KELLY CAPITAL GROWTH
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1 World Scientific Handbook in Financial Economic Series Vol. 3 THEORY and PRACTICE THE KELLY CAPITAL GROWTH INVESTMENT CRITERION Editors ' jj Leonard C MacLean Dalhousie University, USA Edward 0 Thorp University of California, Irvine, USA William T Ziemba Mathematical Institute, Oxford University, UK and University of British Columbia, Canada i World Scientific NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI
2 Contents Preface List of Contributors Acknowledgments Pictures xv xvii xxi xxv Part I: The Early Ideas and Contributions 1. Introduction to the Early Ideas and Contributions 3 2. Exposition of a New Theory on the Measurement of Risk 11 (translated by Louise Sommer) D. Bernoulli Econometrica, 22, (1954) 3. A New Interpretation of Information Rate 25 J. R. Kelly, Jr. Bell System Technical Journal, 35, (1956) 4. Criteria for Choice among Risky Ventures 35 H. A. Latane Journal of Political Economy, 67, (1959) 5. Optimal Gambling Systems for Favorable Games 47 L. Breiman Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, 1, (1961)
3 viii Contents 6. Optimal Gambling Systems for Favorable Games 61 E. O. Thorp Review of the International Statistical Institute, 37(3), (1969) 7. Portfolio Choice and the Kelly Criterion 81 E. O. Thorp Proceedings of the Business and Economics Section of the American Statistical Association, (1971) 8. Optimal Investment and Consumption Strategies under Risk 91 for a Class of Utility Functions N. H. Hakansson Econometrica, 38, (1970) 9. On Optimal Myopic Portfolio Policies, with and without 113 Serial Correlation of Yields N. H. Hakansson Journal of Business, 44, (1971) 10. Evidence on the "Growth-Optimum-Model" 125 R. Roll The Journal of Finance, 28(3), (1973) Part II: Classic Papers and Theories 11. Introduction to the Classic Papers and Theories Competitive Optimality of Logarithmic Investment 147 R. M. Bell and T. M. Cover Mathematics of Operations Research, 5(2), (1980) 13. A Bound on the Financial Value of Information 153 A. R. Barron and T. M. Cover IEEE Transactions of Information Theory, 34(5), (1988)
4 Contents ix 14. Asymptotic Optimality and Asymptotic Equipartition 157 Properties of Log-Optimum Investment P. H. Algoet and T. M. Cover Annals of Probability, 16(2), (1988) 15. Universal Portfolios 181 T. M. Cover Mathematical Finance, 1(1), 1-29(1991) 16. The Cost of Achieving the Best Portfolio in Hindsight 211 E. Ordentlich and T. M. Cover Mathematics of Operations Research, 23(4), (1998) 17. Optimal Strategies for Repeated Games 235 M. Finkelstein and R. Whitley Advanced Applied Probability, 13, (1981) 18. The Effect of Errors in Means, Variances and Co-Variances 249 on Optimal Portfolio Choice V. K. Chopra and W. T. Ziemba Journal of Portfolio Management, 19, 6-11 (1993) 19. Time to Wealth Goals' in Capital Accumulation 259 L. C. MacLean, W. T. Ziemba, and Y. Li Quantitative Finance, 5(4), (2005) 20. Survival and evolutionary Stability of Rule the Kelly 273 I. V. Evstigneev, T. Hens, and K. R. Schenk-Hoppe (2010)
5 x Contents 21. Application of the Kelly Criterion to Ornstein-Uhlenbeck 285 Processes Y. Lv and B. K. Meister Lecture Notes of the Institute for Computer Sciences, 4, (2009) Part III: The Relationship of Kelly Optimization to Asset Allocation 22. Introduction to the Relationship of Kelly Optimization to 301 Asset Allocation 23. Survival and Growth with a Liability: Optimal Portfolio 307 Strategies in Continuous Time S. Browne Mathematics of Operations Research, 22(2), (1997) 24. Growth versus Security in Dynamic Investment Analysis 331 L. C. MacLean, W. T. Ziemba, and G. Blazenko Management Science, 38(11), (1992) 25. Capital Growth with Security 355 L. C. MacLean, R. Sanegre, Y. Zhao, and W. T. Ziemba Journal of Economic Dynamics and Control, 28(4), (2004) 26. Risk-Constrained Dynamic Active Portfolio Management 373 S. Browne Management Science, 46(9), (2000) 27. Fractional Kelly Strategies for Benchmark Asset Management 385 M. Davis and S. Lleo (2010) 28. A Benchmark Approach to Investing and Pricing 409 E. Platen (2010)
6 Contents xi 29. Growing Wealth with Fixed-Mix Strategies 427 " M. A. H. Dempster, I. V. Evstigneev, and K. R. Schenk-Hoppe (2010) Part IV: Critics and Assessing the Good and Bad Properties of Kelly 30. Introduction to the Good and Bad Properties of Kelly Lifetime Portfolio Selection by Dynamic Stochastic 465 Programming P. A. Samuelson Review of Economics and Statistics, 51, (1969) 32. Models of Optimal Capital Accumulation and Portfolio 473 Selection and the Captial Growth Criterion W. T. Ziemba and R. G. Vickson (2010) 33. The "Fallacy" of Maximizing the Geometric Mean in Long 487 Sequences of Investing or Gambling P. A. Samuelson Proceedings National Academy of Science, 68(10), (1971) 34. Why We Should Not Make Mean Log of Wealth Big Though 491 Years to Act Are Long P. A. Samuelson Journal of Banking and Finance, 3, (1979) 35. Investment for the Long Run: New Evidence for an Old Rule 495 H. M. Markowitz Journal of Finance, 31(5), (1976) 36. Understanding the Kelly Criterion 509 E. O. Thorp Wilmott, May and September (2008)
7 xii Contents 37. Concave Utilities Are Distinguished by Their 525 Optimal Strategies E. O. Thorp and R. Whitley Colloquia Mathematica Societatis Janos Bolyai, (1972) 38. Medium Term Simulations of the Full Kelly and 543 Fractional Kelly Strategies Investment L. C. MacLean, E. O. Thorp, Y. Zhao, and W. T. Ziemba (2010) 39. Good and Bad Kelly Properties of the Kelly Criterion 563 L. C. MacLean, E. O. Thorp, and W. T. Ziemba (2010) Part V: Utility Foundations 40. Introduction to the Utility Foundations of Kelly Capital Growth Theory 577 N. H. Hakansson and W. T. Ziemba In R. A. Jarrow, V. Maksimovic, and W. T. Ziemba (Eds.), Finance, Handbooks in OR & MS, Volume 9, North Holland (1995) 42. A Preference Foundation for Log Mean-Variance Criteria in 599 Portfolio Choice Problems D. G. Luenberger Journal of Economic Dynamics and Control, 17, (1993) 43. Portfolio Choice with Endogenous Utility: A Large 619 Deviations Approach M. Stutzer Journal of Econometrics, 116, (2003)
8 Contents xiii 44. On Growth-Optimality vs. Security against Underperformance 641 M. Stutzer (2010) Part VI: Evidence of the Use of Kelly Type Strategies by the Great Investors and Others 45. Introduction to the Evidence of the Use of Kelly Type 657 Strategies by the Great Investors and Others 46. Efficiency of the Market for Racetrack Betting 663 D. B. Hausch, W. T. Ziemba, and M. E. Rubinstein Management Science, 27, (1981) 47. Transactions Costs, Extent of Inefficiencies, Entries and 681 Multiple Wagers in a Racetrack Betting Model D. B. Hausch and W. T. Ziemba Management Science, 31, (1985) 48. The Dr. Z Betting System in England 695 W. T. Ziemba and D. B. Hausch In D. B. Hausch, V. Lo, and W. T. Ziemba (Eds.), Efficiency of Racetrack Betting Markets, World Scientific (2008) 49. A Half Century of Returns on Levered and Unlevered Portfolios 703 of Stocks, Bonds and Bills, with and without Small Stocks R. R. Grauer and N. H. Hakansson Journal of Business, 592, (1986) 50. A Dynamic Portfolio of Investment Strategies: Applying 735 Capital Growth with Drawdown Penalties J. M. Mulvey, M. Bilgili, and T. M. Vural (2010)
9 xiv Contents 51. Intertemporal Surplus Management 753 M. Rudolf and W. T. Ziemba Journal of Economic Dynamics and Control, 28, (2004) 52. The Symmetric Downside-Risk Sharpe Ratio and the 769 Evaluation of Great Investors and Speculators W. T. Ziemba Journal of Portfolio Management, 32(1), (2005) 53. Postscript: The Renaissance Medallion Fund 785 R. E. S. Ziemba and W. T. Ziemba In Scenarios for Risk Management and Global Investment Strategies, Wiley (2007) 54. The Kelly Criterion in Blackjack Sports Betting and the 789 Stock Market E. O. Thorp In S. A. Zenios and W. T. Ziemba (Eds.), Handbook of Asset and Liability Management, Volume 1, Elsevier (2006) Bibliography 833 Author Index 839 Subject Index 843
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