مواجهه با نرخ ارز : یک رویکرد غیر پارامتری

The typical conclusion reached when researchers examine exchange rate exposure is that only a few firms are exposed. This finding is puzzling since institutional knowledge and theory suggests a larger effect. In this paper, we compare results obtained using a linear approach with those from nonlinear and nonparametric models. Among firms that don't have a linear exposure, we find that a considerable proportion of these are exposed when nonlinear or nonparametric models are used. This exposure is most striking when a nonparametric model is used. We also find that firms' hedging activities decrease linear exposure but don't affect nonparametric exposure.

In the aftermath of the emerging market currency crises, linked mainly to speculative attacks on fixed exchange rate regimes, countries have announced limited commitments, if at all, to pegging their exchange rates. Even so, substantial evidence shows that these countries intervene heavily in foreign exchange markets to limit the volatility of exchange rates. Balance sheet effects have been argued as one of the main reasons for this intervention. More specifically, the large amounts of unmatched foreign currency denominated liabilities firms carry have been a source of concern for emerging market central banks. Therefore, it is important to understand the effects of exchange rate risk on firms' balance sheets and value, and develop methods to measure firms' exposures to such risks. While it is well established that exchange rate fluctuations are an important source of risk for a firm, the literature does not agree on a benchmark methodology to be used in measuring exposure. One branch of the literature quantifies the idiosyncratic effects of exchange rate fluctuations on a firm's stock return by using various extensions of the Adler and Dumas (1984) model. The main conclusion of this line of work (c.f. Jorion, 1990 and Griffin and Stulz, 2001) is that exchange rate exposure, measured by the proportion of firms with significant exposure, is trivial. This finding contrasts with the predictions of finance theory and substantial anecdotal evidence suggesting a considerable vulnerability to exchange rate movements. Indeed, Bartram and Bodnar (2007) define the inability to find exposure – even for firms that have extensive operations abroad – as the exchange rate exposure puzzle. Empirical studies using various estimation techniques, sample selection, and different exchange rates report limited success in capturing exchange rate exposure. Most of this literature agrees that the linear relationship between exchange rates and stock returns assumed under the Adler and Dumas (1984) model may understate the level of exposure. This is especially agreed to be true if exchange rates have nonlinear effects on a firm's cash flow or firms' operational decisions. Indeed, some studies (Allayannis, 1997, Allayannis and Ihrig, 2001, Bartram, 2004, Bodnar et al., 2002, Bodnar and Wong, 2003, Broll et al., 2001, Doidge et al., 2000, Griffin and Stulz, 2001, Odegaard and Priestley, 2007, Taylor and Peel, 2000 and Taylor et al., 2001) show that using various functional forms such as quadratic and cubic can more effectively capture, for some firms, the degree of exposure when a linear model cannot. Nevertheless, the use of different functional forms does not change the conclusions considerably and does not solve the exchange rate exposure puzzle. It is important to point out further that these studies do not agree on a specific functional form to use in estimating exchange rate exposures. In the literature, we identified three important reasons why conventional models may not capture exchange rate exposure accurately or why there may be a lack of exposure. First, using the same functional form for each firm can be restrictive and could generate low levels of exchange rate exposure. This is especially true if firms differ in the way they are affected by exchange rate movements. Indeed, it is agreed that the degree of exposure depends on firm and industry characteristics such as size, monopoly power, external orientation, degree of import penetration and the substitutability between domestically produced and imported inputs. More importantly, the theoretical studies mentioned above suggest that these characteristics not only determine the degree of exposure but also have implications for the functional relationship between exchange rate movements and firms' value. Second, there are a large number of studies (c.f. Allayannis and Ihrig, 2001, Jorion, 1990, Koutmos and Knif, 2002, Brunner et al., 2000 and Williamson, 2001) arguing or finding that exchange rate–stock return relationship does not follow a time invariant functional form. Exchange rate exposures in these studies vary over time as firm and market characteristics such as markup and market shares change. Therefore, the time invariant functional form assumption of the Adler–Dumas model can falsely predict that exposure is insignificant. Third, some studies argue that firms use foreign currency derivatives (c.f. Allayanis and Ofek, 2001 and Bartram and Bodnar, 2007) and pass through part of currency changes to customers (Bartram et al., 2010) effectively to protect against unanticipated exchange rate fluctuations. Therefore, it is possible that the lack of exposure does not reflect the inadequacy of the methodology but may be due to the hedging behavior and exchange rate pass through. In this paper, we offer a different approach and estimate exchange rate exposure nonparametrically. In so doing, we are able to account for two of the main shortcomings of the conventional methods mentioned above. Specifically, a nonparametric (NP) approach allows us to estimate a different functional form for each firm and allows this functional form to change over time. We choose to use the local linear regression method developed by Stone (1977) as our NP estimation strategy due to its high asymptotic efficiency compared to alternative NP methods. Although we are not the first to use this approach to study exchange rate exposure,1 our paper makes a first attempt at comparing the results from NP models with those from parametric and partially parametric (PP) models. Using stock return data from firms in five emerging market countries and the U.S., we provide a comparison of the number of firms with exchange rate exposure where we have computed exposure using linear, nonlinear (NL), PP and NP models.2 Including U.S. firms is advantageous for two reasons. First, it allows us to compare our results to those from the large body of work on exchange rate exposure of U.S. firms. More importantly, the data that is available for these firms (and not available for other firms) is convenient for measuring the effects of hedging and testing the soundness of our NP methodology. Our results show that when NL and PP models are used, a number of firms classified as exposed are considerable. When we use a NP methodology, we find that the number of firms exposed and the economic significance of exposure increases substantially in each country. This striking result clearly shows that utilizing only a linear model to measure exchange rate exposure significantly underestimates the degree of exposure. Next, we investigate the role that foreign exchange hedging plays using the notional amounts of foreign currency derivatives held by S&P 500 firms (disclosed in the notes of their annual reports). Although we would have liked to examine the effects of hedging in emerging markets, data on derivatives is not publicly available to the best of our knowledge. Our findings reveal that while firms reduce their linear exposure using foreign currency derivatives, this does not carry over to the NP case. These results are robust to altering the choice of exchange rate and return horizons. Additionally, using several tests we find no evidence that the high level of exposure is artificially generated by the NP methodology. The rest of the paper is organized as follows. Section 2 presents the linear, NL, PP and the NP models used to measure exchange rate exposure and the methodology used to measure the effects of hedging on exchange rate exposure. Section 3 discusses the data. Section 4 presents the results. Section 5 reports the results from some robustness checks and Section 6 concludes.

Our results demonstrate that when exchange rate exposure is measured using only a linear model, the proportion of firms with exposures are understated in both emerging markets and an advanced economy such as the U.S.. We show that if NL, PP and NP models are used as an estimation strategy the frequency of exposure increases. Among these models, however, we find that only NP results display the high frequencies of exposure that are parallel to anecdotal evidence, finance theory and institutional knowledge. Consistent with these results, our second stage regression results implied that firms are able to lower their linear exposures but not the NP (and nonlinear in some cases) exposures by using foreign currency derivatives. Although the NP approach used in this paper has several advantages for every country, this approach would be most useful for countries that have a high degree of variety among their firms (in terms of openness and economic exposure) and/or are experiencing structural breaks (for example those that are in the process of integrating with global capital markets). Indeed, by estimating the nature (or the functional form) of the relationship between stock prices and exchange rates uniquely for each firm and by more effectively accounting for the dynamics of this relationship before and after structural breaks, a NP approach can be more advantageous over parametric approaches. The latter characteristic would be especially useful when using long sample periods.