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.
    ---><---

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. John Lintner, 1965. "Security Prices, Risk, And Maximal Gains From Diversification," Journal of Finance, American Finance Association, vol. 20(4), pages 587-615, December.
    7. 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, Oxford University Press, vol. 112(2), pages 647-661.
    8. Samuelson, Larry, 2001. "Introduction to the Evolution of Preferences," Journal of Economic Theory, Elsevier, vol. 97(2), pages 225-230, April.
    9. R. H. Strotz, 1955. "Myopia and Inconsistency in Dynamic Utility Maximization," Review of Economic Studies, Oxford University Press, vol. 23(3), pages 165-180.
    10. 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.
    11. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    12. Clark, Andrew E. & Oswald, Andrew J., 1996. "Satisfaction and comparison income," Journal of Public Economics, Elsevier, vol. 61(3), pages 359-381, September.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Corneo, Giacomo & Jeanne, Olivier, 1997. "On relative wealth effects and the optimality of growth," Economics Letters, Elsevier, vol. 54(1), pages 87-92, January.
    19. 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.
    20. Jack Hirshleifer, 1978. "Natural Economy Versus Political Economy," UCLA Economics Working Papers 129, UCLA Department of Economics.
    21. 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.
    22. Blume, Lawrence & Easley, David, 1992. "Evolution and market behavior," Journal of Economic Theory, Elsevier, vol. 58(1), pages 9-40, October.
    23. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    24. 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.
    25. Rogers, Alan R, 1994. "Evolution of Time Preference by Natural Selection," American Economic Review, American Economic Association, vol. 84(3), pages 460-481, June.
    26. 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.
    27. 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.
    28. 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.
    29. Waldman, Michael, 1994. "Systematic Errors and the Theory of Natural Selection," American Economic Review, American Economic Association, vol. 84(3), pages 482-497, June.
    30. Luo Guo Ying, 1995. "Evolution and Market Competition," Journal of Economic Theory, Elsevier, vol. 67(1), pages 223-250, October.
    31. 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.
    32. Biais, Bruno & Shadur, Raphael, 2000. "Darwinian selection does not eliminate irrational traders," European Economic Review, Elsevier, vol. 44(3), pages 469-490, March.
    33. Alvaro Sandroni, 2000. "Do Markets Favor Agents Able to Make Accurate Predicitions?," Econometrica, Econometric Society, vol. 68(6), pages 1303-1342, November.
    34. Hirshleifer, Jack, 1977. "Economics from a Biological Viewpoint," Journal of Law and Economics, University of Chicago Press, vol. 20(1), pages 1-52, April.
    35. Stroyan, K. D., 1983. "Myopic utility functions on sequential economies," Journal of Mathematical Economics, Elsevier, vol. 11(3), pages 267-276, July.
    36. Sandroni, Alvaro, 2005. "Market selection when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 91-104, February.
    37. 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.
    38. Arthur J. Robson, 2001. "The Biological Basis of Economic Behavior," Journal of Economic Literature, American Economic Association, vol. 39(1), pages 11-33, March.
    39. Hansson, Ingemar & Stuart, Charles, 1990. "Malthusian Selection of Preferences," American Economic Review, American Economic Association, vol. 80(3), pages 529-544, June.
    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. 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.
    2. 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.
    3. 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.
    4. Chung-Han Hsieh, 2021. "On Asymptotic Log-Optimal Buy-and-Hold Strategy," Papers 2103.04898, 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. 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. 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.
    3. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, Open Access Journal, vol. 9(2), pages 1-67, May.
    4. 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.
    5. Hongjun Yan, 2008. "Natural Selection in Financial Markets: Does It Work?," Management Science, INFORMS, vol. 54(11), pages 1935-1950, November.
    6. H. Allen Orr, 2018. "Evolution, finance, and the population genetics of relative wealth," Journal of Bioeconomics, Springer, vol. 20(1), pages 29-48, April.
    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. Wei Xiong, 2013. "Bubbles, Crises, and Heterogeneous Beliefs," NBER Working Papers 18905, National Bureau of Economic Research, Inc.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Emanuela Sciubba, 2006. "The evolution of portfolio rules and the capital asset pricing model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 29(1), pages 123-150, September.
    15. 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.
    16. Luo, Guo Ying, 2012. "Conservative traders, natural selection and market efficiency," Journal of Economic Theory, Elsevier, vol. 147(1), pages 310-335.
    17. Giulio Bottazzi & Pietro Dindo & Daniele Giachini, 2018. "Long-run heterogeneity in an exchange economy with fixed-mix traders," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 66(2), pages 407-447, August.
    18. 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.
    19. Witte, Björn-Christopher, 2011. "Fund managers - why the best might be the worst: On the evolutionary vigor of risk-seeking behavior," BERG Working Paper Series 81, Bamberg University, Bamberg Economic Research Group.
    20. 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.

    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.

    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). General contact details of provider: http://www.springer.com .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.