تغییر زمان مدل سازی و عدم تقارن در مواجهه با ارز خارجی

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.

There has been a significant amount of effort devoted to investigating the impact of foreign exchange (FX) risk on firm value over the past 15 years. Much of this interest stems from the question of whether portfolio managers and corporate managers are able to diversify FX risk. To the extent that FX risk is not diversifiable, exposure to this risk is of concern to portfolio managers and corporate financial managers in constructing asset portfolios and in hedging strategies. While initial studies did not find FX risk to be priced (e.g., Jorion, 1991), recent studies that allow for time variation in the pricing of exchange rate risk have found FX risk to be priced (e.g., Dumas and Solnik, 1995 and De Santis and Gerard, 1998). Concurrent with this literature, studies began to analyze the magnitude and determinants of exposure to FX risk. The first prominent study that empirically estimated FX exposure was conducted by Jorion (1990). Modifying the Adler and Dumas (1984) approach by including a market portfolio return, he found only 5% of U.S. multinational firms to have significant return sensitivity to an exchange rate index. Subsequently, several studies have attempted to improve upon the methods used to estimate exposure.2 One of our primary objectives is improving the estimation methodology by allowing exposure to vary over time. Several studies have shown improvement in the detection of foreign exchange exposure. Chow et al. (1997) assert that long-horizon regressions more readily identify significant exposure, based on their view that market participants likely make errors in assessing the longer-term consequences of FX risk. Due to asymmetric pricing behavior, hysteresis, and asymmetric hedging, Koutmos and Martin, 2003a and Koutmos and Martin, 2003b, Bartram (2004), Carter et al. (2005), and Tai (2005) evaluate asymmetric responses to appreciations and depreciations and improve upon the detection of exposure. Choi and Prasad (1995) and Di Iorio and Faff (2000) also provide some evidence of asymmetric responses to currency appreciations and depreciations. It has also been argued that due to an averaging out effect, broadly defined exchange rate indexes may obscure the detection of exposure (e.g., Bartov and Bodnar, 1994, Martin et al., 1999, Allayannis and Ofek, 2001 and Koutmos and Martin, 2003b). Lastly, Bodnar and Wong (2003) recommend using size-based portfolios to control for market conditions when estimating foreign exchange exposure. In addition to the studies above that show time variation in exposure by incorporating the possibility of asymmetric responses to appreciations and depreciations, there are studies that provide evidence that exposure is more generally time dependent. Brunner et al. (2000) find the exposure coefficients of the German market and German corporations are not stable over time. Allayannis and Ihrig (2001) show that exposure varies with industry markups; Williamson (2001) concludes that exposure of automotive firms changes with market share; while Bodnar et al. (2002) demonstrate that exposure varies with pass through. Patro et al. (2002) find the exposure of OECD equity markets vary year to year due to imports, exports, credit ratings and tax revenues. Bodnar and Wong (2003) show that exposure estimates generated from a model that controls for market movements (i.e., residual exposures) are more stable over time than exposures estimated without controlling for market movements (i.e., total exposures). Lastly, Ihrig and Prior (2005) find some firms have significant exposure only during crisis periods. None of the studies thus far, however, provide a simple and unifying framework for the study of the dynamic properties of foreign exchange exposure. We propose a dynamic vector GARCH framework that allows for simultaneous estimation of the daily time-varying exposure parameter as well as potential asymmetries in the exposure mechanism. While Koutmos and Martin, 2003a and Koutmos and Martin, 2003b model asymmetries with respect to appreciations and depreciations, they do not test for time variation in the exposure parameter, and instead assume that the base exposure is fixed. Their work documents, however, that the distributions of stock returns and exchange rate changes are conditionally heteroscedastic, which suggests that exposure itself might be time varying. Our study details the time series properties of the time-varying exposure parameters. Furthermore, we evaluate whether sector portfolios and size-based portfolios have time varying exposures. We use sector portfolios to allow for comparisons between our findings and those of Koutmos and Martin (2003a). We use size-based portfolios to investigate whether these portfolios capture some portion of time-varying exposures, since Bodnar and Wong (2003) recommend using size-based portfolios to control for market conditions when evaluating firm-level foreign exchange exposure. While there are mixed views on the relationship between exposure and firm size,3Bodnar and Wong (2003) believe the relation between exposure and firm size is anomalous and that the influence of size on exposure becomes less prominent when the estimation model for exposure controls for size-based market returns. This study finds that exchange rate exposures of size-based as well as sector-based portfolios from the U.S. stock market are time varying, and the exposure parameters are mean reverting with low persistence. Moreover, the response of return variance to past innovations is asymmetric for the majority of the decile and sector portfolios. Asymmetric exposure is pervasive across the size-based portfolios, as well as the financial and industrial sector portfolios. Lastly, we find that the variability in the time-varying exposure is smaller (larger) for the largest (smallest) firms and for industrial (technology) firms.

This paper studies the dynamic properties of exchange rate exposure of stock returns using a dynamic framework based on a vector GARCH. This framework allows for simultaneous estima- tion of the time-varying variance covariance matrix of stock returns and exchange rate changes and the time-varying exposure parameter, thus eliminating possible simultaneity biases. The exposure parameters are mean-reverting and exhibit low persistence, ranging from 1 to less than 2 days. Moreover, the response of return variance to past innovations is asymmetric for the majority of decile and sector portfolios. We find that exchange rate exposures of size-based and sector-based portfolios are time varying. Furthermore, the results show that the variability in the time-varying exposure is smaller (larger) for larger (smaller) firms and for industrial firms (technology firms).