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The Kelly Capital Growth Investment Criterion

Author: Leonard C. MacLean
Publisher: World Scientific
ISBN: 9814293490
Size: 39.62 MB
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This volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.

The Kelly Capital Growth Investment Criterion

Author: Edward O Thorp
Publisher: World Scientific
ISBN: 981446581X
Size: 27.23 MB
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This volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.Contents: "The Early Ideas and Contributions: "Introduction to the Early Ideas and ContributionsExposition of a New Theory on the Measurement of Risk (translated by Louise Sommer) "(D Bernoulli)"A New Interpretation of Information Rate "(J R Kelly, Jr)"Criteria for Choice among Risky Ventures "(H A Latan‚)"Optimal Gambling Systems for Favorable Games "(L Breiman)"Optimal Gambling Systems for Favorable Games "(E O Thorp)"Portfolio Choice and the Kelly Criterion "(E O Thorp)"Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions "(N H Hakansson)"On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields "(N H Hakansson)"Evidence on the ?Growth-Optimum-Model? "(R Roll)""Classic Papers and Theories: "Introduction to the Classic Papers and TheoriesCompetitive Optimality of Logarithmic Investment "(R M Bell and T M Cover)"A Bound on the Financial Value of Information "(A R Barron and T M Cover)"Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment "(P H Algoet and T M Cover)"Universal Portfolios "(T M Cover)"The Cost of Achieving the Best Portfolio in Hindsight "(E Ordentlich and T M Cover)"Optimal Strategies for Repeated Games "(M Finkelstein and R Whitley)"The Effect of Errors in Means, Variances and Co-Variances on Optimal Portfolio Choice "(V K Chopra and W T Ziemba)"Time to Wealth Goals in Capital Accumulation "(L C MacLean, W T Ziemba, and Y Li)"Survival and Evolutionary Stability of Rule the Kelly "(I V Evstigneev, T Hens, and K R Schenk-Hopp‚)"Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes "(Y Lv and B K Meister)""The Relationship of Kelly Optimization to Asset Allocation: "Introduction to the Relationship of Kelly Optimization to Asset AllocationSurvival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time "(S Browne)"Growth versus Security in Dynamic Investment Analysis "(L C MacLean, W T Ziemba, and G Blazenko)"Capital Growth with Security "(L C MacLean, R Sanegre, Y Zhao, and W T Ziemba)"

The Kelly Capital Growth Investment Criterion

Author: Leonard C. MacLean
Publisher: World Scientific Publishing Company
ISBN: 9789814383134
Size: 39.73 MB
Format: PDF, Mobi
View: 1942
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This volume provides the definitive treatment of fortune's formula or the Kelly capital growth criterion as it is often called. The strategy is to maximize long run wealth of the investor by maximizing the period by period expected utility of wealth with a logarithmic utility function. Mathematical theorems show that only the log utility function maximizes asymptotic long run wealth and minimizes the expected time to arbitrary large goals. In general, the strategy is risky in the short term but as the number of bets increase, the Kelly bettor's wealth tends to be much larger than those with essentially different strategies. So most of the time, the Kelly bettor will have much more wealth than these other bettors but the Kelly strategy can lead to considerable losses a small percent of the time. There are ways to reduce this risk at the cost of lower expected final wealth using fractional Kelly strategies that blend the Kelly suggested wager with cash. The various classic reprinted papers and the new ones written specifically for this volume cover various aspects of the theory and practice of dynamic investing. Good and bad properties are discussed, as are fixed-mix and volatility induced growth strategies. The relationships with utility theory and the use of these ideas by great investors are featured.

Stochastic Optimization Models In Finance

Author: W. T. Ziemba
Publisher: Academic Press
ISBN: 1483273997
Size: 57.87 MB
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Stochastic Optimization Models in Finance focuses on the applications of stochastic optimization models in finance, with emphasis on results and methods that can and have been utilized in the analysis of real financial problems. The discussions are organized around five themes: mathematical tools; qualitative economic results; static portfolio selection models; dynamic models that are reducible to static models; and dynamic models. This volume consists of five parts and begins with an overview of expected utility theory, followed by an analysis of convexity and the Kuhn-Tucker conditions. The reader is then introduced to dynamic programming; stochastic dominance; and measures of risk aversion. Subsequent chapters deal with separation theorems; existence and diversification of optimal portfolio policies; effects of taxes on risk taking; and two-period consumption models and portfolio revision. The book also describes models of optimal capital accumulation and portfolio selection. This monograph will be of value to mathematicians and economists as well as to those interested in economic theory and mathematical economics.

Fortune S Formula

Author: William Poundstone
Publisher: Hill and Wang
ISBN: 9780374707088
Size: 63.68 MB
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In 1956, two Bell Labs scientists discovered the scientific formula for getting rich. One was mathematician Claude Shannon, neurotic father of our digital age, whose genius is ranked with Einstein's. The other was John L. Kelly Jr., a Texas-born, gun-toting physicist. Together they applied the science of information theory—the basis of computers and the Internet—to the problem of making as much money as possible, as fast as possible. Shannon and MIT mathematician Edward O. Thorp took the "Kelly formula" to Las Vegas. It worked. They realized that there was even more money to be made in the stock market. Thorp used the Kelly system with his phenomenally successful hedge fund, Princeton-Newport Partners. Shannon became a successful investor, too, topping even Warren Buffett's rate of return. Fortune's Formula traces how the Kelly formula sparked controversy even as it made fortunes at racetracks, casinos, and trading desks. It reveals the dark side of this alluring scheme, which is founded on exploiting an insider's edge. Shannon believed it was possible for a smart investor to beat the market—and William Poundstone's Fortune's Formula will convince you that he was right.

Calendar Anomalies And Arbitrage

Author: William T Ziemba
Publisher: World Scientific
ISBN: 9814405477
Size: 54.74 MB
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This book discusses calendar or seasonal anomalies in worldwide equity markets as well as arbitrage and risk arbitrage. A complete update of US anomalies such as the January turn-of-the year, turn-of-the-month, January barometer, sell in May and go away, holidays, days of the week, options expiry and other effects is given concentrating on the futures markets where these anomalies can be easily applied. Other effects that lend themselves to modified buy and hold cash strategies include the presidential election and factor models based on fundamental anomalies. The ideas have been used successfully by the author in personal and managed accounts and hedge funds. Contents:Introduction — Calendar Anomalies (C S Dzhabarov and W T Ziemba)Playing the Turn-of-the-Year Effect with Index Futures (R Clark and W T Ziemba)Arbitrage Strategies for Cross-Track Betting on Major Horse Races (D B Hausch and W T Ziemba)Locks at the Racetrack (D B Hausch and W T Ziemba)Arbitrage and Risk Arbitrage in Team Jai Alai (D Lane and W T Ziemba)Miscellaneous InsertsRisk Arbitrage in the Nikkei Put Warrant Market of 1989–1990 (J Shaw, E O Thorp and W T Ziemba)Design of Anomalies Funds: Concepts and Experience (D R Capozza and W T Ziemba)Land and Stock Prices in Japan (D Stone and W T Ziemba)The Chicken or the Egg: Land and Stock Prices in Japan (W T Ziemba)Japanese Security Market Regularities: Monthly, Turn-of-the-Month and Year, Holiday and Golden Week Effects (W T Ziemba)Seasonality Effects in Japanese Futures Markets (W T Ziemba)Day of the Week Effects in Japanese Stocks (K Kato, S L Schwartz and W T Ziemba)Comment on “Why a Weekend Effect?” (W T Ziemba)The Turn-of-the-Month Effect in the World's Stock Markets, January 1988 – January 1990 (T Martikainen, J Perttunen and W T Ziemba)The Turn-of-the-Month Effect in the U.S. Stock Index Futures Markets, 1982–1992 (C Hensel, and G A Sick and W T Ziemba)Worldwide Security Market Anomalies (W T Ziemba and C R Hensel)Worldwide Security Market Regularities (W T Ziemba)Cointegration Analysis of the Fed Model (M Koivu, T Pennanen and W T Ziemba)The Predictive Ability of the Bond-Stock Earnings Yield Differential Model (K Berge, G Consigli and W T Ziemba)Efficiency of Racing, Sports, and Lottery Betting Markets (W T Ziemba)The Favorite-Longshot Bias in S&P500 and FTSE 100 Index Futures Options: The Return to Bets and the Cost of Insurance (R G Tompkins, W T Ziemba and S D Hodges)The Dosage Breeding Theory for Horse Racing Predictions (M Gramm and W T Ziemba)An Application of Expert Information to Win Betting on the Kentucky Derby, 1981–2005 (R S Bain, D B Hausch and W T Ziemba) Readership: Students, researchers and professionals who are interested in stock market investment and futures trading strategies. Keywords:Calendar Anomalies;Arbitrage;Stock Prices;Stock Returns;US Stock Market;Futures Markets;Betting;Trading Strategies;Sports Market;Lottery Market;Capital Growth Theory;Semi-Strong Market Efficiency;Speculative Investments;Index Futures;Factor Models Based on Fundamental Anomalies;Worldwide Stock Market StrategiesReviews: “For several decades William T. Ziemba has focused on documenting, explaining, and trading on, calendar-based and other anomalies. This collection contains not only the original papers, but updates that examine whether the patterns persist.” Jay R Ritter Professor of Finance University of Florida “A question I am frequently asked is whether stock market regularities persist into the future. My answer is always the same. If you think an anomaly looks interesting, don't invest a penny until you have read what William T Ziemba has to say about it. He is the master of research on anomaly strategies.” Elroy Dimson Professor Emeritus London Business School “Research on return anomalies touches upon central topics in financial economics: Are markets informationally efficient? Are smart arbitrageurs able to correct mispricing swiftly, or at all? Are patterns of predictability in securities markets the consequences of risk premia, psychological bias, or mere ex post data-mining? To address these questions it is valuable to have an extensive inventory of careful studies of different kinds of markets, assets, countries, frequencies, institutional settings, and time periods. As such, this volume is a valuable source of ideas and stylized facts for the building of new theoretical insight.” David Hirshleifer Professor of Finance UC Irvine “Can you beat the market by using historical patterns in financial data? Here is the latest and most comprehensive treatment of these anomalies by a leading theorist and practitioner—what paid, what is working, and what might be profitable in the future.” Edward O Thorp Edward O Thorp & Associates Author of “Beat the Dealer” and “Beat the Market” “This lively retrospective takes readers on an informative anomalies tour, featuring both breadth and depth, across Japan, Europe, and the US in markets for equities, fixed income securities, land, and horse race betting.” Hersh Shefrin Professor of Finance Santa Clara University

Rational Decisions

Author: Ken Binmore
Publisher: Princeton University Press
ISBN: 9781400833092
Size: 18.49 MB
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It is widely held that Bayesian decision theory is the final word on how a rational person should make decisions. However, Leonard Savage--the inventor of Bayesian decision theory--argued that it would be ridiculous to use his theory outside the kind of small world in which it is always possible to "look before you leap." If taken seriously, this view makes Bayesian decision theory inappropriate for the large worlds of scientific discovery and macroeconomic enterprise. When is it correct to use Bayesian decision theory--and when does it need to be modified? Using a minimum of mathematics, Rational Decisions clearly explains the foundations of Bayesian decision theory and shows why Savage restricted the theory's application to small worlds. The book is a wide-ranging exploration of standard theories of choice and belief under risk and uncertainty. Ken Binmore discusses the various philosophical attitudes related to the nature of probability and offers resolutions to paradoxes believed to hinder further progress. In arguing that the Bayesian approach to knowledge is inadequate in a large world, Binmore proposes an extension to Bayesian decision theory--allowing the idea of a mixed strategy in game theory to be expanded to a larger set of what Binmore refers to as "muddled" strategies. Written by one of the world's leading game theorists, Rational Decisions is the touchstone for anyone needing a concise, accessible, and expert view on Bayesian decision making.

Financial Derivatives

Author: Jamil Baz
Publisher: Cambridge University Press
ISBN: 9780521815109
Size: 26.15 MB
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This book offers a complete, succinct account of the principles of financial derivatives pricing. The first chapter provides readers with an intuitive exposition of basic random calculus. Concepts such as volatility and time, random walks, geometric Brownian motion, and Ito's lemma are discussed heuristically. The second chapter develops generic pricing techniques for assets and derivatives, determining the notion of a stochastic discount factor or pricing kernel, and then uses this concept to price conventional and exotic derivatives. The third chapter applies the pricing concepts to the special case of interest rate markets, namely, bonds and swaps, and discusses factor models and term structure consistent models. The fourth chapter deals with a variety of mathematical topics that underlie derivatives pricing and portfolio allocation decisions such as mean-reverting processes and jump processes and discusses related tools of stochastic calculus such as Kolmogorov equations, martingale techniques, stochastic control, and partial differential equations.

Efficiency Of Racetrack Betting Markets

Author: Donald B. Hausch
Publisher: World Scientific
ISBN: 9812819193
Size: 52.13 MB
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A reprint of one of the classic volumes on racetrack efficiency, this book is the only one in its field that deals with the racetrack betting market in-depth, containing all the important historical papers on racetrack efficiency. As evidenced by the collection of articles, the understanding of racetrack betting is clearly drawn from, and has correspondingly returned something to, all the fields of psychology, economics, finance, statistics, mathematics and management science.