Bank's Equity-Asset Ratio Bounds Under Exchange Rate Risk : A Tool for Stress Testing

A large fraction of bank's assets and debts in developing countries are usually denominated in foreign currencies (e.g. US dollars, euros). Therefore, fluctuations of the exchange rate is likely to affect their financial wealth. The equity-asset ratio is a usual measure of bank's financial strength. As we will see, this ratio is very sensitive to exchange rate movements. In this paper, we establish some bounds of the expectation of the equity-asset ratio considering limited information of the underlying stochastic exchange rate. Specially, we are interested in finding the lower bound of the expectation of this ratio, that is knowing the worst case scenario of bank financial wealth. We also characterize the conditions under which the equity-ratio remains unchanged considering both direct and indirect effects of exchange rate movements. Our results could shed some light on the complex world of financial regulation and serve regulators as an additional tool for stress testing