Risk in Risk Aversion

Abstract

Behind every investment portfolio, there are sources and uses of its funds, each with their own risks. Though funding risks are pervasive, their implication for setting appropriate risk aversion for portfolio construction is too little exploited. In this article, the authors extend single-period decision making to combine risk in assumed funding supply and uses with risk in investment returns to provide a joint optimization. Their approach uses expected utility maximization based either on the constant relative risk aversion property or on the generalized logarithmic utility model, the latter somewhat sharper in controlling tail risk. Mathematics is greatly simplified by matrix calculation using discrete preference states. The authors also employ investment leverage on surplus over subsistence requirements to estimate the need for conservatism. Examples are given for both the generic moderate errors in judging appropriate risk aversion and the more extreme funding risk arising from uncertainty as to retirement longevity.