Mean-Variance Preferences and Investor Behavior

We study the comparative statics implications of mean-variancepreferences for optimal portfolios. Specifically, we show thatall risk averse mean-variance investors raise their investmentin a risky asset in response to a change in that asset's returndistribution if and only if the change lowers both the mean andstandard-deviation of the return by the same percentage. Thus, raising the mean while keeping the standard deviation constant or lowering the standard deviation while keeping the mean constant will not increase investment for all mean-variance investors. If, however, we truncate the distribution from above in such a way that the mean and standard deviation fall by the same percentage, then investment does increase for all risk averse mean-variance investors. Besides being of interest in its own right, our result allows us to compare the comparative statics implications of the expected utility and mean-variance models systematically