Banks’ expected equity-to-asset ratio bounds under foreign exchange risk

Abstract

In this paper, we develop optimal bounds of the expectation equity-to-asset ratio when the bank faces foreign exchange shocks. These bounds can be established with limited information on the underlying stochastic foreign exchange rate. Specifically, we are interested in finding the highest lower bound on the expectation of this ratio, as it indicates the worst case scenario of a bank's net worth. Comparative statics of these bounds, when the moments of the foreign exchange rate distribution vary, are studied as well. We characterize the conditions under which the expected equity ratio remains unchanged by foreign exchange rate movements. We also establish the optimal bounds of this expected ratio when the foreign exchange rate behaves as a mixture distribution. To our knowledge, the bounds of the type developed here have not previously been proposed in the banking literature.