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Mean-risk analysis of risk aversion and wealth effects on optimal portfolios with multiple investment opportunities
Authors:Masaaki Kijima  Masamitsu Ohnishi
Institution:(1) Graduate School of Systems Management, The University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 112 Tokyo, Japan;(2) Department of Business Management, Faculty of Economics, Tohoku University, Kawauchi, Aoba-ku, 980 Sendai, Japan
Abstract:In this paper, we first define risk in an axiomatic way and a class of utility functions suitable for the so-called mean-risk analysis. Then, we show that, in a portfolio selection problem with multiple risky investments, an investor who is more risk averse in the Arrow-Pratt sense prefers less risk, in the sense of this paper, with less mean return, and an investor who displays increasing (decreasing) relative risk aversion becomes more conservative (aggressive) as the initial capital increases. The risk aversion effect for diversification on optimal portfolios is also discussed.
Keywords:Portfolio theory  risk aversion  utility function  diversification
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