PORTFOLIO SELECTION AND CAPITAL ASSET PRICING FOR A CLASS OF NON-SPHERICAL DISTRIBUTIONS OF ASSETS RETURNS

The joint distribution that describes the return generating process here is modeled to distinguish between two aspects of portfolio risk by breaking down the variance of the portfolio distribution into two components: Spherical variance and a non-spherical variance. The latter determines skewness and other odd higher cummulants whereas the even cummulants are determined by both components. While any risk averse investor exhibits aversion to the spherical component, he may exhibit either a preference or an aversion to the non-spherical variance depending on his specific utility function. The problem of portfolio selection, for any risk averse investor, is equivalent to a quadratic programming problem that minimizes the spherical variance for a given mean and a non-spherical variance pair. Ranking of portfolio distributions collapses to a ranking of their respective means and risk measures. The mean-variance-skewness efficient set is derivable as a function of the joint distribution parameters and estimatable from observable security returns. This framework allows an analytical evaluation of the practical optimality of the mean-variance investment strategy for all constant absolute risk averse investors. An optimization premium that reflects the foregone opportunity cost of the mean-variance strategy is derived as a function of the absolute risk aversion measure and the joint distribution parameters. Utilizing monthly returns on ten securities, the derived optimization premium is operationalized empirically. When there is a riskless asset, the optimization premium does not exceed...