the 1960s and ’70s, some academics and Wall Street practitioners didn’t buy into the coin-tossing view of finance. Many old-school bankers and traders were put off by the mathematical demands it came with, but numbered among the skeptics were also some technically adept economists, including Sanford Grossman, of Wharton, and Joseph Stiglitz, who is now at Columbia.

The defenders of VAR sidestepped this problem by redefining risk as volatility and assuming that the future would resemble recent history. In the simplest version of VAR, which involves a portfolio consisting of a single asset class, the risk modeler calls up some data and looks at how much the portfolio has jumped around in the past, perhaps by calculating its standard deviation. The next step involves invoking the ghost of Louis Bachelier—this is where the illusion of predictability comes in—and assuming that daily movements in financial prices follow the bell curve, or normal distribution, which places exact numbers on the likelihood of unlikely events. (For example, in any given trading session the probability of a stock rising or falling by more than three times its standard deviation is about 0.003, less than one in three hundred.)


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Crisis Economics: A Crash Course in the Future of Finance by Nouriel Roubini, Stephen Mihm

Alan Greenspan, Asian financial crisis, asset-backed security, balance sheet recession, bank run, banking crisis, barriers to entry, Bear Stearns, behavioural economics, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, bond market vigilante , bonus culture, Bretton Woods, BRICs, British Empire, business cycle, call centre, capital controls, Carmen Reinhart, central bank independence, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency risk, dark matter, David Ricardo: comparative advantage, debt deflation, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, fiat currency, financial deregulation, financial engineering, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, Glass-Steagall Act, global pandemic, global reserve currency, Gordon Gekko, Greenspan put, Growth in a Time of Debt, housing crisis, Hyman Minsky, information asymmetry, interest rate swap, invisible hand, Joseph Schumpeter, junk bonds, Kenneth Rogoff, laissez-faire capitalism, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, market bubble, market fundamentalism, Martin Wolf, means of production, Minsky moment, money market fund, moral hazard, mortgage debt, mortgage tax deduction, new economy, Northern Rock, offshore financial centre, oil shock, Paradox of Choice, paradox of thrift, Paul Samuelson, Ponzi scheme, price stability, principal–agent problem, private sector deleveraging, proprietary trading, pushing on a string, quantitative easing, quantitative trading / quantitative finance, race to the bottom, random walk, regulatory arbitrage, reserve currency, risk tolerance, Robert Shiller, Satyajit Das, Savings and loan crisis, savings glut, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, subprime mortgage crisis, Suez crisis 1956, The Great Moderation, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, too big to fail, tulip mania, Tyler Cowen, unorthodox policies, value at risk, We are all Keynesians now, Works Progress Administration, yield curve, Yom Kippur War

Samuels, Jeff E. Biddle, and John B. Davis, eds., A Companion to the History of Economic Thought (Oxford: Blackwell, 2003), 112-29; Alessandro Roncaglia, The Wealth of Ideas: A History of Economic Thought (Cambridge, U.K.: Cambridge University Press, 2005), 179-243, 278-96, 322-83. 40 Louis Bachelier: Louis Bachelier, “Théorie de la spéculation,” in Annales Scientifiques de l’École Normale Supérieure 3 (1900): 21-86; Justin Fox, The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street (New York: Harper Business, 2009), 6-8. 40 “The consensus of judgment . . .”: Lawrence quoted in John Kenneth Galbraith, The Great Crash, 1929 (Boston: Houghton Mifflin, 1954), 75. 41 postwar academic departments: Fox, Myth of the Rational Market, 89-107. 41 “random walk” theory: Burton G.

Faith in the fundamental stability of markets gave rise to an important corollary: if markets are fundamentally self-regulating, and their collective wisdom is always right, then the prices of assets bought and sold in the market are accurate and justified. Early-twentieth-century economists tried to give this theory some mathematical validity. They relied in part on the work of French mathematician Louis Bachelier, whose Théorie de la spéculation, completed in 1900, argued that an asset’s price accurately reflects all known information about it. There is no such thing, in his view, as an undervalued or overvalued asset; the market is a perfect reflection of the underlying fundamentals. To be sure, asset prices change, often dramatically, but merely as a rational and automatic response to the arrival of new information.


The Fractalist by Benoit Mandelbrot

Albert Einstein, Benoit Mandelbrot, Brownian motion, business cycle, Claude Shannon: information theory, discrete time, double helix, financial engineering, Georg Cantor, Henri Poincaré, Honoré de Balzac, illegal immigration, Isaac Newton, iterative process, Johannes Kepler, John von Neumann, linear programming, Louis Bachelier, Louis Blériot, Louis Pasteur, machine translation, mandelbrot fractal, New Journalism, Norbert Wiener, Olbers’ paradox, Paul Lévy, power law, Richard Feynman, statistical model, urban renewal, Vilfredo Pareto

Two Pictures of Price Variation How do prices vary on the organized markets called bourses, stock exchanges, or commodity exchanges? For centuries, such markets have thrived without the benefit of a systematic mathematical model. The first such model was put forward in 1900 by an outsider in French mathematics, Louis Bachelier (1870–1946). It came out astonishingly early—well ahead of its time—and was odd indeed. It became the standard financial model, and was the one Houthakker was using with cotton prices. The model was advanced financially, but not buttressed by any data whatsoever. Originally, it drew little attention, but over time two events revived it.

While I would be elected on the basis of my work in finance, I could teach anything I chose. This mattered to few persons other than me. I realize now that I was about to be pushed out of the economic mainstream by a major step in academic economics: the 1972 revival by Black-Scholes-Merton of the formula of Louis Bachelier. Could I have both fought and outwaited them in a protected site? Unfortunately, the downside was big. From the viewpoint of the dream that ruled my life, the timing was dreadful. Fractal geometry was on a roll, and at IBM I had squirreled away sufficient resources to prepare the 1975 French book and undertake a longer English one.


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

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", Albert Einstein, anti-communist, asset allocation, Bear Stearns, beat the dealer, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bletchley Park, Brownian motion, buy and hold, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, Edward Thorp, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial engineering, Henry Singleton, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John Meriwether, John von Neumann, junk bonds, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Michael Milken, Myron Scholes, New Journalism, Norbert Wiener, offshore financial centre, Paul Samuelson, publish or perish, quantitative trading / quantitative finance, random walk, risk free rate, risk tolerance, risk-adjusted returns, Robert Shiller, Ronald Reagan, Rubik’s Cube, short selling, speech recognition, statistical arbitrage, Teledyne, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond, zero-sum game

It was rumored that Savage’s peripatetic career had something to do with his habit of informing associates of their stupidity. In 1954 Savage was looking for a book on a library shelf. He came across a slim volume by Louis Bachelier. The thesis of Bachelier’s book was that the changes in stock prices are completely random. Savage sent postcards to a number of people he thought might be interested, including Samuelson. On the cards Savage wrote, “Ever hear of this guy?” The answer was no. The world had forgotten Louis Bachelier. His 1900 thesis, “A Theory of Speculation,” argued that the day-to-day changes in stock prices are fundamentally unpredictable. When a stock’s price reflects everything known about a company and all reasonable projections, then future changes in price should be, by definition, unpredictable.


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, book value, Bretton Woods, Brownian motion, business cycle, capital asset pricing model, Cass Sunstein, classic study, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, Cornelius Vanderbilt, 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, equity risk premium, financial engineering, 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, land bank, Louis Bachelier, low interest rates, 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, public intellectual, quantitative trading / quantitative finance, random walk, Richard Thaler, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, subprime mortgage crisis, Suez canal 1869, Suez crisis 1956, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, tontine, too big to fail, trade liberalization, trade route, transatlantic slave trade, tulip mania, wage slave

We meet several interesting figures; the first is the Parisian broker and financial economist Jules Regnault, who developed the theory of efficient markets. The second is Henri Lefèvre, the accountant for the Rothschild bank in Paris who designed a way to calculate complex positions of stocks and bonds simultaneously. The third is Louis Bachelier, the French academic mathematician whose fascination with pricing options trading on the Paris Bourse led to the discovery of Brownian motion—an abstract model of how a system evolves through time. Together, their insights led to virtually all the tools of modern financial engineering. The limitations of these tools ultimately exposed the potential for failure of even our most complex models.

., two years rather than one month) should also be worth more money because of the rule Jules Regnault came up with: the expected price change (up or down) grows with time. BROWNIAN MOTION These general intuitions about what makes options more or less expensive can only get you so far. Toward the end of the nineteenth century, a French mathematician, Louis Bachelier (1870–1946), developed a mathematical technique for calculating the precise prices of options. As expected, it required as an input to the equation the riskiness of the stock—what Regnault had earlier called its “vibration.” It also required the time period for which the option is granted (the “maturity” of the option).

Lévy’s research focused on “stochastic processes”: mathematical models that describe the behavior of some variable through 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.


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Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures by Frank J. Fabozzi

algorithmic trading, Benoit Mandelbrot, Black Monday: stock market crash in 1987, capital asset pricing model, collateralized debt obligation, correlation coefficient, distributed generation, diversified portfolio, financial engineering, fixed income, global macro, index fund, junk bonds, Louis Bachelier, Myron Scholes, p-value, power law, quantitative trading / quantitative finance, random walk, risk free rate, risk-adjusted returns, short selling, stochastic volatility, subprime mortgage crisis, Thomas Bayes, transaction costs, value at risk

Complex derivative instruments such as options, caps, floors, and swaptions can only be valued (i.e., priced) using tools from probability and statistical theory. While the model for such pricing was first developed by Black and Scholes (1976) and known as the Black-Scholes option pricing model, it relies on models that can be traced back to the mathematician Louis Bachelier (1900). In the remainder of this introductory chapter, we do two things. First, we briefly distinguish between the study of probability and the study of statistics. Second, we provide a roadmap for the chapters to follow in this book. PROBABILITY VS. STATISTICS Thus far, we have used the terms “probability” and “statistics” collectively as if they were one subject.

For example, in equation (D.3), we bound the integral by the P(Sτ ≤ K)-quantile K of the probability distribution of Sτ.313 Then, we saw how quantiles changed as we replace one random variable with another. This was displayed, for example, in the second equation of equation (D.6) where K was the P(Sτ ≤ K)-quantile of Sτ, which translated into the P(Sτ ≤ K)-quantile K/S0 of the new random variable Y = Sτ/S0. References Bachelier, Louis. [1900] 2006. Louis Bachelier’s Theory of Speculation: The Origins of Modern Finance. Translated by Mark Davis and Alison Etheridge. Princeton, N.J.: Princeton university Press. Barndorff-Nielsen, Ole E. 1997. “Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling.” Scandinavian Journal of Statistics 24 (1): 1-13.


pages: 741 words: 179,454

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

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", "there is no alternative" (TINA), "World Economic Forum" Davos, affirmative action, Alan Greenspan, Albert Einstein, algorithmic trading, Andy Kessler, AOL-Time Warner, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Bear Stearns, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, book value, Bretton Woods, BRICs, British Empire, business cycle, buy the rumour, sell the news, capital asset pricing model, carbon credits, Carl Icahn, Carmen Reinhart, carried interest, Celtic Tiger, clean water, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, corporate raider, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency risk, Daniel Kahneman / Amos Tversky, deal flow, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Dr. Strangelove, Dutch auction, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Everybody Ought to Be Rich, Fall of the Berlin Wall, financial engineering, financial independence, financial innovation, financial thriller, fixed income, foreign exchange controls, full employment, Glass-Steagall Act, global reserve currency, Goldman Sachs: Vampire Squid, Goodhart's law, Gordon Gekko, greed is good, Greenspan put, happiness index / gross national happiness, haute cuisine, Herman Kahn, high net worth, Hyman Minsky, index fund, information asymmetry, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, James Carville said: "I would like to be reincarnated as the bond market. You can intimidate everybody.", job automation, Johann Wolfgang von Goethe, John Bogle, John Meriwether, joint-stock company, Jones Act, Joseph Schumpeter, junk bonds, Kenneth Arrow, Kenneth Rogoff, Kevin Kelly, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, market bubble, market fundamentalism, Market Wizards by Jack D. Schwager, Marshall McLuhan, Martin Wolf, mega-rich, merger arbitrage, Michael Milken, Mikhail Gorbachev, Milgram experiment, military-industrial complex, Minsky moment, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Myron Scholes, Naomi Klein, National Debt Clock, negative equity, NetJets, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, Paul Samuelson, pets.com, Philip Mirowski, Phillips curve, planned obsolescence, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, proprietary trading, public intellectual, quantitative easing, quantitative trading / quantitative finance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, Reminiscences of a Stock Operator, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Thaler, Right to Buy, risk free rate, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Rod Stewart played at Stephen Schwarzman birthday party, rolodex, Ronald Reagan, Ronald Reagan: Tear down this wall, Satyajit Das, savings glut, shareholder value, Sharpe ratio, short selling, short squeeze, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, stock buybacks, survivorship bias, tail risk, Teledyne, 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 new new thing, The Predators' Ball, The Theory of the Leisure Class by Thorstein Veblen, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, two and twenty, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond, zero-sum game

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.

Insurance, with its long history, offered guidance on valuation. The insurer’s profit was the difference between statistical loss experience, based on historical knowledge of claims, and the premiums paid, plus investment income on the premiums. Applying insurance theory to options proved difficult. Louis Bachelier applied random walk models to pricing options. Paul Cootner and Paul Samuleson worked on the problem. In their 1967 book Beat the Market, mathematicians Sheen Kassouf and Edward Thorp outlined the relationship between the price of an option and the price of the underlying stock. Thorp, whose interest was gambling and beating the casino at roulette and baccarat, developed a model, anticipating the Black-Scholes equation.


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 engineering, 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

This includes a discussion of the difference between hedging stock portfolios with forwards and hedging with futures; 11. an entry into understanding swaps, by viewing them as structured products, based on the forward concept; 12. the difference between commodity and interest rate swaps, and a detailed explanation of what it means to pay fixed and receive floating in an interest rate swap; 13. understanding Eurodollar futures strips, notation shifts, and the role of the quote mechanism; 14. discussion of swaps as a zero-sum game, and research challenges to the comparative advantage argument; 15. swaps pricing and alternative interpretations of the par swap rate; 16. a step-by-step approach to options starting in Chapter 9 with the usual emphasis on the quote mechanism, as well as incorporation of real asset options examples; 17. an American option pricing model in Chapter 9, and its extension to European options in Chapter 11; 18. the importance of identifying short, not just long, positions in an underlying asset and the hedging demand they create; 19. two chapters on option trading strategies; one basic, one advanced, including the three types of covered calls, the protective put strategy, and their interpretations; 20. a logical categorization of rational option pricing results in Chapter 11, and the inclusion of American puts and calls; 21. neither monotonicity nor convexity, which are usually assumed, are rational option results; 22. partial vs. full static replication of European options; 23. working backwards from payoffs to costs as a method for devising and interpreting derivatives strategies; 24. the introduction of generalized forward contracts paves the way for the connection between (generalized) forward contracts and options, and the discussion of American put-call parity; 25. the Binomial option pricing model, N=1, and why it works—which is not simply no-arbitrage; 26. three tools of modern mathematical finance: no-arbitrage, replicability and complete markets, and dynamic and static replication, and a rule of thumb on the number of hedging vehicles required to hedge a given number of independent sources of uncertainty; 27. static replication in the Binomial option pricing model, N=1, the hedge ratio can be 1.0 and a preliminary discussion in Chapter 13 on the meaning of risk-neutral valuation; 28. dynamic hedging as the new component of the BOPM, N>1, and a path approach to the multi-period Binomial option pricing model; 29. equivalent martingale measures (EMMs) in the representation of option and stock prices; 30. the efficient market hypothesis (EMH) as a guide to modeling prices; 31. arithmetic Brownian motion (ABM) and the Louis Bachelier model of option prices; 32. easy introduction to the tools of continuous time finance, including Itô’s lemma; 33. Black–Scholes derived from Bachelier, illustrating the important connection between these two models; 34. modeling non-constant volatility: the deterministic volatility model and stochastic volatility models; 35. why Black–Scholes is still important; 36. and a final synthesis chapter that includes a discussion of the different senses of risk-neutral valuation, their meaning and economic basis, and a complete discussion of the dynamics of the hedge portfolio in the BOPM, N=1.

Black–Scholes derived from Bachelier, illustrating the important connection between these two models; 34. modeling non-constant volatility: the deterministic volatility model and stochastic volatility models; 35. why Black–Scholes is still important; 36. and a final synthesis chapter that includes a discussion of the different senses of risk-neutral valuation, their meaning and economic basis, and a complete discussion of the dynamics of the hedge portfolio in the BOPM, N=1. I would like to thank the giants of the derivatives field including: Louis Bachelier, Fischer Black, John Cox, Darrell Duffie, Jonathan Ingersoll, Kiyoshi Itô, Robert Merton, Paul Samuelson, Myron Scholes, Stephen Ross, Mark Rubinstein, and many others. I sincerely hope that the reader enjoys traveling along the path to understanding Derivatives Markets. David Goldenberg Independent researcher, NY, USA ACKNOWLEDGMENTS I would like to thank everyone at Routledge for their hard work on this book.


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, Alan Greenspan, Albert Einstein, Andrei Shleifer, asset allocation, Atul Gawande, backtesting, beat the dealer, Black Swan, book value, 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, financial engineering, forensic accounting, Henry Singleton, hindsight bias, intangible asset, Jim Simons, Louis Bachelier, p-value, passive investing, performance metric, quantitative hedge fund, random walk, Richard Thaler, risk free rate, risk-adjusted returns, Robert Shiller, shareholder value, Sharpe ratio, short selling, statistical model, stock buybacks, survivorship bias, systematic trading, Teledyne, The Myth of the Rational Market, time value of money, transaction costs

They started meeting together once a week in an effort to solve the warrant valuation conundrum. Thorp found the answer in an unlikely place. 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.


pages: 345 words: 86,394

Frequently Asked Questions in Quantitative Finance by Paul Wilmott

Abraham Wald, Albert Einstein, asset allocation, beat the dealer, Black-Scholes formula, Brownian motion, butterfly effect, buy and hold, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, currency risk, delta neutral, discrete time, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial engineering, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, lateral thinking, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, power law, quantitative trading / quantitative finance, random walk, regulatory arbitrage, risk free rate, 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

This idea of the random walk has permeated many scientific fields and is commonly used as the model mechanism behind a variety of unpredictable continuous-time processes. The lognormal random walk based on Brownian motion is the classical paradigm for the stock market. See Brown (1827). 1900 Bachelier Louis Bachelier was the first to quantify the concept of Brownian motion. He developed a mathematical theory for random walks, a theory rediscovered later by Einstein. He proposed a model for equity prices, a simple normal distribution, and built on it a model for pricing the almost unheard of options. His model contained many of the seeds for later work, but lay ‘dormant’ for many, many years.


pages: 335 words: 94,657

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

asset allocation, behavioural economics, book value, buy and hold, buy low sell high, corporate governance, correlation coefficient, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, endowment effect, estate planning, financial engineering, financial independence, financial innovation, high net worth, index fund, John Bogle, junk bonds, late fees, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, margin call, market bubble, mental accounting, money market fund, passive investing, Paul Samuelson, random walk, risk tolerance, risk/return, Sharpe ratio, statistical model, stocks for the long run, survivorship bias, the rule of 72, transaction costs, Vanguard fund, yield curve, zero-sum game

They have given us sophisticated theories that we can use to select our investments and combine them in the most efficient manner to give us maximum return with minimum volatility. THE EFFICIENT MARKET THEORY (EMT) To understand EMT, we'll go back to the year 1900 when a young French mathematician named Louis Bachelier wrote his Ph.D. thesis, which contained the seeds of the Efficient Market Theory. EMT can be described as "an investment theory that states that it is impossible to `beat the market' because existing share prices already incorporate and reflect all relevant information." Another student of the stock market was Alfred Cowles, who came to prominence about 20 years later.


Concentrated Investing by Allen C. Benello

activist fund / activist shareholder / activist investor, asset allocation, barriers to entry, beat the dealer, Benoit Mandelbrot, Bob Noyce, Boeing 747, book value, business cycle, buy and hold, carried interest, Claude Shannon: information theory, corporate governance, corporate raider, delta neutral, discounted cash flows, diversification, diversified portfolio, Dutch auction, Edward Thorp, family office, fixed income, Henry Singleton, high net worth, index fund, John Bogle, John von Neumann, junk bonds, Louis Bachelier, margin call, merger arbitrage, Paul Samuelson, performance metric, prudent man rule, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, shareholder value, Sharpe ratio, short selling, survivorship bias, technology bubble, Teledyne, transaction costs, zero-sum game

His research led him to fill three library shelves with books, including Adam Smith’s Wealth of Nations, John von Neumann and Oskar Morgenstern’s Theory of Games and Economic Behavior, Paul Samuelson’s Economics, and Fred Schwed’s Where Are the Customer’s Yachts? In a notebook Shannon recorded a varied list of thinkers, including French mathematician Louis Bachelier, Benjamin 74 Concentrated Investing Graham, and Benoit Mandelbrot. He took notes about margin trading; short selling; stop‐loss orders; the effects of market panics; capital gains taxes and transaction costs. The only surviving document from Shannon’s research is a mimeographed handout from one of the lectures he delivered at MIT in the spring term of 1956, in a class called Seminar of Information Theory.


pages: 289 words: 95,046

Chaos Kings: How Wall Street Traders Make Billions in the New Age of Crisis by Scott Patterson

"World Economic Forum" Davos, 2021 United States Capitol attack, 4chan, Alan Greenspan, Albert Einstein, asset allocation, backtesting, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, bitcoin, Bitcoin "FTX", Black Lives Matter, Black Monday: stock market crash in 1987, Black Swan, Black Swan Protection Protocol, Black-Scholes formula, blockchain, Bob Litterman, Boris Johnson, Brownian motion, butterfly effect, carbon footprint, carbon tax, Carl Icahn, centre right, clean tech, clean water, collapse of Lehman Brothers, Colonization of Mars, commodity super cycle, complexity theory, contact tracing, coronavirus, correlation does not imply causation, COVID-19, Credit Default Swap, cryptocurrency, Daniel Kahneman / Amos Tversky, decarbonisation, disinformation, diversification, Donald Trump, Doomsday Clock, Edward Lloyd's coffeehouse, effective altruism, Elliott wave, Elon Musk, energy transition, Eugene Fama: efficient market hypothesis, Extinction Rebellion, fear index, financial engineering, fixed income, Flash crash, Gail Bradbrook, George Floyd, global pandemic, global supply chain, Gordon Gekko, Greenspan put, Greta Thunberg, hindsight bias, index fund, interest rate derivative, Intergovernmental Panel on Climate Change (IPCC), Jeff Bezos, Jeffrey Epstein, Joan Didion, John von Neumann, junk bonds, Just-in-time delivery, lockdown, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, Mark Spitznagel, Mark Zuckerberg, market fundamentalism, mass immigration, megacity, Mikhail Gorbachev, Mohammed Bouazizi, money market fund, moral hazard, Murray Gell-Mann, Nick Bostrom, off-the-grid, panic early, Pershing Square Capital Management, Peter Singer: altruism, Ponzi scheme, power law, precautionary principle, prediction markets, proprietary trading, public intellectual, QAnon, quantitative easing, quantitative hedge fund, quantitative trading / quantitative finance, Ralph Nader, Ralph Nelson Elliott, random walk, Renaissance Technologies, rewilding, Richard Thaler, risk/return, road to serfdom, Ronald Reagan, Ronald Reagan: Tear down this wall, Rory Sutherland, Rupert Read, Sam Bankman-Fried, Silicon Valley, six sigma, smart contracts, social distancing, sovereign wealth fund, statistical arbitrage, statistical model, stem cell, Stephen Hawking, Steve Jobs, Steven Pinker, Stewart Brand, systematic trading, tail risk, technoutopianism, The Chicago School, The Great Moderation, the scientific method, too big to fail, transaction costs, University of East Anglia, value at risk, Vanguard fund, We are as Gods, Whole Earth Catalog

It was a problem, he said, that went back a century to the work of a neurotic French economist in Paris. “Prices of course go up and down, that was known to everybody, and there are all kinds of nice maxims about it,” Mandelbrot said in a thick French accent. “In 1900, an incredible genius looked at the problem. His name was Louis Bachelier. Nobody noticed him. He had a very miserable life. But he wrote in 1900 a [dissertation] in mathematics, believe it or not, called ‘The Theory of Speculation.’ Speculation meant speculation on the stock market or bond market. And he introduced for the first time in loose and incomplete fashion Brownian motion,” he said, referring to the nineteenth-century observation by Scottish botanist Robert Brown that the motion of pollen in a liquid is a random process.


Capital Ideas Evolving by Peter L. Bernstein

Albert Einstein, algorithmic trading, Andrei Shleifer, asset allocation, behavioural economics, Black Monday: stock market crash in 1987, Bob Litterman, book value, business cycle, buy and hold, buy low sell high, capital asset pricing model, commodity trading advisor, computerized trading, creative destruction, currency risk, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, diversification, diversified portfolio, endowment effect, equity premium, equity risk premium, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, fixed income, high net worth, hiring and firing, index fund, invisible hand, Isaac Newton, John Meriwether, John von Neumann, Joseph Schumpeter, Kenneth Arrow, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, market bubble, mental accounting, money market fund, Myron Scholes, paper trading, passive investing, Paul Samuelson, Performance of Mutual Funds in the Period, price anchoring, price stability, random walk, Richard Thaler, risk free rate, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, seminal paper, Sharpe ratio, short selling, short squeeze, Silicon Valley, South Sea Bubble, statistical model, survivorship bias, systematic trading, tail risk, technology bubble, The Wealth of Nations by Adam Smith, transaction costs, yield curve, Yogi Berra, zero-sum game

If capital goes to the wrong uses or does not f low at all, the economy will operate inefficiently, and ultimately economic growth will be low.”1 The data of financial markets reveal, for better or for worse, “the brain of the economy” and “the lifeblood of economic activity.” This extraordinary data bank was the key mechanism that revealed the fundamental character of financial markets as early as 1900 to Louis Bachelier, little-known but surely among the most powerful of finance theorists (see Capital Ideas, pp. 18–23), and later to all to the creators of Capital Ideas. Much more was to follow.* Although time had to pass before practitioners could persuade themselves to accept the implications of theory, the data bank became the stepping-stone to implementation, from the first index fund at Wells Fargo Investment Advisors in 1971 to the diverse activities of today’s practitioners described in this book.


pages: 354 words: 26,550

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

algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business cycle, business process, buy and hold, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, computerized trading, diversification, equity premium, fault tolerance, financial engineering, financial intermediation, fixed income, global macro, high net worth, implied volatility, index arbitrage, information asymmetry, interest rate swap, inventory management, Jim Simons, law of one price, Long Term Capital Management, Louis Bachelier, machine readable, margin call, market friction, market microstructure, martingale, Myron Scholes, New Journalism, p-value, paper trading, performance metric, Performance of Mutual Funds in the Period, pneumatic tube, profit motive, proprietary trading, purchasing power parity, quantitative trading / quantitative finance, random walk, Renaissance Technologies, risk free rate, 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, tail risk, trade route, transaction costs, value at risk, yield curve, zero-sum game

The strong form deals with all kinds of public and nonpublic information; the semistrong form excludes nonpublic information from the information set. As in most contemporary academic literature on market efficiency, we restrict the tests to the weak form analysis only. Non-Parametric Runs Test Several tests of market efficiency have been developed over the years. The very first test, constructed by Louis Bachelier in 1900, measured the probability of a number of consecutively positive or consecutively negative price changes, or “runs.” As with tossing a fair coin, the probability of two successive price changes of the same sign (a positive change followed by a positive change, for example) is 1/(22 ) = 0.25.


pages: 407 words: 104,622

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman

affirmative action, Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, Andrew Wiles, automated trading system, backtesting, Bayesian statistics, Bear Stearns, beat the dealer, behavioural economics, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black Monday: stock market crash in 1987, blockchain, book value, Brownian motion, butter production in bangladesh, buy and hold, buy low sell high, Cambridge Analytica, Carl Icahn, Claude Shannon: information theory, computer age, computerized trading, Credit Default Swap, Daniel Kahneman / Amos Tversky, data science, diversified portfolio, Donald Trump, Edward Thorp, Elon Musk, Emanuel Derman, endowment effect, financial engineering, Flash crash, George Gilder, Gordon Gekko, illegal immigration, index card, index fund, Isaac Newton, Jim Simons, John Meriwether, John Nash: game theory, John von Neumann, junk bonds, Loma Prieta earthquake, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, Mark Zuckerberg, Michael Milken, Monty Hall problem, More Guns, Less Crime, Myron Scholes, Naomi Klein, natural language processing, Neil Armstrong, obamacare, off-the-grid, p-value, pattern recognition, Peter Thiel, Ponzi scheme, prediction markets, proprietary trading, quantitative hedge fund, quantitative trading / quantitative finance, random walk, Renaissance Technologies, Richard Thaler, Robert Mercer, Ronald Reagan, self-driving car, Sharpe ratio, Silicon Valley, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, Steve Bannon, Steve Jobs, stochastic process, the scientific method, Thomas Bayes, transaction costs, Turing machine, Two Sigma

During the 1970s, Thorp helped lead a hedge fund, Princeton/Newport Partners, recording strong gains and attracting well-known investors—including actor Paul Newman, Hollywood producer Robert Evans, and screenwriter Charles Kaufman. Thorp’s firm based its trading on computer-generated algorithms and economic models, using so much electricity that their office in Southern California was always boiling hot. Thorp’s trading formula was influenced by the doctoral thesis of French mathematician Louis Bachelier, who, in 1900, developed a theory for pricing options on the Paris stock exchange using equations similar to those later employed by Albert Einstein to describe the Brownian motion of pollen particles. Bachelier’s thesis, describing the irregular motion of stock prices, had been overlooked for decades, but Thorp and others understood its relevance to modern investing.


pages: 453 words: 111,010

Licence to be Bad by Jonathan Aldred

"Friedman doctrine" OR "shareholder theory", Affordable Care Act / Obamacare, Alan Greenspan, Albert Einstein, availability heuristic, Ayatollah Khomeini, behavioural economics, Benoit Mandelbrot, Berlin Wall, Black Monday: stock market crash in 1987, Black Swan, Capital in the Twenty-First Century by Thomas Piketty, Carmen Reinhart, Cass Sunstein, Charles Babbage, clean water, cognitive dissonance, corporate governance, correlation does not imply causation, cuban missile crisis, Daniel Kahneman / Amos Tversky, Donald Trump, Douglas Engelbart, Douglas Engelbart, Dr. Strangelove, Edward Snowden, fake news, Fall of the Berlin Wall, falling living standards, feminist movement, framing effect, Frederick Winslow Taylor, From Mathematics to the Technologies of Life and Death, full employment, Gary Kildall, George Akerlof, glass ceiling, Glass-Steagall Act, Herman Kahn, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, Jeff Bezos, John Nash: game theory, John von Neumann, Linda problem, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, meta-analysis, Mont Pelerin Society, mutually assured destruction, Myron Scholes, Nash equilibrium, Norbert Wiener, nudge unit, obamacare, offshore financial centre, Pareto efficiency, Paul Samuelson, plutocrats, positional goods, power law, precautionary principle, profit maximization, profit motive, race to the bottom, RAND corporation, rent-seeking, Richard Thaler, ride hailing / ride sharing, risk tolerance, road to serfdom, Robert Shiller, Robert Solow, Ronald Coase, Ronald Reagan, scientific management, Skinner box, Skype, Social Responsibility of Business Is to Increase Its Profits, spectrum auction, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tragedy of the Commons, transaction costs, trickle-down economics, Vilfredo Pareto, wealth creators, zero-sum game

The eighteenth-century French mathematician Abraham de Moivre was the first to realize that repeated random events such as these generate a bell-curve distribution.fn4 The problems begin when we carry over these ideas to the wrong places. Again, Jimmie Savage played a key role. Savage had discovered the work of Louis Bachelier, an obscure French mathematician who in 1900 had published a ‘theory of speculation’ suggesting prices in financial markets move completely randomly. Savage produced the first English translation of Bachelier’s theory, and Bachelier’s ideas gained further attention with the emergence of the ‘efficient market hypothesis’ in the 1960s.


pages: 288 words: 16,556

Finance and the Good Society by Robert J. Shiller

Alan Greenspan, Alvin Roth, bank run, banking crisis, barriers to entry, Bear Stearns, behavioural economics, benefit corporation, Bernie Madoff, buy and hold, 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, democratizing finance, Deng Xiaoping, diversification, diversified portfolio, Donald Trump, Edward Glaeser, eurozone crisis, experimental economics, financial engineering, financial innovation, financial thriller, fixed income, full employment, fundamental attribution error, George Akerlof, Great Leap Forward, Ida Tarbell, income inequality, information asymmetry, invisible hand, John Bogle, joint-stock company, Joseph Schumpeter, Kenneth Arrow, Kenneth Rogoff, land reform, loss aversion, Louis Bachelier, Mahatma Gandhi, Mark Zuckerberg, market bubble, market design, means of production, microcredit, moral hazard, mortgage debt, Myron Scholes, Nelson Mandela, Occupy movement, passive investing, Ponzi scheme, prediction markets, profit maximization, quantitative easing, random walk, regulatory arbitrage, Richard Thaler, Right to Buy, road to serfdom, Robert Shiller, Ronald Reagan, selection bias, self-driving car, shareholder value, Sharpe ratio, short selling, Simon Kuznets, Skype, social contagion, Steven Pinker, tail risk, telemarketer, Thales and the olive presses, Thales of Miletus, The Market for Lemons, The Theory of the Leisure Class by Thorstein Veblen, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, Vanguard fund, young professional, zero-sum game, Zipcar

It can be attacked empirically, but this method of research is likely to be costly.8 It may seem strange that a well-developed options trading industry existed in Schwed’s day and yet there was still no theory of options pricing—a prerequisite that would seem essential to trading in that market. Actually a serviceable options pricing theory had been published in 1900 by the French mathematician Louis Bachelier.9 But there is no evidence that anyone in the options market had even heard of his paper. That did not change until 1964, when the mathematical treatises of A. J. Boness and Case Sprenkle appeared.10 Boness remarked on the strangeness of this: “Investment analysis is largely in a pre-theoretic stage of development.


pages: 436 words: 127,642

When Einstein Walked With Gödel: Excursions to the Edge of Thought by Jim Holt

Ada Lovelace, Albert Einstein, Andrew Wiles, anthropic principle, anti-communist, Arthur Eddington, Benoit Mandelbrot, Bletchley Park, Brownian motion, cellular automata, Charles Babbage, classic study, computer age, CRISPR, dark matter, David Brooks, Donald Trump, Dr. Strangelove, Eddington experiment, Edmond Halley, everywhere but in the productivity statistics, Fellow of the Royal Society, four colour theorem, Georg Cantor, George Santayana, Gregor Mendel, haute couture, heat death of the universe, Henri Poincaré, Higgs boson, inventory management, Isaac Newton, Jacquard loom, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, Large Hadron Collider, Long Term Capital Management, Louis Bachelier, luminiferous ether, Mahatma Gandhi, mandelbrot fractal, Monty Hall problem, Murray Gell-Mann, new economy, Nicholas Carr, Norbert Wiener, Norman Macrae, Paradox of Choice, Paul Erdős, Peter Singer: altruism, Plato's cave, power law, probability theory / Blaise Pascal / Pierre de Fermat, quantum entanglement, random walk, Richard Feynman, Robert Solow, Schrödinger's Cat, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, Skype, stakhanovite, Stephen Hawking, Steven Pinker, Thorstein Veblen, Turing complete, Turing machine, Turing test, union organizing, Vilfredo Pareto, Von Neumann architecture, wage slave

Why should the pattern of ups and downs in the market for cotton bear such a striking resemblance to the wildly unequal way wealth was spread through society? This was certainly not consistent with the orthodox model of financial markets, which was originally proposed in 1900 by a French mathematician named Louis Bachelier (who had copied it from the physics of a gas in equilibrium). According to the Bachelier model, price variation in a stock or commodity market is supposed to be smooth and mild; fluctuations in price, arranged by size, should line up nicely in a classic bell curve. This is the basis of what became known as the efficient market hypothesis.


pages: 505 words: 142,118

A Man for All Markets by Edward O. Thorp

"RICO laws" OR "Racketeer Influenced and Corrupt Organizations", 3Com Palm IPO, Alan Greenspan, Albert Einstein, asset allocation, Bear Stearns, beat the dealer, Bernie Madoff, Black Monday: stock market crash in 1987, Black Swan, Black-Scholes formula, book value, Brownian motion, buy and hold, buy low sell high, caloric restriction, caloric restriction, carried interest, Chuck Templeton: OpenTable:, Claude Shannon: information theory, cognitive dissonance, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Edward Thorp, Erdős number, Eugene Fama: efficient market hypothesis, financial engineering, financial innovation, Garrett Hardin, George Santayana, German hyperinflation, Glass-Steagall Act, Henri Poincaré, high net worth, High speed trading, index arbitrage, index fund, interest rate swap, invisible hand, Jarndyce and Jarndyce, Jeff Bezos, John Bogle, John Meriwether, John Nash: game theory, junk bonds, Kenneth Arrow, Livingstone, I presume, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, Mason jar, merger arbitrage, Michael Milken, Murray Gell-Mann, Myron Scholes, NetJets, Norbert Wiener, PalmPilot, passive investing, Paul Erdős, Paul Samuelson, Pluto: dwarf planet, Ponzi scheme, power law, price anchoring, publish or perish, quantitative trading / quantitative finance, race to the bottom, random walk, Renaissance Technologies, RFID, Richard Feynman, risk-adjusted returns, Robert Shiller, rolodex, Sharpe ratio, short selling, Silicon Valley, Stanford marshmallow experiment, statistical arbitrage, stem cell, stock buybacks, stocks for the long run, survivorship bias, tail risk, The Myth of the Rational Market, The Predators' Ball, the rule of 72, The Wisdom of Crowds, too big to fail, Tragedy of the Commons, uptick rule, Upton Sinclair, value at risk, Vanguard fund, Vilfredo Pareto, Works Progress Administration

Though it was not sufficiently mispriced then, the history of how warrant prices behaved indicated this could happen before it expired in 1975. When it did we bet a significant part of the partnership’s net worth. — We were guided in this trade and thousands of others by a formula that had its beginnings in 1900 in the PhD thesis of French mathematician Louis Bachelier. Bachelier used mathematics to develop a theory for pricing options on the Paris stock exchange (the Bourse). His thesis adviser, the world-famous mathematician Henri Poincaré, didn’t value Bachelier’s effort, and Bachelier spent the rest of his life as an obscure provincial professor. Meanwhile a twenty-six-year-old Swiss patent clerk named Albert Einstein would soon publish in his single “miraculous year” of 1905 a series of articles that would transform physics.


pages: 431 words: 132,416

No One Would Listen: A True Financial Thriller by Harry Markopolos

Alan Greenspan, backtesting, barriers to entry, Bernie Madoff, buy and hold, call centre, centralized clearinghouse, correlation coefficient, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, family office, financial engineering, financial thriller, fixed income, forensic accounting, high net worth, index card, Long Term Capital Management, Louis Bachelier, low interest rates, Market Wizards by Jack D. Schwager, offshore financial centre, payment for order flow, Ponzi scheme, price mechanism, proprietary trading, quantitative trading / quantitative finance, regulatory arbitrage, Renaissance Technologies, risk-adjusted returns, risk/return, rolodex, Sharpe ratio, statistical arbitrage, too big to fail, transaction costs, two and twenty, your tax dollars at work

Like me, maybe even more than me, he could glance at numbers and draw meaningful conclusions from them. At Bentley College, he played a lot of poker, ran a small bookie operation, and came to believe firmly in the efficient markets hypothesis. Believing that concept was where Neil and I differed most. The efficient markets hypothesis, which was first suggested by French mathematician Louis Bachelier in 1900 and was applied to the modern financial markets by Professor Eugene Fama at the University of Chicago in 1965, claims that if all information is simultaneously and freely available to everyone in the market, no one can have an edge. In this hypothesis having an edge means that for all intents and purposes you have accurate information that your competitors don’t have.


pages: 586 words: 159,901

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

accounting loophole / creative accounting, activist fund / activist shareholder / activist investor, affirmative action, Alan Greenspan, Andrei Shleifer, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, bond market vigilante , book value, borderless world, Bretton Woods, British Empire, business cycle, buy the rumour, sell the news, capital asset pricing model, capital controls, Carl Icahn, central bank independence, computerized trading, corporate governance, corporate raider, correlation coefficient, correlation does not imply causation, credit crunch, currency manipulation / currency intervention, currency risk, David Ricardo: comparative advantage, debt deflation, declining real wages, deindustrialization, dematerialisation, disinformation, diversification, diversified portfolio, Donald Trump, equity premium, Eugene Fama: efficient market hypothesis, experimental subject, facts on the ground, financial deregulation, financial engineering, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, George Akerlof, George Gilder, Glass-Steagall Act, hiring and firing, Hyman Minsky, implied volatility, index arbitrage, index fund, information asymmetry, interest rate swap, Internet Archive, invisible hand, Irwin Jacobs, Isaac Newton, joint-stock company, Joseph Schumpeter, junk bonds, kremlinology, labor-force participation, late capitalism, law of one price, liberal capitalism, liquidationism / Banker’s doctrine / the Treasury view, London Interbank Offered Rate, long and variable lags, Louis Bachelier, low interest rates, market bubble, Mexican peso crisis / tequila crisis, Michael Milken, microcredit, minimum wage unemployment, money market fund, moral hazard, mortgage debt, mortgage tax deduction, Myron Scholes, oil shock, Paul Samuelson, payday loans, pension reform, planned obsolescence, plutocrats, Post-Keynesian economics, price mechanism, price stability, prisoner's dilemma, profit maximization, proprietary trading, publication bias, Ralph Nader, random walk, reserve currency, Richard Thaler, risk tolerance, Robert Gordon, Robert Shiller, Savings and loan crisis, selection bias, shareholder value, short selling, Slavoj Žižek, South Sea Bubble, stock buybacks, The inhabitant of London could order by telephone, sipping his morning tea in bed, the various products of the whole earth, 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

In more popular, more ideological versions of efficient market theory, expectations are imbued with an almost mystical importance: the collective wisdom of "the market" is treated as if it were omniscient. Notions of market efficiency have their roots in a long-standing observation that it's damn hard to beat the market, and that prices seem to move in random ways. Louis Bachelier argued in a 1900 study (that was ignored WALL STREET for 60 years) that over the long term, speculators should consistently earn no extraordinary profits; market prices, in other words, are a "fair game." Another precursor of EM theory was Alfred Cowles, who showed in two studies (Cowles 1933; 1944) that a variety of forecasts by pundits and investment professionals yielded results that were at best no better than the overall market, and often quite worse.


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

Alan Greenspan, Albert Einstein, AOL-Time Warner, asset allocation, backtesting, behavioural economics, Benoit Mandelbrot, Black Monday: stock market crash in 1987, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, Charles Babbage, Charles Lindbergh, compound rate of return, corporate governance, COVID-19, credit crunch, currency risk, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, Donald Trump, Edward Glaeser, equity premium, equity risk premium, estate planning, Eugene Fama: efficient market hypothesis, fake news, family office, fear index, fiat currency, financial engineering, 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, Jim Simons, John Bogle, John Meriwether, John von Neumann, joint-stock company, junk bonds, Kenneth Arrow, linear programming, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, managed futures, 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 Solow, Ronald Reagan, Savings and loan crisis, selection bias, seminal paper, 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

(To be fully precise, the stock price should follow a random walk after adjustment for dividends and a risk premium.) The notion of random walks can be traced back to 1827, when botanist Robert Brown used a microscope to examine dust grains floating in water and noticed their erratic behavior, later memorialized as Brownian motion. On March 29, 1900, a French postgraduate student, Louis Bachelier, successfully defended his dissertation, “The Theory of Speculation,” in which he proposed a model of Brownian motion to explain a similarly random movement but in security prices rather than dust grains—five years before Albert Einstein famously determined the cause of Brown’s observations, providing evidence that atoms and molecules existed.2 Bachelier’s research was largely forgotten for half a century until it was rediscovered by University of Chicago mathematician Leonard Jimmie Savage, who translated the work and brought it to the attention of Paul Samuelson, the first American recipient of the Nobel Prize in Economics.


pages: 512 words: 162,977

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

backtesting, beat the dealer, Benoit Mandelbrot, Berlin Wall, Black-Scholes formula, book value, butterfly effect, buy and hold, commodity trading advisor, computerized trading, currency risk, Edward Thorp, Elliott wave, fixed income, full employment, implied volatility, interest rate swap, Louis Bachelier, margin call, market clearing, market fundamentalism, Market Wizards by Jack D. Schwager, money market fund, paper trading, pattern recognition, placebo effect, prediction markets, proprietary trading, Ralph Nelson Elliott, random walk, Reminiscences of a Stock Operator, risk tolerance, risk/return, Saturday Night Live, Sharpe ratio, the map is not the territory, transaction costs, uptick rule, War on Poverty

There are very powerful scientific methods of cyclical analysis, particularly Fourier analysis, which was invented in the nineteenth century, William Eckhardt / 123 essentially to understand heat transfer. Fourier analysis has been tried again and again on market prices, starting in the late nineteenth century with the work of the French mathematician Louis Bachelier. All this scientific research has failed to uncover any systematic cyclic components in price data. This failure argues strongly against the validity of various trading systems based on cycles. And, I want to stress that the techniques for finding cycles are much stronger than the techniques for finding trends.


pages: 442 words: 39,064

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

Alan Greenspan, Asian financial crisis, asset allocation, behavioural economics, Berlin Wall, Black Monday: stock market crash in 1987, Bretton Woods, Brownian motion, business cycle, buy and hold, buy the rumour, sell the news, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial engineering, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, information asymmetry, intangible asset, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, low interest rates, 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, Paul Samuelson, power law, quantitative trading / quantitative finance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, selection bias, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, stocks for the long run, 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

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.


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

3Com Palm IPO, accelerated depreciation, accounting loophole / creative accounting, Airbus A320, Alan Greenspan, AOL-Time Warner, Asian financial crisis, asset allocation, asset-backed security, banking crisis, Bear Stearns, Bernie Madoff, big-box store, Black Monday: stock market crash in 1987, Black-Scholes formula, Boeing 747, book value, break the buck, Brownian motion, business cycle, buy and hold, buy low sell high, California energy crisis, capital asset pricing model, capital controls, Carl Icahn, 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-border payments, cross-subsidies, currency risk, discounted cash flows, disintermediation, diversified portfolio, Dutch auction, equity premium, equity risk premium, eurozone crisis, fear index, financial engineering, 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, James Webb Space Telescope, junk bonds, Kenneth Rogoff, Larry Ellison, law of one price, linear programming, Livingstone, I presume, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, low interest rates, market bubble, market friction, money market fund, moral hazard, Myron Scholes, new economy, Nick Leeson, Northern Rock, offshore financial centre, PalmPilot, 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, Scaled Composites, shareholder value, Sharpe ratio, short selling, short squeeze, Silicon Valley, Skype, SpaceShipOne, Steve Jobs, subprime mortgage crisis, sunk-cost fallacy, systematic bias, 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, vertical integration, yield curve, zero-coupon bond, zero-sum game, Zipcar

These are discussed in Chapter 18. 2See M. G. Kendall, “The Analysis of Economic Time Series, Part I. Prices,” Journal of the Royal Statistical Society 96 (1953), pp. 11–25. Kendall’s idea was not wholly new. It had been proposed in an almost forgotten thesis written 53 years earlier by a French doctoral student, Louis Bachelier. Bachelier’s accompanying development of the mathematical theory of random processes anticipated by five years Einstein’s famous work on the random Brownian motion of colliding gas molecules. See L. Bachelier, Théorie de la Speculation (Paris: Gauthiers-Villars, 1900). Reprinted in English (A.

Finance, finance.yahoo.com Now look at the quotes for options maturing in April 2012 and January 2013. Notice how the option price increases as option maturity is extended. For example, at an exercise price of $400, the December 2011 call option costs $24.30, the April 2012 option costs $44.05, and the January 2013 option costs $70.00. In Chapter 13 we met Louis Bachelier, who in 1900 first suggested that security prices follow a random walk. Bachelier also devised a very convenient shorthand to illustrate the effects of investing in different options. We use this shorthand to compare a call option and a put option on Apple stock. The position diagram in Figure 20.1(a) shows the possible consequences of investing in Apple April 2012 call options with an exercise price of $400 (boldfaced in Table 20.1).


pages: 1,336 words: 415,037

The Snowball: Warren Buffett and the Business of Life by Alice Schroeder

affirmative action, Alan Greenspan, Albert Einstein, anti-communist, AOL-Time Warner, Ayatollah Khomeini, barriers to entry, Bear Stearns, Black Monday: stock market crash in 1987, Bob Noyce, Bonfire of the Vanities, book value, Brownian motion, capital asset pricing model, card file, centralized clearinghouse, Charles Lindbergh, collateralized debt obligation, computerized trading, Cornelius Vanderbilt, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, desegregation, do what you love, Donald Trump, Eugene Fama: efficient market hypothesis, Everybody Ought to Be Rich, Fairchild Semiconductor, Fillmore Auditorium, San Francisco, financial engineering, Ford Model T, Garrett Hardin, Glass-Steagall Act, global village, Golden Gate Park, Greenspan put, Haight Ashbury, haute cuisine, Honoré de Balzac, If something cannot go on forever, it will stop - Herbert Stein's Law, In Cold Blood by Truman Capote, index fund, indoor plumbing, intangible asset, interest rate swap, invisible hand, Isaac Newton, it's over 9,000, Jeff Bezos, John Bogle, John Meriwether, joint-stock company, joint-stock limited liability company, junk bonds, Larry Ellison, Long Term Capital Management, Louis Bachelier, low interest rates, margin call, market bubble, Marshall McLuhan, medical malpractice, merger arbitrage, Michael Milken, Mikhail Gorbachev, military-industrial complex, money market fund, moral hazard, NetJets, new economy, New Journalism, North Sea oil, paper trading, passive investing, Paul Samuelson, pets.com, Plato's cave, plutocrats, Ponzi scheme, proprietary trading, Ralph Nader, random walk, Ronald Reagan, Salesforce, Scientific racism, shareholder value, short selling, side project, Silicon Valley, Steve Ballmer, Steve Jobs, supply-chain management, telemarketer, The Predators' Ball, The Wealth of Nations by Adam Smith, Thomas Malthus, tontine, too big to fail, Tragedy of the Commons, transcontinental railway, two and twenty, Upton Sinclair, War on Poverty, Works Progress Administration, Y2K, yellow journalism, zero-coupon bond

Inevitably, therefore, he became the target of a group of finance professors who were at that very moment attempting to prove that someone like Buffett was a mere accident who should not be paid attention, much less worshipped. These academics had started by positing the reasonable but not necessarily obvious truth that if a whole lot of people were trying to be better than average, they would become the average. Paul Samuelson, an MIT economist, revived and circulated the 1900 work of Louis Bachelier, who observed that the market is made up of speculators who cohere into a whole that operates according to a “random walk.”38 A professor from the University of Chicago, Eugene Fama, took Bachelier’s work and tested it empirically in the modern-day market, which he described as “efficient.” The scrabbling efforts of legions of investors to beat the market made those very efforts futile, he said.