A Risk-Return Model with Risk and Return Measured as Deviations from a Target Return

Abstract

Two-attribute risk and return models are very popular in the economics and finance literature for analyzing decisions under uncertainty. Their popularity stems primarily from the intuitive appeal of the dichotomy into risk and return, and from the ease with which the concepts can be diagrammed in two dimensions. The most commonly used risk-return model is the mean-variance model in which risk is measured as the variance and return by the mean of the probability distribution over outcomes. The mean-variance model has a number of shortcomings which are widely known, but of particular concern here are the facts that 1) mean-variance dominance is neither necessary nor sufficient for second-degree stochastic dominance; 2) unless the form of the probability distribution is restricted, mean-variance is consistent with von Neumann-Morgenstern utility theory only if the utility function is quadratic; and 3) as Peter Fishburn has noted,