Department of Economics Working Paper Series

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1 Department of Economcs Workng Paper Seres Exchange rate exposure: A nonparametrc approach Uluc Aysun Unversty of Connectcut Melane Guld Mount Holyoke College Workng Paper June Mansfeld Road, Unt 1063 Storrs, CT Phone: (860) Fax: (860) Ths workng paper s ndexed on RePEc,

2 Abstract The typcal concluson reached when researchers examne exchange rate exposure usng a lnear model s that only a few frms are exposed. Ths fndng s puzzlng snce nsttutonal knowledge and basc fnance theory ponts to a larger effect. In ths paper, we compare results obtaned usng a lnear approach wth those from nonlnear, partally parametrc and nonparametrc models. Our data consst of nonfnancal frms n fve emergng market countres and the US. Among frms that were not found to have a lnear exposure, we fnd that a consderable proporton of these are exposed when nonlnear, partally parametrc or nonparametrc models are used. The ncrease n exposure s most strkng when a nonparametrc model s used. We also fnd evdence that frms hedgng actvtes decrease lnear exposure but do not affect nonparametrc exposure. Journal of Economc Lterature Classfcaton: E44; F31; F41 Keywords: nonparametrc, exchange rate exposure, hedgng.

3 1. Introducton In the aftermath of the emergng market currency crses, lnked manly to speculatve attacks on fxed exchange rate regmes, countres have announced lmted commtments, f at all, to peggng ther exchange rates. Even so, substantal evdence shows that these countres ntervene heavly n foregn exchange markets to lmt the volatlty of exchange rates. Balance sheet effects have been argued as one of the man reasons for ths nterventon. More specfcally, the large amounts of unmatched foregn currency denomnated labltes frms carry have been a source of concern for emergng market central banks. Therefore, t s mportant to understand the effects of exchange rate rsk on frms balance sheets and value, and develop methods to measure frms exposures to such rsks. Whle t s well establshed that exchange rate fluctuatons are an mportant source of rsk for a frm, the lterature does not agree on a benchmark methodology to be used n measurng exposure. One branch of the lterature quantfes the dosyncratc effects of exchange rate fluctuatons on a frm s stock return by usng varous extensons of the Adler-Dumas (1984) model. The man concluson of ths lne of work (c.f. Joron, 1990; Grffn and Stulz, 2001) s that exchange rate exposure, measured by the proporton of frms wth sgnfcant exposure, s trval. Ths fndng contrasts wth the predctons of fnance theory and substantal anecdotal evdence suggestng a consderable vulnerablty to exchange rate movements. Indeed, Bartram and Bodnar (2007) defne the nablty to fnd exposure -- even for frms that have extensve operatons abroad -- as the exchange rate exposure puzzle. Emprcal studes usng varous estmaton technques, sample selecton, and dfferent exchange rates report lmted success n capturng exchange rate exposure. Most of ths lterature 1

4 agrees that the lnear relatonshp between exchange rates and stock returns assumed under the Adler-Dumas (1984) model may understate the level of exposure. Ths s especally agreed to be true f exchange rates have nonlnear effects on a frm s cash flow or frms operatonal decsons. Indeed, some studes (Allayanns, 1997; Allayanns and Ihrg, 2001; Bartram, 2004; Bodnar et al., 2002; Bodnar and Wong 2003; Broll, 2001; Dodge et al., 2000; Grffn and Stulz, 2001; Prestly and Odegaard, 2007, Taylor and Peel, 2000; Taylor et al., 2001) show that usng varous functonal forms such as quadratc and cubc can more effectvely capture, for some frms, the degree of exposure when a lnear model can not. Nevertheless, the use of dfferent functonal forms does not change the conclusons consderably and does not solve the exchange rate exposure puzzle. It s mportant to pont out further that, these studes do not agree on a specfc functonal form to use n estmatng exchange rate exposures. In the lterature, we dentfed three mportant reasons why conventonal models may not capture exchange rate exposure accurately or why there may be a lack of exposure. Frst, usng the same functonal form for each frm can be restrctve and could generate low levels of exchange rate exposure. Ths s especally true f frms dffer n the way they are affected by exchange rate movements. Indeed, t s agreed that the degree of exposure depends on frm and ndustry characterstcs such as sze, monopoly power, external orentaton, degree of mport penetraton and the substtutablty between domestcally produced and mported nputs. More mportantly, the theoretcal studes mentoned above suggest that these characterstcs not only determne the degree of exposure but also have mplcatons for the functonal relatonshp between exchange rate movements and frms value. Second, there are a large number of studes (c.f. Allayanns and Ihrg, 2001; Joron, 1990, Koutmos and Knf, 2002; Brunner et al., 2000; Wllamson, 2001) argung or fndng that 2

5 exchange rate-stock return relatonshp does not follow a tme nvarant functonal form. Exchange rate exposures n these studes vary over tme as frm and market characterstcs such as markup and market shares change. Therefore, the tme nvarant functonal form assumpton of the Adler-Dumas model can falsely predct that exposure s nsgnfcant. Thrd, some studes (c.f. Allayanns and Ofek, 2001; Bartram and Bodnar, 2007) argue that frms use foregn currency dervatves effectvely to protect themselves aganst unantcpated exchange rate fluctuatons. Therefore, t s possble that the lack of exposure does not reflect the nadequacy of the methodology, but may be due to the hedgng behavor of frms. In ths paper, we offer a dfferent approach and estmate exchange rate exposure nonparametrcally. In so dong, we are able to account for two of the man shortcomngs of the conventonal methods mentoned above. Specfcally, a nonparametrc (NP) approach allows us to estmate a dfferent functonal form for each frm and allows ths functonal form to change over tme. We choose to use the local lnear regresson method developed by Stone (1977) as our NP estmaton strategy due to ts hgh asymptotc effcency compared to alternatve NP methods. Although we are not the frst to use ths approach to study exchange rate exposure 1, our paper makes a frst attempt at comparng the results from NP models wth those from parametrc and partally parametrc (PP) models. Usng stock return data from frms n 5 emergng market countres and the U.S., we provde a comparson of the number of frms wth exchange rate exposure where we have computed exposure usng lnear, nonlnear (NL), PP and NP models. 2 Includng U.S. frms s 1 Guo and Wu (1998) study the effect of fnancal lberalzaton on the exchange rate exposure of Tawanese ndustres usng a nonparametrc model. 2 Few papers n the lterature analyze the exchange rate exposure of frms n emergng market economes, partally due to nsuffcent data (c.f. Chue and Cook, 2008; Domnguez and Tesar, 2001; Kho and Stulz, 2000; Parsley and Popper, 2008). The conclusons of these papers are mxed at best. However, there s some evdence for a larger degree of exposure n these economes. Therefore, we also nclude frms from these economes n our sample. 3

6 advantageous for two reasons. Frst, t allows us to compare our results to those from the large body of work on exchange rate exposure of U.S frms. More mportantly, the data that s avalable for these frms (and not avalable for other frms) s convenent for measurng the effects of hedgng and testng the soundness of our NP methodology. Our results show that when NL and PP models are used, the number of frms classfed as exposed s consderable. More strkngly, when we use a NP methodology, we fnd that the number of frms exposed and the economc sgnfcance of exposure ncreases substantally n each country. Ths result clearly shows that utlzng only a lnear model to measure exchange rate exposure sgnfcantly underestmates the degree of exposure. Next, we nvestgate the role that foregn exchange hedgng plays usng the notonal amounts of foregn currency dervatves held by S&P 500 frms (dsclosed n the notes to ther annual reports). Although we would have lked to examne the effects of hedgng n emergng markets, data on dervatves s not publcally avalable to the best of our knowledge. Our fndngs reveal that whle frms reduce ther lnear exposure usng foregn currency dervatves, ths does not carry over to the NP case. These results are robust to alterng the choce of exchange rate and return horzons. Addtonally, usng several tests we fnd no evdence that the hgh level of exposure s artfcally generated by the NP methodology. The rest of the paper s organzed as follows. Secton 2 presents the lnear, NL, PP and the NP models used to measure exchange rate exposure and dscusses the methodology followed to measure the effects of hedgng on exchange rate exposure. Secton 3 dscusses the data. Secton 4 presents the results. Secton 5 reports the results from some robustness checks and Secton 6 concludes. 2. Methodology 4

7 In ths secton, we descrbe the models used to approxmate frm level exchange rate exposures. We start wth the commonly used lnear model. Next we dscuss NL and then PP models. Then we detal our preferred NP model. Fnally, we dscuss the effects of hedgng wthn the context of these models. Lnear Model Intally we follow the standard practce n the lterature, and use the followng extenson of the Adler-Dumas (1984) model to measure exchange rate exposure: R t = β 1 Rmt + β2 et + γ t (1) where Rt and R mt are the returns on frm s stock and a value weghted stock market ndex respectvely, and et s the percent change n the foregn exchange rate. The regresson model measures the dosyncratc effects of exchange rate volatlty on a frm s stock return. The market ndex s ncluded to account for economy wde shocks faced by every frm. Ths ncludes for example an expansonary monetary polcy that would nflate stock prces and deprecate the currency concurrently. One reason behnd the wdespread use of ths equaton s the low lkelhood of encounterng endogenety problems snce exchange rates can be assumed to be exogenous for an ndvdual frm. 3 We estmate ths model for every frm n our sample usng OLS as an emprcal strategy, and classfy a frm as exposed to exchange rates f ts β 2 coeffcent s sgnfcant. 4 In so dong, we orthogonolze the market return and replace ths varable wth the resduals obtaned from the estmaton of the followng regresson: 3 Notce that t s more probable for an ndvdual frm to affect exchange rate fluctuatons n developng countres characterzed by shallow fnancal markets. Nevertheless, we dd not thnk t was unreasonable to follow the wdely used model, especally for the U.S. and for the large emergng market economes consdered n our analyss. 4 In the Appendx of Adler Dumas (1984), t s shown how the coeffcent of the exchange rate varable n (1) would represent the economc exposure of a frm to exchange rates fluctuatons. 5

8 R = α 1 + κ (2) mt e t t Ths approach has been followed by Allayanns (1996), Grffn and Stulz (2001), Joron (1991), Prestley and Odegaard (2007) and addresses the possblty of a lack of sgnfcance due to the hgh collnearty between market returns and exchange rates. 5 Specfcally, when the estmaton of equaton (1) yelds an nsgnfcant ˆ β, ths does not mply that the frm s not exposed to exchange rate fluctuatons but rather that the exposure of the frm s greater than the market portfolo. Therefore, by orthogonalzng the market return, we are able to measure absolute rather than relatve exchange rate exposures of frms. We follow the same approach n all the other models descrbed below. Nonlnear (NL) Model Fnance theory provdes several reasons why there may be a nonlnear relatonshp between exchange rates and stock returns. Among these are, the nonlnear effects of exchange rates on cash flows (Stulz, 2003), shftng of producton actvtes to dfferent locatons n response to exchange rate movements (Kogut and Kulatlaka, 1994; Ware and Wnter, 1988), the absence of nonlnear hedgng strateges (Bodnar and Gebhart, 1999; Bodnar, Hayt and Marston, 1998), default rsk (Stulz, 2003), and prcng to market (Knetter, 1994). Therefore, the lterature dentfes nonlnear effects and decsons of frms as a possble source of exchange rate exposure and hghlghts the mportance of measurng these exposures. To gauge the sgnfcance of these nonlnear exposures, researchers (c.f. Bartram, 2004; Prestly and Odegaard, 2007) use varous nonlnear functons of the exchange rate and estmate the followng: 2 5 We also expermented wth the standard model (wthout orthogonolzaton) and found smlar results. However, for all the models we used the proporton of frms that were exposed was sgnfcantly hgher when we orthogonalzed market returns. 6

9 R t = Rmt + β 2 ( et ) ιt β 1 f + (2) where f ( e t ) has taken generc functonal forms such as quadratc (Prestly and Odegaard, 2007) and cubc (Bartram, 2004). The latter functonal forms have been argued to do a better ob of evaluatng asymmetrc effects of deprecatons and apprecatons. 6 These studes use other functonal forms such as the cubcal functon, the snus hyperbolcus, the cubcal root functon, and the nverse snus hyperbolcus. The man dfference between these functonal forms s the ablty to capture convex and concave exposures. Theory does not, however, dentfy a benchmark functonal form to use for each frm and for every pattern of exchange rate movements. 7 To be clear, we do not attempt to offer a dfferent method for measurng nonlnear exposures. We estmate nonlnear exposure n order to provde a bass of comparson to our NP results. We follow several approaches to measure nonlnear exposures. Specfcally, we estmate the above equaton usng the quadratc, cubcal, snus hyperbolcus, the cubcal root, and the nverse snus hyperbolcus functonal forms. Partally Parametrc (PP) Model One common observaton n the lterature s the postve relatonshp between the magntude and the sgnfcance of the exchange rate exposure coeffcents and the sze of the exchange rate shock (c.f. Bartram, 2004; Dodge, Grffn and Wllamson, 2000; Odegaard and Prestly, 2007). Ths s partally explaned by the nablty to dentfy the effects that small exchange rate shocks have on stock returns when other prce relevant nformaton are the man determnants of stock returns. However, when exchange rate shocks are large the effects on stock 6 See for example: Bartram (2004), Carter et al. (2005), D Ioro and Faff (2000), Koutmos and Martn (2003a,b), Cho and Prasad (1995), Ta (2005). 7 For example t s argued that some functonal forms such as the cubc root do a better ob of capturng vulnerablty to large movements but unreasonably predct hgh vulnerablty to smaller movements. 7

10 returns are observed more clearly. Therefore, t s mportant to measure the effects of these large dsturbances separately. To measure the effect of these large exchange rate movements on stock returns, we estmate the followng model: R t = γ 1 Rmt + γ 2 et + γ 3 D1 t et + γ 4 D1 t + γ 5 D2t et + γ 6 D2t + ν t (3) D D f 0.5se < et < 0.5s t = 0 otherwse 1 f 0.5se < e t t = 0 otherwse et where D 1 t and D 2 t are the dummy varables that are used to dfferentate exchange rate movements based on sze and sgn respectvely, and se s the standard devaton of the exchange t rate varable n the sample perod. Ths formulaton allows us to capture the effects of small, large, postve and negatve exchange rate movements separately. 8 To decde whether a frm has sgnfcant exposure, we wll use the null hypothess that all the exchange rate coeffcents are equal to zero (reecton of ths hypothess wll ndcate sgnfcant exposure). Nonparametrc (NP) Model All three of the estmaton strateges used above mpose a functonal form and also assume that ths functonal form does not change durng the sample perod. Furthermore, these methodologes rule out the possblty of dfferent functonal forms for dfferent frms. In ths secton, we address these ssues by estmatng the relatonshp between exchange rate fluctuatons and stock returns wthout adherng to a functonal form. Therefore, we are able to 8 Some studes (c.f. Bartram, 2004; Domnguez and Tesar, 2001, 2006) use sgn and sze bas tests to check whether the sgn and the sze of exchange rate shocks have dfferent effects on stock returns. Followng the methodology n Bartram (2004), we found evdence for both sgn and sze bas. Ths evdence ponts to the separate effects that large, small, postve and negatve exchange rate shocks have on stock returns, and further hghlghts the msspecfcaton of the lnear model n equaton (1). 8

11 avod specfcaton problems that parametrc approaches are subect to. We use the local lnear regresson method developed by Stone (1977) as our NP strategy. We chose ths method snce t s characterzed by hgher asymptotc effcency and has faster convergence at boundary ponts compared to other NP methods. 9 Usng ths strategy, we estmate the followng for each frm: e t ( et ) + ε t R ˆ = f (4) where R ˆ e t R βˆ R = t mt s the excess return on frm s stock. mt R s orthogonalzed as n equaton (2), and β s estmated usng the followng lnear regresson: R = β R + v (5) t mt t Although the exact form for f e ) ( t s not known, the local lnear estmaton methodology approxmates the relatonshp between et and seres expanson around each observaton of exchange rates such that, t ( e e ) = a + b ( e e ) t t e R t by makng use of the Taylor s f ( e ) f ( e ) + f '( e ) for each (6) Next, t fts a lne for each observaton of e by mnmzng the followng: N e ( R [ a + b ( et e )]) t t= 1 2 K (7) where K K( e e ) h = and h are the normal kernel and the regresson smoother t / 5 bandwdth respectvely. Followng the standard practce, we set h equal to σ e / N, where σ e s the standard devaton of the exchange rate. Notce that only observatons close to ncluded n the mnmzaton problem so that the coeffcents a and b are functons of e. e are 9 See Fan and Gbels (1992) and Pagan and Ullah (1999) for a dscusson of these propertes. 9

12 After estmatng b for every pont n the sample, we calculate bˆ N / = 1 = bˆ N to quantfy the relatonshp between the exchange rate and a frm s excess stock return. Smlarly we N measure the varance of bˆ s as var( bˆ ) = ˆ ˆ b b /( N 1). Rlstone (1991) shows that ths = 1 estmator s consstent and asymptotcally normal. Furthermore, ths estmator s wdely used snce (as shown n Rlstone, 1991) the standard errors of ths estmator are comparable to standard errors obtaned from parametrc estmaton. Therefore, comparng the t-ratos obtaned usng these coeffcent estmates to t-ratos obtaned from parametrc approaches s not unreasonable. Effects of Hedgng The exposure levels found usng the models descrbed above can be low, f frms are successful n hedgng ther exchange rate exposures. Therefore, t s nterestng to nvestgate how the exposure levels found n these models are related to the dervatve usage, and to observe how results dffer across models. We test the effect of frms foregn currency dervatve usage on ther exchange rate exposure usng the two stage regresson process of Cragg (1971). Specfcally, we estmate the followng model. ( DER / TA) + λ ( FS / TS ) + λ ( Sze / TSze) + k { L, NL, PP, } ˆ k β = λ1 + λ2 3 4 ε = NP (8) 2 where ˆ β, ˆ β L NL, ˆ β PP, ˆ β NP represent the coeffcents of the exchange rate varable estmated usng a lnear, NL, PP and a NP model respectvely. The rght-hand sde varables ( DER / TA), ( FS / TS ) and ( TSze) Sze / denote frm s foregn currency dervatves to total assets, foregn sales to total sales ratos and ts total assets as a fracton of the sum of the total assets of every frm n the country (and n our sample) respectvely. It s wdely observed (c.f. Joron, 1990; Kho 10

13 and Stulz, 2000; Nance et al., 1993; Parsley and Popper, 2008) that exposure s postvely related to openness and negatvely related to the sze of the frm. The latter observaton s generally attrbuted to the hgher lkelhood of larger frms to be multnatonal companes that therefore, have natural hedges nherent n ther operatons. Gven ths substantal evdence, these varables are ncluded n equaton (8). It s mportant to pont out that ths second stage regresson s not a contrbuton of our paper. Indeed, studes such as Allayanns and Ofek (2001), Hageln and Pramborg (2004), Muller and Verschoor (2006) Pantzals, Smkns and Laux (2001) have used a smlar methodology to study the determnants of exchange rate exposure. We add to ths work by also consderng exposures as measured by NP, as well as NL, PP and lnear models. The lterature offers several optons for measurng the extent of dervatve usage. In contrast to a maorty of the lterature that uses bnary or survey data to ndcate whether frms use dervatves or not, Allayanns and Ofek (2001) were to frst to use a contnuous varable (notonal dervatve usage). Ths approach has become the benchmark recently as t s more convenent for controllng frm characterstcs (such as sze and openness) when measurng the effects of dervatve usage on exposure. Therefore, we use notonal fgures n our estmaton snce we have no reason to use bnary data and ths data was not avalable. There are two other noteworthy ssues n the estmaton of equaton (8). Frst s related to the choce of the dependent varable. A number of studes use only the sgnfcant coeffcents from the frst stage, others use all. Furthermore, some studes use the absolute value of these coeffcents. Second s related to the choce of an estmaton strategy. Although, a maorty of the lterature uses OLS, there are some studes that use Weghted Least Squares (WLS) and Probt models (those that nclude only the sgnfcant coeffcents). 10 To check for robustness, we 10 Weghts n the WLS regresson are generally the standard devaton of the exposure coeffcents (c.f. Allayanns and Ofek, 2001). 11

14 used all of these approaches. The reader should rest assured that there were no noteworthy dfferences when comparng the results of regressons obtaned by usng each of the k βˆ as dependent varables. 11,12 Therefore, we only report the OLS estmaton results and use absolute values but do not omt the nsgnfcant coeffcents. The man reason for followng ths conventon was to be compatble wth a maorty of the studes that use a smlar approach Data In our data set, we nclude nonfnancal frms from the U.S. and 5 relatvely large emergng market economes. 14 The contents of the data set are dsplayed n Table 1. We used Datastream Internatonal to gather data for the frms n emergng market economes and used CRISP to obtan stock prces and total assets for the U.S frms lsted n the S&P 500. Our choce of emergng market countres was determned by data avalablty. We ncluded U.S. frms snce data on dervatves markets partcpaton was only avalable for these frms. The dataset ncludes daly observatons for stock returns, exchange rates, return on market ndces for the perod. In our smulatons, we use value weghted market ndces and the standard monthly return horzon. 15 We check the senstvty of exposure to return horzons, however n our robustness secton. We follow the standard practce n the exposure 11 We found that the coeffcent of the dervatve varable was consderably larger and more sgnfcant n every model when only the sgnfcant coeffcents were ncluded and a Probt model was used as an estmaton strategy.. 12 When usng the absolute values of the coeffcents, we corrected for the resultng truncaton bas by usng the methodology n Domnguez and Tesar (2001) 13 Note that snce the number of sgnfcant coeffcents wll be dfferent for each model we use, by not excludng the nsgnfcant coeffcents we are able to avod any effects that the dfferent degrees of freedom may have on the comparson of the results across models. Nevertheless, ncludng nsgnfcant coeffcents could understate any effect that hedgng may have on exposure coeffcents. As mentoned above, however, the two methods dd not generate any notceable dfferences when comparng across models. 14 The emergng market economes are: Brazl, Chle, Korea, Mexco and Turkey. 15 Bodnar and Wong, 2003 demonstrate that value weghted ndex can ntroduce a bas by gvng more weght to frms that are large and trade more and thus, suggest that an equally weghted market ndex maybe a better opton. Therefore, we also consdered equally weghted ndces. However, the effects were mmateral to our conclusons. 12

15 lterature and exclude fnancal frms from our data set. These frms are generally excluded due to ther market makng property n both foregn exchange and dervatves markets. Notonal amounts of foregn exchange hedgng contracts used by the S&P 500 frms were collected from the footnotes n the annual reports of these frms. 16 Out of the 367 nonfnancal frms n our sample, 268 reported a notonal amount for foregn currency dervatve n ther annual reports. We gathered ths nformaton from the Mergent database for the perod. In general, frms that report the notonal amounts of foregn currency dervatves, also report the foregn sales/total sales ratos. Furthermore, some of these frms also reveal the currency to whch they are most exposed. We utlze ths nformaton n the estmaton of the model n equaton (8). To measure the rght hand sde varables n equaton (8), we take the smple and weghted (usng total assets as weghts) averages of these varables over the perod for each frm. Snce there was no consderable dfference between usng smple and weghted averages, we only report the results from smulatons that use smple averages. For consstency, we also measure the dependent varable (exchange rate exposure) for the perod usng weekly returns. 17 At ths pont we should pont out a potental caveat to our analyss. In partcular, the utlzaton of notonal amount of dervatves reported can also ntroduce a bas snce most frms do not report whether they have short or long postons n the underlyng currency. However, ths should not be a maor concern as frms appear to be nettng foregn currency postons when 16 A maorty of these frms used forward contracts to manage foregn exchange rsk. However, our sample also ncludes foregn currency dervatves such as optons and futures contracts. Swap contracts were not ncluded snce they are manly used to translate foregn debt to domestc labltes. 17 We do not have any reason for expectng asymmetrc effects of usng a shorter sample perod on the exposures found usng dfferent functonal forms. Nevertheless, we ncreased the number of observatons and measured exchange rate exposures usng daly and weekly overlappng observatons for monthly return horzons. Smulatons revealed smlar results and are avalable upon request. 13

16 aggregatng them. 18 Furthermore, snce we are studyng the relatonshp between absolute exposure and the absolute value of dervatve usage, whether a frm has a long or a short poston should not present a systematc bas n our results. Choce of Exchange Rates To date, there s no consensus n the lterature on the choce of exchange rates when measurng exposure. Prevous studes have used maor currences, trade weghted exchange rates, broad exchange rate ndces, or have ncluded exchange rates smultaneously n equaton (1). In choosng the exchange rate we consder several optons. Frst, we nclude exchange rates measured as local currency per maor currences such as the US Dollar, Euro, Japanese Yen, Brtsh pound and the trade weghted exchange rates ndvdually. Second, usng the output of the regressons wth ndvdual currences, we dentfy, for each frm the exchange rate that generates the maxmum sgnfcance of exposure (denoted as ERMAX n the rest of the paper) and report the results obtaned usng ths methodology. Ths methodology, dfferent from prevous work, allows the data to predct the exchange rate nstead of restrctng the analyss by measurng exposure of every frm to a sngle currency or a basket of currences. Thrd, for U.S. frms we measure frms exposure to the currences they dentfy n ther footnotes n addton to ther exposures to the maor currences mentoned above (denoted as ERStated n the rest of the paper). 4. Results Proporton of Frms exposed to exchange rate shocks Table 2 shows the percentages of frms wth sgnfcant (at the 5% level usng robust standard errors) exposures. Columns correspond to the dfferent models used to measure exchange rate exposure and the last row represents the number of regressons for whch we fnd evdence for frst and/or second order seral correlaton n the resduals. For convenence, we 18 When frms reported both short and long postons we netted these postons for each currency. 14

17 report the results obtaned usng the local currency/us Dollar exchange rate for emergng markets and the US Dollar/Euro exchange rate for the U.S. As mentoned n the prevous secton, we report the senstvty of some of our results to alternatve exchange rate measures. We only report the results from the nonlnear model wth a quadratc functonal form snce the other generc nonlnear forms resulted n consderably lower proportons of exposure. The latter conventon s followed n the rest of the paper. Fgures reported n the frst column of Table 2 are wthn the range of values found n studes that use lnear models and show that only a few frms are exposed to exchange rate movements. 19 Notce also that our models appear to be reasonably specfed as we faled to fnd substantal evdence of frst and/or second order seral correlaton n the resduals. More mportantly, we fnd that exchange rate exposures n each country are substantally underestmated f NL, PP, and NP models are not consdered. Ths can be seen clearly n columns 2 to 4 whch show the proporton of frms that dd not have lnear exposure but had sgnfcant NL, PP, or a NP exposure to exchange rate movements. Indeed, the number of frms wth lnear or NL, and lnear or PP exposure s sgnfcantly hgher (100 percent hgher n a maorty of the cases) than the number of frms wth lnear exposure only. More strkngly, we fnd that NP estmaton produces proportons that are sgnfcantly hgher for each country. These results, however, are qualtatvely smlar to the results from the lnear model. For example, we fnd that Korea has the hghest percentage of frms that are exposed and Brazl and Mexco have the lowest percentages when usng ether model. These fgures are not too unreasonable f we consder that Korea and Brazl have the most open and 19 Most of the studes use U.S. data and fnd frequency of exposure less than 15%. We can not do ustce to the vast amount of research. Albet, here are some of the exposure proportons we found: Joron (1990), 5.2%; Walsh (1994), 5.6%; Prasad and Raan (1995), 15.0%; Dukas, Fatem and Tavakkol (1996), 5%-8.3%. For other countres: Prasad and Raan (1995), 4% (JPN), 5.9% (GBR), 16.7 % (DEU); Dodge, Grffn and Wllamson (2006), 8.2% (18 countres). 15

18 closed economes n the sample, respectvely. 20 Furthermore, NP results show that n general proportons of exposure n emergng markets are hgher than the U.S. 21 Ths s n contrast to some studes (c.f. Domnguez and Tesar, 2001; Kho and Stulz, 2000) that do not fnd materal evdence for ths dfference. Ths contrast can partally be explaned by the dfferent exchange rates and return horzons we employ. However, the man dfference n ths paper s the orthogonalzaton of the market return varable. Usng ths method, we capture the absolute effects of exchange rate movements on a frm s stock return rather than only measurng the relatve exposure of frms. Therefore, our results demonstrate that absolute exposure to exchange rates s more frequent n emergng markets. 22 Next we consder the economc sgnfcance of exposure. The average coeffcent values that represent ths magntude of exposure are dsplayed n Table 3. In contrast to the results n Table 2, we do not fnd a unform ncrease or decrease n the sze (economc sgnfcance) of exposure when we compare the results from the lnear and NP models. Averages are computed usng the absolute values of the exchange rate coeffcents and equal weghts. 23 Therefore, the NP model only predcts hgher frequency of exposure and not a larger sze of exposure. The results also show, compared to studes usng advanced economes that the sze of lnear 20 The average values for the (Exports+Imports)/GDP ratos between 1998 and 2008 for Korea and Brazl were 77.3 and 24.9 percent respectvely. 21 Note however that we do not measure relatve exposure (relatve to the market ndex) as n Domnguez and Tesar (2001) and Kho and Stulz (2000) and use orthogonalzed market returns n our experments. 22 Usng an alternatve strategy to measure absolute exposure Chue and Cook (2008) fnd results smlar to ths paper. Although t s not our mmedate concern, we ran smulatons usng the methodology n Chue and Cook (2008). Specfcally, we replaced domestc stock market ndex wth the world stock market ndex and used nstrumental varables for the exchange rate varable. The results revealed slghtly hgher levels of exposure. However, the conclusons drawn from the comparson of the results from the dfferent models dd not change. 23 We also used weghted averages (wth total assets as weghts) and obtaned smlar results. 16

19 exposures s hgher n emergng market economes and that exposure of US frms are wthn the range of values found n the lterature. 24 The Effects of Hedgng The results of our second stage regresson descrbed n equaton (8) are presented n Table 4. When generatng the dependent varable for each frm, we use ERMAX as the exchange rate varable. We use ths method snce we assume that frms use foregn currency hedgng nstruments to lmt ther vulnerabltes to the fluctuatons of the currences to whch they are most exposed. Our man fndng s that hedgng has a negatve and sgnfcant (at the 5% level usng robust standard errors) effect on exposures estmated usng lnear and PP models but does not have a sgnfcant effect on exposure when NL and NP models are used. The sgns of the sze and openness coeffcents, as expected mply that small and open frms are more exposed. Alternatvely, we use the exchange rates that frms state as the man currences they are exposed to n ther annual reports. Results are dsplayed n Table 5. We fnd that the sze and the sgnfcance of the dervatve usage varable ncreases. Furthermore, we fnd that frms were able to reduce ther nonlnear exposures to the currences ther most vulnerable to by hedgng. However, we fnd that NP exposures reman unaffected by the level of dervatve usage. Fnancal optons provde nonlnear payoff schedules, whch would be convenent for reducng nonlnear exposures. However, our results ndcate that ether nonlnear exposures are not dentfed clearly or that these fnancal nstruments are not beng used effectvely by frms. 4. Testng the soundness of the NP methodology 24 For example for U.S., Joron (1990) estmates a maxmum exposure of 0.56 over the perod, Domnguez and Tesar (2006) smlarly estmate a maxmum exposure of over the perod n 6 non-us advanced economes. Hageln and Pramborg (2002) estmate t to be 0.52 over the perod n Sweden. 17

20 In ths secton we use several experments to test the soundness of the results from the NP model. In so dong, we attempt to determne whether the substantal dfferences n results obtaned usng a NP model versus alternatve models are due to the NP estmaton methodology tself. We use the S&P 500 frms n ths secton. Ths sample set was chosen manly for brevty and consstency. The data requred to conduct the frst two tests were only avalable for U.S. frms and we could not fnd evdence pontng to dfferent conclusons when we used data from emergng markets n the last three tests. Frms that declare no exposure Sxty-nne of the S&P 500 frms explctly declare that they do not have sgnfcant exposure to foregn currency fluctuatons and therefore do not carry any foregn currency dervatves. Convenently, ths nformaton allows us to scrutnze the results obtaned from the NP model. Specfcally, by comparng exposure coeffcents obtaned usng NP and other methods for these frms, we are able to nvestgate whether the hgher frequency of exposure found wth a NP estmaton s artfcally generated by ths methodology. Results are dsplayed n Panel A of Table 6. Consstent wth frms declaratons, we see that the proporton of frms wth estmated exposure (among frms who state no exposure) s low regardless of the dfferent models used n estmaton. Furthermore, the results also suggest that the relatvely hgh proporton of exposure found usng a NP approach s unlkely due to the approach tself (to the extent that the nformaton provded by these frms are accurate). Profle of frms that have a nonparametrc exposure In ths secton, we analyze the characterstcs of frms that are classfed as exposed when a NP approach s used, but are not classfed as exposed f parametrc models are used. Specfcally, we estmate the followng model to determne the effects of dervatve usage, 18

21 foregn sales and sze on the lkelhood of fndng exposure n a NP model but not n the other models. In so dong, we use data for U.S. frms that have NP exposure. D NP, 0 1 ( DER TA) + ψ ( FS / TS ) + ψ ( Sze / TSze) + = L, NL, PP = ψ + ψ ν / 2 3 (9) D NP, = 1 f ˆ β NP s sgnfcant and ˆ β s not D NP, = 0 f ˆ β NP and ˆ β are both sgnfcant We estmate ths model usng 3 dfferent dependent varables. The dependent varable, NP D, s set equal to 1 f there s NP exposure but no lnear, NL or PP exposure, respectvely. In Secton 3 we found, consstent wth the lterature, that frms smaller n sze and/or frms wth hgher foregn sales are relatvely more exposed to exchange rate fluctuatons. Accordngly, we would expect to observe these characterstcs n frms that have NP exposure but are classfed as not exposed when parametrc specfcatons are used. Conversely, f we observe that the NP approach s -- naccurately -- fndng a sgnfcant exposure for frms that have no operatons abroad nor any economc exposure, ths would pont to methodology related shortcomngs. The results obtaned from a probt estmaton strategy are dsplayed n Panel B of Table 6. We fnd that frms classfed as exposed under a NP approach but not exposed usng the other methods (L, NL, PP) have relatvely hgh foregn sales and are smaller n sze. Ths s consstent wth our fndngs descrbed n the prevous secton. Also consstent wth our man results, we fnd that dervatve usage does not affect the lkelhood of fndng exposure when usng a NP model. Specfcaton Tests As mentoned above, we dentfy the usage of the same parametrc form for each frm as a possble determnant of our results. To test whether ths constrant s a determnant of the low 19

22 exposure found usng parametrc models, we follow the methodology of L and Whang (1998). The authors propose a method for testng for specfc functonal forms aganst alternatve functonal forms. Ths method s especally convenent for our purposes snce the alternatve functonal forms do not have to be specfed. The constructon of the author s test statstc and ts propertes s summarzed n Appendx A. Panel C of Table 6 dsplays the results of our specfcaton tests usng US data. Columns correspond to the functonal forms that were tested under the null hypothess. To be concse, we only report the proporton of frms for whch the functonal form lsted n the correspondng column was reected at the 5% level. The results suggest that a lnear model provdes a better overall ft compared wth the other parametrc models. However, for a maorty of the frms n our sample, the parametrc forms were reected. 25 Return horzons and the choce of exchange rates In ths secton, we replcate our smulatons usng dfferent exchange rates and return horzons and measure the proporton of S&P 500 frms exposed under these scenaros. We focus on the weekly, monthly, quarterly and semannual horzons when measurng the change n exchange rates, stock prces and returns to market n equaton (1). Note that comparng exposure across dfferent return horzons n ths way would be questonable due to the large dfferences n the degrees of freedom assocated wth each return horzon. To overcome the lack of power and make sgnfcance more comparable across dfferent frequences, we use overlappng observatons smlar to Domnguez and Tesar (2006) and Bodnar and Wong (2003). In so dong, we use daly overlappng observatons for weekly return horzons, and weekly 25 When we used the same test for emergng market frms n our sample we found that the functonal forms were reected for a larger proporton of frms compared to the US. These results are avalable upon request. We also expermented wth other nonlnear functonal forms and found proportons that were larger than under the lnear specfcaton. 20

23 overlappng observatons for monthly, quarterly and semannual horzons. We correct for seral correlaton stemmng from the usage of overlappng observatons by employng the Newey and West (1987) method. The results from the estmaton of equaton (1) (usng the US Dollar/Euro exchange rate) are dsplayed n Panel D of Table 6. Consstent wth a maorty of the research (c.f., Allayanns, 1997; Bartov and Bodnar, 1994; Bodnar and Wong, 2003; Chow and Chen, 1998; Chow, Lee and Solt, 1997; Domnguez and Tesar, 2001, 2006; Jongen, Muller and Verschoor, 2007), we fnd, n general, that the proporton of frms wth sgnfcant exposure ncreases wth the return horzon. Notce, however that the conclusons drawn from our benchmark model reman the same. Specfcally, we observe that NL, PP, and NP models capture the exposure of a notceable number of frms and that these numbers are consderably hgher for the NP model. We reach a smlar concluson when we use dfferent exchange rates. Results (usng monthly return horzons) dsplayed n Panel E of Table 6 demonstrate that the number of frms wth exposure accordng to the NP model s hgher for every exchange rate we use. We also fnd that exchange rate exposure s not as frequent when a trade weghted exchange rate s used, and that the proportons are the hghest for ERStated and -- by defnton -- for ERMAX. Subsamples and the lagged effects of exchange rate fluctuatons There s evdence n the lterature that suggests a lagged effect of exchange rate movements on stock prces. Partally ndcatng delayed processng of nformaton by nvestors when evaluatng frms exchange rate rsk. Furthermore, some studes (c.f. Domnguez and Tesar, 2006) argue that measurng exchange rate exposures usng a long sample perod may understate the level of exposure. Ths especally true for frms n countres where sgnfcant exchange rates 21

24 fluctuatons are lmted to short perods of tme. 26 Our smulatons ncludng the lagged effects of exchange rates and lmtng the sample to perods wth hgh exchange rate volatlty generally yelded larger exchange rate coeffcents. However, smulaton results from the lnear, NL, PP and NP models were qualtatvely smlar Concluson Our results demonstrate that when exchange rate exposure s measured usng only a lnear model, the proporton of frms wth exposures are understated n both emergng markets and an advanced economy such as the US. We show that f NL, PP and NP models are used as an estmaton strategy the frequency of exposure ncreases. Among these models, however we fnd that only NP results dsplay the hgh frequences of exposure that are parallel to anecdotal evdence, fnance theory and nsttutonal knowledge. Consstent wth these results, our second stage regresson results mpled that frms are able to lower ther lnear exposures but not the NP (and nonlnear n some cases) exposures by usng foregn currency dervatves. Although the NP approach used n ths paper has several advantages for every country, ths approach would be most useful for countres that have a hgh degree of varety among ther frms (n terms of openness and economc exposure) and/or are experencng structural breaks (for example those that are n the process of ntegratng wth global captal markets). Indeed, by estmatng the nature (or the functonal form) of the relatonshp between stock prces and exchange rates unquely for each frm and by more effectvely accountng for the dynamcs of ths relatonshp before and after structural breaks, a NP approach can be more advantageous over parametrc approaches. The latter characterstc would be especally useful when usng long sample perods. 26 Although our partally nonparametrc approach accounts for these large fluctuatons, lmtng the sample to specfc perods marked by hgh volatlty can do a better ob of capturng the dynamcs governng these perods. 27 These results are avalable upon request. 22

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