Strong Increases in Downside Risk Aversion. Issue 2 (September 2016) - Keenan, Donald; Snow, Arthur
Abstract A ranking of risk preferences is of economic interest insofar as it leads to unambiguous comparative statics predictions, and for this to be the case, the ranking must be a strict partial ordering. The ranking by greater risk aversion meets this demand at the second order, and yields a variety of well-known predictions concerning the effect of greater risk aversion on demands for insurance and risky assets, among many other applications. There has been less success at the third order, where ranking preferences by aversion to downside risk has not produced a strict partial ordering. The problem is that account has not been taken of the fact that an increase in downside risk aversion must induce changes in risk aversion as well. We propose a definition of stronger downside risk aversion that does yield a strict partial ordering by requiring a nested increase in both second- and third-order risk aversion, so thatv is more strongly downside risk averse thanu ifv is more risk averse and more downside risk averse thanu . We demonstrate thatv being more strongly downside risk averse thanu is characterized byv never liking any change in the probability distribution fory that induces a third-order stochastic dominance deterioration in the distribution foru (y ). We apply the definition to obtain intuitive comparative statics predictions in the precautionary saving problem, and relate the definition to alternatives proposed in the literature.