Modeling time variation and asymmetry in foreign exchange exposure

Many recent studies suggest that exchange rate exposure is unstable over time and exhibits asymmetric behavior during currency appreciations and depreciations. This paper proposes a dynamic framework for the study of such questions and our empirical findings show that exchange rate exposure of U.S. stocks is time varying. Using decile and sector portfolios, we find asymmetric exposure to be pervasive across the decile portfolios as well as the financial and industrial sectors. Moreover, the response of return variance to past innovations is asymmetric for the majority of cases. The dynamic exchange rate exposure parameters are found to be mean-reverting with low persistence, generally ranging from 1 to less than 2 days. The average time-varying exposure is statistically significant for the size-based and sector-based portfolios. Lastly, the variability in the time-varying exposure is smaller (larger) for the largest (smallest) firms and for industrial (technology) firms.