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The Growth of Relative Wealth and the Kelly Criterion

24 Pages Posted: 19 Jan 2017 Last revised: 10 Sep 2017

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Allen Orr

University of Rochester

Ruixun Zhang

MIT Laboratory for Financial Engineering

Date Written: September 10, 2017

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, whether the investor is myopic across a single time period, or is maximizing wealth with an infinite horizon. We relate these results to population genetics, and discuss testable consequences of these findings using experimental evolution.

Keywords: Kelly Criterion, Portfolio Optimization, Adaptive Markets Hypothesis, Evolutionary Game Theory

JEL Classification: G11, G12, D03, D11

Suggested Citation

Lo, Andrew W. and Orr, Allen and Zhang, Ruixun, The Growth of Relative Wealth and the Kelly Criterion (September 10, 2017). Available at SSRN: https://ssrn.com/abstract=2900509 or http://dx.doi.org/10.2139/ssrn.2900509

Andrew W. Lo (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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National Bureau of Economic Research (NBER) ( email )

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Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Stata Center
Cambridge, MA 02142
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Allen Orr

University of Rochester ( email )

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Rochester, NY 14627
United States

Ruixun Zhang

MIT Laboratory for Financial Engineering ( email )

77 Massachusetts Ave. E62-663
Cambridge, MA 02142
United States

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