Paulos J.A. — A Mathematician Plays the Stock Market
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Íàçâàíèå: A Mathematician Plays the Stock Market
Àâòîð: Paulos J.A.
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In A Mathematician Plays the Stock Market, best-selling author John Allen Paulos demonstrates what the tools of mathematics can tell us about the vagaries of the stock market. Employing his trademark stories, vignettes, paradoxes and puzzles (and even a film treatment), Paulos addresses every thinking reader's curiosity about the market: Is it efficient? Is it rational? Is there anything to technical analysis, fundamental analysis, and other supposedly time-tested methods of picking stocks? How can one quantify risk? What are the most common scams? What light do fractals, network theory, and common psychological foibles shed on investor behavior? Are there any approaches to investing that truly outperform the major indexes? Can a deeper knowledge of mathematics help beat the odds? All of these questions are explored with the engaging erudition that made Paulos's A Mathematician Reads the Newspaper and Innumeracy favorites with both armchair mathematicians and readers who want to think like them. Paulos also shares the cautionary tale of his own long and disastrous love affair with WorldCom. In the tradition of Burton Malkiel's A Random Walk Down Wall Street and Jeremy Siegel's Stocks for the Long Run, this wry and illuminating book is for anyone, investor or not, who follows the markets — or knows someone who does.
"Blow up" investor118 "Butterfly effect" of nonlinear systems174 "Dominance" principle, game theory198 "Double-dip" recession46 "Efficient frontier" of portfolios (Markowitz)157 "Flocking effect" Internet178 "Ghosts" investors118 "Head and shoulders" pattern46 "Maximization of expected value" principle198 "Single index model" (Sharpe)159 "The Imp in the Bottle" (Stevenson)94 A New Kind of Science (Wolfram)170—171 A Non-Random Walk Down Wall Street (Lo and MacKinlay)48 A Random Walk Down Wall Street (Malkiel)4862 Accounting practices, assumptions vs. Practices115 Accounting practices, auditors and115—116 Accounting practices, comparing corporate and personal accounting25 Accounting practices, conflict of interest and111—112 Accounting practices, deciphering company financial health111 Accounting practices, Enron112 Accounting practices, reforms114 Accounting practices, transparency115 Accounting practices, vagueness and subjectivity of114 Accounting practices, value investing and110 Accounting practices, worldcom (WCOM)112 Accounting scandalssee also "Fraud" Accounting scandals, Benford’s Law and74 Accounting scandals, deciphering company financial health111 Accounting scandals, Efficient Market Hypothesis and63 Accounting scandals, psychology of cover ups24 Accounting scandals, volatility and15 Accounting scandals, WCOM fraud200 Al Qaeda124 Albert, Reka178—179 Anchoring effect, financial numbers and20 Anchoring effect, number experiments19—20 Anchoring effect, online chatroom example32 Arithmetic meansee also "Mean value" Arithmetic mean, IPO purchases/sales96—98 Arithmetic mean, outstripping geometric mean rate of return99 Arthur Andersen112 Arthur, W. Brian9 Auditors115—116 Aumann, Robert10165 Availability error21 Average values, compared with distribution of incomes132—133 Average values, risk as variance from136—137 Averages, average return compared with median return99 Averages, average value compared with distribution of incomes132—133 Averages, buy-sell rules and43 Averages, outguessing average guess6—7 Averages, risk as variance from average value136—137 Averaging down13—14 Bachelier, Louis59122 Bak, Per178—179 Barabasi, Albert-Lazlo178—179 Bartiromo, Maria199 Bear markets, investor self-descriptions and58 Bear markets, shorting and distorting strategy in35—36 Benford, Frank73 Benford’s law72—74 Benford’s Law, applying to corporate fraud74 Benford’s Law, background of73 Benford’s Law, frequent occurrence of numbers governed by73—74 Bernoulli, Daniel148 Beta (B) values, causes of variations in161 Beta (B) values, comparing market against individual stocks or funds160—161 Beta (B) values, strengths and weaknesses of161—162 Beta (B) values, technique for finding161 Beta (B) values, volatility and160 big bang16 Billiards, as example of nonlinear system172—173 Binary system71 Biorhythm theory39 Black — Scholes option formula122 Black, Fischer121—122129 Blackjack strategies50—51 Blackledge, Todd108 Blue chip companies, P/E ratio of101 Bogle, John60 Bonds will not necessarily continue to be outperformed by stocks145—146 Bonds, Barry108 Bonds, Greenspan’s impact on bond market86 Bonds, history of stocks outperforming143—145 bookkeepingsee "Accounting practices" Bottom-line investing92 Brock, William48 Brokerssee "Stock brokers" Buffet, Warren6585 Bull markets, investor self-descriptions and58 Bull markets, pump and dump strategy in33 Butterfly Economics (Ormerod)169 Buy-sell rules43 Buying on the margin127129see Calendar effects49 Call optionssee also "Stock options" Call options, covering121 Call options, how they work120 Call options, selling120 Call options, strategies121—122 Call options, valuation tools122—123 Campaign contributions126 Capital asset pricing model160 Capital gains vs. Dividends91—92 Central limit theorem140 Ceos, arrogance of184—185 Ceos, benefits in manipulating stock prices123—124 Ceos, remuneration compared with that of average employee183 Ceos, volatility due to malfeasance of15 Chain letters92—95 Chaitin, Gregory193 Chancesee also "Whim" Chance, as undeniable factor in market63 Chance, trading strategies and28 Chaos theory172see CHARITY156 Clayman, Michelle107 Cognitive illusions21—26 Cognitive illusions, availability error21 Cognitive illusions, confirmation bias21—22 Cognitive illusions, heuristics rules of thumb for saving time25—26 Cognitive illusions, mental accounts24—25 Cognitive illusions, status quo bias22—23 Cohen, Abby Joseph147 Coin flipping63—64 Common knowledge, accounting scandals and63 Common knowledge, definition and importance to investors9—10 Common knowledge, dynamic with private knowledge191 Common knowledge, insider trading and164—165 Common knowledge, parable illustrating10—12 Common knowledge, private information becoming165—167 Companies/corporations, adjusting results to meet expectations21 Companies/corporations, applying Benford’s Law to corporate fraud74 Companies/corporations, comparing corporate and personal accounting25 Companies/corporations, financial health and102 Companies/corporations, P/E ratio of blue chips101 Competition vs. Cooperation, prisoner’s dilemma191—192 Complexity of sequences (mathematics)193 Complexity of trading strategies191192194—196 Complexity, changing over time195—196 Complexity, horizon195 Compound interest, as basis of wealth86 Compound interest, doubling time and90 Compound interest, formulas for88—89 Compound interest, future value and89—90 Compound interest, present value and89 Confirmation bias, definition of21—22 Confirmation bias, investments reflecting13 Confirmation bias, stock-picking and22 Connectednesssee also "Networks"
Connectedness, European market causing reaction on Wall Street163 Connectedness, interactions based on whim168—169 Connectedness, interactions between technical traders and value traders167—168 Connectedness, irrational interactions between traders169—170 Connectedness, Wolfram model of interactions between traders170—171 Consumer Confidence Index (CCI)9 Contrarian investing, dogs of the Dow105 Contrarian investing, measures of excellence and107 Contrarian investing, rate of return and106—107 Cooperation vs. Competition, prisoner’s dilemma191—192 Correlation coefficient152see Counter-intuitive investment54 Counterproductive behavior psychology of17—18 Covariance, calculation of152—153 Covariance, portfolio diversification based on154 Covariance, portfolio volatility and152 Covariance, stock selection and159 Cramer, James199 Crowd, following or not37 Crowd, herd-like nature of price movements181 Dart throwing, stock-picking contest in the Wall Street Journal63 Data mining, illustrated by online chatrooms32 Data mining, moving averages and44 Data mining, survivorship bias and30—31 Data mining, trading strategies and28—30 DeBondt, Werner106—107 Deciding What’s News (Gans)185 Decimalization reforms70—71 Decision making, minimizing regret23 Decision making, selling WCOM200 Depression of1873113 Derivatives trading, Enron112 Despair and guilt over market losses118 Deviation from the meansee also "Mean value" Deviation from the mean, covariance152 Deviation from the mean, standard deviation (d)137—139 Deviation from the mean, variance136—137 Dice, probability and50 Digex55 Discounting process, present value of future money91—92 Distribution of incomes132 Distribution of wealth, dynamic of concentration182—183 Distribution of wealth, UN report on182 Diversified portfoliossee "Stock portfoliosdiversifying" Dividends, earnings and100 Dividends, proposals benefitting returns from92 Dodd, David106 Dogs of the Dow strategy105 Dot com IPOs, as a pyramid scheme93 Double entry bookkeeping115 Double-bottom trend reversal46 Doubling time, compound interest and90 Dow, dogs of the Dow strategy105 Dow, percentages of gains and losses15 e (exponential growth), compound interest and86—88 e (exponential growth), higher mathematics and88—89 Earnings, anchoring effect and20 Earnings, complications with determination of100 Earnings, inflating (WCOM)112 Earnings, P/E ratio and100 Earnings, stock valuation and100 East, Steven, H.147 Ebbers, Bernie, acquisition appetite of93 Ebbers, Bernie, arrogance of183 Ebbers, Bernie, author emails offer of help199 Ebbers, Bernie, Digex purchase55 Ebbers, Bernie, down-home style of181—182 Ebbers, Bernie, forced to sell WCOM stock23 Ebbers, Bernie, fraud by112—113 Ebbers, Bernie, pump and dump strategy and34 Ebbers, Bernie, purchase of worldcom stock by129 Economics, human behavior and16—17 Efficient Market Hypothesis, background of59 Efficient Market Hypothesis, impact of accounting scandals on63 Efficient Market Hypothesis, increased efficiency results in decreased predictability61—62 Efficient Market Hypothesis, investors beliefs impacting189 Efficient Market Hypothesis, moving averages and44 Efficient Market Hypothesis, paradoxes of187—189 Efficient Market Hypothesis, randomness and57 Efficient Market Hypothesis, rationale for60—61 Efficient Market Hypothesis, resistance and support levels and46 Efficient Market Hypothesis, versions of59—60 Elliott, Ralph Nelson38—39 Ellison, Larry184 Employee remuneration vs. CEO remuneration183 Endowment effect22 Enron, accounting practices112 Enron, margin calls on CEO Ken Lay129 Environmental exploitation, as Ponzi scheme93—94 Equity-risk premium146 Erdoes, Paul75177 Escher, M.C.54 European stock market163 Euros, benefits of standardizing European currencies71 Euros, euro-pound/pound-euro exchange rate39—40 Expected excess return158160 Expected valuesee also "Mean value" Expected value, "maximization of expected value"198 Expected value, covariance and152 Expected value, formula for obtaining133—134 Expected value, graphing against risk (Markowitz optimal portfolios)157 Expected value, insurance company example135 Expected value, mu (m)133138 Expected value, probability theory and135—136 Exploitable opportunities, tendency to disappear61 Fama, Eugene59105 Fibonacci numbers, Elliott wave theory and38 Fibonacci numbers, golden ratio and40—41 Fibre-optic cable113—144 Fifty-two-week highs20 Fooled by Randomness (Taleb)134 Formulas, Black — Scholes options122 Formulas, compound interest88—89 Formulas, expected value133—134 Fractals38174—175 Frank, Robert183 Fraudsee also "accounting scandals" Fraud, applying Benford’s Law to corporate fraud74 Fraud, applying Benford’s law to income tax fraud73 Fraud, Bemie Ebbers112—113 Fraud, Salomon Smith Barney benefiting illegally from IPOs34 Fraud, WCOM fraud200 Fraud, wrongdoing of brokers at Merrill Lynch34 Free market economy184 French, Ken105 Full House: The Spread of Excellence from Plato to Darwin (Gould)61 Fund managers149see Fundamental analysis, as sober investment strategy85 Fundamental analysis, determining fundamental value by discounting process91—92 Fundamental analysis, evidence supporting104 Fundamental analysis, present value and90 Fundamental analysis, sequence complexity and trading rules and195 Fundamental analysis, stock valuation with99—100 Fundamental analysis, unexciting nature of86 Future value, P/E ratio as measure of future earnings expectations101 Future value, present value and89—90 Gambler’s fallacy64 Games, gambling and probability50—51 Games, game theory198 Games, guessing games6—9 Games, Monopoly141—142 Games, Parrondo’s paradox52—54 Games, St. Petersburg paradox147—149 Games, ultimatum games17 Games, worldcom board game142 Gans, Herbert185 Gates, Bill182184 Geometric mean, illustrated by IPO purchases/sales96—98 Geometric mean, rate of return99 Gilder, George2
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