Comparative Statics Under Uncertainty : The Case of Mean-Variance Preferences

We analyze the comparative statics of optimal decisions under uncertainty when preferences are represented by two-moment, mean-variance utility functions. We relate our findings to concepts for risk attitudes that have recently been proposed for the expected utility approach. In the two-parameter approach, a number of plausible comparative static effects already emerges under the assumption of decreasing absolute risk aversion (DARA). DARA is, however, not sufficient to determine comparative static effects when changes in background risks are considered. Instead, risk vulnerability, temperance and standardness imply, appropriately transferred to the mean-variance framework, the plausible effect that risk taking will be reduced if the riskiness of background risks increases