Currency excess returns and global downside market risk

Transcription

1 Currency excess reurns and sde marke rsk by Vcora Galsband * and Thomas Nschka * Vcora Galsband, Deusche Bundesbank, Economcs Deparmen, Wlhelm-Epsen-Srasse 14, 6432 Frankfur am Man, Germany. Phone: , Fax: , E-Mal: vcora.galsband@bundesbank.de Thomas Nschka, Swss Naonal Bank, Moneary Polcy Analyss, Börsensrasse 15, P.O.Box, 822 Zürch, Swzerland. Phone: , Fax: , E-Mal: homas.nschka@snb.ch

2 Currency excess reurns and sde marke rsk Absrac We assess cross-seconal dfferences n 19 blaeral, condonal currency excess reurns n an emprcal model ha dsngushes beween US- and rsks, condonal on US bull (sde) or bear (sde) markes. A frs glance, our resuls sugges ha sde rsk s compensaed n blaeral currency reurns hus corroborang relaed sudes on currency porfolo reurns. However, we fnd ha sde rsk and fnancal marke volaly exposures are closely relaed. Moreover, he sde rsk evdence s mosly drven by emergng markes currences. Hence, sde rsk models canno fully address he ssue of currency reurns beng largely unrelaed o sandard rsk facors.

3 1 Inroducon The dfference beween curren forward and spo exchange raes,.e. he forward dscoun, should be a good predcor of fuure exchange rae movemens accordng o he uncovered neres rae pary condon (UIP). However, a wealh of sudes naed by Tryon (1979), Hansen and Hodrck (198) and Fama (1984) fnd ha exchange rae changes do no follow forward dscouns or, equvalenly, neres rae dfferenals. Regressng realzed spo exchange rae changes on he prevous perod s forward dscouns ypcally produces negave or nsgnfcan pon esmaes. 1 Ths amouns o sayng ha currences wh a forward dscoun end o deprecae whle he forward dscoun, n general, should predc an apprecaon. Ths ex pos devaon from he UIP, also known as he forward premum puzzle, can be poenally raonalzed by means of a me-varyng rsk premum ha nvesors demand on foregn currency denomnaed nvesmens. 2 Rsk prema on foregn currences ha lead o volaons of he UIP mgh reflec crash rsk or rare evens (e.g. Brunnermeer e al., 29; Farh e al., 213; Farh and Garbax, 211) or dfferences n he sensvy of currences o sysemac rsk facors (e.g. Ang and Chen, 21; Chrsansen e al., 211; Lusg and Verdelhan, 26, 27; Lusg e al., 211; Menkhoff e al., 212a; Verdelhan, 21, 212). However, he leraure explanng ex pos devaons from he UIP wh exposures o sysemac rsk facors faces crcsms on hree man grounds. Frs, ypcally reles on he formaon of currency porfolos o documen he emprcal relaon beween sysemac rsk facors and devaons from he UIP condon n he cross-secon (e.g. Ang and Chen, 21; Galsband and Nschka, 213; Lusg and Verdelhan, 27, Lusg e al., 211; Menkhoff e 1 Bansal and Dahlqus (2) show ha hs observaon does no peran o hgh nflaon counres. Meredh and Chnn (25) use long-erm governmen bond yelds as proxes for rsk-free raes o evaluae he explanaory power of long-erm yeld dfferenals for exchange rae changes a long horzons. They fnd ha he UIP holds a me horzons of 5 years or beyond. Lohan and Wu (25) show ha he UIP holds n a long sample perod unl he 198s. Husman e al. (1998) use a panel se o show ha he UIP s volaed bu wh sgnfcan, non-negave regresson coeffcens. 2 Backus e al. (21) provde a heorecal model n whch moneary polcy, cenral banks n bg closed and small open economes followng dfferen Taylor Rules, could generae volaons of he UIP. Burnsde e al. (211) argue ha peso problems accoun for volaons from he UIP. 1

4 al., 212; Raffery, 211). The use of currency porfolos srongly lms he degrees of freedom n cross-seconal asse prcng es whch poenally oversaes he explanaory power of he models for currency reurns (Burnsde, 211). Second, general, emprcal prcng models ha are successful n explanng excess reurns on currency porfolos mply mplausble values of rsk averson. For example, he consumpon-based models examned n Lusg and Verdelhan (27) raonalze he cross-seconal dsperson n currency porfolo reurns only wh mpled rsk averson parameer values around 1. A smlar value of rsk averson s needed n an neremporal CAPM seng o explan currency porfolo reurns (Galsband and Nschka, 213). Thrd, confroned wh blaeral currency excess reurns, he mos successful emprcal currency prcng models employ raher ad hoc rsk facors. Examples nclude he carry rade facor,.e. he reurn dfferenal on hgh and low forward dscoun sored currency porfolos, nroduced by Lusg e al. (211) or a measure of volaly on foregn exchange markes (Menkhoff e al., 212a). More general proxes of sysemac rsk canno accoun for (blaeral) currency excess reurns well (Barroso and Sana- Clara, 213; Burnsde e al., 27; Burnsde e al., 211; Burnsde, 211). Agans hs backdrop, we assess f recen models based on non-sandard nvesor preferences ha lnk currency porfolo reurns and radonal rsk facors are successful n explanng blaeral, currency excess reurns as well. In addon, our assessmen akes a closer, emprcal look on he underlyng economc raonale of hese models and res o augmen hem by explong basc nsghs from currency- prcng models such as Lusg e al. (211). Ths assessmen s based on Dobrnskaja (21) and Leau e al. (213) who argue ha he weak lnk beween sandard rsk facors and currency excess reurns can be overcome by consderng a CAPM verson ha dsngushes beween exposure o he marke reurn n mes of negave marke reurns (sde rsk) and mes of posve marke reurns (sde rsk). We already know ha hese sde rsk models are helpful n explanng average 2

5 reurns on sock markes (Ang e al., 26; Boshekan e al., 212; Galsband, 212). The basc raonale for he success of hese models s nvesors loss averson (Kahnemann and Tversky, 1979; Gul, 1991). In such a seng, nvesors care dfferenly abou an asse s comovemen wh fallng markes as opposed o an asse s comovemen wh rsng markes. Ths sounds lke a descrpon of he lnk beween he ypcal carry rade gong long n hgh forward dscoun currences and shor n low forward dscoun currences and he reurn on he US sock marke durng he 27/28 crss perod. Lusg and Verdelhan (211) depc hs relaon n her Fgure 4, here reproduced as Fgure 1. 3 The correlaon beween he ypcal carry rade reurn and he US sock marke s abou.7 durng ha crss perod. By conras, s vrually zero n normal mes. Hence, s naural o confron sde rsk models wh excess reurns on foregn currences. [abou here Fgure 1] Indeed, Dobrynskaja (21) shows ha he margnal conrbuon of sde rsk on op of he exposure o he uncondonal marke reurn s prced n excess reurns on porfolos of foregn currences and socks. She sors he currency porfolos on pas perods neres rae dfferenals. More recenly, Leau e al. (213) use a smlar verson of a sde rsk model o undersand reurns on neres rae dfferenal sored porfolos of currences as well as porfolos of oher asse classes such as commodes and bonds. Moreover, hey examne more generally he relaon of sde rsk models o rsk facors exraced from he prncpal componen analyss of currency porfolo reurns. However, none of hese papers dsngushes beween and counry- componens n he marke reurn despe recen evdence on he success of rsk facors o explan average excess reurns on currency porfolos (Lusg and Verdelhan, 211; Lusg e al., 211; Menkhoff e al., 212a). 4 Snce Verdelhan (212) shows ha also counry- 3 We hank Adren Verdelhan for provdng us wh he orgnal graphc fle. 4 Verdelhan (212) shows ha also counry- rsk can generae devaons from he UIP as emphaszed n Backus e al. (21). 3

6 rsk can generae devaons from he UIP, s no clear f he explanaory power of he sde rsk model s due o counry- or rsk. In addon, he focus of hese sudes s on a relavely small number of currency porfolos whch mgh be problemac n her cross-seconal analyses gven he low degrees of freedom (Burnsde, 211). Therefore, we examne blaeral foregn currency reurns ha are condonal on he prevous monh s forward dscoun o ncrease he number of es asses n he emprcal analyss. In addon, we dsngush beween and counry- componens of he marke reurn n sde and sde saes of he world and assess f he rsk explanaon documened for currency porfolos also perans o blaeral currency excess reurns. We show ha exposure o he componen of he US marke reurn n sde rsk saes s margnally prced n 19 blaeral, condonal currency excess reurns on developed and emergng counres US dollar exchange raes durng he sample perod from January 1999 o March A frs glance, hs fndng corroboraes Dobrnskaja (21) and Leau e al. (213) and lnks he sde rsk model o he rsk sory ha underles he success of he currency rsk facors proposed by Lusg e al. (211) or Menkhoff e al. (212). However, our subsample analyss reveals ha he sde rsk explanaon of counry-level excess reurns on foregn currences s largely drven by he emergng markes n he sample. Ths sands n marked conras o he evdence based on currency porfolos (Leau e al., 213). The relaon beween blaeral excess reurns on developed markes currences and sde rsk s, n conrary, vrually non-exsen. We confrm hs observaon n a longer sample perod from January 1985 o March 213. Furhermore, we 5 Our source of exchange rae daa s Daasream whch provdes mos US dollar forward and spo exchange raes only snce January 1997 (see also Burnsde a al., 211). Greenway-McGrevy e al. (212), for nsance, also sar her analyss of exchange rae predcably based on prncpal componens of US dollar exchange raes n January

7 show ha conrollng for equy marke volaly subsanally weakens he explanaory power of he sde rsk model for blaeral currency excess reurns because equy marke volaly s hgh n mes of fallng sock marke reurns. The economc raonale of he sde rsk model s explanaory power for currency excess reurns s hence unclear. Accordng o our emprcal resuls, s no necessarly loss averson ha explans he seemng success of sde rsk model varees n explanng average currency excess reurns. Averson o uncerany, as poenally refleced n equy marke volaly, mgh be a dfferen explanaon. In sum, our resuls sugges ha sde rsk models leave he crque of Burnsde e al. (27) and Burnsde (211) vald. I s hard o fnd a sgnfcan lnk beween radonal rsk facors, such as sock marke reurns, and currency excess reurns. Evdence based on currency porfolos should be accompaned by an analyss of blaeral currency excess reurns as hey consue a bgger challenge n cross-seconal analyss. The remander of he paper s organzed as follows. We presen he defnon of currency excess reurns n secon 2. We show our exenson of he emprcal verson of he CAPM n Secon 3 and descrbe he daa n Secon 4. Secon 5 provdes our economerc framework and he man resuls as well as a se of robusness checks. Fnally, Secon 6 concludes. 2 Defnon of currency excess reurns We defne currency excess reurns as ex pos devaons from he uncovered neres rae pary condon (UIP),.e. φ + 1 = s+ 1, (1) n whch φ + 1 represens he currency excess reurn, s he counry shor-erm neres rae, s home counry, here US counerpar, and he change n he log spo exchange rae s + 1 5

8 of counry relave o he home currency. An ncrease n s corresponds o an apprecaon of he home or deprecaon of he foregn currency. We regard excess reurns a he monhly frequency a whch covered neres rae pary usually holds (Akram e al., 28). Thus neres rae dfferenals are roughly equal o forward dscouns f s, (2) where f s he log forward exchange rae and he log currency excess reurn can be wren as a dfference beween he log forward dscoun and he log spo rae change φ = s ) s. (3) + 1 ( f + 1 Ths represenaon s equvalen o buyng a foregn currency n he forward marke and sellng one perod, here one monh, laer n he spo marke: φ + 1 = f s+ 1. (4) In order o ake ransacon coss no accoun we examne condonal, blaeral foregn currency excess reurns. The condonng varable for he excess reurn n +1 s he sgn of he dfference beween forward and spo raes observed a me. If hs dfference s posve, hen we go long n he foregn currency,.e. φ f s (5), l, b, a + 1 = + 1 If he dfference s negave, hen we go shor n he foregn currency nex perod,.e. φ f s (6), s, a, b + 1 = where a and b abbrevae ask and bd prces and l and s abbrevae long and shor posons, respecvely. Snce we focus on currency pars, here s a lo of varaon wh respec o long and shor posons n each blaeral exchange rae over our sample perod. In addon, by usng condonal currency excess reurns we capure smlar feaures of exchange rae daa as porfolos of currences ha are sored on forward dscouns. The dsadvanage of he use of 6

9 blaeral currency reurns s he loss of he sample perod lengh when emergng marke currences are ncluded n he sample. The advanage s relaed o he gans n he number of es asses and degrees of freedom n he cross-seconal regressons (Burnsde, 211). 3 Mehodology Ths secon brefly movaes an emprcal verson of he Sharpe (1964) and Lnner (1965) CAPM as he sarng pon of our analyss. In a second sep, we explan how we ncorporae he dsncon beween counry- and rsk no he emprcal model. Fnally, we nroduce sde and sde rsks no he emprcal model. 3.1 Why do we use an emprcal model based on a CAPM? Sandard models confroned wh currency excess reurns mply mplausbly hgh esmaes of he coeffcen of relave rsk averson. For nsance, he consumpon-based models n Lusg and Verdelhan (27) delver a rsk averson coeffcen of around 1. Galsband and Nschka (213) sudy excess reurns on currency porfolos n an neremporal verson of he CAPM and also fnd mpled rsk averson values of hs magnude. In hs paper, we evaluae f we can crcumven hs requremen. To mpose dscplne n hs respec, we op for an emprcal verson of he CAPM as a sarng pon. As hghlghed by Cochrane (25) we can easly nfer a CAPM from a consumponbased model under he assumpon of logarhmc uly (Rubensen, 1976). In he case of logarhmc uly, u ( C) = ln( C), and under he assumpon ha he marke or oal wealh porfolo s a clam o fuure consumpon flows, he prce of he marke porfolo, wren as M P, can be P M = E = 1 u'( C+ ) δ C u'( C ) + δ = C, 1 δ (7) where E s he expecaon operaor and δ denoes he ndvdual me preference parameer. The reurn on he marke porfolo, M R, s hen proporonal o consumpon growh: 7

10 R M = P M C P M + 1 = ( δ /(1 δ ) + 1) C+ 1 1 C+ 1 =. δ /(1 δ ) C δ C (8) Clearly, oher movaons of a CAPM are possble bu he logarhmc uly case llusraes he resrcon of he coeffcen of relave rsk averson. To see hs, remember ha a power uly funcon 6, 1γ C 1 u ( C) =, n whch γ reflecs he coeffcen of relave rsk averson, 1 γ converges o logarhmc uly when he rsk averson coeffcen approaches uny. We choose hs represenaon wh low mposed levels of rsk averson as a sarng pon o sudy he cross-seconal dsperson n blaeral, condonal currency excess reurns. 3.2 Incorporang counry- and rsk n he marke reurn A smple dsncon beween counry- and rsk facors n he framework of he sandard CAPM allows o easly accoun for he prevous leraure on he mporance of rsks for foregn exchange markes (Lusg e al., 211; Lusg and Verdelhan, 211; Menkhoff e al., 212a). From a US nvesor s perspecve, a sandard CAPM seng mples ha dfferences n he sensves o he US marke reurn should explan average currency excess reurns. Sensves of he blaeral currency excess reurn vs-à-vs counry obey M, US, M cov( φ, r ) =. (9) M, US var( r ) where M US r, s he reurn on he US sock marke n excess of he rsk-free rae. We nroduce he dsncon beween counry- and componens of he US marke excess reurn by regressng he US marke reurn on a world marke reurn. The fed value of hs regresson,.e. ha par of he US marke reurn ha comoves perfecly wh he world marke reurn, s henceforh referred o as marke reurn componen. 6 For smplcy, here we show he case when we add a consan o he ypcal power uly funcon. 8

11 We refer o he resdual of hs regresson as he US- componen whch s orhogonal o he componen by consrucon. In he emprcal analyss, we explcly dsngush beween sensves o counry and componens n he US marke reurn. The exposure o he counry- componen s measured as M,, cov( φ, r ) =, (1) M, var( r ) whle he exposure o he componen s defned as M,, cov( φ, r ) =. (11) M, var( r ) 3.3 Upsde and sde rsks Lusg and Verdelhan (211) show ha he payoff from a ypcal carry rade sraegy and he excess reurn on he US sock marke are hghly correlaed n he recen crss perod bu vrually uncorrelaed n more ranqul mes. In addon, Chrsansen e al. (211) and Cenedese (212) show ha he sensvy o he marke reurn s regme-dependen. These fndngs could be a reflecon of a more general noon of loss averson. Invesors n foregn exchange markes place a greaer emphass on he dsuly of large losses han on uly mprovemens from equally hgh gans (Kahnemann and Tversky, 1979). The general concep of loss averson plays an mporan role n he early porfolo heory leraure (Markowz, 1959) and asse prcng heory (Bawa and Lndenberg, 1977; Harlow and Rao, 1989; Hogan and Warren, 1974; Jahankhan, 1976). However, Ang e al. (26) were he frs o show ha sde rsk s acually prced n average sock reurns. Sock reurns whch covary srongly wh he fallng sock marke reurn should offer relavely hgh average reurns o compensae for sde rsk exposure. Downsde rsk, however, appears o be only one deermnan of sock reurns. Sze or he rao of book-o- 9

12 marke equy sll have an mpac on expeced sock reurns a he frm-level afer conrollng for sde rsk exposure. Based on he evdence ha reurns on carry rade sraeges are hghly correlaed wh he marke reurn n mes of dsress (Lusg and Verdelhan, 211), we apply hs reasonng o blaeral currency excess reurns. Dobrynskaja (21) and Leau e al. (213) analyse currency porfolos formed accordng o neres rae dfferenals n a smlar framework. One mporan dfference o hese sudes s our dsncon beween US- and componens n he marke reurn. Snce dfferences n he exposure o rsks can raonalze dfferences n average reurns on currency porfolos (Lusg e al., 211; Menkhoff e al., 212a), we assess f a smlar observaon can be made for blaeral excess reurns. The baselne defnon of sde and sde saes s based on he US marke reurn. If he marke reurn s negave, we are hen n a sde sae. If he marke reurn s bgger han or equal o zero, we are hen n an sde sae. Dobrnskaja (21) makes he same assumpon n her assessmen of currency porfolo and sock porfolo reurns whle Leau e al. (213) argue ha he hreshold should be defned as mulple of he marke reurn s sandard devaon around s mean. They chose one sandard devaon below he mean as a benchmark. We frs evaluae he defnon of sde and sde rsk saes accordng o posve or negave hresholds for he marke reurn and hen consder he Leau e al. (213) defnon of he sde rsk sae. Taken ogeher, our baselne emprcal model can dsngush beween four varans of currency excess reurns sensvy o he marke reurn: Upsde rsk as well as sde rsk n he US- and he componen of he marke reurn. More formally, hese sensves are M, M, US, cov( φ, r r ) = (12) M, M, US var( r r ) 1

13 M, M, US, cov( φ, r r < ) = (13) M, M, US var( r r < ) and M, M, US, cov( φ, r r ) =. (14) M, M, US var( r r ) M, M, US, cov( φ, r r < ) =. (15) M, M, US var( r r < ) 4 Daa In our benchmark aon, we examne a sample of monhly US dollar exchange raes from 19 economes for whch spo and forward exchange raes are avalable durng he enre sample perod from January 1999 o March 213. Accordng o he Morgan Sanley Capal Inernaonal (MSCI) classfcaon of sock markes our sample comprses 1 developed and 9 emergng markes. Table 1 gves an overvew and presens he mean condonal excess reurn on each currency par along wh s sandard error. All of he momens are n percen p.a. There s a large dsperson n he mean, condonal excess reurns across currency pars. For example, from a US nvesor s perspecve, he condonal excess reurn,.e. gong long and shor accordng o he sgn of he prevous perod s forward dscoun, on an nvesmen n he Ausralan dollar delvers a reurn of more han 7% p.a. By conras, he condonal excess reurn on a Swss franc nvesmen les around -4% p.a. The sandard errors of he condonal, currency excess reurns are raher large. A majory of he mean blaeral, condonal currency excess reurns s no sgnfcanly dfferen from zero a convenonal sgnfcance levels. Due o her subsanal nosness, blaeral currency excess reurns are a challenge for asse prcng and macroeconomc models alke. However, here are sgnfcan cross-seconal dfferences beween hese blaeral currency excess reurns. These dfferences are he focus of our sudy. Dobrynskaja (21) and Leau e al. (213) analyse neres rae 11

14 dfferenal or forward dscoun sored currency porfolo reurns and fnd he dsncon beween sde and sde saes of he marke reurn useful n undersandng her average excess reurns. We examne wheher hs fndng holds for excess reurns on currency pars. The focus on blaeral currency reurns, however, lms he sample perod compared wh sudes ha focus on currency porfolos. Ths s a prce o pay when one aemps o sudy a broad cross-secon of exchange raes ha are de faco a leas close o a floang exchange rae regme. Renhar and Rogoff (24) pon ou ha afer he demse of Breon Woods and well no he 199s many de ure floang exchange raes were de faco pegs. For example, Dobrynskaja (213) sresses ha before he nroducon of he euro n January 1999 nne oher European currences de faco ed her currency very closely o he Deuschmark. These nsghs are ypcally gnored n he currency reurn rsk facor leraure by rounely ncludng de faco pegged currences n he formaon of currency porfolos. I s no clear how he emprcal analyss of currency porfolos s affeced f, say, we have hry US dollar currency reurns o form porfolos bu nne of hese currences are pegged o he Deuschmark, such ha one hrd of he sample essenally mmcs he Deuschmark s flucuaons agans he US dollar. Wh hese caveas n mnd, we sar our baselne sample wh he nroducon of he euro n January 1999 and focus on blaeral, condonal currency excess reurns relave o he US dollar. Wh respec o he choce of currences, we only use currences for whch forward and spo rae daa s avalable over he enre sample perod. Moreover, counres whch essenally peg or offcally e her currences o oher sngle currences are no ncluded. For nsance, we do no consder he Dansh krone as s closely ed o he euro. The krone s only allowed o flucuae whn a narrow band around he euro (+/- 2.5%) even hough he European Exchange Rae Mechansm II (ERM II) would allow flucuaons of +/- 15%. By conras, we nclude Sngapore n our sample as manages s currency agans an 12

15 undsclosed baske of oher currences. Please noe ha Easern European counres such as Czech Republc, Poland or Hungary are no ye members of ERM II. As a robusness check, we consder he me perod from January 1985 o March 213 for our subsample of developed marke currences. The daa sources for he spo and foregn exchange raes (bd and ask) are WM/Reuers and Barclays avalable va Daasream. 7 End of monh values are consruced from daly raes. [abou here Table 1] To dsenangle US from marke componens n he US sock marke reurn, we use he MSCI sandard prce ndex for he US and he MSCI World prce ndex. Boh ndces are denomnaed n US dollars and measured a he end of he monh. These daa are freely avalable on hp:// MSCI ndces have he advanage ha hey are broad and calculaed usng he same mehodology. We use daly daa on he MSCI counry sock ndces (prce ndces denomnaed n local currency) o calculae a measure of equy marke volaly. We follow Lusg e al. (211) and calculae hs measure n wo seps. Frs, we compue he sandard devaon of daly reurns n a monh for each of he counry ndexes. Then we ake he cross-seconal mean of hese monhly volaly seres o oban he measure of equy marke volaly. We use hese volaly seres as conrol varables n our robusness checks snce fallng sock markes are ypcally assocaed wh rsng volaly. So, a pror, s no clear f exposure o he marke reurn n sde saes s dfferen han exposure o fnancal marke volaly. Fnally, we use he 1-monh T-bll rae from he Fama and French Research Facors fle as he rsk-free rae o calculae excess reurns on he sock marke ndces from he U.S. nvesor s perspecve. Ths daa s publshed on Kenneh French s webse. 8 7 Mos US dollar exchange raes on Daasream are only avalable snce January 1997 and no for all of he currences under sudy. 8 hp://mba.uck.darmouh.edu/pages/faculy/ken.french/ 13

16 5 Economerc framework, baselne resuls and robusness checks In hs secon, we presen our basc economerc framework, he baselne resuls and a varey of robusness checks. 5.1 Economerc framework and baselne resuls Our assessmen of he ably of CAPM-based models o explan he cross-seconal dsperson n blaeral currency excess reurns explos he sandard bea represenaon of he basc asse prcng equaon. We esmae he bea represenaon va he Fama-MacBeh mehodology (Fama-MacBeh, 1973) n a seres of cross-seconal regressons of he excess reurns on her sensves o he underlyng rsk facors a each pon n me. To form a bass for comparson, we sudy four model varans wh he 19 blaeral, condonal currency excess reurns under sudy. The frs varan s he sandard CAPM whch mples ha sensvy o he US marke reurn s he only deermnan of average currency excess reurns. The resuls of he cross-seconal regresson of he followng form M φ = +, (16) M ˆ, v are summarzed n Panel A of Table 2. The able provdes a cross-seconal 2 R, he average rsk prce esmae,, he mean squared prcng errors (mspe) and he mean absolue prcng errors (mape) n percenage pons per annum. Panel A of Table 2 shows ha he sandard CAPM from he US perspecve summarzed n Equaon (16), seems o capure some of he dsperson n he 19 monhly currency excess reurns under sudy. The rsk prce esmae s posve and sgnfcan. However, he sandard CAPM explans only 15% of he cross-seconal varaon n currency excess reurns a he counry level durng he perod beween January 1999 and March 213. In addon, he prcng errors are que large and he rsk prce esmae above 4% p.a. s far bgger han he sample mean of he US marke excess reurn of.27% p.a. over he sample perod or he long-run mean US marke excess reurn of abou 5% p.a. The mean reurn s 14

17 approxmaely he heorecally correc prce of marke rsk snce a regresson of he marke reurn on self delvers a sensvy of uny. Agans hs background, he sandard CAPM does no seem o be parcularly helpful n undersandng average currency excess reurns n lne wh he pons made by Burnsde (211) and Burnsde e al. (211). Nex we queson wheher a dsncon beween counry- and componens n he marke reurn does a beer job n hs respec. Panel B of Table 2 dsplays he esmaes of Fama-MacBeh cross-seconal regressons of currency excess reurns on her exposure o he US- and he componen of he marke reurn ˆ, ˆ, φ = + +,. (17) In lne wh several sudes (Lusg and Verdelhan, 211; Lusg e al., 211; Menkhoff e al., 212a), rsk s relavely more mporan han counry- rsk n explanng he paerns n he daa. In conras o he counry- componen, sensvy o he componen of he US marke reurn seems o be prced n blaeral currency excess reurns. Ths CAPM varan produces lower prcng errors han he sandard CAPM and he crossseconal f s rased o more han 4%. However, he rsk prce of sensvy o he marke reurn componen s sll far oo hgh. The dsncon beween counry- and componens of he marke reurn s hence no suffcen o explan average currency excess reurns. To assess he poenal explanaory power of sde rsk models for blaeral currency excess reurns, we closely follow Ang e al. (26) n he se of he emprcal model bu augmen wh he dsncon beween and counry- componens of he US marke reurn. e Ths leads o he followng aon ˆ,,,,, v, ˆ, ˆ, ˆ φ = ,, (18) where he sde and sde sensves follow he defnons n Equaons (12) o (15) n Panel C of able 2. v 15

18 Our resuls confrm ha he dsncon beween sde and sde rsks maers. I s he sde marke rsk ha s margnally, sgnfcanly prced n average currency excess reurns. The prcng errors drop compared wh he esmaes n panels A and B of Table 2. Furhermore, hs emprcal model explans roughly 6% of he cross-seconal dsperson n he blaeral currency excess reurns wh lower rsk prce esmaes as compared wh he case of he uncondonal CAPM aons. Leau e al. (213) defne sde saes as saes of he world n whch he marke reurn s one sandard devaon below s sample mean. If s above hs value, hen hs sae of he world s consdered as an sde rsk sae. We follow hs defnon and repor hese resuls n panel D of able 2. The rsk prce esmaes vary a b. Upsde rsk as defned above ncluded also negave marke reurn values bu he general concluson prevals. Global sde rsk s refleced n condonal, blaeral currency excess reurns. Mos of he evdence for a sde rsk compensaon comes from saes of he world n whch he marke reurn ook relavely large negave values. In our baselne sample perod, here are 26 daes whch qualfy as sde rsk saes accordng o he Leau e al. (213) defnon. [abou here: Table 2] A general crcsm of he aemps o lnk excess reurns on currences o radonal rsk facors such as he marke reurn or consumpon growh s he observaon ha he ndvdual sensves from me seres regressons n he Fama-MacBeh regressons are no sascally dfferen from zero (Burnsde, 211). Ths crcsm apples o he sde rsk models as well. Table 3 provdes an overvew of he esmaed sensves o he four marke reurn componens from panel D of able 2 along wh her Newey-Wes (1987) correced sandard errors applyng a lag lengh of four monhs n he correcon. Indvdually, mos of he sensves o he marke reurn componens are ndsngushable from zero. [abou here Table 3] 16

19 However, Lusg and Verdelhan (211) argue ha he economcally mporan queson s f he sensves dffer from each oher and wheher hese dfferences are refleced n cross-seconal dsperson n currency excess reurns. In erms of our esmaes of sde rsk sensves, le us consder he Ausralan dollar reurn (abou 7% p.a. mean reurn) and he Brsh pound excess reurn (abou -1.2% p.a. mean reurn). Table 3 esmaes he exposure of he excess reurn on he Ausralan dollar o be.38 wh a sandard error of abou.26, whle he correspondng bea of he Brsh pound s equal o -.29 wh a sandard error of.19. The respecve ranges of he pon esmaes are.12 o.64 and -.1 o Hence, despe mprecse measuremen of he pon esmaes, here are crossseconal, sgnfcan dfferences n he sensves n he sde rsk beas ha seem o be relaed n he dfferences beween mean blaeral currency excess reurns. We challenge hs vew n he subsequen secon. 5.2 Robusness Checks Ths secon provdes several robusness checks of he baselne resuls presened n panel D of able 2 o provde a comparson wh Leau e al. (213) n erms of he defnon of sde rsk saes Downsde rsk, uncondonal marke reurn exposure and equy marke volaly As emphaszed by Ang e al. (26), s mporan o conrol he sensves o he marke reurn n he sde and sde saes for he uncondonal marke reurn exposure as sde and sde saes could smply concde wh perods of low and hgh uncondonal sensves o he marke reurn. Therefore, we augmen our baselne aon summarzed n equaon (18) o accoun for he margnal conrbuon of sde rsk on op of he uncondonal marke reurn exposure: φ = +,, ( ˆ, ( ˆ,, M, M ) + ) + v,,, ( ˆ,, M ) +, ( ˆ,, M ) (19) 17

20 Panel A of able 4 presens he correspondng rsk prce esmaes as well as cross-seconal measures of f. In sum, despe slghly lower measures of f, our baselne resuls are unchanged boh n economc and sascal erms. A relaed, naural concern s ha our rsk measures could be a reflecon of he exposure of foregn currences o equy marke volaly. Volaly ends o be hgh when he marke reurn s fallng and vce versa. Moreover, Ranaldo and Söderlnd (21) fnd a relaon beween currency reurns and sock marke volaly levels n her assessmen of safe haven currences. Safe haven currences apprecae when fnancal marke volaly s hgh. In addon, Lusg e al. (211) show ha her carry rade facor, he decsve rsk facor o explan he cross-secon of average excess reurns on currency porfolos, s posvely correlaed wh changes n equy marke volaly. We follow Lusg e al. (211) n calculang equy marke volaly from daly reurns on he MSCI sock ndces of he counres under sudy. We regress our blaeral, condonal currency excess reurns on he level as well as on log changes n he equy volaly seres o oban he currency excess reurns sensves o equy marke volaly n he sde and sde marke saes as conrols n our sde rsk model. The crossseconal regresson hen obeys φ = +,, ( ˆ, ( ˆ,, VOL, VOL ) + ) + v,,, ( ˆ,, VOL ) +, ( ˆ,, VOL ) (2) for he level of equy marke volaly, VOL, and φ = +,, ( ˆ, ( ˆ,, VOL, VOL ) + ) + v,,, ( ˆ,, VOL ) +, ( ˆ,, VOL ) (21) for he log changes n he equy marke volaly, ΔVOL. The respecve esmaes are presened n panel B and panel C of able 4. The resuls n panel B of able 4 qualfy he noon of a sde rsk premum n condonal blaeral currency excess reurns. Afer conrollng for he level of equy 18

21 marke volaly, we fnd no srong spor for a gh lnk beween sde rsk and average currency excess reurns. In fac, hese resuls raher sugges ha sde and sde rsk canno be clearly dsngushed from equy marke volaly. Ths observaon hence quesons wha exacly s he underlyng economc raonale of emprcal sde rsk models whch are movaed wh nvesors loss averson. Uncerany averson could also be refleced n sde rsk exposures as he resuls n panel B of able 4 sugges. Ineresngly, panel C of able 4 hghlghs ha once we conrol for changes n equy marke volaly our baselne resuls reman unaffeced. [abou here Table 4] Counry subsamples and sde rsk bea sored currency porfolos Our sample of currences consss of 1 developed and 9 emergng economes accordng o he MSCI classfcaon of sock markes. In hs secon we nvesgae how our resuls peran o each class of counres separaely. Ths exercse s based on he baselne prcng relaon presened n equaon (18). The resuls are presened n able 5. Panel A of able 5 presens he resuls for he subsample of nne currency reurns from emergng markes over he baselne sample perod from January 1999 o March 213. For hs counry subsample, he esmaed rsk prces are sascally ndsngushable from zero despe beer measures of cross-seconal f. Panel B of able 5 adds nsul o njury by suggesng ha s sde rsk ha s prced n he cross-secon of developed markes currences. The rsk prce of sde rsk s sascally sgnfcan as opposed o he rsk prce of sde rsk. Ths laer fndng s corroboraed by he resuls provded n panel C of able 5. Tess of developed markes currency excess reurns over an exended sample perod from January 1985 o March 213 rejec he sde rsk sory oo. In sum, he resuls presened n able 5 sugges ha a sde rsk explanaon of crossseconal dfferences n blaeral, condonal currency excess reurns s largely confned o emergng markes currences f a all. 19

22 An alernave would be o addonally allow for me-varaon n he sensves o sde and sde rsk componens of he marke reurn. For nsance, Lusg e al. (211) sress ha s mporan o allow for me varaon n he sensvy o her carry rade facor n order o raonalze he cross-secon of blaeral currency excess reurns n her model. However, followng he Leau e al. (213) defnon of sde saes of he world, n our baselne sample perod 26 daes qualfy as sde rsk saes only and here are 44 respecve daes n he long sample perod from 1985 o 213. In vew of he low number of observaons, appears nfeasble o allow for addonal me varaon n he marke reurn exposures condonal on sde and sde rsk saes. One mgh also objec ha he blaeral currency excess reurns are smply oo nosy. Insead, porfolos sored on sde rsk bea mgh provde a beer hn a he explanaory power of sde rsk for currency excess reurns. In addon, should be he covaraon of exchange rae changes, s, wh rsk facors followng from he defnon of currency excess reurns n equaon (3), ha deermnes he rsk premum on foregn currency nvesmens. Currency porfolos based on sensves of exchange rae changes o rsk facors mgh shed lgh on hs ssue oo. We hus regress s for each currency on he conemporaneously measured four dfferen marke reurn componens o oban he exchange raes analogues of he sensves n equaons (12) o (15). For ease of comparson, we hold he sample perod consan from January 1999 o March 213. Table 6 repors hese sensves along wh he correspondng Newey-Wes correced sandard errors. [abou here Table 6] Based on hese full sample beas we form wo porfolos focused on exposure o sde rsk. One porfolo consss of he fve currences wh he hghes sde rsk bea over he whole sample perod and anoher porfolo consss of he fve currences wh he lowes sde rsk bea over he sample perod. To ake no accoun ransacon coss we ake a long poson n he hgh sde rsk porfolo and a shor poson n he 2

23 low sde rsk currency porfolo. The excess reurns n he porfolos are equally weghed averages of he counry-level excess reurns as s common n he leraure on currency porfolos sored on neres rae dfferenals. In addon, we delberaely focus on he wo exreme porfolos. The mos sgnfcan spread n currency porfolo reurns s beween he exreme porfolos (Lusg and Verdelhan, 27; Lusg e al., 211). Moreover, by usng he beas obaned from regressons usng he full n-sample nformaon, we gve he sde rsk model a furher advanage as we are here merely neresed n he queson f developed or emergng markes currences drve our emprcal resuls. Panel A of able 7 presens he mean excess reurns on he wo porfolos separaely, her reurn dfference and he assocaed sandard errors of hese porfolo reurns n parenheses below he mean reurns. All momens are expressed n % p.a. The hgh sde rsk porfolo consss of reurns relave o he currences of Ausrala, Hungary, Mexco, Norway and Poland. The low sde rsk porfolo consss of reurns on currences of Inda, Japan, Kuwa, Sngapore and Swzerland. A long poson n he hgh sde rsk porfolo delvers an annualzed excess reurn of abou 3.6% p.a. whle shorng he low sde rsk bea currences gves a reurn of -2.7% p.a. such ha gong long n hgh and shor n low sde rsk currences delvers a reurn of 6.2% p.a. The sandard errors ndcae ha he mean reurns are sascally dfferen from zero. Ths sorng exercse confrms our baselne resuls for currency pars whch sugges ha sde rsk s prced n currency excess reurns. Panel B of able 7 gves he same sascs when we focus on he en currences from developed markes. In hs case we use hree currences o form he hgh and low sde rsk porfolos. 9 Evdenly, he low sde rsk porfolo reurn s no dsngushable from zero. The reurn dfference beween hgh and low sde rsk currency porfolos s only margnally dfferen from zero. 9 The hgh sde rsk porfolo hen conans he reurns on currences of Ausrala, New Zealand and Norway. The low sde rsk porfolo comprses currences of Japan, Sngapore and Swzerland. 21

24 The pcure s fundamenally dfferen when we focus on he emergng markes sample. 1 Panel C of able 7 shows ha he reurn dfference beween he porfolos of hgh and low sde rsk sored currency porfolos s larger and more sgnfcan. Sporng our baselne conclusons, he porfolo formaon exercse confrms ha a sde rsk explanaon of currency excess reurns s o mos exen drven by he emergng markes n our sample. [abou here Table 7] Wha s he mpac of he fnancal crss snce 27? In hs crque on sudes ha documen an economcally mporan as well as sascally sgnfcan relaon beween sandard rsk facors and currency excess reurns, Burnsde (211) sresses ha he lnk s ndeed srong n he recen crss perod bu very much confned o ha perod. Relaed o hs pon, Grsse and Nschka (213) follow Verdelhan (212) and assess safe haven characerscs of Swss franc exchange rae pars vs-à-vs mosly developed counres n UIP regressons augmened wh rsk facors. They fnd ha crossseconal dfferences n he sensvy of hese Swss franc exchange raes o rsk are manly due o he perod from 27 o 29. The underlyng economc concep of sde rsk models s loss averson whch could be parcularly pronounced durng crss perods bu should be more general han ha. Therefore, we assess he explanaory power of our baselne sde rsk model aon bu resrc he sample perod o January 1999 o June 27. Thus he sample ends before frs ensons on money markes whch mark he onse of he fnancal crss (Brunnermeer e al., 29). We repor he cross-seconal prcng resuls for our sample of 19 blaeral, condonal currency excess reurns durng hs resrced pre-crss perod. In addon, we repea he porfolo formaon exercse from secon and repor excess reurns on porfolos sored on he exposure of he uncondonal exchange rae changes o 1 In hs case, he hgh sde rsk currency porfolo comprses currences of Hungary, Poland and Mexco. The low sde rsk porfolo covers currences of Inda, Kuwa and Thaland. 22

25 sde rsk for perod from January 1999 o June 27. Lmng he sample perod reduces he number of sde saes of he world o 12 compared wh 26 over our baselne sample. Recall ha we use he defnon of sde saes employed by Leau e al. (213),.e. when he marke reurn s one sandard devaon below s sample average. We presen he sensves of he blaeral, condonal currency excess reurns o he four marke reurn componens n able 8. The esmaes of sensves o he marke reurn componens vary que a b compared wh he baselne esmaes presened n able 3. Ineresngly, however, he esmaes of sde rsk sensves are n general slghly more precsely esmaed. We observe more beas ha are clearly or a leas margnally dfferen from zero. Hence, by resrcng he sample perod we do no necessarly lose precson n he esmaon of he sde rsk sensves. [abou here Table 8] Wha does hs mply for he cross-seconal prcng of he blaeral, condonal currency excess reurns under sudy? Panel A of able 9 gves a frs answer. I presens rsk prce esmaes and he measures of cross-seconal f. I s apparen ha he cross-seconal f deeroraes sgnfcanly once we exclude he crss perod snce md-27. The prcng errors ncrease drascally and he 2 R sasc drops from 6% n he baselne resuls o 25%. In addon, based on he rsk prce esmaes and he uncerany surroundng hese esmaes we canno ell f s he sde raher han sde rsk whch s a poenally prced source of rsk n he blaeral currency excess reurns. Ye, he sensves of he blaeral, condonal currency excess reurns are sll mprecsely measured. Sorng porfolos based on he exposure of uncondonal exchange rae changes o he sde rsk componen of he marke reurn mgh provde a sharper pcure. Panel B of able 9 presens mean excess reurns and sandard errors of currency porfolos ha are sored accordng o he exposure of uncondonal, log exchange rae changes over he sample perod from January 1999 o June 27 o he sde 23

26 rsk componen of he US marke reurn. These sensves are addonally presened n able 1. We repor excess reurns on long posons n he hgh bea porfolos and shor posons n he low bea porfolos. Agan, n he full sample of counres he hgh and low bea porfolos each comprse fve currences. The sraegy of akng a long poson n he porfolo of he hgh sde rsk currences and smulaneously shorng he low sde rsk currences produces a sgnfcan reurn of roughly 9% p.a. Ths resul s very much n lne wh he porfolo formaon for he baselne sample perod presened n able 7. We oban smlar evdence from he counry subsamples as n he baselne sample perod,.e. almos no relaon beween sensves o sde rsk and developed markes currency excess reurns bu a srong lnk n he emergng markes subsample. The porfolo formaon exercse hence suggess ha s no so much he recen crss perod ha drves he evdence n favour of a sde rsk explanaon of currency excess reurns bu he presence of emergng markes n our sample. [abou here Table 9] [abou here Table 1] 6 Conclusons The correlaon beween sandard rsk facors, such as he reurn on he marke porfolo, and he excess reurns on foregn currences s srong n mes of crss. Based on hs observaon, models ha explcly dsngush beween saes of he world n whch he marke reurn s fallng or rsng are successful n explanng excess reurns on currency porfolos and porfolos of oher asse classes (Dobrynskaja, 21; Leau a al., 213). The economc raonale behnd hese models s he noon of loss averson,.e. nvesors end o value he dsuly of a ceran loss of wealh more han he uly of an equally hgh gan. A frs glance, our emprcal resuls for blaeral, condonal currency excess reurns seem o corroborae he resuls obaned for currency porfolos. We exend hs leraure by provdng 24

27 evdence on he mporance of he componen n sde rsk for cross-seconal explanaons of average excess reurns on currency pars. However, our emprcal analyss reveals a leas wo addonal pons whch lead o a more scepcal apprasal of sde rsk models for currency reurns. Frs, we show ha conrollng for volaly on equy markes leads o a sgnfcan deeroraon of he explanaory power of sde rsk models for blaeral currency excess reurns. Ths fndng rases doubs on he role of loss averson as opposed o uncerany averson or relucance o load on crash rsk as he underlyng economc concep of he emprcal sde rsk model ha we use n our asse prcng exercses. Second, he evdence n favour of a sde rsk explanaon for excess reurns on currency pars sems from he currences of emergng markes n our sample. The lnk beween sde rsk and average excess reurns on developed markes currences s subsanally weaker. Taken ogeher, our paper provdes furher spor for Burnsde (211) cauonng agans he weak lnk beween currency excess reurns and sandard rsk facors. 25

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