Characterizations of optimal portfolios by univariate and multivariate risk aversion

Abstract

In a portfolio selection model with two risky investments having bivariate normally distributed returns, we show that Rubinstein's measures of risk aversion can yield the desirable characterizations of risk aversion and wealth effects on the optimal portfolios. These properties are analogous to those of the Arrow-Pratt measures of risk aversion in the portfolio selection model with one riskless and one risky investment. If investors' preferences are represented by multi-attributed utility functions and returns on different investments and other relevant factors have a joint normal distribution, we show that optimal portfolios can be characterized by a matrix measure of risk aversion.