Scandinavian Working Papers in Economics

Discussion Papers,
Norwegian School of Economics, Department of Business and Management Science

No 2006/23: On the Evolution of Investment Strategies and the Kelly Rule – A Darwinian Approach

Terje Lensberg () and Klaus Reiner Schenk-Hoppé ()
Additional contact information
Terje Lensberg: Dept. of Finance and Management Science, Norwegian School of Economics and Business Administration, Postal: NHH , Department of Finance and Management Science, Helleveien 30, N-5045 Bergen, Norway
Klaus Reiner Schenk-Hoppé: Leeds University Business School, University of Leeds, Postal: Leeds University Business School, The Maurice Keyworth Building, University of Leeds, Leeds LS2 9JT, United Kingdom

Abstract: This paper complements theoretical studies on the Kelly rule in evolutionary finance by studying a Darwinian model of selection and reproduction in which the diversity of investment strategies is maintained through genetic programming. We find that investment strategies which optimize long-term performance can emerge in markets populated by unsophisticated investors. Regardless whether the market is complete or incomplete and whether states are i.i.d. or Markov, the Kelly rule is obtained as the asymptotic outcome. With price-dependent rather than just state-dependent investment strategies, the market portfolio plays an important role as a protection against severe losses in volatile markets.

Keywords: Evolutionary finance; portfolio choice; asset pricing; genetic programming

JEL-codes: C63; G11

29 pages, December 19, 2006

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