Mean-risk analysis of risk aversion and wealth effects on optimal portfolios with multiple investment opportunities

In this paper, the authors first define risk in an axiomatic way and a class of utility functions suitable for the co-called mean-risk analysis. Then, they 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.