TAILIEUCHUNG - Evolutionary Stable Stock Markets ∗

These severe problems may come as a surprise, since the sample covariance matrix has appealing properties, such as being maximum likelihood under normality. But this is to forget what maximum likelihood means. It means the most likely parameter values given the data. In other words: let the data speak (and only the data). This is a sound principle, provided that there is enough data to trust the data. Indeed, maximum likelihood is justified asymptotically as the number of observations per variable goes to infinity. It is a general drawback of maximum likelihood that it can perform poorly in small sample. For the covariance matrix, small sample problems. | Evolutionary Stable Stock Markets Igor Evstigneev a Thorsten Hens b Klaus Reiner Schenk-Hoppe b c October 27 2003 Abstract This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded by portfolio rules that will gain market wealth and hence change the valuation. In the model the valuation of assets is given by the wealth average of the portfolio rules in the market. The wealth dynamics is modelled as a random dynamical system. Necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when relative dividend payoffs form a stationary Markov process. These local stability conditions lead to a unique evolutionary stable strategy according to which assets are evaluated by expected relative dividends. JEL-Classification G11 D52 D81. Keywords evolutionary finance portfolio theory incomplete markets. We are grateful to Jarrod Wilcox and William Ziemba for very valuable comments. 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. aSchool of Economic Studies University of Manchester Oxford Road Manchester M13 9PL UK. bInstitute for Empirical Research in Economics University of Zurich Blumlisalpstrasse 10 8006 Zurich Switzerland. cInstitute of Economics University of Copenhagen Studiestrffide 6 DK-1455 Copenhagen K Denmark. Email thens@ klaus@ 1 1 Introduction The expected discounted dividends model is one of the cornerstones of finance. According to this model the rational and fair value of common stocks is given by the discounted sum of future dividends paid out by the company. Indeed in the very long run half a century the trend of stock market prices coincides with the trend of the .

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