IDEAS home Printed from https://ideas.repec.org/a/kap/jbioec/v20y2018i1d10.1007_s10818-017-9253-z.html
   My bibliography  Save this article

The growth of relative wealth and the Kelly criterion

Author

Listed:
  • Andrew W. Lo

    (Massachusetts Institute of Technology
    Massachusetts Institute of Technology
    Massachusetts Institute of Technology)

  • H. Allen Orr

    (University of Rochester)

  • Ruixun Zhang

    (Massachusetts Institute of Technology)

Abstract

We propose an evolutionary framework for optimal portfolio growth theory in which investors subject to environmental pressures allocate their wealth between two assets. By considering both absolute wealth and relative wealth between investors, we show that different investor behaviors survive in different environments. When investors maximize their relative wealth, the Kelly criterion is optimal only under certain conditions, which are identified. The initial relative wealth plays a critical role in determining the deviation of optimal behavior from the Kelly criterion regardless of whether the investor is myopic across a single time period or maximizing wealth over an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.

Suggested Citation

  • Andrew W. Lo & H. Allen Orr & Ruixun Zhang, 2018. "The growth of relative wealth and the Kelly criterion," Journal of Bioeconomics, Springer, vol. 20(1), pages 49-67, April.
  • Handle: RePEc:kap:jbioec:v:20:y:2018:i:1:d:10.1007_s10818-017-9253-z
    DOI: 10.1007/s10818-017-9253-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10818-017-9253-z
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s10818-017-9253-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrew E. Clark & Paul Frijters & Michael A. Shields, 2008. "Relative Income, Happiness, and Utility: An Explanation for the Easterlin Paradox and Other Puzzles," Journal of Economic Literature, American Economic Association, vol. 46(1), pages 95-144, March.
    2. Amir, Rabah & Evstigneev, Igor V. & Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Market selection and survival of investment strategies," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 105-122, February.
    3. Aurell, Erik & Baviera, Roberto & Hammarlid, Ola & Serva, Maurizio & Vulpiani, Angelo, 2000. "Growth optimal investment and pricing of derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 505-521.
    4. Richard H. Thaler & Amos Tversky & Daniel Kahneman & Alan Schwartz, 1997. "The Effect of Myopia and Loss Aversion on Risk Taking: An Experimental Test," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 112(2), pages 647-661.
    5. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 23(3), pages 165-180.
    6. Hirshleifer, David & Luo, Guo Ying, 2001. "On the survival of overconfident traders in a competitive securities market," Journal of Financial Markets, Elsevier, vol. 4(1), pages 73-84, January.
    7. Igor Evstigneev & Thorsten Hens & Klaus Schenk-Hoppé, 2006. "Evolutionary stable stock markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 449-468, January.
    8. Jack Hirshleifer, 1978. "Natural Economy Versus Political Economy," UCLA Economics Working Papers 129, UCLA Department of Economics.
    9. Leonid Kogan & Stephen A. Ross & Jiang Wang & Mark M. Westerfield, 2006. "The Price Impact and Survival of Irrational Traders," Journal of Finance, American Finance Association, vol. 61(1), pages 195-229, February.
    10. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-857, July.
    11. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    12. Rogers, Alan R, 1994. "Evolution of Time Preference by Natural Selection," American Economic Review, American Economic Association, vol. 84(3), pages 460-481, June.
    13. De Long, J Bradford & Andrei Shleifer & Lawrence H. Summers & Robert J. Waldmann, 1990. "Noise Trader Risk in Financial Markets," Journal of Political Economy, University of Chicago Press, vol. 98(4), pages 703-738, August.
    14. Clark, Andrew E. & Oswald, Andrew J., 1996. "Satisfaction and comparison income," Journal of Public Economics, Elsevier, vol. 61(3), pages 359-381, September.
    15. Lawrence Blume & David Easley, 2006. "If You're so Smart, why Aren't You Rich? Belief Selection in Complete and Incomplete Markets," Econometrica, Econometric Society, vol. 74(4), pages 929-966, July.
    16. Hens, Thorsten & Schenk-Hoppe, Klaus Reiner, 2005. "Evolutionary stability of portfolio rules in incomplete markets," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 43-66, February.
    17. Robson, Arthur J., 1996. "A Biological Basis for Expected and Non-expected Utility," Journal of Economic Theory, Elsevier, vol. 68(2), pages 397-424, February.
    18. Biais, Bruno & Shadur, Raphael, 2000. "Darwinian selection does not eliminate irrational traders," European Economic Review, Elsevier, vol. 44(3), pages 469-490, March.
    19. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    20. De Long, J Bradford & Shleifer, Andrei & Summers, Lawrence H & Waldmann, Robert J, 1991. "The Survival of Noise Traders in Financial Markets," The Journal of Business, University of Chicago Press, vol. 64(1), pages 1-19, January.
    21. Hirshleifer, Jack, 1977. "Economics from a Biological Viewpoint," Journal of Law and Economics, University of Chicago Press, vol. 20(1), pages 1-52, April.
    22. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    23. Terence C. Burnham & Aimee Dunlap & David W. Stephens, 2015. "Experimental Evolution and Economics," SAGE Open, , vol. 5(4), pages 21582440156, November.
    24. Hubertus J. E. Beaumont & Jenna Gallie & Christian Kost & Gayle C. Ferguson & Paul B. Rainey, 2009. "Experimental evolution of bet hedging," Nature, Nature, vol. 462(7269), pages 90-93, November.
    25. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
    26. Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk‐Hoppé, 2002. "Market Selection Of Financial Trading Strategies: Global Stability," Mathematical Finance, Wiley Blackwell, vol. 12(4), pages 329-339, October.
    27. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, vol. 39(1), pages 11-33, March.
    28. Hansson, Ingemar & Stuart, Charles, 1990. "Malthusian Selection of Preferences," American Economic Review, American Economic Association, vol. 80(3), pages 529-544, June.
    29. Arthur J. Robson & Larry Samuelson, 2009. "The Evolution of Time Preference with Aggregate Uncertainty," American Economic Review, American Economic Association, vol. 99(5), pages 1925-1953, December.
    30. Thomas J. Brennan & Andrew W. Lo, 2011. "The Origin of Behavior," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 55-108.
    31. Bakshi, Gurdip S & Chen, Zhiwu, 1996. "The Spirit of Capitalism and Stock-Market Prices," American Economic Review, American Economic Association, vol. 86(1), pages 133-157, March.
    32. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    33. Samuelson, Larry, 2001. "Introduction to the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 225-230, April.
    34. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    35. Hirshleifer, David & Subrahmanyam, Avanidhar & Titman, Sheridan, 2006. "Feedback and the success of irrational investors," Journal of Financial Economics, Elsevier, vol. 81(2), pages 311-338, August.
    36. Hakansson, Nils H, 1970. "Optimal Investment and Consumption Strategies Under Risk for a Class of Utility Functions," Econometrica, Econometric Society, vol. 38(5), pages 587-607, September.
    37. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
    38. Arthur J. Robson, 2001. "Why Would Nature Give Individuals Utility Functions?," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 900-929, August.
    39. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    40. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    41. Waldman, Michael, 1994. "Systematic Errors and the Theory of Natural Selection," American Economic Review, American Economic Association, vol. 84(3), pages 482-497, June.
    42. Luo Guo Ying, 1995. "Evolution and Market Competition," Journal of Economic Theory, Elsevier, vol. 67(1), pages 223-250, October.
    43. Stroyan, K. D., 1983. "Myopic utility functions on sequential economies," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 267-276, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thomas J. Brennan & Andrew W. Lo & Ruixun Zhang, 2018. "Variety Is the Spice of Life: Irrational Behavior as Adaptation to Stochastic Environments," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 1-39, September.
    2. Rabah Amir & Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2022. "An evolutionary finance model with short selling and endogenous asset supply," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 655-677, April.
    3. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, arXiv.org.
    4. Evstigneev, Igor & Hens, Thorsten & Potapova, Valeriya & Schenk-Hoppé, Klaus R., 2020. "Behavioral equilibrium and evolutionary dynamics in asset markets," Journal of Mathematical Economics, Elsevier, vol. 91(C), pages 121-135.
    5. Hsieh, Chung-Han, 2024. "On solving robust log-optimal portfolio: A supporting hyperplane approximation approach," European Journal of Operational Research, Elsevier, vol. 313(3), pages 1129-1139.
    6. Sergei Belkov & Igor V. Evstigneev & Thorsten Hens, 2020. "An evolutionary finance model with a risk-free asset," Annals of Finance, Springer, vol. 16(4), pages 593-607, December.
    7. Chung-Han Hsieh, 2022. "On Solving Robust Log-Optimal Portfolio: A Supporting Hyperplane Approximation Approach," Papers 2202.03858, arXiv.org.
    8. Mu-En Wu & Jia-Hao Syu & Chien-Ming Chen, 2022. "Kelly-Based Options Trading Strategies on Settlement Date via Supervised Learning Algorithms," Computational Economics, Springer;Society for Computational Economics, vol. 59(4), pages 1627-1644, April.
    9. I. V. Evstigneev & T. Hens & M. J. Vanaei, 2023. "Evolutionary finance: a model with endogenous asset payoffs," Journal of Bioeconomics, Springer, vol. 25(2), pages 117-143, August.
    10. Chung-Han Hsieh, 2020. "Necessary and Sufficient Conditions for Frequency-Based Kelly Optimal Portfolio," Papers 2004.12099, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Hirshleifer, David & Lo, Andrew W. & Zhang, Ruixun, 2023. "Social contagion and the survival of diverse investment styles," Journal of Economic Dynamics and Control, Elsevier, vol. 154(C).
    2. Thomas J. Brennan & Andrew W. Lo & Ruixun Zhang, 2018. "Variety Is the Spice of Life: Irrational Behavior as Adaptation to Stochastic Environments," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(03), pages 1-39, September.
    3. Lensberg, Terje & Schenk-Hoppé, Klaus Reiner, 2006. "On the Evolution of Investment Strategies and the Kelly Rule – A Darwinian Approach," Discussion Papers 2006/23, Norwegian School of Economics, Department of Business and Management Science.
    4. Thomas J Brennan & Andrew W Lo, 2012. "An Evolutionary Model of Bounded Rationality and Intelligence," PLOS ONE, Public Library of Science, vol. 7(11), pages 1-8, November.
    5. H. Allen Orr, 2018. "Evolution, finance, and the population genetics of relative wealth," Journal of Bioeconomics, Springer, vol. 20(1), pages 29-48, April.
    6. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    7. Dindo, Pietro, 2019. "Survival in speculative markets," Journal of Economic Theory, Elsevier, vol. 181(C), pages 1-43.
    8. Mikhail Zhitlukhin, 2021. "Capital growth and survival strategies in a market with endogenous prices," Papers 2101.09777, arXiv.org.
    9. Peter A. F. Fraser‐Mackenzie & Tiejun Ma & Ming‐Chien Sung & Johnnie E. V. Johnson, 2019. "Let's Call it Quits: Break‐Even Effects in the Decision to Stop Taking Risks," Risk Analysis, John Wiley & Sons, vol. 39(7), pages 1560-1581, July.
    10. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    11. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    12. Emilio Barucci & Marco Casna, 2014. "On the Market Selection Hypothesis in a Mean Reverting Environment," Computational Economics, Springer;Society for Computational Economics, vol. 44(1), pages 101-126, June.
    13. Yao, Jing & Li, Duan, 2013. "Bounded rationality as a source of loss aversion and optimism: A study of psychological adaptation under incomplete information," Journal of Economic Dynamics and Control, Elsevier, vol. 37(1), pages 18-31.
    14. Leonid Kogan & Stephen A. Ross & Jiang Wang & Mark M. Westerfield, 2006. "The Price Impact and Survival of Irrational Traders," Journal of Finance, American Finance Association, vol. 61(1), pages 195-229, February.
    15. Witte, Björn-Christopher, 2012. "Fund managers - Why the best might be the worst: On the evolutionary vigor of risk-seeking behavior," Economics Discussion Papers 2012-20, Kiel Institute for the World Economy (IfW Kiel).
    16. Brock, W.A. & Hommes, C.H. & Wagener, F.O.O., 2009. "More hedging instruments may destabilize markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(11), pages 1912-1928, November.
    17. Thorsten Hens & Klaus Reiner Schenk-Hoppé & Martin Stalder, 2002. "An Application of Evolutionary Finance to Firms Listed in the Swiss Market Index," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(IV), pages 465-487, December.
    18. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2019. "Momentum and reversal in financial markets with persistent heterogeneity," Annals of Finance, Springer, vol. 15(4), pages 455-487, December.
    19. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    20. Kogan, Leonid & Ross, Stephen A. & Wang, Jiang & Westerfield, Mark M., 2017. "Market selection," Journal of Economic Theory, Elsevier, vol. 168(C), pages 209-236.

    More about this item

    Keywords

    Kelly criterion; Portfolio optimization; Adaptive Markets Hypothesis; Evolutionary game theory;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jbioec:v:20:y:2018:i:1:d:10.1007_s10818-017-9253-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.