Globally evolutionarily stable portfolio rules

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Globally Evolutionarily Stable Portfolio Rules ^*

Igor V. Evstigneev ^a , Thorsten Hens ^b and Klaus Reiner Schenk-Hopp´ e ^c

September 20, 2005

Abstract

The paper examines a dynamic model of a financial market with endogenous asset prices determined by short run equilibrium of supply and demand. As- sets pay dividends, that are partially consumed and partially reinvested. The traders use fixed-mix investment strategies (portfolio rules), distributing their wealth between assets in fixed proportions. Our main goal is to identify glob- ally evolutionarily stable strategies, allowing an investor to “survive,” i.e., to accumulate in the long run a positive share of market wealth, regardless of the initial state of the market. It is shown that there is a unique portfolio rule with this property—an analogue of the famous Kelly (1956) rule of “betting one’s beliefs.”

JEL-Classification: G11, C61, C62.

Keywords: Evolutionary Finance, Wealth Dynamics, Survival and Extinction of Portfolio Rules, Evolutionary Stability, Kelly Rule.

* Financial support by the national center of competence in research “Financial Valuation and Risk Management” is gratefully acknowledged. The national centers in research are managed by the Swiss National Science Foundation on behalf of the federal authorities.

a Economic Studies, School of Social Sciences, University of Manchester, Oxford Road, Manch- ester M13 9PL, United Kingdom. E-mail: [email protected].

b Institute for Empirical Research in Economics, University of Zurich, Bl¨ umlisalpstrasse 10, 8006 Z¨ urich, Switzerland and Norwegian School of Economics and Business Administration, Helleveien 30, N-5045 Bergen, Norway. E-mail: [email protected].

c Leeds University Business School and School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom. E-mail: [email protected].

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