The Precautionary Premium and the Risk-Downside Risk Tradeoff

Abstract

This paper shows that the precautionary premium embodies a tradeoff between risk and downside risk. It is the size of a mean-preserving spread for thish the strength of aversion to risk just offsets the strength of aversion to downside risk. Using this result, decreasing absolute prudence can be interpreted as meaning that the amount of exposure to risk (as measured by a spread) for which aversion to risk just offsets aversion to downside risk decreases as wealth increases. This happens when an increase in wealth causes a smaller percentage change in absolute downside risk aversion than in absolute risk aversion.