Stochastic Dominance for Decreasing Absolute Risk Aversion

Abstract

In recent years the expected-utility approach to decision making under risk has gained increasing acceptance among portfolio theorists. On the other hand, the mean-variance (MV) approach of Markowitz [13], which has dominated portfolio theory in the past, continues to enjoy great popularity. In MV theory, the investor is assumed to rank his preferences for risky returns solely in terms of their means and variances, with higher means and lower variances, being preferred. Tobin [20] showed that MV theory is consistent with expected utility theory in the special case of joint-normally distributed asset returns. The MV approach enjoys a ready acceptance among practitioners, and requires only modest informational and computational inputs. Perhaps its most attractive feature is its ability to decompose the overall portfolio problem into a sequence of much simpler problems: first, the “efficient” set of portfolios (which minimize variance for any given mean return) is calculated, and then the investor chooses one of the efficient portfolios in a manner consistent with his personal preferences. This efficient set is the same for all investors having the same mean-variance-covariance estimates of risky-asset returns, and can, in principle, be determined once and for all using parametric quadratic programming [12, 22] Despite these real advantages, the MV theory embodies certain problems of principle in the case of nonnormally distributed asset returns, and this fact has led to increasing emphasis on the presumably more rational expected-utility theory.

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