Diversification and risk attitudes toward two risks

Abstract

In this paper, we examine risk attitudes toward two risks within the set of bivariate utility functions that are risk averse to one risk in isolation and correlation averse (correlation loving). Specifically, correlation averters (correlation lovers) exhibit risk loving or risk aversion to one risk in the presence of another, depending on whether the riskiness of the former risk is below or above a positive threshold. The prevalence of such risk attitudes toward two risks uniquely describes the dependence structure of the two risks being characterized by the notion of negative (positive) expectation dependence. We then propose to use the positive threshold as an intensity measure of risk aversion with two risks, which is shown to be equivalent to the concept of generalized Ross risk aversion. We offer two applications regarding primary prevention for health risks and the motive for precautionary saving in the presence of wealth and interest rate risks, both of which involve random variables whose dependence structure is governed by the notion of expectation dependence.