The Kelly Capital Growth Investment Criterion - Contents 715f2u
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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
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
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
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
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