Allocative Downside Risk Aversion

Traditionally, downside risk aversion is the study of the placement of a pure risk (a secondary risk) on either the upside or the downside of a primary two-state risk. When the decision maker prefers to have the secondary risk placed on the upside rather than the downside of the primary lottery, he is said to display downside risk aversion. The literature on the intensity of downside risk aversion has been clear on the point that greater prudence is not equivalent to greater downside risk aversion, although the two concepts are linked. In the present paper we present a new, and we argue equally natural, concept of the downside risk aversion of a decision maker, namely the fraction of a zero mean risk that the decision maker would optimally place on the upside. We then consider how this measure can be used to identify the intensity of downside risk aversion. Specifically, we show that greater downside risk aversion in our model can be accurately measured by a relationship that is very similar to, although somewhat stronger than, greater prudence.