Expectation Dependence: The Banking Firm Under Risk

Abstract

This paper examines the optimal lending and hedging decisions of a bank facing uncertain returns on its loans. The bank's preferences are state-dependent in that the utility function depends on a state variable, i.e. the business cycle of the economy. The purpose of this paper is to complement the results of the banking literature. To characterize the bank's optimal use of financial instruments to hedge, we show that the concept of expectation dependence (Wright, 1987) is useful. While the current hedging literature specifies price risk as a monotonically increasing or decreasing function of the state-variable plus noise, expectation dependence provides much more general bivariate dependence structure. The bank's optimal futures position is an under-hedge or an over-hedge, depending on whether the random return on loans is positively or negatively correlated with the business cycle of the economy in the sense of expectation dependence, respectively. The bank as such takes dependencies into consideration when devising its optimal hedging strategy.