The Rise of the Quants Great Minds in Finance Series Editor: Professor Colin Read This series explores the lives and times, theories and applications of those who have contributed most significantly to the formal study of finance It aims to bring to life the theories that are the foundation of modern finance, by examining them within the context of the historical backdrop and the life stories and characters of the “great minds” behind them Readers may be those interested in the fundamental underpinnings of our stock and bond markets; college students who want to delve into the significance behind the theories; or experts who constantly look for ways to more clearly understand what they do, so they can better relate to their clients and communities Titles include: The The The The Life Cyclists Portfolio Theorists Rise of the Quants Efficient Market Hypothesists Great Minds in Finance Series Standing Order ISBN 978–0–230–27408–2 (outside North America only) You can receive future titles in this series as they are published by placing a standing order Please contact your bookseller or, in case of difficulty, write to us at the address below with your name and address, the title of the series and the ISBN quoted above Customer Services Department, Macmillan Distribution Ltd, Houndmills, Basingstoke, Hampshire RG21 6XS, England The Rise of the Quants Marschak, Sharpe, Black, Scholes, and Merton Colin Read Palgrave macmillan © Colin Read 2012 Softcover reprint of the hardcover 1st edition 2012 978-0-230-27417-4 All rights reserved No reproduction, copy or transmission of this publication may be made without written permission No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6–10 Kirby Street, London EC1N 8TS Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages The author has asserted his right to be identified as the author of this work in accordance with the Copyright, Designs and Patents Act 1988 First published 2012 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS Palgrave Macmillan in the US is a division of St Martin’s Press LLC, 175 Fifth Avenue, New York, NY 10010 Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world Palgrave® and Macmillan® are registered trademarks in the United States, the United Kingdom, Europe and other countries ISBN 978-1-349-32433-0 DOI 10.1057/9781137026149 ISBN 978-1-137-02614-9 (eBook) This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin A catalogue record for this book is available from the British Library A catalogue record for this book is available from the Library of Congress 10 21 20 19 18 17 16 15 14 13 12 Contents List of Figures vii Preface to the Great Minds in Finance series viii Introduction A Roadmap to Resolve the Big Questions Part I Jacob Marschak The Early Years The Times 16 The Theory 19 Applications 28 Life and Legacy 35 Part II William Forsyth Sharpe, John Lintner, Jan Mossin, and Jack Treynor The Early Years 43 The Times 55 10 The Theory 61 11 Applications 69 12 Life and Legacy 75 Part III Fischer Black and Myron Scholes 13 The Early Years 83 14 The Times 96 15 The Black-Scholes Options Pricing Theory 109 16 Applications 117 17 The Nobel Prize, Life, and Legacy 125 Part IV Robert Merton 18 The Early Years 135 19 The Times 146 20 The Theory 152 v vi Contents 21 Applications 157 22 The Nobel Prize, Life, and Legacy 163 Part V What We Have Learned 23 Combined Contributions 177 24 Conclusions 179 Notes 182 Glossary 188 Index 193 List of Figures 3.1 The Marschak family tree 10 8.1 The Sharpe family tree 45 8.2 The Lintner family tree 50 8.3 The Treynor family tree 52 10.1 The capital allocation line 10.2 63 Various choices of risk and return along the capital allocation line 13.1 The Scholes family tree 64 84 13.2 The Black family tree 89 18.1 The Merton family tree 136 vii Preface to the Great Minds in Finance series This series covers the gamut of the study of finance – from the significance of financial decisions over time and through the cycle of one’s life to the ways in which investors balance reward and risk; from how the price of a security is determined to whether these prices properly reflect all available information – we will look at the fundamental questions and answers in finance We delve into theories that govern personal decision-making, those that dictate the decisions of corporations and other similar entities, and the public finance of government This will be done by looking at the lives and contributions of the key players upon whose shoulders the discipline rests By focusing on the great minds in finance, we draw together the concepts that have stood the test of time and have proven themselves to reveal something about the way humans make financial decisions These principles, which have flowed from individuals, many of whom have been awarded the Nobel Memorial Prize in Economics for their insights (or perhaps shall be awarded some day), allow us to see the financial forest for the trees The insights of these contributors to finance arose because these great minds were uniquely able to glimpse a familiar problem through a wider lens From the greater insights provided by a more expansive view, they were able to focus upon details that have eluded previous scholars Their unique perspectives provided new insights that are the measure of their genius The giants who have produced the theories and concepts that drive financial fundamentals share one important characteristic: they have developed insights that explain how markets can be used or tailored to create a more efficient economy The approach taken is one taught in our finance programs and practiced by fundamentals analysts We present theories to enrich and motivate our financial understanding This approach is in contrast to the tools of technicians formulated solely on capitalizing on market inefficiencies without delving too deeply into the very meaning of efficiency in the first place From a strictly aesthetic perspective, one cannot entirely condemn the tug-of-war of profits sought by the technicians, even if they little to enhance – and may even detract from – efficiency The mathematics and physics of price movements viii Preface to the Great Minds in Finance series ix and the sophistication of computer algorithms is fascinating in its own right Indeed, my appreciation for technical analysis came from my university studies toward a Bachelor of Science degree in physics, followed immediately by a PhD in economics However, as I began to teach economics and finance, I realized that the analytic tools of physics that so pervaded modern economics have strayed too far from explaining this important dimension of human financial decision-making To better understand the interplay between the scientific method, economics, human behavior, and public policy, I continued with my studies toward a Master of Accountancy in taxation, an MBA, and a Juris Doctor of Law As I taught the economics of intertemporal choice, the role of money and financial instruments, and the structure of the banking and financial intermediaries, I recognized that my students had become increasingly fascinated with investment banking and Wall Street Meanwhile, the developed world experienced the most significant breakdown of financial markets in almost eight decades I realized that this once-in-a-lifetime global financial meltdown arose because we had moved from an economy that produced things to one in which, by 2006, generated a third of all profits in financial markets, with little to show but pieces of paper representing wealth that had value only if some stood ready to purchase them I decided to shift my research from academic research in esoteric fields of economics and finance and toward the contribution to a better understanding of markets by the educated public I began to write a regular business column and a book that documented the unraveling of the Great Recession The book, entitled Global Financial Meltdown: How We Can Avoid the Next Economic Crisis, described the events that gave rise to the most significant economic crisis in our lifetime I followed that book with The Fear Factor, which explained the important role of fear as a sometimes constructive and at other times destructive influence in our financial decision-making I then wrote a book on why many economies at first thrive and then struggle to survive in The Rise and Fall of an Economic Empire Throughout, I try to impart to you, the educated reader, the intuition and the understanding that would, at least, help you to make informed decisions in increasingly volatile global economies and financial markets As I describe the theories that form the foundations of modern finance, I show how individuals born without great fanfare can come to be regarded as geniuses within their own lifetime The lives of each Conclusions 181 a crystal ball to foresee the future The world is uncertain because we never know how markets, economies, resources, or institutions will be abused or used in ways that could not have been broadly anticipated The failure of Long Term Capital Management in 1999 and the credit crisis of 2008 brought about by a freezing-up of the derivatives market in credit default swaps and collateralized debt obligations demonstrates that, while risk can be hedged, it can never be reduced to zero Notes Introduction John Maynard Keynes, “The General Theory of Employment,” Quarterly Journal of Economics, 51 (1937), 209–23, at p 214 The Early Years www.newschool.edu/nssr/het/profiles/neisser.htm, date accessed January 23, 2012 A Cowles, “Can Stock Market Forecasters Forecast?” Econometrica, (1933), 309–24 The Theory Frank Knight, Risk, Uncertainty and Profit Boston: Houghton Mifflin, 1921 J Marschak and H Makower, “Money and the Theory of Assets,” Econometrica, (1938), 311–25 Keynes, “The General Theory of Employment,” pp 213–14 Frank Plumpton Ramsey, “Truth and Probability,” in R.B Braithwaite (ed.), Foundations of Mathematics and Other Logical Essays London: Routledge & Kegan Paul, 1931 J.R Hicks, “A Suggestion for Simplifying the Theory of Money,” Economica, (1935), 1–19 Jacob Marschak, “Money and the Theory of Assets,” Econometrica, (1938), 311–25 Ibid., p 320 Ibid Jacob Marschak, “Rational Behavior, Uncertain Prospects, and Measurable Utility,” Econometrica, 18(2) (1950), 111–41 10 Ibid., p 120 11 Jacob Marschak, “Probability in the Social Sciences,” Cowles Commission Paper, 82 (1954), referring to a lecture given on December 6, 1950 12 Ibid., p 179 13 Kenneth Arrow and Frank Hahn, General Competitive Analysis San Francisco: Holden-Day, 1971, pp 361 and 369 Applications Kenneth Arrow, “The Theory of Risk Aversion,” in Aspects of the Theory of Risk Bearing Helsinki: Yrjo Jahnssonin Saatio, 1965 Reprinted in Essays in the Theory of Risk Bearing Chicago: Markham, 1971, pp 90–109 182 Notes 183 J.W Pratt, “Risk Aversion in the Small and in the Large,” Econometrica, 32(1/2) (1964), 122–36 S.A Ross, “Some Stronger Measures of Risk Aversion in the Small and in the Large with Applications,” Econometrica, 49(3) (1981), 621–39 John Burr Williams, The Theory of Investment Value Cambridge, MA: Harvard University Press, 1938 Henry Lowenfeld, Investment, an Exact Science London: Financial Review of Reviews, 1909, p 49 Colin Read, The Portfolio Theorists, Great Minds in Finance series Basingstoke: Palgrave Macmillan Life and Legacy Roy Radner, “Equilibrium of Spot and Futures Markets under Uncertainty,” Center for Research in Management Science Technical Report no 24, University of California, Berkeley, 1967 Roy Radner, “Competitive Equilibrium Under Uncertainty,” Econometrica, 36 (1968), 31–58 Jacob Marschak and Roy Radner, Economic Theory of Teams New Haven, CT: Yale University Press, 1972 The Early Years www.rand.org/about/history.html, date accessed January 23, 2012 http://en.wikipedia.org/wiki/George_Dantzig, date accessed January 23, 2012 Ibid Harry Markowitz, “Portfolio Selection,” Journal of Finance, 7(1) (1952), 77–91 http://en.wikipedia.org/wiki/Jack_L._Treynor, date accessed January 23, 2012 William Sharpe, “How to Rate Management of Investment Funds,” Harvard Business Review, 43 (1965), 63–75 William Sharpe and Kay Mazuy, “Can Mutual Funds Outguess the Market?” Harvard Business Review, 44 (1966), 131–6 The Times http://en.wikipedia.org/wiki/IBM_System/360, date accessed January 23, 2012 10 The Theory William F Sharpe, “A Simplified Model for Portfolio Analysis,” Management Science, 9(2) (1963), 277–93 F Modigliani and M Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review, 48(3) (1958), 261–97 184 Notes 11 Applications G Chamberlain, “A Characterization of the Distributions that Imply Mean-Variance Utility Functions,” Journal of Economic Theory, 29 (1983), 185–201 Kent D Daniel, David Hirshleifer, and Avanidhar Subrahmanyam, “Overconfidence, Arbitrage, and Equilibrium Asset Pricing,” Journal of Finance, 56(3) (2001), 921–65 Mark Rubinstein, “The Valuation of Uncertain Income Streams and the Pricing of Options,” Bell Journal of Economics, (1976), 407–25 Douglas T Breeden, “An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities,” Journal of Financial Economics, (1979), 265–96 Richard Roll, “A Critique of the Asset Pricing Theory’s Tests Part I: On Past and Potential Testability of the Theory,” Journal of Financial Economics, 4(2) (1977), 129–76 Fischer Black, Michael C Jensen, and Myron Scholes, “The Capital Asset Pricing Model: Some Empirical Tests,” in Michael C Jensen (ed.), Studies in the Theory of Capital Markets New York: Praeger, 1972, pp 79–121 James Tobin, “Liquidity Preference, Separation and Asset Pricing,” Zeitschrift für Betriebswirtschaft, (1983), 53–7 12 Life and Legacy Jonathan Burton, “Revisiting the Capital Asset Pricing Model,” Dow Jones Asset Manager (1998), pp 20–8 William F Sharpe, “Capital Asset Prices – A Theory of Market Equilibrium Under Conditions of Risk,” Journal of Finance, XIX(3) (1964), 425–42 13 The Early Years www.nytimes.com/1998/11/14/business/when-theory-met-reality-specialreport-teachings-two-nobelists-also-proved-their.html?pagewanted=all&src=pm, date accessed January 23, 2012 Ibid 14 The Times Lyndon Moore and Steve Juh, “Derivative Pricing 60 Years Before Black-Scholes: Evidence from the Johannesburg Stock Exchange,” Journal of Finance, 61(6) (2006), 3069–98 Aristotle, Politics, Book I, Chapter 11, Sections 5–10 John O’Farrell, An Utterly Impartial History of Britain – Or 2000 Years of Upper Class Idiots in Charge London: Doubleday, 2007 J de la Vega (1688), Confusion de Confusiones; reprinted in M Fridson (ed.), Extraordinary Popular Delusions and the Madness of Crowds; and Confusion de Confusiones (New York: Wiley, 1996) Notes 185 Isaac de Pinto (1771), An Essay on Circulation of Currency and Credit in Four Parts and a Letter on the Jealousy of Commerce, translated with annotations by S Baggs (1774), London; reprinted by Gregg International Publishers (1969) Robert J Leonard, “Creating a Context for Game Theory,” History of Political Economy, 24 (Supplement) (1992), 29–76, at p 39 http://en.wikipedia.org/wiki/Louis_Bachelier, date accessed January 23, 2012 Alfred Cowles and H Jones, “Some A Posteriori Probabilities in Stock Market Action,” Econometrica, 5(3) (1937), 280–94 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 Perry Mehrling, Fischer Black and the Revolutionary Idea of Finance Hoboken, NJ: Wiley, 2005, p 138 Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81(3) (1973), 637–54 http://articles.chicagotribune.com/2011-01-19/business/ ct- biz-0119confidential-oconnor-20110119_1_cboe-edmund-o-connor-trading, date accessed January 23, 2012 J.M Harrison and D.M Krebs, “Martingales and Arbitrage in Multi-period Securities Markets,” Journal for Economic Theory, 20(3) (1979), 381–408 John C Cox, Stephen A Ross, and Mark Rubinstein, “Option Pricing: A Simplified Approach,” Journal of Financial Economics, (1979), 229–63 Richard Roll, “An Analytical Formula for Unprotected American Call Options on Stocks with Known Dividends,” Journal of Financial Economics, (1977), 251–8 Robert Geske, “The Valuation of Compound Options,” Journal of Financial Economics (1979), 63–81 Robert E Whaley, “On the Valuation of American Call Options on Stocks with Known Dividends,” Journal of Financial Economics, 9(1) (1981), 207–11 17 The Nobel Prize, Life, and Legacy www.thedailybeast.com/newsweek/2008/10/17/600-000-000-000-000.html, date accessed January 23, 2012 F Black, E Derman, and W Toy, “A One-Factor Model of Interest Rates and its Application to Treasury Bond Options,” Financial Analysts Journal (1990), 24–32 F Black, “How to Use the Holes in Black-Scholes,” Journal of Applied Corporate Finance, 1(4) (1989), 67–73 Mehrling, Fischer Black and the Revolutionary Idea of Finance, p 288 www.nobelprize.org/nobel_prizes/economics/laureates/1997/press.html, date accessed January 23, 2012 Justin Fox, “Myron Scholes, Intellectual Godfather of the Credit Default Swap, Says Blow ‘em All Up,” Time Magazine, March 6, 2009: http://curiouscapitalist 186 Notes blogs.time.com/2009/03/06/myron-scholes-intellectual-godfather-of-thecredit-default-swap-says-blow-em-all-up/, date accessed January 23, 2012 18 The Early Years www.nytimes.com/2003/02/24/nyregion/ robert- k- merton- versatilesociologist-and-father-of-the-focus-group-dies-at-92.html?pagewanted=3, date accessed January 23, 2012 www.nobelprize.org/nobel_prizes/economics/laureates/1997/ mertonautobio.html, date accessed January 23, 2012 19 The Times Robert C Merton, “An Intertemporal Capital Asset Pricing Model,” Econometrica, 41(5) (1973), 867–87 Robert C Merton, “The Relationship between Put and Call Option Prices: Comment,” Journal of Finance, 28(1) (1973), 183–4 Robert C Merton, “An Analytical Derivation of the Efficient Portfolio Frontier,” Journal of Financial and Quantitative Analysis, 10 (1972), 1851–72 Robert C Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4(1) (1973), 141–83 Paul A Samuelson and Robert C Merton, “A Complete Model of Warrant Pricing that Maximizes Utility,” Industrial Management Review, 10 (1969), 17–46 Robert C Merton, “A Golden Golden-Rule for Welfare-Maximization in an Economy with a Varying Population Growth Rate,” Western Economic Journal, (1969), 307–18 Robert C Merton, “Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case,” Review of Economics and Statistics, 51 (1969), 247–57 Robert C Merton, “A ‘Motionless’ Motion of Swift’s Flying Island,” Journal of the History of Ideas, 27 (1966), 275–7 20 The Theory Robert C Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science, 4(1) (1973), 141–83 Robert C Merton, “On the Pricing of Contingent Claims and the ModiglianiMiller Theorem,” Journal of Financial Economics, 5(3) (1977), 241–9 21 Applications http://en.wikipedia.org/wiki/American_International_Group, date accessed January 23, 2012 Notes 187 22 The Nobel Prize, Life, and Legacy Paul Samuelson, “Mathematics of Speculative Price,” in R.H Day and S.M Robinson (eds), Mathematical Topics in Economic Theory and Computation, Philadelphia, PA: Society for Industrial and Applied Mathematics, 1972 Reprinted in SIAM Review, 15(1) (1973), 1–42 Peter L Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street New York: Free Press, 1992, p 223 www.nobelprize.org/nobel_prizes/economics/laureates/1997/press.html, date accessed January 23, 2012 www.alumni.hbs.edu/bulletin/1997/december/theory.html, date accessed January 23, 2012 Gretchen Morgenson and Michael M Weinstein, “When Theory Met Reality: A Special Report; Teachings of Two Economists Also Proved Their Undoing,” New York Times, November 14, 1998 Dennis Overbye, “They Tried to Outsmart Wall Street,” New York Times, March 29, 2009 Glossary Alpha ␣ – the excess return on a security or over what is predicted by the CAPM American options – an option to purchase (a call) or sell (a put) an underlying security at a specified exercise price on (or, in the case of American options, before) a specified settlement date Arrow-Pratt measure of risk aversion – a measure of the relative degree of risk aversion as measured by the rate of ratio of an individual’s second and first derivatives of utility Beta  – a measure of the systematic risk of a relative to the market Binomial model – an options pricing methodology that breaks the dynamic path of the derivatives into a series of steps at various points in time between the valuation date and the expiration date Black-Scholes model – a model that can determine the price of a European call option based on the assumption that the underlying security follows a geometric Brownian motion with constant drift and volatility Bond – a financial instrument that provides periodic (typically semi-annual) interest payments and the return of the paid-in capital upon maturity in exchange for a fixed price Brownian motion – the simplest of the class of continuous-time stochastic processes that describes the random motion of a particle or a security that is buffeted by forces that are normally distributed in strength Calculus of variations – a mathematical technique that can determine the optimal path of a variable, like savings or consumption, over time Call – an option to purchase a specified security at a specified future time and price Capital allocation line – a line drawn on the graph of all possible combinations of risky and risk-free assets that shows the best risk–reward horizon Capital Asset Pricing Model (CAPM) – a methodology that shows the relationship between risk and expected return for a financial security Cardinal theory – a theory in economics and finance that requires the measurement of the objective function rather than the mere ordering of alternative outcomes Chicago Board Options Exchange (CBOE) – an exchange founded in 1973 to trade options on securities It is the world’s largest options exchange Chicago Board of Trade (CBOT) – a commodity exchange established in 1848 that permitted the trading of financial and commodity contracts Chicago School – a philosophy of economic and financial thought based on the premise that unfettered markets are the most efficient Classical model – a microeconomic-based approach to economic decisionmaking that assumes that all actors are rational and maximize their selfinterest, and is driven by the principle that prices adjust to ensure supply is equal to demand Collateralized debt obligations – investment-grade securities backed by a package of loans, mortgages, bonds, or other debt obligations 188 Glossary 189 Consumption CAPM – an extension of the CAPM that includes future consumption preferences Corporate finance – the study of financial decisions made by corporations to maximize shareholder value Correlation – the statistical relationship between two variables, typically measured by demonstrating that the movement of one variable is associated with movement of the other Covariance – a measure of the degree to which returns on two risky assets are correlated in their movement Cowles Commission – a research institute founded by Alfred Cowles to stimulate new theories in the decision sciences that can help explain financial markets Coupon rate c – the periodic payment to the owner of a bond Credit default swaps – securities that allow the exchange of risk by the underwriting of instruments prone to default risk Delta ⌬ – the optimal ratio between the option and stock for a hedge that reduces risk to the theoretical floor Derivative – in mathematics, the instantaneous rate of change of one variable as a function of the change of another; in finance, a financial instrument that derives its value from another underlying asset or instrument Differential equation – an equation that specifies the relationship between the rates of change of a collection of variables Discount rate – the rate at which humans will reduce the value of future income in the determination of its present value This term is also used to signify the interest rate set by a nation’s central bank Diversification – a technique that uses the combination of assets to reduce the risk of the portfolio without lowering its return Dynamic – the analysis of a process as it changes over time Econometrics – the set of tools used to demonstrate predictable statistical correlations between financial and economic variables Efficient market hypothesis – a theory based on the premise that one cannot systematically beat the market because market prices already properly incorporate all available information Elliptical distribution of returns – a pattern of returns that is symmetric in that the return could deviate upward or downward with equal probability The normal distribution is a member of the family of all elliptical distributions Equilibrium – a state in which a relationship converges upon a constant balance European options – options that can only be exercised at the exercise date Existence – the premise used in a theory of equilibrium that an equilibrium will actually occur Expectations – the set of beliefs over the future value of an economic or financial variable Face value F – the nominal value of a bond that is returned to the bondholder upon maturity First moment – the mean of a variable that can be described by a known probability distribution function Full information – the desirable quality that all knowable information about the value of a security is revealed Fundamentals analysis – estimation of the price of a security based on the underlying pattern of future profitability of the enterprise 190 Glossary Gamma ␥ – the rate of change of the optimal combination of an option and the underlying security over time Infinite time horizon – an economic planning horizon that has no end For instance, an infinitely lived individual or society would make decisions with due consideration to an infinite future Interest rate – the rate of periodic payments, as a share of the principal amount borrowed, to compensate for humans’ inherent preference for the present over the future Intertemporal – a reference to decisions made across time Intertemporal CAPM – an extension of the CAPM beyond the simple consideration of variances to also include additional consumption and investment opportunities over time Keynesian model – a model developed by John Maynard Keynes that demonstrates savings may not necessarily be balanced with new investment and the gross domestic product may differ from that which would result in full employment Kurtosis – a statistical measure of the distribution of observations about the expected mean as a deviation from that predicted by the normal distribution Life cycle – the characterization of a process from its birth to death Life Cycle Model – a model of household consumption behavior from the beginning of its earning capacity to the end of the household Markov process – a stochastic process with the memorylessness property for which the present state, future state, and past observations are independent Markowitz bullet – the upper boundary of the efficient frontier of various portfolios when graphed according to risk and return Martingale – a model of a process for which past events cannot predict future outcomes Mean – a mathematical technique that can be calculated based on a number of alternative weightings to produce an average for a set of numbers MIT School – an approach to economic and financial studies that favors dynamic (time-variant) modeling and simple, elegant, but predictively powerful theories Modern Portfolio Theory – the set of techniques developed in the 1950s by Harry Markowitz to design optimal portfolios and the most efficient risk–reward trade-off Monte Carlo simulations – an algorithm that repeats simulations of a postulated financial relationship with random elements The Monte Carlo simulation often reveals patterns that cannot be gleaned by analytic methods Mortgage-backed securities – a financial instrument that derives its asset value on a collection of underlying mortgages; in other words, a financial security that is backed by a collection of financial securities Naked short – selling of securities for which one does not own the title or a right to sell Normal distribution of returns – a distribution that follows a prescribed and symmetric pattern that occurs frequently in natural processes Optimal control theory – an extension of the calculus of variations that is a powerful tool in the modeling of dynamic processes Options – the contractual right to purchase a security at a future date under specified terms Glossary 191 Options pricing theory – a theory used to determine the rational price of an option or derivative Ordinal theory – a theory that has as an objective function and ordering that can rank the preference of various outcomes but not the degree of the preference Ordinary least squares – a method to solve for the relationship between a dependent variable as a weighted sum of independent variables This technique minimizes the squared difference between the dependent variable and the predicted amount from an estimate of a weighted combination of the independent variables Before the recent advent of significant computing power, this readily calculable technique was used to estimate relationships between dependent and independent variables Perfect market – a market that is characterized by a very large number of buyers and sellers, each with no market power, and full information and access to credit Personal finance – the study of household and personal savings decisions as a method to enhance lifetime consumption Price-earnings ratio – the ratio of a security’s price to its earnings as a measure of its payback period Put – the right to sell a security at a specified date and price Quadratic utility function – a utility function that rises with wealth, income, or consumption that can be described by a quadratic equation One with such a quadratic utility function will only be sensitive to the mean and variance parameters of a security Random walk – the expectation that a security return at time t is equal to its last period value plus a stochastic (random) component that is independent and identically distributed with zero mean and variance 2 Rational – decision-making based on full and objective analysis Regression – a technique used to fit a dependent variable as a weighted sum of independent variables Representative agent – the use of a single representative entity to determine the rational decision of a financial or economic process Return – the expected surplus offered to entice individuals to hold a financial instrument Rho – the effect on the option price for a single percentage point change in the risk-free rate of return Risk – in finance, the degree of uncertainty associated with exchanging a known sum for a larger future but less certain sum Risk-averse – a property that states an agent would prefer less risk to more for an equal return Risk-free asset – an asset that yields a certain return over all possible states Risk-free rate of return – the return offered by an asset that does not vary over future states Risk–reward trade-off – an individual’s determination of the required reward to compensate for additional risk Second moment – a weighted measure of the deviation of a random variable from its mean, or first moment Securities market line – a graph that compares the systematic market risk for the market as a whole compared to its return Security – a financial contract that establishes the rights of ownership of an asset 192 Glossary St Petersburg Paradox – a scenario which presents a simple decision rule that only regards the expected value of the outcome but which no rational person would be willing to take Static – the consideration of mathematical, physical, or economic relationships that not change over time Stochastic calculus – the extension of the tools of calculus to processes that are stochastic Stochastic process – a random process in which there is indeterminacy that cannot be fully known and instead is described by a probability distribution Systematic risk – the unavoidable risk that inherently affects the entire market Taylor’s series – the expression of the range of a function arising from deviations of its domain as represented by an infinite series of the function’s derivatives and the deviations of its domain Theta τ – the effect of a one-day reduction in the time to expiry on the option price Transactions costs – the sunk or upfront cost of participating in a transaction beyond the cost of exchange of the transacted items themselves These could include contracting or participation fees Uncertainty – the degree to which the value of future variables cannot be fully known today Unsystematic risk – the inherent security- or industry-specific risk that can be reduced through optimal diversification Variance – a specific measure of the deviation of a set of data points around the mean value in which the deviations from the mean are squared It is calculated as the expected squared deviations of a variable from its mean Vega – the sensitivity of the option price to a single percentage point change in measured volatility Volatility – a measure of the degree of uncertainty and unexplained movements of a variable over time Warrant – a derivative that is offered by a firm as a right to purchase the underlying security at a specific price within a certain timeframe Wealth line – a locus of points that connect various levels of consumption of goods over time for a given and known level of income or wealth Weiner process – a continuous-time random walk with random jumps at each point in time Index Alpha, 67, 73, 110, 121 American options, 100, 101, 116, 123 Arrow, Kenneth, 23 Arrow-Pratt measure of risk aversion, 29 Beta, 66, 67, 69, 72, 73, 110, 111, 112, 121, 152 Binomial model, 122 Black-Scholes equation, 96, 97, 113, 117, 121, 122, 124, 125, 128, 150, 153, 158, 159, 160, 161, 163, 179, 180 Bond, 5, 33, 59, 96, 106, 121, 126, 140, 142, 154, 159, 160, 168, 169, 170, 185 Brownian motion, 32, 105, 113, 120, 155 Calculus of variations, 143 Call, 98, 99, 100, 101, 104, 106, 107, 108, 112, 114, 115, 116, 122, 123, 136, 151, 153, 160, 165, 166, 167, 185, 186 Capital allocation line, 63, 64, 67 Capital Asset Pricing Model (CAPM), 4, 41, 48, 49, 51–3, 57, 60, 61, 65–81, 87, 88, 89, 93, 94, 96, 106, 109–12, 118, 121, 124, 141, 150, 152, 158, 177, 179, 180 Chicago Board Options Exchange (CBOE), 100, 101, 102, 117, 118, 119, 120, 122, 125, 129, 158, 159 Chicago Board of Trade (CBOT), 100, 101, 109, 119, 156 Chicago School, 86, 120, 152, 153 Classical model, 17 Collateralized debt obligation, 181 Consumption, 23 Consumption CAPM, 72 Corporate finance, 32, 76, 81, 106, 127, 143, 144 Correlation, 23, 34, 36, 59, 62, 67, 73, 155 Coupon rate c, 168 Covariance, 23, 32, 34, 58, 59, 60, 62, 65, 66, 74, 93 Cowles Commission, 13, 14, 15, 18, 19, 23, 24, 25, 36, 55, 61, 69, 105, 141 Credit default swaps, 5, 129, 130, 160, 161, 181, 185 Debreu, Gerard, 23 Delta, 123, 124 Derivative, 5, 25, 26, 27, 29, 30, 81, 101, 106, 109, 121, 125, 128, 129, 130, 131, 142, 155, 159, 160, 162, 169, 173, 174, 175, 179, 181, 184 Differential equation, 111, 112, 113, 115, 121, 125, 127, 139, 142, 143, 148, 149, 152, 153, 154, 155, 157, 158, 179 Discount rate, 53, 58, 93, 106, 108, 111, 113 Diversification, 23, 32, 59, 66, 67, 76 Dynamic, 5, 14, 67, 68, 71, 114, 124, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 179 Econometric, 14, 19, 36, 39, 61, 78, 79, 141, 144, 150, 173 Efficient market hypothesis, 13, 32, 70, 72, 73, 94, 95, 111, 124 Elliptical distribution of return, 69 Equilibrium, 2, 13, 14, 17, 18, 23, 24, 36, 38, 56, 57, 61, 74, 77, 89, 119, 147, 150, 175, 183, 184 European option, 100, 101, 115, 116, 122 Face value F, 96 First moment, 23, 26, 70, 112, 177 Irving, Friedman, Milton, Full information, 14, 71 Fundamentals analysis, 33, 58, 158 193 194 Index Gamma, 124 Hicks, John, 21, 22 Homogenity, 65 Infinite time horizon, 25 Interest rate, 1, 58, 59, 96, 106, 110, 114, 115, 116, 126, 152, 153, 154, 168, 185 Intertemporal CAPM, 71 Intertemporal choice, 1, 69, 71, 75, 124, 125, 143, 150, 184, 186 Keynes, John Maynard, Kurtosis, 121 Life cycle, 1, 76, 125, 143, 144, 149, 150 Life Cycle Model, 1, 125, 144, 150 Markov process, 116, 120, 126 Markowitz, Harry, 23, 63 Markowitz bullet, 63 Marschak, Jacob, 22, 23, 24 Martingale, 105, 120, 121, 185 Mean, 4, 20, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 41, 43, 48, 58, 59, 60, 63, 66, 69, 70, 72, 104, 118, 121, 126, 154, 155, 177, 179, 184 MIT School, 141, 142 Modern Portfolio Theory, 2, 3, 4, 19, 23, 24, 34, 41, 43, 44, 46, 48, 56, 57, 61, 64, 68, 69, 72, 73, 74, 76, 89, 95, 125, 177 Modigliani, Franco, Monte Carlo simulation, 122 Mortgage-backed securities, Naked short, 129 Normal distribution of return, 116, 161 Options pricing theory, 5, 32, 68, 71, 72, 77, 109, 111, 113, 115, 116, 120, 124, 180 Ordinal theory, 22 Ordinary least squares, 70 Perfect market, 71, 154 Personal finance, 76, 146, 175, 179 Price/earnings ratio, 58 Put, 100, 122, 123 Quadratic utility function, 26, 70 Ramsey, Frank Plumpton, 1, 24 Random walk, 13, 32, 103, 104, 105, 113, 161 Rational, 21, 23, 37, 38, 58, 66, 70, 151, 156 Regression, 67, 70, 75 Representative agent, 65, 73, 74, 111, 142, 143 Return, 2, 4, 22, 23, 25, 26, 27, 28, 53, 58, 59, 60, 61, 62, 63, 64, 65, 66–7, 68, 70, 79, 88, 92, 93, 104, 111, 112, 113, 114, 115, 118, 121, 122 Rho, 124 Risk aversion, 29, 31, 61, 107, 117 Risk-free asset, 2, 59, 62, 63, 65, 70, 73 Risk-free rate of return, 66, 67, 111, 112, 113, 114, 124, 153 Risk–reward trade-off, 46, 87 Savage, Leonard Jimmie, 23 Second moment, 4, 23, 26, 27, 28, 34, 43, 59, 69, 70, 105, 112, 177 Securities market line, 2, 140, 156 Security, 32–33, 35, 43–4, 57–8, 66–7, 96 St Petersburg Paradox, 20, 102 Static, 1, 5, 13, 68, 71, 143, 149, 152, 153, 179 Steinhaus, Hugo, 102 Stochastic calculus, 105, 120, 143, 157 Stochastic process, 126 Subjective probability, 24 Systematic risk, 2, 67, 70 Taylor’s series, 25, 27, 28 Theta, 124 Transactions cost, 66, 71, 75, 100, 101, 110 Uncertainties, 2, 20, 36, 53, 101 Uncertainty, 1, 2, 4, 15, 16, 19, 20, 21, 22, 23, 24, 25, 27, 29, 35, 36, Index 37, 38, 43, 47, 61, 68, 69, 79, 98, 137, 151, 157 Unsystematic risk, 2, 67 Variance, 4, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 41, 43, 48, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 69, 70, 72, 93, 104, 111, 112, 121, 154, 177, 179, 184 195 Vega, 99, 124, 184 Volatility, 30, 32, 33, 59, 96, 113, 122, 123, 124, 126, 158, 160 Von Neumann, John, 22, 23 Warrant, 96, 97, 98, 99, 100, 107, 109, 111, 112, 118, 140, 142, 143, 149, 151, 156, 162, 185, 186 Weiner process, 104, 105, 154 ... describe the center of gravity and the inertia of an object The discipline of finance used the same technique in what we now know as the mean and variance approach With measures of the mean and variance... primitive and simplistic state The modern quants, and trillions The Rise of the Quants of dollars of financial investment each year, now rely on the pricing tools provided by William Sharpe, Fischer... condemn the tug -of- war of profits sought by the technicians, even if they little to enhance – and may even detract from – efficiency The mathematics and physics of price movements viii Preface to the