The Kelly Capital Growth Investment Criterion - Contents

World Scientific Handbook in Financial Economic Series — Vol. 3

THEORY and PRACTICE

THE

KELLY CAPITAL GROWTH INVESTMENT CRITERION

Editors

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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

Contents Preface

xv

List of Contributors

xvii

Acknowledgments

xxi

Pictures

xxv Part I: The Early Ideas and Contributions

1. Introduction to the Early Ideas and Contributions 2. Exposition of a New Theory on the Measurement of Risk (translated by Louise Sommer)

3 11

D. Bernoulli Econometrica, 22, 23-36 (1954) 3. A New Interpretation of Information Rate

25

J. R. Kelly, Jr. Bell System Technical Journal, 35, 917-926 (1956) 4. Criteria for Choice among Risky Ventures

35

H. A. Latane Journal of Political Economy, 67, 144-155 (1959) 5. Optimal Gambling Systems for Favorable Games L. Breiman Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, 1, 63-68 (1961)

47

viii Contents

6. Optimal Gambling Systems for Favorable Games

61

E. O. Thorp Review of the International Statistical Institute, 37(3), 273-293 (1969) 7. Portfolio Choice and the Kelly Criterion

81

E. O. Thorp Proceedings of the Business and Economics Section of the American Statistical Association, 215-224 (1971) 8. Optimal Investment and Consumption Strategies under Risk for a Class of Utility Functions

91

N. H. Hakansson Econometrica, 38, 587-607 (1970) 9. On Optimal Myopic Portfolio Policies, with and without Serial Correlation of Yields

113

N. H. Hakansson Journal of Business, 44, 324-334 (1971) 10. Evidence on the "Growth-Optimum-Model"

125

R. Roll The Journal of Finance, 28(3), 551-566 (1973) Part II: Classic Papers and Theories 11. Introduction to the Classic Papers and Theories

143

12. Competitive Optimality of Logarithmic Investment

147

R. M. Bell and T. M. Cover Mathematics of Operations Research, 5(2), 161-166 (1980) 13. A Bound on the Financial Value of Information A. R. Barron and T. M. Cover IEEE Transactions of Information Theory, 34(5), 1097-1100 (1988)

153

Contents ix

14. Asymptotic Optimality and Asymptotic Equipartition Properties of Log-Optimum Investment

157

P. H. Algoet and T. M. Cover Annals of Probability, 16(2), 876-898 (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), 960-982 (1998) 17. Optimal Strategies for Repeated Games

235

M. Finkelstein and R. Whitley Advanced Applied Probability, 13, 415-428 (1981) 18. The Effect of Errors in Means, Variances and Co-Variances on Optimal Portfolio Choice

249

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), 343-355 (2005) 20. Survival and evolutionary Stability of Rule the Kelly I. V. Evstigneev, T. Hens, and K. R. Schenk-Hoppe (2010)

273

x Contents

21. Application of the Kelly Criterion to Ornstein-Uhlenbeck Processes

285

Y. Lv and B. K. Meister Lecture Notes of the Institute for Computer Sciences, 4, 1051-1062 (2009) Part III: The Relationship of Kelly Optimization to Asset Allocation 22. Introduction to the Relationship of Kelly Optimization to Asset Allocation

301

23. Survival and Growth with a Liability: Optimal Portfolio Strategies in Continuous Time

307

S. Browne Mathematics of Operations Research, 22(2), 468-493 (1997) 24. Growth versus Security in Dynamic Investment Analysis

331

L. C. MacLean, W. T. Ziemba, and G. Blazenko Management Science, 38(11), 1562-1585 (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), 937-954 (2004) 26. Risk-Constrained Dynamic Active Portfolio Management

373

S. Browne Management Science, 46(9), 1188-1199 (2000) 27. Fractional Kelly Strategies for Benchmark Asset Management

385

M. Davis and S. Lleo (2010) 28. A Benchmark Approach to Investing and Pricing E. Platen (2010)

409

Contents

29. Growing Wealth with Fixed-Mix Strategies

xi

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

459

31. Lifetime Portfolio Selection by Dynamic Stochastic Programming

465

P. A. Samuelson Review of Economics and Statistics, 51, 239-246 (1969) 32. Models of Optimal Capital Accumulation and Portfolio Selection and the Captial Growth Criterion

473

W. T. Ziemba and R. G. Vickson (2010) 33. The "Fallacy" of Maximizing the Geometric Mean in Long Sequences of Investing or Gambling

487

P. A. Samuelson Proceedings National Academy of Science, 68(10), 2493-2496 (1971) 34. Why We Should Not Make Mean Log of Wealth Big Though Years to Act Are Long

491

P. A. Samuelson Journal of Banking and Finance, 3, 305-307 (1979) 35. Investment for the Long Run: New Evidence for an Old Rule

495

H. M. Markowitz Journal of Finance, 31(5), 1273-1286 (1976) 36. Understanding the Kelly Criterion E. O. Thorp Wilmott, May and September (2008)

509

xii Contents

37. Concave Utilities Are Distinguished by Their Optimal Strategies

525

E. O. Thorp and R. Whitley Colloquia Mathematica Societatis Janos Bolyai, 813-830 (1972) 38. Medium Term Simulations of the Full Kelly and Fractional Kelly Strategies Investment

543

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

575

41. 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, 65-86. North Holland (1995) 42. A Preference Foundation for Log Mean-Variance Criteria in Portfolio Choice Problems

599

D. G. Luenberger Journal of Economic Dynamics and Control, 17, 88-906 (1993) 43. Portfolio Choice with Endogenous Utility: A Large Deviations Approach M. Stutzer Journal of Econometrics, 116, 365-386 (2003)

619

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 Strategies by the Great Investors and Others

657

46. Efficiency of the Market for Racetrack Betting

663

D. B. Hausch, W. T. Ziemba, and M. E. Rubinstein Management Science, 27, 1435-1452 (1981) 47. Transactions Costs, Extent of Inefficiencies, Entries and Multiple Wagers in a Racetrack Betting Model

681

D. B. Hausch and W. T. Ziemba Management Science, 31, 381-394 (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, 567-574. World Scientific (2008) 49. A Half Century of Returns on Levered and Unlevered Portfolios of Stocks, Bonds and Bills, with and without Small Stocks

703

R. R. Grauer and N. H. Hakansson Journal of Business, 592, 287-318 (1986) 50. A Dynamic Portfolio of Investment Strategies: Applying Capital Growth with Drawdown Penalties J. M. Mulvey, M. Bilgili, and T. M. Vural (2010)

735

xiv

Contents

51. Intertemporal Surplus Management

753

M. Rudolf and W. T. Ziemba Journal of Economic Dynamics and Control, 28, 975-990 (2004) 52. The Symmetric Downside-Risk Sharpe Ratio and the Evaluation of Great Investors and Speculators

769

W. T. Ziemba Journal of Portfolio Management, 32(1), 108-122 (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, 295-298. Wiley (2007) 54. The Kelly Criterion in Blackjack Sports Betting and the Stock Market

789

E. O. Thorp In S. A. Zenios and W. T. Ziemba (Eds.), Handbook of Asset and Liability Management, Volume 1, 387-428. Elsevier (2006) Bibliography

833

Author Index

839

Subject Index

843