Foreign Exchange Volatility and Stock Returns

Transcription

1 Foregn Exchange Volaly and Sock Reurns Workng Paper Seres Ocober 2012 Dng Du Norhern Arzona Unversy The W. A. Franke College of Busness PO Box Flagsaff, AZ (928) Fax: (928) Ou Hu Deparmen of Economcs Youngsown Sae Unversy Youngsown, OH (330)

2 Foregn Exchange Volaly and Sock Reurns 1. Inroducon The Inernaonal Capal Asse Prcng Model of Solnk (1974), Sercu (1980), and Adler and Dumas (1983) suggess ha he covarance of sock reurns wh foregn exchange changes should be a prced facor when purchasng power pary s volaed. Movaed by hs nsgh, emprcal sudes on foregn exchange rsk ypcally add foregn exchange changes o he sandard asse-prcng models as an addonal facor. However, hs approach usually fnds ha only low proporons of U.S. socks have sgnfcan foregn exchange exposure and foregn exchange rsk s no prced. 1 Recenly, Menkhoff, Sarno, Schmelng, and Schrmpf (2011) (MSSS) fnd ha (G)lobal FX volaly s a key drver of rsk prema n he cross-secon of carry rade reurns. The prcng power of volaly also apples o oher cross-secons, such as a common FX momenum sraegy, ndvdual currences' excess reurns, domesc U.S. corporae bonds, U.S. equy momenum, as well as FX opon porfolos and nernaonal bond porfolos. (p. 3) Alhough MSSS focus on undersandng carry rade reurns n foregn exchange markes, he pervasveness of he prcng power of foregn exchange volaly across such a varey of es asses (documened n her sudy) suggess a poenally promsng approach o undersandng foregn exchange rsk n he equy marke. Tha s, may be foregn exchange volaly (second momens) no foregn exchange changes (frs momens) ha maer for he cross-secon of sock reurns. Ths perspecve also has a number of heorecal jusfcaons. Frs, as MSSS argue, volaly can be a sae varable n he Meron (1973) sense. Second, Shapro (1974), Dumas (1978), and Lev (1990) among ohers sugges ha foregn exchange changes can affec frms cash flows, whch mples ha foregn exchange volaly can nfluence frms cash flow volaly and, herefore, he dscoun rae. Movaed by he above observaons, we sudy wheher foregn exchange volaly s a prced facor n he US sock marke n hs paper. If foregn exchange volaly s a prced facor n he sock marke, should help reduce prcng errors of sandard asse-prcng models, such as he CAPM of Sharpe (1964) and Lnner (1965) and he four-facor model of Carhar (1997). 2 Therefore, we focus on he comparson beween he performance of he sandard models and ha of her enhanced versons wh foregn exchange volaly as an addonal facor. Emprcally, we use a wde varey of es asses commonly used n nernaonal fnance and emprcal asse prcng, ncludng 25 sze and BM porfolos, 25 sze and momenum porfolos, 10 porfolos formed on earnngs-o-prce, 10 porfolos formed on dvdend yeld, 10 porfolos formed on shor-erm reversal, 10 porfolos formed on long-erm reversal, and 30 ndusry porfolos. In erms of emprcal mehodology, we employ he cross-seconal regresson mehodology of Fama and MacBeh (1973) as well as he me-seres regresson approach of Fama and French (1996). For robusness, we also use he mmckng porfolo approach of Fama and French (1993). Our fndngs can be easly summarzed: emprcally, foregn exchange volaly has no power n explanng eher he me-seres or he cross-secon of sock reurns. Our fndngs call 1 See also Joron (1990, 1991), Khoo (1994), Barov and Bodnar (1994), Allayanns (1997), Chow, Lee and Sol (1997), Vassalou (2000), Bodnar and Wong (2003), Barram (2004), Barram and Bodnar (2005), Marn and Mauer (2005), Barram (2007), Barram (2008), Francs, Hasan, and Huner (2008), Kolar, Moorman, and Sorescu (2008), Barram, Brown, and Mnon (2010), Du and Hu (2012), and Anell and Vahekosk (2012). 2 The four facor model augmens he hree-facor model of Fama and French (1993) wh a momenum facor, snce he hree-facor model s well-known o be unable o accoun for sock momenum of Jegadeesh and Tman (1993) (e.g. Fama and French, 1996). 1

3 for more research on foregn exchange rsk. In heory, foregn exchange volaly can affec frms cash flow volaly. Therefore, should be a prced facor for equy reurns. Barov, Bodnar, and Kaul (1996) and Adran and Rosenberg (2008) mply ha mgh be he long-erm componen of foregn exchange volaly ha affecs sysemac rsk of frms. Therefore, fuure research may decompose foregn exchange volaly no dfferen componens and examne her dfferenal effecs on he me-seres and he cross-secon of sock reurns. The remander of he paper s organzed as follows: Secon 2 descrbes he daa. Secon 3 presens emprcal mehodology. Secon 4 repors emprcal resuls when foregn exchange volaly nnovaons are measured by he frs dfference of foregn exchange volaly. Secon 5 presens he resuls when foregn exchange volaly nnovaons are measured by facormmckng porfolo reurns. Secon 6 concludes he manuscrp. 2. Daa Our full sample ncludes 34 counres whose daly exchange rae daa are avalable from he Federal Reserve Bank of S. Lous. They are Ausra, Ausrala, Belgum, Brazl, Canada, Chna, Denmark, Euro Area, Fnland, France, Germany, Greece, Hong Kong, Inda, Ireland, Ialy, Japan, Korea, Malaysa, Mexco, Neherlands, New Zealand, Norway, Porugal, Sngapore, Souh Afrca, Span, Sr Lanka, Sweden, Swzerland, Tawan, Thaland, Venezuela, and Uned Kngdom. Our sample perod s from January 1973 o December The sar of our sample perod concdes wh he sar of flucuang exchange raes (see Barov, Bodnar, and Kaul, 1996). Monhly daa of relevan facors ncludng he rsk-free rae (RF), he excess marke reurn (MKT), he momenum facor (WML), he sze facor (SMB), and he book-o-marke-equy facor (HML) are from Kenneh French s webse. 3 We follow MSSS o consruc he foregn exchange (FX) volaly seres. Specfcally, we frs compue he absolue daly log reurn for each currency on each day n our sample. We hen average over all currences avalable on any gven day. Fnally, we average daly values whn a gven monh o oban he monhly FX volaly. We measure FX volaly nnovaons n wo ways. The frs way s o ake he frs dfference of he FX volaly as n Ang, Hodrck, Xng, and Zhang (2006). 4 The second way s o consruc a facor- mmckng porfolo along he same lne as Fama and French (1993). For wo reasons, hs second approach, n prncple, should be more powerful han he frs one. Frs, FX volaly changes are a macroeconomc varable (no reurns), whch may conan nformaon ha s rrelevan o asse prcng (and may also have measuremen errors). In conras, a facormmckng porfolo n prncple capures only he nformaon n FX volaly nnovaons ha s pernen o sock reurns, and herefore should reduce he nose n esmaons. 5 Second, o consruc our facor-mmckng porfolo, we esmae frms FX volaly sensves n a rollng regresson fashon, whch allows me varaon n volaly sensvy n a non-srucural framework. 6 Panel A of Fgure 1 shows he me seres of he FX volaly; Panel B presens he FX volaly nnovaons as he frs dfference; Panel C depcs he nnovaons as he facormmckng porfolo reurn. Table 1 presens he descrpve sascs for he FX volaly and s nnovaons. 3 We hank Fama and French for makng hese daa avalable a hp://mba.uck.darmouh.edu/pages/faculy/ken.french/. 4 Usng he AR(1) resduals as n MSSS yelds qualavely smlar resuls. However, as MSSS pon ou, hs approach no only may nroduce an errors-n-varables problem bu also requres esmaon on he full sample whch s no mplemenable (snce marke parcpans do no have such nformaon n real me). 5 See Chan, Karcesk and Lakonshok (1998 and 1999) for more dscusson and applcaons of he mmckng porfolo approach. 6 See Dodge, Grffn, and Wllamson (2006) for more dscusson. 2

4 Fgure 1 Foregn exchange volaly: Panel A: The FX volaly Panel B: The frs dfference of he FX volaly Panel C: Facor-mmckng porfolo of he FX volaly nnovaons Panel A of Fgure 1 shows he me seres of he FX volaly; Panel B presens he FX volaly nnovaons as he frs dfference; Panel C depcs he nnovaons as he facor-mmckng porfolo reurn. 3

5 Table 1: Descrpve sascs of he FX volaly and s nnovaons Mean Sd Error Mnmum Maxmum FX volaly Frs dfference of he FX volaly Facor-mmckng porfolo of he FX volaly nnovaons Table 1 presens he descrpve sascs for he FX volaly and s nnovaons. When FX volaly nnovaons are measured by he frs dfference of he FX volaly, we focus on 25 sze and book-o-marke (BM) porfolos (whch are commonly used n he leraure) as our es asses. For robusness, besdes 25 sze and book-o-marke (BM) porfolos, we expand our se of es asses o nclude 25 sze and momenum porfolos, 10 porfolos formed on earnngs-o-prce, 10 porfolos formed on dvdend yeld, 10 porfolos formed on shor-erm reversal, 10 porfolos formed on long-erm reversal, and 30 ndusry porfolos. 7 When FX volaly nnovaons are measured by facor-mmckng porfolo reurns, n lne wh Fama and French (1993), we consruc 25 sze and volaly-sensvy porfolos as our esng asses. Usng such volaly-sensvy porfolos can maxmze he power of he ess, because hese porfolos are formed on he sensvy o FX volaly nnovaons. 3. Emprcal mehodology To examne wheher he FX volaly has margnal power o explan he me-seres and cross-secon of sock reurns, we focus on he comparson beween he performance of wo sandard asse-prcng models and ha of her enhanced versons wh he FX volaly as an addonal facor. The frs sandard model s he CAPM of Sharpe (1964) and Lnner (1965) (MKT): r b MKT (1) r where s he excess reurn on asse n perod, and MKT s he excess marke reurn. If foregn exchange volaly s a prced facor, should reduce prcng errors of he CAPM. Thus, we consder an enhanced verson of he CAPM, a wo-facor model, whch augmens he CAPM wh an FX volaly facor (MKT+VOL): r b MKT c VOL (2) where VOL s he volaly nnovaons measured by eher he frs dfference of he FX volaly or he facor-mmckng porfolo reurn. I s well known ha he CAPM fals o capure he sze, value and momenum effecs (e.g. Fama and French, 1993; Jegadeesh and Tman, 1993). Therefore, he second sandard model we consder s he four-facor model of Carhar (1997) (MKT+SMB+HML+WML), whch enhances he CAPM wh he sze, value and momenum facors: r b MKT s SMB v HML m WML (3) 7 All he monhly porfolo reurn daa are from Kenneh French s webse. The deals of he consrucon of hese porfolos are also avalable a Kenneh French s webse. 4

6 where SMB s he dfference beween he reurns on dversfed porfolos of small socks and bg socks, HML s he dfference beween he reurns on dversfed porfolos of hgh book-omarke (value) socks and low book-o-marke (growh) socks, and WML s he dfference beween he monh reurns on dversfed porfolos of he wnners and losers of he pas year. Agan, f foregn exchange volaly s a prced facor, should reduce prcng errors of hs model. Thus, we also consder an enhanced verson of hs model, a fve-facor model (MKT+SMB+HML+WML+VOL) wh he FX volaly as an addonal facor. r b MKT s SMB v HML m WML c VOL (4) To evaluae he performance of hese asse-prcng models, we carry ou wo complemenary ses of ess. The frs se focuses on he me-seres of sock reurns wh he me-seres regresson approach of Fama and French (1993, 1996). Essenally, Eqs. (1) hrough (4) are esmaed for each es asse wh monhly daa. Followng relevan leraure (e.g. Fama and French, 2011), we evaluae each model based on he magnude of prcng errors (he average absolue value of he nerceps and he average of he sandard errors of he nerceps), he explanaory power (he average adjused R 2 ), and he Gbbons, Ross, and Shanken (1989) (GRS) F-es sasc for he hypohess ha he nerceps are jonly equal o zero for all es asses. The second se of ess concenraes on he cross-secon of sock reurns wh he Black, Jensen, and Scholes (1972) and Fama and MacBeh (1973) wo-pass mehodology esmang facor loadngs n he frs pass, and usng hose o oban rsk premums n he second pass wh sandard refnemens: he Shanken (1992) correcon o oban errors-n-varables (EIV) robus sandard errors, accounng for he fac ha facor sensves are esmaed, and he Shanken and Zhou (2007) correcon o generae msspecfcaon (MIS) robus sandard errors. We also ake no consderaon he suggesons of Lewellen, Nagel and Shanken (2010) regardng crossseconal asse-prcng ess: (1) we expand he se of es asses beyond porfolos formed on sze and BM; (2) we repor no only he OLS resuls bu also he GLS resuls. We evaluae each model based on he adjused R 2 (.e. he prcng error). 4. FX volaly nnovaon as he frs dfference of he FX volaly 4.1 Man resuls Panel A of Table 2 summarzes me-seres regressons o explan monhly excess reurns on 25 sze-bm porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R 2 (R 2 ), and he GRS F-es sasc (GRS). We focus on he comparson beween he sandard models and her enhanced versons wh he FX volaly as an addonal facor. Frs, we examne he CAPM (Eq. 1) and s enhanced verson (Eq. 2). As we can see, enhancng he CAPM wh he FX volaly does no mprove he performance of he CAPM a all. From he CAPM o s enhanced verson, he average absolue value of he nerceps, he average adjused R 2, and he GRS sascs all say he same. Thus, dsapponngly, he me-seres evdence based on he CAPM suggess ha he FX volaly s no prced. 5

7 Table 2: Summary sascs of me-seres and cross-seconal regressons for 25 sze-bm porfolos: Panel A: Summary sascs of me-seres regressons Model α S(α) R 2 GRS MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * Panel B: Two-pass OLS cross-seconal regressons Model Facor γ EIV MIS R 2 MKT Alpha 1.38* MKT MKT+VOL Alpha 1.59* MKT VOL MKT+SMB+HML+WML Alpha MKT SMB HML 0.47* WML Alpha MKT+SMB+HML+WML+VOL MKT SMB HML 0.47* WML VOL Panel A summarzes me-seres regressons o explan monhly excess reurns on 25 sze-bm porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R 2 (R 2 ), and he GRS F-es sasc (GRS). Panel B repors he Fama and MacBeh (1973) wo-pass OLS regressons (wh a consan) wh 25 sze-bm porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R 2. The asersk ndcaes he sgnfcance a he 5% level. Nex, we compare he four-facor model of Carhar (1997) (Eq. 3) wh s enhanced verson (Eq. 4). 8 I s evden ha augmenng he four-facor model wh he FX volaly does no mprove he performance of he model. From he four-facor model o s enhanced verson, he average absolue value of he nerceps, he average adjused R 2, and he GRS sascs all say he same. Thus, he me-seres evdence based on he four-facor model does no suppor he noon ha he FX volaly s prced eher. Panel B of Table 1 repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 25 sze-bm porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each 8 The four-facor model performs noceably beer han he CAPM. From he CAPM o he four-facor model, he average absolue value of he nerceps decreases from 0.31 o 0.10; he average adjused R 2 ncreases from 0.74 o 0.91; and he GRS sascs reduces from 3.95 o Our resuls are n general conssen wh prevous sudes (e.g. Fama and French, 2011). 6

8 Table 3 Sub-sample resuls for 25 sze-bm porfolos Panel A: Summary sascs of me-seres regressons 1973:1 1985:9 1985: :12 Model α S(α) R 2 GRS α S(α) R 2 GRS MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * Panel B: Two-pass OLS cross-seconal regressons 1973:1 1985:9 1985: :12 Model Facor γ EIV MIS R 2 γ EIV MIS R 2 MKT Alpha * MKT MKT+VOL Alpha * MKT VOL MKT+SMB+HML+WML Alpha MKT SMB 0.48* HML 0.76* WML * MKT+SMB+HML+WML+VOL Alpha MKT SMB HML 0.77* WML * VOL Panel A summarzes me-seres regressons o explan monhly excess reurns on 25 sze-bm porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). Panel B repors he Fama and MacBeh (1973) wo-pass OLS regressons (wh a consan) wh 25 sze-bm porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R 2. From he CAPM o s enhanced verson, he nercep (Alpha) ncreases slghly from 1.38 o 1.59 (boh are sgnfcan a he 5% level based on eher EIV or MIS ); and he crossseconal R 2 ncreases nsgnfcanly from 0.13 o From he four-facor model of Carhar (1997) o s augmened verson, he nercep (Alpha) ncreases from 0.69 o 0.73 (boh are no sgnfcan a he 5% level based on eher EIV or MIS ); and he cross-seconal R 2 says he same a 9 Lewellen, Nagel and Shanken (2010) show ha a sample adjused R 2 mgh need o be as hgh as 44% o be sascally sgnfcan n models wh one facor, 62% n models wh hree facors, and 69% n models wh fve facors. (p. 176) 7

9 0.71. Furhermore, he FX volaly facor s never sgnfcan. Taken ogeher, conssen wh he me-seres regresson resuls, he cross-seconal regresson resuls also sugges ha he FX volaly s no prced. 4.2 Robusness check Sub-sample resuls Snce here s evdence suggesng ha foregn exchange exposure and rsk premum can be me varyng, 10 for robusness, we examne wo sub-sample perods. One s from 1973:1 o 1985:9, and he oher s from 1985:10 o 2010:12. Ths dvson of he sample s based on he consderaon of he Plaza Accord n 1985:9. The sub-sample resuls are repored n Table 3 n he same fashon as Table 2. As we can see, for boh sub-sample perods, addng he FX volaly o he sandard models such as he CAPM and he four-facor model of Carhar (1997) does no reduce prcng errors n me seres and cross-seconal regressons. Furhermore, he FX volaly does no have a sgnfcan rsk premum n eher perod. Therefore, he sub-sample evdence confrms he whole-sample evdence, suggesng ha he FX volaly s no prced Tes resuls for he expanded se of es asses To relax he gh facor srucure of sze-b/m porfolos (Lewellen, Nagel and Shanken 2010, p. 182), we expand our se of es asses o 120 porfolos formed on, besdes sze-bm, szemomenum, earnngs-o-prce, dvdend yeld, shor-erm reversal, long-erm reversal, and ndusry. Tables 4 and 5 summarze me-seres and cross-seconal regressons n he same fashon as Table 2. In Table 4, we repor summary me-seres regresson sascs for he porfolos formed on ndvdual characerscs (.e. earnngs-o-prce) as well as hose for all 120 asses. Regardless of wheher we look a he porfolos formed on ndvdual characerscs or all 120 porfolos, he same paern emerges: he enhanced versons of he sandard models ha nclude he FX volaly do no reduce he prcng errors or ncrease he explanaory power n me-seres regressons. Consder he summary sascs for regressons wh 120 porfolos as es asses, he average absolue values of he nerceps from 120 me-seres regressons are 0.24 for he CAPM, 0.24 for s enhanced verson, 0.12 for he four-facor model of Carhar (1997), and 0.12 for s augmened verson. For hese models, he average adjused R 2 s are 0.72, 0.72, 0.82 and 0.82; and he GRS sascs are 2.65, 2.66, 2.28 and 2.28, respecvely. Panel A of Table 5 repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 120 porfolos as he es asses. The resuls are, n general, conssen wh hose n Table 2. The models ha nclude he FX volaly do no ouperform he sandard models whou hs facor. For nsance, he OLS R 2 s are 0.01 for he CAPM, 0.02 for s enhanced verson, 0.60 for he four-facor model of Carhar (1997), and 0.61 for s augmened verson. Furhermore, he FX volaly facor s never sgnfcan. Thus, he evdence confrms ha he FX volaly has no power o explan eher he me-seres or he cross-secon of sock reurns for a wde varey of es asses GLS regressons Lewellen, Nagel and Shanken (2010) sugges researchers repor no only he OLS resuls bu also he GLS resuls, especally he GLS cross-seconal R 2. As hey pon ou, The broader pon s ha, whle he OLS R 2 mgh be relevan for some quesons for example, askng wheher a model s predcons of expeced reurns are accurae for a gven se of asses (subjec o he lmaons dscussed n Secon 2) he GLS R 2 s probably more relevan for oher 10 See for nsance Francs, Hasan, and Huner (2008). 8

10 Table 4 Summary sascs of me-seres regressons for a varey of es asses, Tes asses Model α S(α) R 2 GRS Sze/Momenum MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * Earnngs/Prce MKT * MKT+VOL * MKT+SMB+HML+WML MKT+SMB+HML+WML+VOL Dvdend Yeld MKT MKT+VOL MKT+SMB+HML+WML MKT+SMB+HML+WML+VOL Shor-Term MKT Reversal MKT+VOL MKT+SMB+HML+WML MKT+SMB+HML+WML+VOL Long-Term MKT * Reversal MKT+VOL * MKT+SMB+HML+WML MKT+SMB+HML+WML+VOL Indusry MKT MKT+VOL MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * 120 asses MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * In Table 4, we repor summary me-seres regresson sascs for he porfolos formed on ndvdual characerscs (.e. earnngs-o-prce) as well as hose for all 120 asses. Table 4 shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). The asersk ndcaes he sgnfcance a he 5% level. quesons for example, askng how well a model explans he rsk-reurn opporunes avalable n he marke. (p. 184). We hus repor he GLS resuls n Panel B of Table 5 for 120 porfolos over he same sample perod from 1973 o The resuls are, n prncple, conssen wh he OLS resuls n Panel A. The models ha nclude he FX volaly do no ouperform he sandard models whou hs facor. Furhermore, he FX volaly facor s never sgnfcan FX volaly nnovaons measured by he AR(1) resduals MSSS use he AR(1) resduals of he FX volaly as FX volaly nnovaons. We hus repea our ess wh 120 porfolos as our es asses and he AR(1) resduals as nnovaons. Panel A of Table 6 summarzes he me-seres and he OLS cross-seconal regressons resuls. We only repor he resuls for he models wh he FX volaly, snce he resuls for he CAPM and he four-facor model of Carhar (1997) are no affeced by he FX nnovaon measures and are he same as hose n Table 4 (for 120 asses) and Table 5. A comparson beween Tables 4 and 5 and Panel A of Table 6 reveals ha usng AR(1) resduals produces almos dencal resuls. For nsance, for he enhanced CAPM, n me-seres regressons, he average absolue value of he nerceps s 0.24 when he FX nnovaons are 9

11 Table 5 Two-pass cross-seconal regressons for 120 es asses, Model Facor Panel A: OLS regressons Panel B: GLS regressons γ EIV MIS R 2 γ EIV MIS R 2 MKT Alpha 0.82* * MKT MKT+VOL Alpha 0.80* * MKT VOL MKT+SMB+HML+WML Alpha * MKT SMB HML 0.34* * WML 0.72* * MKT+SMB+HML+WML+VOL Alpha * MKT SMB HML 0.35* * WML 0.74* * VOL Panel A repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 120 porfolos as he es asses, where Panel B presens he GLS resuls. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS and GLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. measured by he frs dfference, and 0.24 when nnovaons are measured by he AR(1) resduals. In OLS cross-seconal regressons, he adjused R 2 s 0.02 n he frs case and 0.08 n he second case. Agan, he FX volaly facor s never sgnfcan Developed counry currences We also follow MSSS and sudy a subsample whch ncludes only he currences of developed counres. These counres are Ausrala, Canada, Denmark, Euro area, France, Germany, Ialy, Japan, Neherlands, Norway, Sweden, Swzerland, and he Uned Kngdom. The resuls for 120 porfolos are repored n Panel B of Table 6. Agan, usng developed counry currences yelds almos dencal resuls, suggesng ha he FX volaly has no power n explanng eher he me-seres or he cross-secon of sock reurns. 5. FX volaly nnovaons as he facor-mmckng porfolo reurns As we pon ou, usng facor-mmckng porfolo reurns o measure FX volaly nnovaons and he porfolos formed on he volaly sensvy as es asses can maxmze he power of ess. Thus, n hs secon, we provde he deals on how o consruc he FX volaly mmckng porfolo and assocaed es asses. We also repor he relevan es resuls. 5.1 Man resuls In lne wh Fama and French (1993), we consruc our facor-mmckng porfolo of he FX volaly n wo seps. The frs sep s o form sx value-weghed sze and volalysensvy porfolos wh all he socks n he Cener for Research n Secury Prces (CRSP). The porfolos, whch are consruced a he end of each June, are he nersecons of wo porfolos formed on sze (marke capalzaon) and hree porfolos formed on volaly sensvy. The sze breakpon for year s he medan NYSE marke equy a he end of June of year. The 10

12 Table 6 Robusness check, Panel A: Innovaons measured as he AR(1) resduals Summary sascs of me-seres regressons Model α S(α) R 2 GRS MKT+VOL * MKT+SMB+HML+WML+VOL * Two-pass OLS cross-seconal regressons Model Facor γ EIV MIS R 2 MKT+VOL Alpha 0.76* MKT VOL MKT+SMB+HML+WML+VOL Alpha MKT SMB HML 0.35* WML 0.74* VOL Panel B: FX volaly based on developed counry currences Summary sascs of me-seres regressons Model α S(α) R 2 GRS MKT+VOL * MKT+SMB+HML+WML+VOL * Two-pass OLS cross-seconal regressons Model Facor γ EIV MIS R 2 MKT+VOL Alpha 0.82* MKT VOL MKT+SMB+HML+WML+VOL Alpha MKT SMB HML 0.35* WML 0.74* VOL Panel A summarzes me-seres and OLS cross-seconal regressons when he AR(1) resduals are employed as nnovaons. Panel B presens he correspondng resuls when only developed counry currences are used. The es asses are 120 porfolos. For me-seres regressons, we repor he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). For cross-seconal regressons, we presen he Fama and MacBeh (1973) wo-pass OLS regresson resuls. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. volaly sensvy for June of year s esmaed wh he pror wo years daa based on he mul-facor model n Eq. (4). 11 The FX volaly s calculaed wh all he currences n our sample. The volaly-sensvy breakpons are he 30h and 70h percenles. These porfolos are held for one year (from July of year o June of year +1) and rebalanced a he end of June of 11 As a resul, our es perod n hs secon s from 1975:7 o 2010:12. 11

13 year +1. By rebalancng he porfolos on an annual bass n a condonal fashon, we allow frms volaly sensvy o be me varyng. The second sep s o defne he facor-mmckng porfolo reurns as he average reurn on he wo posve sensvy porfolos mnus he average reurn on he wo negave sensvy porfolos. Tha s, our FX volaly rsk facor s BP SP BN SN VOL (6) 2 2 where BP, SP, BN and SN are he reurns on large and posve sensvy, small and posve sensvy, large and negave sensvy, and small and negave sensvy porfolos, respecvely. Agan, n lne wh Fama and French (1993), we consruc 25 sze and volalysensvy porfolos as our esng asses. These 25 porfolos are consruced n a smlar way as he sx sze and volaly-sensvy porfolos. Table 7 summarzes he resuls of he me-seres and he OLS cross-seconal regressons. As we can see, even f we use an approach ha can maxmze he power of ess, he FX volaly sll has no power o explan he me-seres or he cross-secon of sock reurns. In boh me seres and cross-seconal regressons, he models ha nclude he FX volaly do no noceably ouperform he sandard models ha exclude hs facor. Furhermore, he FX volaly facor s never sgnfcan n he cross-seconal ess. Thus, he evdence confrms ha he FX volaly s no prced. 5.2 Robusness check We perform a varey of robusness ess. The frs one s o examne he wo sub-sample perods, 1975:7 o 1985:9 and 1985:10 o 2010:12. The resuls are repored n Table 8. As we can see, for boh sub-sample perods, addng he FX volaly o he sandard models does no reduce prcng errors n me seres and cross-seconal regressons. Furhermore, he FX volaly does no have a sgnfcan rsk premum n eher perod. Therefore, he sub-sample evdence confrms he whole-sample evdence, suggesng ha he FX volaly s no prced. The second robusness es s o use he developed counry currences o consruc he FX volaly mmckng porfolo and assocaed sze and volaly-sensvy porfolos. The resuls are repored n Table 9. As we can see, he resuls are qualavely smlar as hose n Table 7 based on all he currences. In boh me seres and cross-seconal regressons, he models wh he FX volaly do no ouperform he sandard models whou hs facor. Furhermore, he FX volaly facor s never sgnfcan n he cross-seconal ess. We also underake a number of oher expermens, ncludng droppng he socks wh a prce less han $5 (o mnmze poenal bases arsng from low-prced and llqud socks), usng a 5-year wndow o esmae frms volaly sensvy (o mgae he mpac of oulers), and employng a one-facor model ha only ncludes he FX volaly nnovaons n he frs sep o consruc he FX volaly mmckng facor and he assocaed es asses. The resuls are all smlar. To save space, we do no repor hese resuls. Bu hey are avalable upon reques. Therefore, all he evdence rejecs he noon ha he FX volaly s a prced facor n he US sock marke, whch calls for more research on FX rsk. 12

14 Table 7 Facor-mmckng porfolo approach resuls based on all he currences, Panel A: Summary sascs of me-seres regressons Model α S(α) R 2 GRS MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * Panel B: Two-pass OLS cross-seconal regressons Model Facor γ EIV MIS R 2 MKT Alpha 1.45* MKT MKT+VOL Alpha 1.35* MKT VOL MKT+SMB+HML+WML Alpha 2.07* MKT -1.68* SMB HML WML MKT+SMB+HML+WML+VOL Alpha 1.86* MKT -1.39* SMB HML WML VOL Table 7 summarzes me-seres and OLS cross-seconal regressons when he facor-mmckng porfolo reurns are used o measure FX volaly nnovaons and he porfolos formed on he volaly sensvy are employed as es asses. Panel A summarzes me-seres regressons o explan monhly excess reurns on 25 volaly sensvy porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). Panel B repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 25 volaly sensvy porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. 13

15 Table 8 Facor-mmckng porfolo approach resuls based on all he currences: sub-sample resuls Panel A: Summary sascs of me-seres regressons 1975:7 1985:9 1985: :12 Model α S(α) R 2 GRS α S(α) R 2 GRS MKT * * MKT+VOL * * MKT+SMB+HML+WML * * MKT+SMB+HML+WML+VOL * * Panel B: Two-pass OLS cross-seconal regressons 1975:7 1985:9 1985: :12 Model Facor γ EIV MIS R 2 γ EIV MIS R 2 MKT Alpha * MKT MKT+VOL Alpha * MKT VOL MKT+SMB+HML+WML Alpha * MKT * SMB HML 1.66* WML MKT+SMB+HML+WML+VOL Alpha * MKT * SMB HML 1.67* WML VOL Panel A summarzes me-seres regressons o explan monhly excess reurns on 25 volaly sensvy porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). Panel B repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 25 volaly sensvy porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. 14

16 Table 9: Facor-mmckng porfolo approach resuls based on developed counry currences, Panel A: Summary sascs of me-seres regressons Model α S(α) R 2 GRS MKT * MKT+VOL * MKT+SMB+HML+WML * MKT+SMB+HML+WML+VOL * Panel B: Two-pass OLS cross-seconal regressons Model Facor γ EIV MIS R 2 MKT Alpha 1.59* MKT MKT+VOL Alpha 1.49* MKT VOL MKT+SMB+HML+WML Alpha 2.17* MKT -1.69* SMB HML WML MKT+SMB+HML+WML+VOL Alpha 2.02* MKT -1.47* SMB HML WML VOL Table 9 summarzes me-seres and OLS cross-seconal regressons when only he developed counry currences are used o consruc he FX volaly mmckng porfolo and assocaed sze and volalysensvy porfolos. Panel A summarzes me-seres regressons o explan monhly excess reurns on 25 volaly sensvy porfolos. Panel A shows he average absolue value of he nerceps ( α ), he average of he sandard errors of he nerceps (s(α)), he average adjused R2 (R2), and he GRS F-es sasc (GRS). Panel B repors he Fama and MacBeh (1973) wo-pass OLS regressons wh 25 volaly sensvy porfolos as he es asses. γ s he esmaed rsk premum assocaed wh each facor. EIV and MIS are he Shanken (1992) errors-n-varables robus -rao and he Shanken and Zhou (2007) msspecfcaon robus -rao, respecvely. We also repor he OLS cross-seconal adjused R2. The asersk ndcaes he sgnfcance a he 5% level. 6. Concluson The pervasveness of he prcng power of foregn exchange volaly across a varey of es asses (documened n Menkhoff, Sarno, Schmelng, and Schrmpf, 2011) suggess a poenally promsng approach o undersandng foregn exchange rsk n he equy marke. Tha s, may be foregn exchange volaly (second momens) no foregn exchange changes (frs momens) ha maers for he cross-secon of sock reurns. Ths perspecve also has a number of heorecal jusfcaons. Movaed by hese emprcal and heorecal consderaons, we explore wheher foregn exchange volaly s a prced facor n he US sock marke n hs paper. Unforunaely, he emprcal evdence n hs paper suggess ha foregn exchange volaly has no power o explan eher he me-seres or he cross-secon of sock reurns. Our fndngs, herefore, call for more research on foregn exchange rsk. In heory and pracce, foregn exchange volaly can affec frms cash flow volaly. Consequenly, should be a prced facor for equy reurns. In hs paper, followng Menkhoff, Sarno, Schmelng, and 15

17 Schrmpf (2011), we measure foregn exchange volaly as a sngle varable. Tha s, we do no dfferenae dfferen componens of volaly (.e. long-run and shor-run componens). Two sudes, however, sugges ha may be more nformave o employ wo-componen volaly models. One s Barov, Bodnar, and Kaul (1996). They fnd ha he marke rsk (bea) of mulnaonal frms ncreases wh he ncrease n foregn exchange volaly when a longerhorzon (5 years) s focused upon. The second sudy s Adran and Rosenberg (2008). The auhors fnd dfferenal effecs of he long-run and shor-run componens of sock marke volaly on expeced reurns of socks. These wo sudes sugges ha fuure research may decompose he foregn exchange volaly no dfferen componens and examne her dfferenal effecs on he me-seres and he cross-secon of sock reurns. 16

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