Some consequences of correlation aversion in decision science

Very often in decision problems with uni- or multivariate objective, many results depend upon the signs of successive direct or cross derivatives of the utility function at least up to the 4th order. The purpose of the present paper is to provide a new and unified interpretation of these signs. It is based on the observation that decision-makers like to combine assets the return of which are negatively correlated (i.e., they have a preference for hedging). More specifically, this attitude is modelled through the concept of an ‘elementary correlation increasing transformation’ defined by Epstein and Tanny (1980). Decision-makers are said to be correlation averse if they dislike such a transformation. It will be shown that correlation aversion underlies many aspects of a decision-maker's behavior under risk, including risk aversion, prudence, and temperance. Hence, correlation aversion provides a unifying, elegant and powerful framework to analyze risky decisions in the bivariate case. In this framework, also the concave version of the bivariate stochastic orderings introduced in Denuit, Lefèvre and Mesfioui (1999) turns out to be appropriate for comparing correlated outcomes and for comparing bivariate distributions with ordered marginals. The main result of this paper states that a decision-maker who is averse to correlation would rank bivariate outcomes as if using such higher order concave stochastic orderings. In particular, some features of decision-making under bidimensional risk, such as cross-prudence and cross-temperance, can also be linked to correlation aversion.