Production and Hedging under Correlated Price and Background Risks

Abstract

This paper examines the competitive firm that has to make its production and hedging decisions under correlated price and background risks. The background risk can be either financial or non-financial, which is accommodated by using a bivariate utility function. The separation theorem is shown to hold in that the firm’s optimal output level depends neither on the firm’s bivariate utility function nor on the joint distribution of the price and background risks. We derive necessary and sufficient conditions under which the firm optimally opts for an over-hedge (under-hedge). We further derive necessary and sufficient conditions under which hedging has positive (negative) effect on the firm’s optimal output level. These conditions are shown to be related to the concept of expectation dependence and bivariate preferences that include correlation aversion (correlation loving) and cross-prudence (cross-imprudence).