The Growth of Relative Wealth and the Kelly Criterion

24 Pages Posted: 6 Feb 2019 Last revised: 19 Oct 2021

See all articles by Andrew W. Lo

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Laboratory for Financial Engineering; Santa Fe Institute

Allen Orr

University of Rochester - Department of Biology

Ruixun Zhang

Peking University; 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) - Laboratory for Financial Engineering ( email )

100 Main Street
E62-618
Cambridge, MA 02142
United States
617-253-0920 (Phone)
781 891-9783 (Fax)

HOME PAGE: http://web.mit.edu/alo/www

Santa Fe Institute

1399 Hyde Park Road
Santa Fe, NM 87501
United States

Allen Orr

University of Rochester - Department of Biology ( email )

Rochester, NY
United States

Ruixun Zhang

Peking University ( email )

5 Yiheyuan Road
Beijing, Beijing 100871
China

HOME PAGE: http://www.math.pku.edu.cn/teachers/ZhangRuixun%20/index.html

MIT Laboratory for Financial Engineering

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

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
638
Abstract Views
3,310
Rank
63,539
PlumX Metrics