Mean-variance preferences and investor behaviour

We study the comparative statics implications of mean-variance preferences for optimal portfolios. Specifically, we show that all risk-averse mean-variance investors raise their investment in a risky asset in response to a change in that asset's return distribution if and only if the change lowers both the mean and standard deviation of the return by the same percentage. Besides being of interest in its own right, our results allow us to compare some comparative statics implications and the expected utility and mean-variance models systematically.