Risk Adjusted Currency Hedging Policies for Minimum Probability of Default

Abstract

Asset risk adjusted currency hedging policy is studied from the perspective of minimum probability of default when foreign investments are partly funded by borrowings and partly by equity. As a base case where assets are in three currencies and the asset risks are the same across currencies, an example is provided that aligning the currency composition of equity to that of assets minimizes the probability default. In the example, it is shown that misalignment of a currency with higher exchange rate volatility results in larger increase in the probability of default. The assumption of the same asset risks across currencies is then relaxed and a method of adjustment for different asset risks is developed. Consistent with an intuition that assets with higher risks have larger unexpected losses and therefore will require larger amount of equity to maintain a certain level of the probability of default, it is shown that the adjustment needs to be made according to the relative asset risks. An example is provided for a case where assets are in three currencies with the composition of 0.5, 0.25, 0.25 and the standard deviations of currency 1, currency 2, and currency 3 assets are 2%, 3%, and 4% respectively. If the asset risks were the same across currencies, then the optimal currency composition would be the same with the currency composition of assets, which is 0.5, 0.25, and 0.25. However, in this example, it is shown that the optimal currency composition of equity becomes 0.36, 0.27, and 0.36 for currency 1, currency 2, and currency 3 respectively. The results of this paper could provide a guideline for framing a currency policy of multilateral financial institutions or of central banks in managing their foreign reserves because their primary objective of financial policies would be to minimize the probability of default or the probability of foreign reserves being depleted.