Taste shocks in preferences and the Risk. Premium in the Exchange rate market #

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1 Tase shocks n preferences and he Rsk Premum n he Exchange rae marke # (a) (*) Juan-Angel Jmenez-Marín a po. de Fundamenos de Análss Económco II, Compluense Unversy, Somosaguas, Madrd, 83, Span. Absrac: Ths paper examnes he conrbuon of ase changes on he rsk premum n he exchange rae markes. I presens a Two-counry, pure exchange, cash-n-advance economy n whch agens have preferences subjec o ase shocks. Under hese preferences one can dsngush beween wo ypes of uncerany ha wll play a promnen role n he rsk premum: he fundamenal uncerany and he preference uncerany. The former refers o he ancpaed uncerany over he fundamenal varables. The laer s assocaed wh ase shocks. Tase shocks n preferences can be jusfed by numerous reasons such as reflecng measuremen errors n he varables, sochasc raes of me preferences, mssspecfcaons of he parameerzaon of preferences, or merely, expeced shfs n he marke srucure. The spr s smlar o Hu s (997) model, bu ase shocks n preferences lead o a sochasc dscoun facor ha should be suffcenly volale o delver a hgher rsk premum. JEL Classfcaon: F3, F4, G, G5 Keywords: Rsk premum, ase shocks, fundamenal uncerany. * Correspondng auhor. Tel.: Fax: ; E_mal: juanangel@ccee.ucm.es #I am graeful o R. Flores, G. Kamnsky, A. Novales, and P. Vega for helpful commens. The paper has benefed from commens from semnar parcpans a he George Washngon Unversy. I would lke o acknowledge he fnancal suppor of he Mnsero de Educacón, Span, hrough Projec BEC and he Fundacon Caja Madrd. Pars of hs work were compleed whle vsng George Washngon Unversy, Washngon, C. The auhor s graeful o hs nsuon for s hospaly.

2 .- INTROUCTION An nense research effor has been pad n recen years o characerze he deermnans of excess reurns n he forward marke for exchange raes [see Hodrck, 987, Bekaer and Hodrck, 99, and Verdelhan 006, among many ohers]. As a consequence, sgnfcan progress has been made n denfyng he facors ha lead o he presence of a rsk premum n exchange raes, alhough characerzng how s sze changes over me remans an open queson. An exensve leraure has analyzed he excess reurns n forward conracs for exchange raes usng neremporal asse valuaon models á la Lucas (98), whch esablshes a lnk beween fnancal markes and markes of goods. Along hs lne, Hansen and Hodrck (983), Kamnsky and Peruga (990), and Hu (997) show ha he exchange rae s a funcon of fundamenal varables such as money supply, oupu, and real ncome. In equlbrum, he excess reurn n he currency marke s deermned by he preferences of prvae agens and he volaly of he fundamenal varables n he economy. However, hese models have faled o conssenly explan he observed daa. The moderae amoun of rsk n fundamenal varables does no guaranee he hgh average excess reurns one observes, unless an unreasonably large relave rsk averson s assumed. We know snce Mehra and Presco (985) ha sochasc dscoun facors mus have a large varance n order o prce sock excess reurns. Varous auhors have aemped o solve he emprcal problem assocaed wh he sandard represenave agen model by nroducng more general preferences ha make margnal uly of consumpon exremely sensve o small varaons n consumpon. Campbell and Cochrane (999) use hab o explan sock marke prces. Backus, Gregory and Telmer (993) and Verdelhan (006) employ hab formaon o explan he exchange rae rsk premum and Bekaer (996) examnes he ably of a model along hese lnes o generae large and varables foregn exchange rsk premum. Ohers papers explore wheher he rsk premum can be explaned by usng preferences subjec o ase shocks, Normandn and S-Amour (998) nvesgae he relave conrbuon of rsk averson, ner-emporal subsuon, and ase shocks on he equy prema. The work presened here s relaed wh hs las lne of research. I examnes he conrbuon of ase shocks on he rsk premum n he exchange rae markes. I presens a Twocounry, pure exchange, cash-n-advance economy n whch agens have preferences subjec o ase shocks. Under hese preferences one can dsngush beween wo ypes of uncerany ha Tase shocks have proved o be useful n varous sengs, such as consumpon (Mron, 986 and Caballero, 990), exchange raes (Jmenez and Flores, 007), money demand (Townsend, 989), and busness cycle behavor (Bencvenga, 99).

3 wll play a promnen role n he rsk premum: he fundamenal uncerany and he preference uncerany. The former refers o he ancpaed uncerany over he fundamenal varables. The laer would be assocaed wh ase shocks. Tase shocks n preferences can be jusfed by numerous reasons such as reflecng measuremen errors n he varables, sochasc raes of me preferences, mss-specfcaons of he parameerzaon of preferences, or merely, expeced shfs n he marke srucure. The spr s smlar o Hu s (997) model, bu ase shocks n preferences lead o a sochasc dscoun facor ha should be suffcenly volale o delver a hgher rsk premum. The ase shocks are represened by a scalng preference parameer ha affecs he domesc and foregn sochasc dscoun facors dfferenly. In order o keep he problem racable I assume ase shocks whose evoluon are no affeced by agens decson. In hs model he ase shocks uncerany ranslaes drecly o he sochasc dscoun facors. Lke n Backus, Fores, and Telmer (00) assumng log-normal dscoun facors, he model relaes he rsk premum o he varances of he domesc and foregn dscoun facors. The man conrbuon of hs paper s o presen a model explanng he deermnans of rsk premum n currency markes as an explc funcon of he amoun of uncerany observed by prvae agens. The model allows us o spl he rsk premum no erms due o he fundamenal macroeconomc uncerany, ase rsk, and he relaonshp beween he wo. Lke n prevous sudes, he model esablshes he relaonshp beween he excess reurn and he observed volaly of money supply and oupu. Addonally, ase rsks nclude anyhng else (non-consumpon shocks) ha maers o agens welfare and may lead o shfs n preferences. In hese economes, even f money supply and oupu processes are smooh, rsk premum can be que volale because ase shocks have a hgh volaly. I es hs model for he ranson perod o he European currency consderng blaeral exchange raes beween he French franc, Brsh pound, and Spansh pesea all of hem wh he German mark. The uncerany on he success of convergence process may explan he excess reurn observed n some European currences n hs perod, even hough he varably of observable macroeconomc varables such as money, oupu, and consumpon dd no change very much. The euro would elmnae exchange rae uncerany and he currency converson cos The agen s ase changes n dfferen ways as he/she ages or due o suaons she/he has never encounered, for nsance, he change from flexble o fxed raes s an essenal shf n marke srucure. A credbly fxed exchange rae has neher volaly nor an expeced rae of change. So he rsk premum dsappears. The suaon s dramacally dfferen when he exchange rae eher floas explcly, or s fxed unrelably so ha speculave aacks are possble. In hs case forces oher han hose from money and goods markes drve he foregn exchange marke. Tase shocks may explan how he agen ner-emporal consumpon audes mgh be affeced for hs suaon. 3

4 among he member saes, whch would spur nernaonal rade and nvesmen. Furhermore, he moneary unon would creae he poenal for some counres o mpor moneary credbly (Herrendorf, 997) from oher member counres wh repuaon for pruden moneary polcy (e.g., Germany). The parcpaon of such counres n he unon would lower expeced nflaon hroughou he unon ha would conrbue o fnancal deepenng and greaer nvesmen. Therefore, euro would have mplcaons for agens nvesmen and savng decsons. Tase shocks n preferences are nended o capure he effec of he expeced new currency on he agen neremporal consumpon audes. Three wesern European counres n he EMS, Uned Kngdom, enmark and Sweden, have no ye adoped he euro. Besdes, he European Unon has ncorporaed welve Easern European counres as new members. Hence, alhough I use he nal convergence process o he euro as an llusraon, our mehodology can be used o analyze possble exchange rae rsk premum n hese counres. A smlar analyss could also be appled f common currency areas n Lan Amerca or Souh Eas Asa are evenually approved. I proceed as follows. In secon wo, I presen he heorecal model and descrbe he relaons among rsk premum, fundamenal uncerany, and ase shocks ha are obaned from he Euler condon. The hrd secon descrbes a parcular model specfyng agens preferences and he sochasc behavor of he man varables. I explo hese assumpons o derve an analycal expresson for he rsk premum allowng for sascal ess o be performed. In he fourh secon, as an llusraon, I apply hs model o accoun for he rsk premum durng he ranson perod o he European currency. Secon fve presens he man conclusons..- THEORETICAL MOEL The consumpon-based asse prcng model s derved n a sandard represenave agen seng followng Lucas (98) and Hu (997). The model consders wo counres (domesc and foregn) and wo pershable commodes, x and x F. In each counry, a dfferen currency s used o pay for ransacons n her respecve commodes. A each perod, he domesc (foregn) counry receves a sochasc endowmen Y (Y F ) of good x (x F ), and zero uns of he oher commody. omesc (foregn) counry also receves a sochasc endowmen M (M F ) of s currency. Thus, R = (Y, Y F ) and N =(M, M F ) defne he sae vecors of real and nomnal endowmens respecvely. Real endowmens and money socks follow a mulvarae sochasc process o be specfed below. 4

5 Consumers are dencal n boh counres. The model s wren from he perspecve of he domesc counry. The represenave consumer has preferences characerzed by: (,, ) s F β s s s s= U = E U c c Z 0 < β < () where E denoes he mahemacal condonal expecaon on nformaon known a he begnnng of perod. c s, c F s represen he consumpon levels of he domesc and foregn goods by he represenave agen of counry a perod s, and Z 3 s s a sochasc ase shock. I assume he uly funcon U(.,.) o be bounded, connuously dfferenable, ncreasng and srcly concave n all he argumens. U CZ, where he subscrp on U denoes he paral dervave of U wh respec o he correspondng argumen, can ake any sgn. β s he consan me dscoun facor. I assume ha each economy s subjec o a cash- n-advance consran. A he begnnng of each perod, consumers receve he endowmens of goods and money. Snce money does no produce any uly by self, consumers wll use o buy consumpon commodes. In order o be able o purchase foregn goods, hey frs need o exchange currency hrough eher spo or forward conracs a her correspondng equlbrum prces. From money marke equlbrum, nomnal prces mus sasfy: where ( ) j j j P R, N = M Y, for j =, F. () j P s he domesc and foregn currency prce for good j a me. In order o descrbe an equlbrum soluon of he model, we requre a dsrbuon of wealh. We have assumed ha wealh of every knd s evenly dvded beween he resdens of he wo counres. Specfcally, he resden of each counry owns half of he domesc and foregn endowmens, and he socks of domesc and foregn money. Gven hs dsrbuon of wealh, consumpon s gven by: 4 j j c = Y, j, =, F. (3) As shown by Hu (997) he equlbrum exchange rae (uns of domesc currency per un of foregn currency) s gven by: 3 In Baksh and Chen (996) Z sands for he spr of capalsm, and n Campbell and Cochrane (999) Z s nroduced hrough me-varyng habs n whch he blss pon s a funcon of pas consumpon. In hs paper Z means a shock o margnal uly. Z mples a knd of sae-dependen preferences. 5

6 ( ) ( ) ( ) ( ) F F U F c, c, Z F U F Y /, Y /, Z P c c M Y S =. =. F F P U c, c, Z M Y U Y /, Y /, Z F F c c (4) As an alernave, currency exchange can ake place hrough forward conracs, whch allows consumers o nsure hemselves agans he uncerany on he fuure purchasng power of her own currences. I assume ha hese conracs las a sngle perod, beng purchased a he end of each perod. Hence, forward conracs deermne he dsrbuon of currency for he followng perod. To oban he forward exchange rae, n uns of domesc currency per un of foregn currency, le us frs consder bonds denomnaed n eher domesc or foregn currency. From he frs order condon descrbng he opmal consumpon and porfolo decsons, he domesc (foregn) value b (b F ) of a bond ha pays one un of domesc (foregn) currency a me + sasfes: j ( + ) j b = E q,,, for j = F (5) where q + (q F + ) denoes he domesc (foregn) neremporal margnal rae of subsuon (IMRS). As shown by Hu (997) he IMRS of hs model s gven by: β U j c U j c ( R, Z ) j ( R, Z ) π π j j = q +, for j =, F, (6) j where ( j ) j j (, ) =, for j, F. π P R N Y M = 5 Followng Backus e al. (00), le s consder a forward conrac specfyng a dae he exchange a + of one un of foregn currency and F + uns of domesc currency. Ths conrac specfes a ne flow of domesc currency a dae + of F + - S +. Snce nvolves no paymens a dae, prcng relaon (5) mples: 4 Ths soluon s he perfecly pooled equlbrum of Lucas (98). ( c + + π + ) 5 To gan same nuon, expresson (6) can be wren as: bu j ( R Z ) π β E U j ( R Z ), =,, for j j j c j=, F. The lef hand sde s he margnal uly cos of consumng b (b F ) uns of domesc (foregn) currency less a me ; he rgh-hand sde s he expeced margnal uly benef form nvesng he uns of domesc (foregn) currency n an asse denomnaed n domesc (foregn) currency a me, obanng one un of domesc (foregn) currency a me +, and consumng he proceeds. The consumer equaes he margnal cos and margnal benef. 6

7 + ( ( + + )) E q F S = (7) 0. From (4) and (6), one can defne he change n he exchange rae as he rao of he wo IMRSs a home and abroad: S S q =. (8) F + + q+ vdng (7) by S and applyng (8), one can oban he forward premum as: 6 F ( q + ) ( + ) + F E = (9) S E q Thus, akng condonal expecaons on he fuure spo rae S + from (4) and subracng he value of he forward rae F + from (9), one can oban he expeced reurn n a forward conrac, ( ) ( ) ( ) ( ) F F F F U F Y /, Y /, Z F U F Y /, Y /, Z + + c + M Y + c M Y E q E[ S+] - F = E. -.. F F F F M+ Y+ U Y /, Y /, Z M Y q U Y /, Y /, Z c E + c Ths s a generalzaon of he resul derved by Hu (997). Equaon (0) shows ha he expeced excess reurn from a forward conrac s deermned by real and moneary varables, as well as by he preferences of he represenave agen lke n Hu (997). Addonally, n hs paper he excess reurn n forward conracs s also deermned by ase shocks. Therefore, n hs economy, even f real and moneary varables were smooh, he rsk premum could be very volale f shocks n preferences, whch are one of he drvng forces behnd he marke uncerany, were suffcenly volale. 3.- EMPIRICAL METHO The characerzaon of rsk premum n (0) s very general and addonal srucure mus be nroduced pror o esng he heory. So now I ncorporae no he model hree assumpons ha lead o a esable analycal formulaon of he rsk premum. Frs, I aler slghly he concep of rsk premum o avod some praccal dffcules. Secondly, I specfy he preferences of he represenave consumer snce hey play a cenral role n he (0) 6 F S + E q E q S E q + F ( + ) = + = ( + ) S 7

8 deermnaon of he rsk premum. Fnally, some assumpons on he sochasc behavor of he varables n he model are made Redefnng he rsk premum The defnon of rsk premum n (0) s no nvaran o changes n he uns of measuremen. Specfcally, s subjec o he Segel paradox, as a consequence of Jensen s nequaly. The value of he rsk premum emergng from hs expresson s dfferen dependng on wheher one measures he exchange rae n uns of domesc currency per un of foregn currency (S ), or he reverse (/S ). To avod hs problem s sandard n he leraure o use a defnon of rsk premum ha ncorporaes a logarhmc ransformaon. ong hs he change of uns only affecs he sgn of he rsk premum: E [ln(/s + )] = -E [ln(s + )]. Then I can defne he new measure of rsk premum as RP e + E [s + - f + ], where s + s he log of S + /S (.e. he + deprecaon rae of he domesc currency), and f s he log of F + /S (.e. he forward premum). Ths measure s relaed o he rsk premum n (0) hrough: E [s + -f + ] E [(S + - F + )/S ] when usng he approxmaon ln (+x) x (for a small value of x). Thus, gven (8) and (9) he rsk premum can be wren as, ( ) ( ) ( ) ( ) RP = E s E log q + E log q = E s + r r, () e F F where r = log E q +, for =, F, s he neres rae of he one-perod bond defned n he prevous secon. Therefore, he exchange rae rsk premum s he excess reurn of a domesc nvesor who borrows one un of domesc currency a home, buys /S worh of foregn currency, lends on he foregn marke for a defned perod and fnally reconvers hs earnngs o he domesc currency. To see more clearly how he moneary and real varables as well as he ase shocks affec he rsk premum, addonal assumpons on consumer preferences and sochasc properes of hese varables have o be done Consumer preferences As a sandard llusraon, I assume a separable uly funcon, F ( ) α F ( c ) ( c ) γ λ λ U c,c = Z + Z αγ, 0 and α, γ α γ F () 8

9 where β and γ are he rsk averson parameers, Z s a sochasc ase shock 7 and λ j, for j=, F, measures he exen o whch ase shocks affec o domesc and foregn goods. 8 Addonally, s necessary o make some assumpons on he jon sochasc behavor of real and nomnal endowmens, as well as on he probably dsrbuon of ase shocks before obanng a racable expresson for he rsk premum The sochasc process for he man varables The rsk premum depends on condonal expecaons of cross producs of random varables. Under general condons, hese producs do no have a well defned probably dsrbuon whch mgh allow for compung her expecaons. Therefore, I need o ncorporae some resrcons on he sochasc behavor of he man varables n he model. Tha wll also allow us o fnd a formulaon for he rsk premum as a funcon of he man sources of uncerany n he economy. Gven (6) and separable preferences n () boh domesc and foregn IMRS are: ( γ ) ( ) ( α ) ( ) F F ( ) F F λ + = + + z + q y m ( ) λ =, z + q y m where y + Y + Y, m + M + M, for =, F and z + Z + Z. (3) More precsely, I consder he case where he oupu and money supply growh as well as ase shock growh are condonally jonly log-normal. Followng Hu (997), I assume ha dscoun facors are log-normal. 9 Assumng log-normal IMRS, Backus e al. (00) show ha he 7 Baksh and Chen (996) analyze he mplcaons for consumpon, porfolo holdngs and sock-marke prces of he hypohess ha nvesors accumulae wealh no only for he sake of consumpon bu also for wealh-nduced socal saus. Accordng Max M. Weber (958), hs hypohess essenally capures he spr of capalsm. Baksh and Chen (996) posulae ha Z s he nvesor s relave socal sandng. They posulae ha Z s srcly ncreasng n wealh (so as o reflec he spr of capalsm), bu decreasng n socal-wealh sandards (so ha saus s only relave). On he conrary ha Baksh and Chen, I assume ha Z evoluon s no affeced by agen s decsons. 8 Usng hs uly funcon he spo exchange rae s gven by, ( ) γ ( ) ( ) ( α ) F α β λ λ F F S = M Y M Y Z When λ F >λ, a posve shock n preferences wll ncrease he margnal uly on foregn goods more han on domesc goods, whch n urn leads o a hgher demand for foregn goods, and hereby ncreasng he relave prce of x F. Hence, he spo exchange rae ncreases, producng a deprecaon n he domesc currency. 9 I s furher from evden ha log-normaly of m, y, and z guaranees ha her produc s also lognormal f hese varables are condonally correlaed. 9

10 rsk premum s equal o half of he dfference beween condonal varances of he wo neremporal margnal raes of subsuon: RP e = F, q q σ σ (4) where σ q+ s he condonal varance of he logarhm of he IMRS for =, F. Ths expresson ells us ha f he domesc IMRS were condonally more volale han he foregn IMRS, one would expec a posve rsk premum. To see hs more clearly, he shor neres rae can be wren as r = log E log ( ) q + = E q + + σ. From (9) he q + expeced change n he exchange rae s: E s E q E q = r + r σ + σ F F log log F + = + + q+ q+. Therefore, f σ > σ, one would expec an exchange rae deprecaon, whch n urn F q+ q+ would mply ha nvesng n he foregn currency should provde a posve excess reurn. The domesc nvesor would expec posve foregn currency excess reurn a perod o compensae hm/her for he expeced loss when hs/her asses are abroad. Fnally, from (3) and (4), I can express he rsk premum n erms of he properes of oupu growh, moneary aggregaes, and preference ases: ( ) e RP = λ λ F ( γ) ( α) ( ) ( ) σ F F m σ m σ y σ y σ + + z ( ) ( ) F γ σ F F α ( ) λ σ F ( α) F σ F y m λ σ z m λ σ z m γ λ σ y z y m y z ( ) where σ x var log ( x + ) and σ x p cov log ( x + ) log ( p + ) ( ) (5). Equaon (5) saes ha expeced rsk premum s deermned by () he condonal varance of he domesc and foregn oupu, () he condonal varance of he domesc and foregn money supply, () he condonal covarance beween oupu and money supply, 0 (v) he condonal varance of he 0 ), ), and ) can be explaned hrough her conrbuon o he volaly of he purchasng power pary of boh currences gven he cash n advance consrans. An ncrease n he volaly of nomnal or real endowmens n he domesc counry, or a decrease n her covarance, ncreases he volaly of he purchasng power of he domesc currency, whch n urn leads o an ncrease on he volaly of he domesc IRMS. An ncrease n he volaly of nomnal or real endowmens for he foregn counry or a decrease n her jon covarance would lead o he oppose effec on he rsk premum. 0

11 ase shocks, and (v) he condonal covarance beween money supply, oupu and he ase shocks. ), ), and ) are relaed o he macroeconomc uncerany, and v) s assocaed o he preference uncerany. Ths model generalzes ha derved by Hu (997). Here he exchange rae rsk premum conans a second source of rsk assocaed o ase shocks. The presence of ase shocks could provde he addonal degree of freedom necessary o reproduce he hgh currency rsk premum whou requrng unreasonable coeffcens of relave rsk averson va he ncremenal ase covarance mples. A large prema would be requred o offse he mpac of shfng margnal ules of consumpon due o he presence of ase shocks. In he nex secon I es wheher hs model can accoun for he observed rsk premum durng he ranson perod o he European currency usng blaeral exchange raes beween he French franc, Brsh pound, and he Spansh pesea, all wh he German mark. Fundamenal macroeconomc uncerany dd no generae suffcen rsk o reconcle he radonal model wh he daa. Forces oher han hose from money and goods markes seem o be he mos mporan sources of uncerany n hese ranson counres. Tase shocks n preferences capurng changes n he ase for domesc and foregn asses because of shfs n he marke srucure- may offer a poenal explanaon for hese oher dsurbances drvng he foregn exchange marke. 4. TESTING THE MOEL To es (5), I use a wo-sep esmaon sraegy: frs, I denfy and esmae he source of he ase shocks and oban he condonal varances and covarances for he exogenous varables. Second, I use ha nformaon o esmae (5) by OLS, applyng sandard specfcaon Lambda measures how he ase shock uncerany affecs o he rsk of domesc and foregn bonds. To gan some nuon, one could assume ha ase shocks are ndependen of he sae of he money supply and producon. From (3): ( ) ( ) ( ) σ = q σ + α m σ y α σ y m + λ and + + σ + z ( ) ( ) ( ) F σ F = γ F F F F q σ y + σ m γ σ + λ Therefore, y m σ z + + he effec on he IMRS volaly of a rse n he preference uncerany,, depends on λ j for j=, F. If λ > λ F, an σ z + ncrease n σ z has a greaer effec on he domesc IMRS han does on he foregn IMRS. As consequence, gven + (4) excess reurn would be hgher. I consder he blaeral relaonshps beween Spansh pesea (SPA), eusche mark (EM), Serlng pound (GBP) and French franc (FRF). The sample sars on January, 986 afer Span became a member of he European Economc Communy and ends n Aprl 998 (In May 998 he European Councl announced he counres ha would form he euro area on January, 999). I use monhly daa for Span (SP), Germany (GER), France (FR) and Uned Kngdom (UK). The ndusral producon (IP) s used as an ndcaor of economc acvy and M as he moneary aggregae. To compue probables of convergence I use neres raes for swaps a 3-year maures for all counres, from 99: o 998:04. Fnally, spo and forward exchange raes represen he value for he las day of he monh. Prelmnary daa analyss (un roo ess and nervenon analyss [Box and Tao (975)]) shows ha all varables, bu rsk premum, are I(). Therefore, all varables are dfferenced n he model for he condonal varance. These resuls are no repored here bu are avalable upon reques.

12 ess. The consan erm n he regresson acs as a proxy for he se of second order condonal momens ha are no me varyng. Snce fundamenal varables are measured dfferenly n each counry, her volales are no drecly comparable, so s no possble o esmae he model under he consrans mposed by nernaonal symmery. Hence, I only esmae he unresrced verson of he model, whch ncorporaes all condonal momens separaely. Therefore, esng he heory mples es he sgnfcance and he sgn of he esmaed parameers. 4.. Measurng varables In order o keep he problem racable, I wll assume ha ase shocks are ndependen of he sae of he money supply and he producon. I assume ha he dynamc of real and moneary varables, represened by he money supply and he ndusral producon, can be summarzed by a VARMA model n logged dfferences wh GARCH nnovaons, whch allows us o capure any possble nonlnear dependence among her nnovaons. The mayor dffculy n esmang he exchange rsk premum expresson s ha ase shocks are no observed. Several approaches are avalable for addressng hs problem such as relang he unobservable componens o an arbrary se of observable varables, or as modelng he ase shock growh from a gven law of moon (.e. Markov Chan). In hs paper I follow a smlar sraegy o ha of he so-called Peso problem (Krasker, 980, Lews, 988 and Kamnsky and Peruga, 99). 3 Agens know ha somehng can and wll affec hem and her ases n he fuure bu hey canno specfy exacly when wll occur. 4 I assume z, he growh of he ase shock, may follow one of wo possble regmes: δ 0, δ, wh δ >δ 0. δ 0 represens he acual sae and δ represens a posve shocks on preferences (n hs case, would mean ha he domesc counry fulflls he convergence crera esablshed n he Maasrch agreemen). There s a probably of a posve shock n preferences and he marke esmaes hs lkelhood as p =Prob (δ + = δ / δ = δ 0 ). Ths probably should be expeced o change over me as a funcon of he evoluon of some economc ndcaors ha agens consder 3 The concep 'peso problem' has s orgn n sudes made on he Mexcan peso a he begnnng of he 70s. Traders n currency markes ancpaed a Mexcan peso devaluaon, and for some me he peso was beng sold a a dscoun n forward markes, even hough he governmen mananed s value unl 976. Ths effec made he forward exchange rae o devae from beng an unbased predcor of fuure spo exchange rae over ha perod of me. 4 To gan some nuon, le us focus on he ranson perod o he European currency. Agens n he economy realze ha her fuure welfare depends on wheher he counry fulflls he convergence crera esablshed n he Maasrch agreemen, wha means ha he currency would ake par on he common European currency snce he begnnng. The euro creaes he poenal for some counres o mpor moneary credbly and a lower expeced nflaon ha would conrbue o fnancal deepenng and greaer nvesmen. These expeced facs could have a large mpac on he opmal consumpon-porfolo plans of he agens, whch n urn leads o changes on he equlbrum asse prces.

13 relevan when predcng fuure polcy decsons. The probably ha he curren sae lass for a leas one more perod s -p = Prob (δ + = δ o / δ = δ 0 ). The condonal expecaon of he shf on preferences ndcaor, z +, s: E [z + ] = p δ + (-p )δ 0, and s varance: Var (z + ) =p (-p )( δ - δ 0 ). Thus equaons (5) can be expressed as: RP e + ( p ) ( ) = λp δ δ 0 σ F F F F m + σ m σ y + σ y y+ m + + ( γ) ( α) ( γ ) σ ( α) σ y m (6) F λ= λ λ + + Because of he shocks n preferences ha ake no accoun he effec of he new expeced currency on he agens nvesmen and savng decsons, he exchange rae rsk premum n (6) depends on he volaly of z +, whch sands for he preference uncerany. In hs case, he preference uncerany s a non lnear funcon of he perceved probably of he success of he convergence process. The varance of z + s zero when p s eher 0 or, reflecng absolue cerany abou he shocks n preferences. The effec of p on he preference uncerany reaches s maxmum value for nermedae values of p. When p </, a larger probably wll ncrease ase shocks uncerany. Whereas, for p >/, a larger probably would reduce he varance of z +. In expresson (6), f λ > 0.e. λ > λ F - a rse n he varance of z + leads o a hgher rsk premum. In he emprcal model, one would expec a posve sgn for p, and a negave sgn for p. As shown n he prevous secon, f λ > λ F a rse n he varance of z + deprecaes he expeced exchange rae and he domesc nvesor would expec posve foregn currency excess reurn a perod o compensae hm/her for he expeced loss when hs/her asses are abroad. 5 Convergence Probably (and how o measure ) The exchange rae rsk premum n (6) depends on he perceved probably of convergence. To subsue for hs unobserved probably assgned by he fnancal markes o he even ha he counry belongs o he EMU by January 999, I use a procedure smlar o JP Morgan EMU calculaor. The basc feaure of he EMU calculaor s ha he observed neres rae spread a me, IR_SPR, s supposed o be a weghed average of he IN spread, IR_SPR IN, whch 5 Assumng λ > λ F s as f (o use a concree example) durng he convergence perod o he euro, he ncrease n he probably of he Spansh pesea parcpang n he euro snce he begnnng had a larger effec on he Spansh economy han on he German economy. 3

14 would apply f he counry adops he sngle currency and he OUT spread, IR_SPR OUT, correspondng o he case when he counry s ou of he EMU. The weghs are he correspondng probables of each even, ( ) IN OUT IR _ SPR = p IR _ SPR + p IR _ SPR (7) In a moneary unon, fnancal nsrumens from dfferen counres wh he same maury, lqudy and cred rsk mus have he same yeld. So, f n January 999 a counry fulflls he convergence crera 6 and eners no he EMU, s rskless neres rae should be equal o hose n he oher counres of he moneary unon. On he oher hand, f he counry does no ener no he unon, s neres rae wll be deermned by a varey of facors ncludng s own moneary polcy and wll generally manan a posve spread relave o counres n he unon. Hence, f IR_SPR IN = 0 and IR_SPR OUT = θ > 0 n (0), one can esmae he probably assgned by he fnancal markes a me o he even ha he counry belongs o he EMU by January 999: p = IR_ SPR θ. (8) When esmang I use a more flexble funconal form by akng (7) o sugges a negave relaonshp beween he convergence probably and he neres rae swap: p = α0 α IR _ SPR, (9) hen p p IR SPR IR SPR ( ) = ( α0 α _ ) ( α0 α _ ). Thus (6) becomes a regresson equaon of he form, RP s f + + = β + β _ + β _ + 0 IR SPR IR SPR ( ) ( ) ( ) ( ) σ F F F F m + σ γ m σ y + α y σ y + γ σ α y m σ m + u (0) h = λ( δ 0- δ ) ; β = hα α ; β = hα α ; β = hα ;. wh ( ) ( ) Expresson () ncludes he excess reurn n forward conracs (RP + ) as dependen varable, projeced on a consan and he neres rae spread (IR_SPR) approxmang he 6 To ener EMU, he Maasrch Treay ndcaes ha canddaes mus lower nflaon o whn.5% of he lowes hree n he European Communy, push budge defcs below 3% of GP, lower deb-o-gp raos o 60% and manan a sable currency. 4

15 convergence probably. The square value of he proxy for he convergence probably s also ncluded n he model. The rsk premum expresson also ncludes condonal varances (,,, F y and F m m σ y ) σ σ σ and covarances ( F F y m and y m ) σ σ The unquesonable parcpaon of Germany n he euro area makes reasonable o focus he analyss on dfferenals wh German neres raes. Therefore, he probably of he counry adopng he sngle currency from he ouse of he EMU s nversely relaed o he spread of neres raes wh Germany. I consder neres raes from swap markes o be more relable han hose from he marke for governmen bonds, whch s raher narrow and llqud n some counres. Furhermore, he ax reamen of reurns on publc deb s dfferen across counres. On he conrary, he swap marke s very lqud and conracs are sandardzed across currences, ncludng he ax reamen of reurns, and hey are no affeced by defaul rsk. 7 Usng he spread of 3-year swap rae as a proxy for he probably of convergence s based on our belef ha a 3-year maury s more lkely o capure expecaons of convergence o he euro area for a counry. Is behavor s smlar o hose of he 5- and 0-year raes, whle he -year rae s very nfluenced by moneary polcy decsons. Ineres rae spread wh Germany and rsk premum values for France, Span, and Uned Kngdom are shown n Fgure for he 994:0-998:04 perod. In all cases, he rsk premum seres s clearly more volale han he spread. Over 994 and he frs par of 995, he spread ncreased for Span, sharply decreasng durng 996, whch could reflec a growng probably ha hs counry could adop he sngle currency from he begnnng. There was a ransory ncrease a he begnnng of 997 and he spread reurned very quckly o a decreasng pah. The spread wh France wdened n he sprng of 995, from zero o abou percenage pon, remanng a ha level unl he end of 996, when fell back o zero. Ths s conssen wh a hgh probably of hs counry n adopng he sngle currency from he begnnng. On he oher hand, he spread showed a posve rend snce he begnnng of 994 for he Uned Kngdom, sablzng afer 996 bu whou he sharp decrease observed for Span and France. These graphs sugges ha for Span and France, an ncrease n IR_SPR (.e. a loss n marke confdence) nduces an ncrease n he volaly of he rsk premum. However, for he Uned Kngdom, he fgure could ndcae ha hs counry was no consdered o be a lkely parcpan n he EMU. Therefore, n hs case he correlaon beween spread and rsk premum s more dffcul o explan. 7 Exracng marke expecaons on a gven even from asse prces s a queson ha has araced a grea deal of neres [see llen and Edlund (997), Favero e al. (000). For revews see Söderlnd and Svensson (997), and Baes (998)]. 5

16 4..- Accounng for he rsk premum I frs presen n Table leas-squares esmaes of (0) for he full sample, 986:0-998:04, and for he hree blaeral relaonshps whou akng no accoun he effec of ase shocks, so ha condonal second order momens are he only explanaory varables. 8 Ths sample explos all avalable daa on condonal second order momens. Usng rsk premum daa correced from exreme values, sharply decreases he evdence of resdual auocorrelaon. R values are raher low, alhough esmaed parameers show her rgh sgn when sgnfcan. However, he overall suggeson s ha macroeconomc uncerany may no be he mos mporan facor deermnng rsk premum n exchange raes. Alernavely, I suded wheher he uncerany mpled by he ase shocks (as measured by he wo spread varables) can accoun for he rsk premum. Usng he longer avalable sample for neres rae swaps, 99:0-998:04, I obaned a poor f, probably because of ncludng he perod pror o formal approval of he Unon Treay. Convergence crera were adoped n he European Unon Treay, whch was approved a he European Councl celebraed a Maasrch n February 99, alhough her fnal approval a he level of he Congress of each counry ook place n November 993. Hence, from 99, governmens consdered he possbly of mplemenng polcy wh a goal of achevng convergence, alhough s jus from 994 ha convergence crera had a formal valdy. When he shorer perod s consdered n Table, 994:0-998:04, resuls become much more sasfacory n erms of explanaory power as well as sgnfcance and sgn of ndvdual coeffcens. Smple and adjused R coeffcens are beween 0% and 5%, well above her values for he larges sample. The neres rae spread s sascally sgnfcan excep for he GBP/GEM relaonshp. In hs case, lack of sgnfcance seems o be a consequence of colneary beween he wo neres rae spread varables. A Wald es for jon sgnfcance of boh varables confrms hs resul. The sgn of he coeffcens s as expeced, excep for he GBP/GEM exchange rae, suggesng ha he lnear probably erm would no capure adequaely all he nformaon regardng he rsk premum n ha currency. I seems ha was only afer 994 when he preference uncerany became a relevan facor n he me evoluon of he rsk premum for hese currences. Table 3 presens he esmaon resuls for he enre model, for he 994:0-998:04 perod, ncludng macroeconomc uncerany and he nonzero probably for he even ha he 8 Appendx shows he specfcaon and esmaon procedure of condonal second order momens. Parameer esmaes are avalable upon reques. 6

17 agen preferences mgh change Condonal second order momens of fundamenal macroeconomc varables are generally no sgnfcan. On he conrary, convergence probably s almos always sgnfcan. One can assess he conrbuon o he fed rsk premum of boh he macroeconomc uncerany and he preference uncerany usng Fgure. The lef column shows, for he 994:0-998:04 perod, he acual exchange rsk premum and he fed values from he model n Table 3; he mddle column shows he par of he fed rsk premum accouned for he macroeconomc uncerany, ˆ β ˆ 3σ ˆ ˆ ˆ ˆ + β F F F 4 F m σ + β m 5σ + β y+ 6σ + β + y+ 7σ β y+m+ 8σ y+m ; and he rgh column dsplays he par of he fed rsk premum accouned for he preference uncerany, ˆ β ˆ IR_ SPR + β3ir_ SPR. Fgure 4 presens several scaer dagrams for he fed rsk premum versus: () he observed exchange rsk premum (lef column), () he macroeconomc uncerany conrbuon (mddle column), and () he preference uncerany conrbuon (rgh column). An nspecon of hese dagrams reveals ha he rsk premum s exremely volale and s more closely relaed o ase shock uncerany han o macroeconomc uncerany. Tha s also refleced n he correlaons coeffcens beween each varable wh he fed rsk premum, whch are sgnfcanly hgher for preference (beween 0.70 and 0.93) han for he macroeconomc uncerany (beween 0.9 and 0.58). The general concluson s ha he uncerany on wheher he counry fulflls he convergence crera esablshed n he Maasrch agreemen s more mporan explanng he rsk premum han he fundamenals of he economy. Furhermore, hs evdence arses only afer 994, suggesng ha was he formal approval of he Maasrch crera, more han he Maasrch agreemen self, he sarng pon for he exchange rae markes o ncorporae he probably of convergence no he deermnaon of he rsk premum. We now have all he nformaon needed o compue he probably ha he marke aaches o he even ha one of he counres analyzed n hs secon jons he European Moneary Unon a a gven dae. The probables compued n hs paper are smlar o hose esmaed usng he J.P. Morgan EMU Calculaor. Nex secon explans how o calculae hese probables from expresson (0) 7

18 4.3. Numercal esmaes of convergence probables From he esmaon of (0) n Table 3 one can recover esmaes 9 for he probables ha France, Span, and UK joned he euro area n Aprl 999. These esmaed probables of jonng he EMU, normalzed so ha p [ 0, ], are shown n Fgure 3. The resuls look farly reasonable. For Span and France he value of he ndcaor rose snce he begnnng of 996. The upward rend confrms he curren percepon of an ncreased probably ha Span and France would adop he sngle currency from he ouse of he EMU. The Uned Kngdom had a hgh probably of enerng he EMU durng lae 993 bu collapsed durng he general wave of pessmsm on he fuure of he currency unon durng 994. Snce hen, he probably connuously decreased unl he end of 997, suggesng, as was fnally he case, ha he lkelhood of hs counry n jonng he euro area was no consdered o be parcularly grea. 5.- CONCLUSIONS I have proposed a general equlbrum model o characerze he rsk premum n he exchange rae marke. The model has a man feaure: agens experence consumpon rsk as well as ase shocks. In hs model he excess reurn s a funcon of wo facors: ) he volaly of fundamenal varables (money and oupu), and ) he preference uncerany (ase shocks). Sochasc dscoun facors are conneced o he properes of money, oupu and ase shocks n preferences. Tase shocks make sochasc dscoun facor more sensve o small varaon n consumpon. Therefore, he emphass placed upon consumpon rsks n capurng acual rsk premum movemens s reduced. The model s conssen wh he observed rsk premum durng he convergence perod o he euro. Expeced shfs n he marke srucure because of he euro had mplcaons for agens nvesmen and savng decsons. I seems ha forces oher han hose from money and goods markes were mporan sources of uncerany durng hs perod, a fac ha was refleced n he rsk premum. Ths makes he model presened n hs paper suable o be used n a scenaro lke hs. Tase shocks are quanavely mporan n reproducng he observed rsk premum over he convergence process. Ineres rae spreads and square spread values, used as proxes for he amoun of observed ase rsk, have an accepable sgnfcan explanaory power n he perod, 9 From he esmaon of (0) n Table 3 one can recover esmaes for α 0, α and h. The sysem of equaons lsed n (0) does no have an analycal soluon and one needs o use a numercal mehod o solve n MATLAB. Then, from (9) s sraghforward o compue he convergence probables. 8

19 once naonal Parlamens approved he Maasrch crera. Regardng fundamenal uncerany, he relevance of condonal varances of money supply and ndusral producon as well as he condonal covarance beween hese wo varables s raher lmed n conssency wh he resuls reached by oher auhors. A naural heorecal exenson s o nvesgae more flexble versons of he uly funcon used n hs paper. Addonally, furher work wll mprove he way o measure he ase shocks n preferences. 9

20 References: Baba, Y., Engle R., Kraf,., Kroner, K., 99. AMulvarae smulaneous generalzed Economcs Workng Paper Seres 89-57r, eparmen of Economcs, UC San ego. Baes,., S., 998. Fnancal Markes assessmen of EMU, paper presened a he Carnege- Rocheser Conference, November. Backus,., Fores, S., Telmer, C., 00. Affne Term Srucure Models and he Forward Premum Anomaly. Journal of Fnance 56,, Backus,., Gregory, A., Telmer, C., 993. Accounng for forward raes n markes for foregn currency. Journal of Fnance 48, Baksh, G., Chen, Z., 996. The spr of capalsm and sock-marke prces. Amercan Economc Revew 86, Bekaer, G., 996. The me-varaon of rsk and reurn n foregn exchange markes: a general equlbrum perspecve. Revew of Fnancal Sudes 9, Bekaer, G., Hodrck, R. J., 99. Characerzng predcable componens n excess reurns on equy and foregn exchange markes Journal of Fnance 47, Bencnvenga, V., 99. An Economerc sudy of hours and oupu varaon wh preferences shocks. Inernaonal Economc Revew 33, Bollerslev, T., 986. Generalzed auoregressve condonal heeroskedascy@, Journal of Economercs 3, Box, G., Tao, G., 975. Inervenon Analyss wh applcaons o economc and envronmenal problems. Journal of Amercan Sascal Assocaon 70, Caballero, R., 989. Slope shocks and consumpon puzzles: A sem-srucural approach. Workng Paper 457, eparmen of Economcs, Columba Unversy. Caballero, R., 988. Iner-emporal subsuon and consumpon flucuaons. Workng Paper 409, eparmen of Economcs, Columba Unversy. Campbell, J., Y., Cochrane, J., H., 999. By force of hab: a consumpon-based explanaon of aggregae sock marke behavour. Journal of Polcal Economy 07, Cole, H., Obsfeld, M., 99. Commody rade and nernaonal rsk sharng: how much do fnancal markes maer?. Journal of Moneary Economcs, llén, H., Edlund, M., 997. EMU expecaons and neres raes. Bank of Sweden, Quarerly Revew /97. Engle, R., 98. AAuoregressve condonal heeroskedascy wh esmaes of he varance of U.K nflaon@. Economerca 50, Favero, C. A., Gavazz, F., Iacone, F., Tabelln, G., 000. Exracng Informaon From Asse Prces: The Mehodology of EMU Calculaors. European Economc Revew, 44,

21 Hansen, L. P. and Hodrck, R. J., 983. Rsk averse speculaon n he forward foregn exchange marke: an economerc analyss of lnear models@, n Frankel, J.A., Exchange Raes and Inernaonal Macroeconomcs, Unversy of Chcago Press. Chcago. Herrendorf, B., 997. "Imporng credbly hrough exchange rae peggng". Economc Journal 07(44), Hodrck, R. J., 989. Rsk, uncerany, and exchange raes. Journal of Moneary Economcs 3, Hodrck, R. J., 987. The emprcal Evdence on he Effcency of Forward and Fuures Foregn Exchange Markes, Harwook Academc Publshers, Chur. Hu, X., 997. Macroeconomc uncerany and rsk premum n he foregn exchange marke, Journal of Inernaonal Money and Fnance, 6, J. P. Morgan, 997. The EMU calculaor handbook, Techncal noe, London. Jmenez-Marn, J., A., Flores-e Fruos, R Seasonal Flucuaons and Equlbrum Models of Exchange Rae, forhcomng Appled Economcs. Kamnsky, G. L. and Peruga, R., 990. Can a me varyng Rsk premum explan excess reurns n he forward marke for foregn exchange?, Journal of Inernaonal Economcs, 8, Kamnsky, G. L and Peruga, R., 99. Credbly crses: The dollar n he early 980s, Journal of Inernaonal Money and Fnance, 0, Krasker, W., 980. The peso problem n esng he effcency of forward exchange markes, Journal of Moneary Ecomomcs, 6, Lews, K., 988. The perssence of he peso problem when polcy s nosy, Journal of Inenaonal Money and Fnance, 7, -. Lucas, R. E. Jr., 98. Ineres raes and currency prces n a wo counry world, Journal of Moneary Economcs, 0, Mehra, R., Presco, E., 985. The equy premum: A puzzle, Journal of Moneary Economcs, 5, 45-6 Mron, J., 986. Seasonal flucuaons and he lfe-cycle permanen-ncome model of consumpon. Journal of Polcal Economy, 94, Normandn, M., S-Amour, P., 998. Subsuon, rsk averson, ase shocks and equy prema. Journal of Appled Economercs, 3, Soderlnd, P. Svensson, L. E. O., 997. New Technques o exrac marke expecaons form fnancal nsrumens. scusson paper, nº 556, CEPR, London, UK. Townsend, R., 989. Currency and cred n a prvae nformaon economy. Journal of Polcal Economy, 97, Verdelhan, A., 006. A hab-based explanaon of he exchange rae rsk premum, Workng paper, Boson Unversy.

22 Weber, M., 958. The Proesan Ehc and he Spr of Capalsm. New York: Charles Scrbner s Sons, 958.

23 Appendx - Specfcaon and esmaon of condonal second order momens Wh regard o fundamenal uncerany, I wll assume, as n Hu (99), ha, condonal on avalable nformaon, growh raes n he fundamenal varables (m + and y +; =, F) follow a jon lognormal dsrbuon. I assume ha he dynamc of real and moneary varables, represened by he money supply and ndusral producon, can be summarzed by a VARMA model n logged dfferences wh GARCH nnovaons, whch allows us o capure any possble nonlnear dependence among her nnovaons. 0 Sandard specfcaon ools suggesed a VARMA(, ) model for (ln(m ), ln(y )) for Span, VAR(3) for Germany, VAR () wh a seasonal VAR() componen for he UK, and a VAR (3) wh a seasonal VAR () for France. Evdence of seasonal componens shows up n spe of usng seasonally adjused me seres daa. All hese models are specal cases of: 3 3 φ φ φ φ φ φ 3 I + B + + B 3 3 B φ φ φ φ φ φ ( ) B B 0 Φ 0 Φ ln λ 0 0 ln m 4 λ Φ Φ θ θ I + + = + I + B ( y ) θ θ εm ε y () εm 0 σm σ my / I ~ N, ε y 0 σmy σ y () Wh B beng he backshf operaor, and ε he nnovaon vecor. As nal condons, I used esmaes under he assumpon of no heeroskedascy. Lagrange mulpler and Ljung-Box sascs on he resduals pon ou o possble condonal heeroskedascy n he money supply for France and he UK, as well as for an auoregressve srucure for he covarance beween he money supply and he ndusral producon n France. These ess led us o a GARCH(, ) model for condonal varances and covarance n (). We esmae he specfcaon: σ m c0 a 0 0 ε m g 0 0 σ m my = c a 0 σ εm ε y + 0 g 0 σ m y c σ a g33 y ε y σ y (3) 0 As proposed by Bollerslev (986) and Baba, Engle, Kraf and Kroner (99), among many ohers. Paral and smple auocorrelaon funcons as well as Akake, Hannan and Qunn, and Schwarz crera. 3

24 I mposed dagonaly consrans ( σ, σ, σ dependng only on her own lags and m y my lags of ε, ε, ε, respecvely). These resrcons are made only o avod he numercal m y my dffcules ha would arse when esmang an over-paramerzed model. I use an alernave VARMA(, ) represenaon of he GARCH (, ) model. Le us consderer he 3 x sochasc vecor: ( ε ε' ) ξ = vech vechσ (4) Where vech( εε' ) = ( ε ε ε ) ', vech ( σ σ σ ) ' m my y Subsung (4) n (3) and rearrangng: = and ξ s a whe nose process. m my y ε m a + g 0 0 μ g 0 0 ξ m I - 0 a + g 0 B εmε y = μ + I - 0 g 0 B ξ my (5) 0 0 a33 g 33 μ g + 33 ξ y ε y n whch he presence of he sum a +g allows us o desgn a drec es for saonary n varance, a +g < [Bollerslev (986)]. Condonal varances for he money supply and he ndusral producon depend on her own nnovaons, whle her condonal covarance depends on nnovaons n boh varables. Condonal heeroskedascy seems o be presen n all counres, alhough no all coeffcens seem o change over me. As suggesed by he prevous ess, we esmaed heeroskedasc effecs for he money supply n France and he UK and he covarance beween he money supply and he ndusral producon n France. However, I also oban a sascally sgnfcan auoregressve srucure for he condonal covarance beween boh varables n Span and Germany. No condonal heeroskedascy n he varances of he money supply or he ndusral producon was found for hese wo counres. 4

25 Appendx Table Leas squares esmaon of he rsk premum assocaed o macroeconomc uncerany. (a)(b) (c) Full sample: 986:0-998:04 Noes: (a) S RP + + u F ESP/EM FRF/EM GBP/EM + ln F + 0 F + = α + α σ + α m σ + α3 4 + m σ y + α σ y + + α 5σ y+m α F 6σ y+m + F σ C * (-.03) (-.88) (-.40) RP(-) (d) 0.430* (.87) * 0.03 y m GER (0.48) (.76) (.33) ˆ GER ˆ σ ˆ σ ˆ σ * 0.043* m y (-.80) ( m (0.83) (-0.9) 0.06 y (0.3) R Adj. R COR() (e) COR() (e) ARCH(6) (f) sascs n parenheses. (b) ˆ σ C var ( log x ( x+ )) σ x p cov ( log ( x + ) log ( p + ) ) + + for =FR, SP, UK (c) An asersk denoes a coeffcen sgnfcan a he 0 % level (d) RP(-) denoes he lagged rsk premum (e) P-value of Breusch-Godfrey es sasc for resdual seral correlaon up o lag order p. (f) Auoregressve condonal heeroskedascy es. ARCH(6) s he p-value of LM es sasc. Table (a) Leas squares esmaon of he rsk premum assocaed o preference uncerany. Sample: 994:0-998:04 RP = γ + 0 γir _ SPR + + γir _ SPR + u ESP/EM (e) FRF/EM GBP/EM C * (-.83) (-.46) 0.04 (.5) IR_SPR 0.465* (.8) * (.87) (-0.80) IR_SPR -0.07* (-.33) -0.* (-.84) (0.3) Tase (b) Uncerany R Adj. R COR() (c) COR() ARCH(6) (d) Noes: (a) -sascs n parenheses. (b) P-value of F-sasc for he null hypohess:h 0 : γ = γ =0. (c) P-value of Breusch-Godfrey es sasc for resdual seral correlaon up o lag order p. (d) Auoregressve condonal heeroskedascy es. ARCH(6) s he p-value of LM es sasc. (e) An asersk denoes a coeffcen sgnfcan a he 0 % level 5