The Kelly Capital Growth Investment Criterion - Contents

World Scientific Handbook in Financial Economic Series Vol. 3

THEORY and PRACTICE

THE

KELLY CAPITAL GROWTHINVESTMENT CRITERION

Editors ' jjLeonard C MacLeanDalhousie University, USA

Edward 0 ThorpUniversity of California, Irvine, USA

William T ZiembaMathematical Institute, Oxford University, UK and University of British Columbia, Canada

i World ScientificNEW 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 3

2. Exposition of a New Theory on the Measurement of Risk 11(translated by Louise Sommer)

D. BernoulliEconometrica, 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. LataneJournal of Political Economy, 67, 144-155 (1959)

5. Optimal Gambling Systems for Favorable Games 47

L. BreimanProceedings of the 4th Berkeley Symposium onMathematical Statistics and Probability, 1, 63-68 (1961)

viii Contents

6. Optimal Gambling Systems for Favorable Games 61

E. O. ThorpReview of the International Statistical Institute, 37(3),273-293 (1969)

7. Portfolio Choice and the Kelly Criterion 81

E. O. ThorpProceedings of the Business and Economics Section ofthe American Statistical Association, 215-224 (1971)

8. Optimal Investment and Consumption Strategies under Risk 91for a Class of Utility Functions

N. H. HakanssonEconometrica, 38, 587-607 (1970)

9. On Optimal Myopic Portfolio Policies, with and without 113Serial Correlation of Yields

N. H. HakanssonJournal of Business, 44, 324-334 (1971)

10. Evidence on the "Growth-Optimum-Model" 125

R. RollThe 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. CoverMathematics of Operations Research, 5(2),161-166 (1980)

13. A Bound on the Financial Value of Information 153

A. R. Barron and T. M. CoverIEEE Transactions of Information Theory, 34(5),1097-1100 (1988)

Contents ix

14. Asymptotic Optimality and Asymptotic Equipartition 157Properties of Log-Optimum Investment

P. H. Algoet and T. M. CoverAnnals of Probability, 16(2), 876-898 (1988)

15. Universal Portfolios 181

T. M. CoverMathematical Finance, 1(1), 1-29(1991)

16. The Cost of Achieving the Best Portfolio in Hindsight 211

E. Ordentlich and T. M. CoverMathematics of Operations Research, 23(4),960-982 (1998)

17. Optimal Strategies for Repeated Games 235

M. Finkelstein and R. WhitleyAdvanced Applied Probability, 13, 415-428 (1981)

18. The Effect of Errors in Means, Variances and Co-Variances 249on Optimal Portfolio Choice

V. K. Chopra and W. T. ZiembaJournal of Portfolio Management, 19, 6-11 (1993)

19. Time to Wealth Goals' in Capital Accumulation 259

L. C. MacLean, W. T. Ziemba, and Y. LiQuantitative Finance, 5(4), 343-355 (2005)

20. Survival and evolutionary Stability of Rule the Kelly 273

I. V. Evstigneev, T. Hens, and K. R. Schenk-Hoppe(2010)

x Contents

21. Application of the Kelly Criterion to Ornstein-Uhlenbeck 285Processes

Y. Lv and B. K. MeisterLecture Notes of the Institute for Computer Sciences, 4,1051-1062 (2009)

Part III: The Relationship of Kelly Optimization toAsset Allocation

22. Introduction to the Relationship of Kelly Optimization to 301Asset Allocation

23. Survival and Growth with a Liability: Optimal Portfolio 307Strategies in Continuous Time

S. BrowneMathematics 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. BlazenkoManagement Science, 38(11), 1562-1585 (1992)

25. Capital Growth with Security 355

L. C. MacLean, R. Sanegre, Y. Zhao, and W. T. ZiembaJournal of Economic Dynamics and Control, 28(4),937-954 (2004)

26. Risk-Constrained Dynamic Active Portfolio Management 373

S. BrowneManagement 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 409

E. Platen (2010)

Contents xi

29. Growing Wealth with Fixed-Mix Strategies 427

" M. A. H. Dempster, I. V. Evstigneev, andK. R. Schenk-Hoppe (2010)

Part IV: Critics and Assessing the Good and BadProperties of Kelly

30. Introduction to the Good and Bad Properties of Kelly 459

31. Lifetime Portfolio Selection by Dynamic Stochastic 465Programming

P. A. SamuelsonReview of Economics and Statistics, 51, 239-246 (1969)

32. Models of Optimal Capital Accumulation and Portfolio 473Selection and the Captial Growth Criterion

W. T. Ziemba and R. G. Vickson (2010)

33. The "Fallacy" of Maximizing the Geometric Mean in Long 487Sequences of Investing or Gambling

P. A. SamuelsonProceedings National Academy of Science, 68(10),2493-2496 (1971)

34. Why We Should Not Make Mean Log of Wealth Big Though 491Years to Act Are Long

P. A. SamuelsonJournal of Banking and Finance, 3, 305-307 (1979)

35. Investment for the Long Run: New Evidence for an Old Rule 495

H. M. MarkowitzJournal of Finance, 31(5), 1273-1286 (1976)

36. Understanding the Kelly Criterion 509

E. O. ThorpWilmott, May and September (2008)

xii Contents

37. Concave Utilities Are Distinguished by Their 525Optimal Strategies

E. O. Thorp and R. WhitleyColloquia Mathematica Societatis Janos Bolyai,813-830 (1972)

38. Medium Term Simulations of the Full Kelly and 543Fractional Kelly Strategies Investment

L. C. MacLean, E. O. Thorp, Y. Zhao, andW. 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. ZiembaIn 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 599Portfolio Choice Problems

D. G. LuenbergerJournal of Economic Dynamics and Control, 17,88-906 (1993)

43. Portfolio Choice with Endogenous Utility: A Large 619Deviations Approach

M. StutzerJournal of Econometrics, 116, 365-386 (2003)

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 theGreat Investors and Others

45. Introduction to the Evidence of the Use of Kelly Type 657Strategies by the Great Investors and Others

46. Efficiency of the Market for Racetrack Betting 663

D. B. Hausch, W. T. Ziemba, and M. E. RubinsteinManagement Science, 27, 1435-1452 (1981)

47. Transactions Costs, Extent of Inefficiencies, Entries and 681Multiple Wagers in a Racetrack Betting Model

D. B. Hausch and W. T. ZiembaManagement Science, 31, 381-394 (1985)

48. The Dr. Z Betting System in England 695

W. T. Ziemba and D. B. HauschIn 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 703of Stocks, Bonds and Bills, with and without Small Stocks

R. R. Grauer and N. H. HakanssonJournal of Business, 592, 287-318 (1986)

50. A Dynamic Portfolio of Investment Strategies: Applying 735Capital Growth with Drawdown Penalties

J. M. Mulvey, M. Bilgili, and T. M. Vural (2010)

xiv Contents

51. Intertemporal Surplus Management 753

M. Rudolf and W. T. ZiembaJournal of Economic Dynamics and Control, 28,975-990 (2004)

52. The Symmetric Downside-Risk Sharpe Ratio and the 769Evaluation of Great Investors and Speculators

W. T. ZiembaJournal of Portfolio Management, 32(1), 108-122(2005)

53. Postscript: The Renaissance Medallion Fund 785

R. E. S. Ziemba and W. T. ZiembaIn Scenarios for Risk Management and GlobalInvestment Strategies, 295-298. Wiley (2007)

54. The Kelly Criterion in Blackjack Sports Betting and the 789Stock Market

E. O. ThorpIn 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