A General Mean-Variance Approximation to Expected Utility for Short Holding Periods

The mean-variance model is precisely consistent with the expected utility hypothesis only in the special cases of normally distributed security returns or quadratic utility functions. There is little evidence, however, that security returns follow normal distributions (see [13] for references) and quadratic preferences can be shown to generate implausible results, exhibiting increasing absolute risk aversion in the Pratt [ll]–Arrow [1, 2] sense and displaying negative marginal utility after some finite wealth level. In addition, Hakansson [4] has shown that single–period, mean-variance-efficient portfolios can have disastrous consequences over time—even when return distributions are stationary. Such criticisms of the mean-variance approach within the Von Neumann-Morgenstern framework have prompted several writers to suggest that investors maximize the expected value of utility functions with more “realistic” properties, while others have criticized the single-period focus of the model. One popular alternative utility function is the logarithmic function which exhibits decreasing absolute risk aversion and (conveniently) leads to myopic decision processes through time (i.e., investors treat each period as if it were the last, basing investment decisions on that period's wealth and return distributions only [8, 4]). (Other utility functions with constant relative risk aversion—such as the power function—also imply myopic decision rules within a multiperiod setting.)