Faculdade de Economia da Universidade de Coimbra

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1 Fculdde de Econom d Unversdde de Combr Grupo de Estudos Monetáros e Fnnceros (GEMF) Av. Ds d Slv, COIMBRA, PORTUGAL gemf@fe.uc.pt JOSÉ A. SOARES DA FONSECA The performnce of the Europen Stock Mrkets: tme-vryng Shrpe rto pproch ESTUDOS DO GEMF N.º PUBLICAÇÃO CO-FINANCIADA PELA FUNDAÇÃO PARA A CIÊNCIA E TECNOLOGIA Impresso n Secção de Textos d FEUC COIMBRA 2009

2 The performnce of the Europen Stock Mrkets: tme-vryng Shrpe rto pproch José A. Sores d Fonsec Abstrct Ths rtcle studes the performnce of the ntonl stock mrkets of sxteen Europen countres (Austr, Belgum, Denmrk, Fnlnd, Frnce, Germny, Greece, Hollnd, Irelnd, Itly, Norwy, Portugl, Spn, Sweden Swtzerlnd nd Unted Kngdom), usng dly dt coverng the perod between 2nd Jnury 200 nd 30th My Dly expected returns, nd the condtonl voltlty of ech ndex, were clculted usng model combnng the mrket model nd n mplct long-term relton between the ndex prces. Fnlly, tme-vryng (condtonl) Shrpe rtos were clculted for ech ndex. These were used s the bss for sttstcl comprson of the performnce of the stock ndexes of ths group of countres, throughout dfferent sub perods correspondng to dfferent condtons (of expnson nd depresson) n the stock mrkets. Keywords: expected return, Shrpe rto, mrket model, condtonl voltlty JEL Clssfcton: F36, G5 Introducton Ths pece of reserch nvestgtes the dly excess expected returns from sxteen Europen stock mrkets, nd ther condtonl vrnce, n order to clculte tme-vryng Shrpe rtos, whch re used to mesure the performnce of these stock mrkets between the begnnng of 200 nd the mddle of The use of these tmevryng rtos llows comprson between performnce n dfferent condtons (of growth nd of contrcton) for ech mrket.

3 Smultneously, these rtos re lso used to evlute the proxmty of the performnce between these countres under dfferent mrket condtons. The stock mrkets under nlyss, represented by ther ntonl stock ndexes, re Austr, Belgum, Denmrk, Fnlnd, Frnce, Germny, Greece, Hollnd, Irelnd, Itly, Norwy, Portugl, Spn, Sweden, Swtzerlnd nd Unted Kngdom. In order to clculte dly tme-vryng Shrpe rtos for ech mrket, we estmted the dly expected return nd the condtonl voltlty of ech mrket, usng model specfed to nclude both Europen mrket model, nd n mplct long-term relton between the levels of the ntonl nd the Europen ndexes. The estmtons were crred out ssumng the hypothess tht the voltlty of the stock return follows GARCH model from whch the condtonl voltlty cn be obtned. It s the jont predctblty of the expected return nd of the condtonl voltlty tht llows the clculton of the tme vryng Shrpe rtos. The ncluson of n mplct error correcton model n the econometrc procedure enbles us to tke nto consderton methodology of fnncl ntegrton nlyss n whch co-ntegrton methods re used for the emprcl nlyss of stock mrket ntegrton. On the other hnd, the fct tht the Shrpe rtos re clculted for mrket portfolo, s s the cse n ths rtcle, they cn be defned s mrket prces of rsk, n greement wth Lelnd (999) nd Adcock (2007). Ths lso mkes the methodology used n ths rtcle close to sset prcng models. In fct, n the pproch to fnncl mrket ntegrton bsed on the sset prcng models, whch begn wth the semnl rtcle of Solnk(974), fnncl mrket ntegrton s consdered s beng verfed when the sme sset prcng model cn be ppled to group of domestc cptl mrkets. The ntl model of Solnk, whch conssted of world cptl sset prcng model contnng world mrket prce of rsk, ws lter tken further by other uthors, such s Stehle (977) Joron nd Schwrtz (986) to nclude both domestc nd world mrket prce of rsk. The hypothess of 2

4 mrket effcency contned n cptl sset prcng models hs cused problems n the emprcl nlyss bsed on these models, becuse t s often contrdcted by emprcl results. Ths s one of the resons why, n some more recent reserch, co-ntegrton models hve become populr n the emprcl nlyss of fnncl mrket ntegrton. Contegrton provdes tool for mesurng the nterdependence between domestc stock mrket nd n nterntonl stock mrket both n the long- nd short-terms. Addtonlly, co-ntegrton models lso tke nto ccount the nfluence exerted by lgged chnges of the vrbles over ther current chnges, whch s observed n the cses n whch mrket effcency s bsent. Frst studes on the subject of Europen stock mrket ntegrton usng the co-ntegrton pproch were publshed erly n ths decde. Rngvd (200) nd Mloud (2003) used contegrton methods s tool for evlutng the ntegrton of the Europen stock mrkets n the yers before the lunch of the sngle currency. Other studes, such s those of Ks (992), Arshnpll nd Douks (993), nd Rchrds (995) lso ppled co-ntegrton to evlute the ntegrton of non-europen stock mrkets. The econometrc method used nd the theoretcl bckground for the clculton of the tme vryng Shrpe rtos In ths reserch ech ntonl stock mrket s represented by ts ntonl MSCI (Morgn Stnley Cptl Interntonl) Index, expressed n euros, nd usng dly dt whch covers the perod between st Jnury 200 nd 3 st My 2009, nd comprses 295 observtons of ech ntonl ndex. The Europen Index (MSCI) nd the Europen Overnght Interest Averge (EONIA) re the two other vrbles used n ths reserch, lso usng dly dt nd coverng the sme perod s the others. Pror to econometrcl testng, ech ndex seres ws trnsformed gvng the bse 00 on 2nd Jnury 200 for ll the seres. 3

5 The logs of these new seres were consequently clculted nd used n the estmtons. The model on whch the estmton of the expected returns for ech of the ntonl ndex s bsed combnes Europen mrket model, nd the long-term relton between the ntonl ndex nd the Europen ndex. The representton of the Europen mrket model s gven by: R = + R + ε () t, Et, t, where R,t nd R E,t re the return of the ntonl portfolo nd the return of the Europen portfolo over perod t respectvely, nd ε,t s the error term, whch hs, by hypothess, zero men. Tkng the opertors of mthemtcl expecttons, the representton of the mrket model becomes: ( ) = + ( ) E R E R t t E (2) where E ( ) t R s the expected return of the domestc portfolo (ndex) over perod t, nd ( ) E R s the expected return of the Europen portfolo t E (ndex) lso over perod t. The ncluson of the long-term relton between the ntonl ndex nd the Europen ndex s bsed on the error correcton model of Engle- Grnger (987). Our tests were conducted usng the logs of the ndex prces, whch, from now on, wll be represented n ths pper by p =. Thus, the error correcton model tkes the followng form: log ( P ) ( ) Δ p = + p p + Δ p + Δ p +ε t, t e, t, 0 Et,, j t, j 2, j Et, j t, j= j= L L (3). whch mens tht the current chnge n the prce log of the ndex t perod t, Δ p t,,s explned by the lgged devton of ts vlue reltve to 4

6 the long-term relton wth the log of Europen ndex, nd by L lgged chnges of the prce logs of both of the domestc nd the Europen ndexes. As the chnges n the prce logs re the returns of the portfolos, the error correcton model cn tke the followng form: ( ) R = + p φ φ p + R + R +ε t, t e, t, 0 Et,, j t, j 2, j Et, j t j= j= L L (4) In the emprcl nlyss conducted n ths rtcle the hypothess tht the returns of ntonl ndex re determned by twce the nfluence of the mrket model, nd of the error correcton model, s tested. The combnton of both nfluences re gven by the followng: R =ϖ +R t, Et, L L +ϖ + ( p p ) + R + R + ε 2 e, t, 0 Et,, j t, j 2, j Et, j t j= j= (5) where ω nd ω 2 re the weghts, respectvely of the mrket model nd of the error correcton model, n the explnton of the dly return of the ntonl ndex. The followng equton ws ssgned to ths model for econometrcl estmton: L L t, = + Et, + t, + 2 Et, +, j t, j+ 2, j Et, j+εt j= j= (6) R R p p R R As Adcock (2007) notes, t s common prctce to embed the bet (mrket) model n models wth uto-regressve nd/or movng verge terms, whch lso tke n consderton the hypothess of ARCH/GARCH effects. Tht s the cse of the model tested n the present pece of reserch. The mn dvntge of ths econometrcl procedure s tht t mkes evdent, smultneously, nd through the 5

7 estmtes of the coeffcents, the mportnce of the Europen mrket model n the explnton of the dly returns of ech ntonl ndex, nd the nfluence exerted by the prces or the lgged returns. The hypothess tht the condtonl vrnce follows GARCH model hs lso been consdered n the tests. Thus, the estmton ws mde v mxmum lkelhood procedure. The results of the tests confrmed tht t s dequte to represent the condtonl vrnce for ll the ntonl ndexes under nlyss usng the GARCH(,)model: σ = + ε + σ (7) t ε, ε t 2, ε t (where σ 2 t s the condtonl vrnce t tme t, nd ε 2 t- s the error term squred). After the estmton, the normlzed resduls (.e. the resduls dvded by the squre root of the condtonl vrnce) were tested for utocorrelton, usng Ljung-Box test, nd for ARCH, usng n F test on the coeffcents of n utoregressve model of the squred normlzed resduls: k 2 2 t bjεt j j= ε = + (8) Both the Ljung-Box test nd the ARCH test were crred out for mxmum of 24 lgs, wth spn of 4 lgs. The results of these two tests determned the choce of the number of lgs n the men equton, nd lso the type nd the order of the GARCH model of the condtonl vrnce. Accordng to the results of these tests, s wll be dscussed n more detl lter, one lg (L=) n the men equton hs been shown to be dequte n lmost ll the cses to elmnte resdul utocorrelton. The only excepton ws the cse of Sweden, n whch t ws necessry to nclude two lgs of the dependent vrble n the men equton n order to elmnte the utocorrelton of the resduls. 6

8 One of the prmry uses of the expected returns, E( R ) nd of the rsk, σ t,s to clculte the Shrpe rto: S ( ) E R r f = (9) σ where r f s the return of the rsk free sset. The clculton of ths rto llows comprson between the performnces of the stock mrket of country nd the stock mrkets of other countres. Lelnd (999) nd Adcock (2007) defned ths Shrpe rto, when relted to stock mrket, s the mrket prce of rsk. Both Lelnd nd Adcock bsed ther nlyss on the non condtonl CAPM, whch mples tht the mrket prce of rsk s constnt durng the perod coverng the dt used to clculte the expected return nd the rsk. As the emprcl model estmted n the present pece of reserch produces dly tme vryng expected returns E ( ) t R, nd tme-vryng mesure of rsk, the condtonl voltlty σ, t., dly tme vryng Shrpe rto, s shown by the followng expresson: S t, ( ), E R r t f t = (0) σ t, cn lso be clculted for ech ntonl ndex, (the rsk-free nterest rte used n the clculton s the Europen Overnght Interest Averge). The use of stochstc dscount fctor s tool for sset prcng forms the theoretcl bss for the economc nterpretton of the tmevryng Shrpe rto. In non-rbtrge economy wth complete mrkets ll the ssets cn be prced usng the stochstc dscount fctor (or prcng kernel) of the Hrrson nd Kreps (979) type, M t+, whch stsfes the followng condton for ny sset, or portfolo : ( ) Et Mt+ R. t+ = () where R,t+ =log(p,t+ /P,t ) 7

9 In greement wth the non-rbtrge condton, equton () cn lso be ppled to the rsk-free sset, whch cn, thus, be represented by the nverse of the expectton of the prcng kernel: ( ) r = E M (2) f, t t t+ Developng Equton () n ccordnce wth the rules of the expectton of the product of two rndom vrbles, nd replcng E t (M t+ ) - by r f,t, t cn be concluded tht the excess expected return of the portfolo s proportonl to ts condtonl covrnce wth the prcng kernel,.e: (, + ),, ( +,, + ) E R r = r Cov M R (3) t t f t f t t t t where Cov t s the condtonl covrnce. Dvdng equton (3) by the condtonl stndrd devton of the portfolo, σ,t, t s possble to conclude tht the condtonl Shrpe rto of the portfolo s proportonl to the condtonl correlton between the return of the portfolo nd the prcng kernel: (, ) S = r Corr M R (4) t, f, tσ M, t t t+ t, + where σ M, t s the condtonl stndrd devton of the prcng kernel, nd Corr t s the condtonl correlton between t nd portolo. As Whtelw (994, 997) underlnes, we cn ntutvely conclude tht substntl prt of the vrton of the condtonl Shrpe rto s ttrbutble to vrton n ths condtonl correlton. On the sme lnes s Whtelw, goes the emprcl evdence of Ayd nd Krysnovsky (2008), tht the use of prcng kernel methodology cn esly encompss tme-vryng mesures of performnce. Both the 8

10 postulte of Whtelw, nd the emprcl evdence of Ayd nd Krysnovsky show the mportnce of clcultng tme-vryng Shrpe rtos s they provde n ndrect wy of obtnng nformton regrdng the condtonl correlton between the return of mrket portfolo nd the stochstc dscount functon (or, n smlr wy, on the condtonl correlton between the return of mrket portfolo nd the vrbles ffectng the stochstc dscount functon). The fnl objectve of ths rtcle s to evlute the co-movement of the condtonl Shrpe rtos of ths group of ntonl ndexes. The use of hstorcl correlton s possble tool for ths objectve. However, t s not sutble for tkng nto ccount the possblty tht the correltons chnge over tme. Thus, t ws used the cross-sectonl dsperson mesure, proposed by Solnk nd Roullet (2000), ntlly to be ppled to stock returns, whch vres nversely wth nstntneous verge correlton, nd so provdes nformton regrdng dynmc correlton. Ths mesure, ppled n ths pper, s represented by the vrnce cross the ntonl ndex Shrpe rtos, nd ws clculted dly. Its representton, referred to ech perod t: 6 ( ) 2, CSDM = S S (5) t t t = where S t s the verge Shrpe rto over perod t. The sttstcl nlyss of the seres of the CSDM, through dfferent subsmples of the perod under nlyss, gves nformton regrdng the nter temporl evoluton of the proxmty of the performnce of the ndexes under nlyss. We cn tke the proxmty of the Shrpe rtos s n ndctor of the degree of ntegrton of the fnncl mrkets. Thus, conductng sttstcl tests on the CSDM over dfferent subsmples, we rrve t conclusons regrdng the evoluton of the ntegrton wthn the group of domestc fnncl mrkets. These tests were conducted on the seres of the CSDM referrng to these 6 countres, nd, seprtely, the sme tests were ppled to the eleven euro re countres. Snce the subsmples consdered n these tests 9

11 correspond to dfferent phses of the stock mrket, t ws possble to rrve t comprtve nlyss of the ntegrton of these mrkets n phses of both fnncl mrket expnson nd contrcton. The estmton of the expected returns, Shrpe rtos nd nlyss of ts evoluton The results of the estmton of the combned mrket model-error correcton model, nd the GARCH, for ech of the stock ndexes re shown n Tbles I. to I.6. Ech of these refers to one of the ntonl ndexes under study. Ech tble s composed of three seprte prts. In the frst prt, ), the results of the estmton of the men equton nd the GARCH model re represented. These nclude, for ech coeffcent, the estmte, the stndrd error, the T sttstc nd the sgnfcnce level. In the second prt, b), results (the Ch-squred test sttstc nd the sgnfcnce level) of the Ljung-Box tests on the utocorrelton of the resduls re shown. These refer to mxmum of 24 lgs wth spn of 4 lgs. In the thrd prt the tests on the resduls heteroskedstcty (ARCH ), whch consst on the F test sttstc nd (ts level of sgnfcnce) clculted through the estmton of utoregressve models of the squred resduls wth mxmum of 24 lgs nd spn of 4 lgs re gven. The results presented n these tbles show tht, n the explnton of the dly returns of mjor prt of the ntonl ndexes, the mrket model domntes the nfluence exerted by the ntonl nd the Europen ndex vlues, snce, for ll the countres, the coeffcent of the return of the Europen ndex s sgnfcntly dfferent from zero. On the other hnd, n the mjorty of the cses, the coeffcents of the ntonl nd the Europen ndex vlues re not sgnfcntly dfferent from zero. The exceptons to ths rule re the cses of Fnlnd, Frnce, Portugl nd Swtzerlnd. In these cses the sttstcs of the coeffcents of the ntonl, nd the Europen ndexes, led to the rejecton of the 0

12 null hypothess tht they re not sgnfcntly dfferent from zero. Snce the coeffcents of the ndex vlues contn nformton regrdng the long-term relton between ech ntonl ndex nd the Europen ndex, t cn be tken tht, n the cse of these four countres, the return of ther ntonl stock ndexes s explned both by Europen mrket model nd by the mplct long-term relton between the ntonl ndex nd the Europen ndex. The Germn cse s peculr becuse the coeffcent of the Europen ndex level s sgnfcntly dfferent from zero, whle the opposte stuton s observed wth the coeffcent of the domestc ndex. Accordng to the results of the Ljung-Box test, shown n prt b) of Tbles I. to I.6, nd lso ccordng to the results of the ARCH test, n prt c) of those tbles, there s no utocorrelton nor ARCH effects observed n the resduls of ny of the regressons. As mentoned bove, the second prt of the tests conducted for ths rtcle nvolved the clculton of dly Shrpe rtos for ech ntonl ndex, nd ther sttstcl nlyss, both over the totl perod of nlyss, nd over dfferent subsmples. The totl perod, between st Jnury 200 nd 3st My 2009, ws broken down nto four subsmples: ) between st Jnury 200 nd 3st December 2002, 2) between st Jnury 2003 nd 3st December 2004, 3) between st Jnury 2005 nd 3st December 2006, nd 4) between st Jnury 2007 nd 3st My Durng the frst nd fourth subsmples phses of mrket contrcton were predomnnt, whle durng the second nd the thrd perods the fnncl mrkets predomnntly went through phses of growth (Ths s llustrted n Fgure, where the seres of the Europen ndex s gven). The mn sttstcs on the tmevryng Shrpe rto of ech country, reltve to the entre perod nd to the four subsmples re presented t the Tble II. In generl, the verge of the tme-vryng Shrpe rtos s postve n the subsmples durng whch the stock mrkets predomnntly experenced phses of growth. On the contrry, n the subsmples durng whch the decrese n prces ws domnnt, the verge of the condtonl Shrpe rto s

13 negtve. The Shrpe rto s negtve when the ndex expected return s less thn the rsk-free nterest rte. Ths stuton s not necessrly precluded by the equlbrum stuton n the stock mrket, f, s Boudoukh, Rchrdson nd Whtelw (997) found, there s nonlner relton between the equty rsk premum nd the slope of the term structure of nterest rtes. These sttstcs (men, stndrd error nd level of sgnfcnce) re complemented by test for equlty cross the subsmples. The results of ths test represented by the Ch-squred sttstcs nd the respectve level of sgnfcnce, presented together wth the other results of ech ntonl ndex, confrm tht the behvour of the Shrpe rtos ws not equl cross subsmples. The ex-post Shrpe rto,: S EP = T t= μ ( Rt, rf, t) T μ 2 (4) where t= μ = T ( Rt, rf, t) T nd T s the number of observtons, ws clculted for the whole smple, nd for the subsmples. The ex-post Shrpe rto hs, n every cse, the sme sgn s the verge condtonl Shrpe rto, s t s lso shown n Tble II. The sttstcs regrdng the seres of the cross secton dsperson mesure (CSDM) of the condtonl Shrpe rtos, between the 6 ntonl stock ndexes under nlyss, re gven n Tble III. These sttstcs were clculted for the entre perod s well s for the four subsmples referred to prevously. These sttstcs (men, stndrd error nd level of sgnfcnce) were lso complemented wth test for equlty cross the subsmples. The results of ths test, represented by the Ch-squred sttstcs nd the respectve level of sgnfcnce, re 2

14 lso gven n Tble III. The verge CSDM shows the lowest verge vlue n the subsmple reltng to , whch ws domnted by perods of growth n the stock mrkets, nd the hghest verge vlue n the lst subsmple, reltng to , whch mostly corresponds to the perod followng the 2007 fnncl crses. Fgure II shows the CSDM seres nd llustrtes these conclusons. The fct tht n ncrese n the CSDM ws prtculrly notble durng the perod followng the 2007 crses suggests tht there ws n ntensve ncrese n domestc bs fter the crses, whch s, qute probbly, one of the mn cuses of the reduced degree of ntegrton. The CSDM ws lso clculted for the Shrpe rtos of the eleven EMU member countres (Austr, Belgum, Fnlnd, Frnce, Germny, Greece, Hollnd, Irelnd, Itly, Portugl nd Spn) nd the sttstcl tests, whch re gven n Tble IV nd llustrted grphclly n Fgure III, led to conclusons smlr to those obtned for the complete group of sxteen countres. The verge CSDM, observed over the lst subsmple ws remrkbly hgher thn those observed over the other subsmples. Ths result cn be nterpreted s menng tht, even wthn the stock mrkets of the EMU members, the 2007 crses cused reducton n ther degree of ntegrton. Conclusons The emprcl nlyss conducted n ths rtcle shows tht tmevryng Shrpe rtos re n dequte tool for comprtve nlyss of the performnce of dfferent stock mrkets, nd lso tht they help us to hve perspectve on the dynmcs of ther ntegrton. To clculte the tme-vryng Shrpe rtos for sxteen Europen stock ndexes, the condtonl men nd the condtonl voltlty of the ndexes were estmted by model whose specfcton combned the mrket model nd the nfluence of the long-term relton between ech ntonl ndex nd the Europen ndex. The results of these estmtons showed tht the mrket model component s domnnt, obscurng the 3

15 nfluence of the mplct long-term relton between the ntonl nd the Europen ndex n lmost ll cses. The exceptons to ths rule were the cses of Fnlnd, Frnce, Portugl nd Swtzerlnd, n whch, there ws evdence of the explntory power of the ndex levels. The sttstcl nlyss of the condtonl Shrpe rtos showed tht they present, on verge, cler dfferences between the growth phses (durng whch hgher performnce ws observed) nd the depresson phses of the stock mrket (durng whch lower performnce domnted). Fnlly, the clculton of cross dsperson mesure, both cross the group of sxteen countres nd cross the EMU members only, showed tht the dsperson of the performnce experenced much more sgnfcnt ncrese over the perod followng the 2007 crss thn tht observed n the yers precedng t. Ths result cn be nterpreted s evdence tht the 2007 crss cused negtve brek n the process of ntegrton between the mrkets under nlyss. References Adcock. C. (2007), Mesurng portfolo performnce usng modfed mesure of rsk, Journl of Asset Mngement, Vol. 7, Ayd, M. nd Krysnovsky, L. (2008), Portfolo performnce sensvty for vrous sset, C prcng kernels, Computers & Opertons Reserch, 35, pp Arshnpll, B. nd Douks, J. (993), Interntonl stock mrket lnkges: Evdence from the pre- nd post-october 987 perod, Journl of Bnkng nd Fnnce, 7, pp Boudoukh,J., Rchrdson, M. And Whtelw (997), Nonlnertes n the Relton Between the Equty Rsk Premum nd the Term Structure, Mngement Scence, 43, pp Engle, R. nd Grnger, C. (987), Contegrton nd Error-Correcton: Representton, Estmton nd Testng, Econometrc, Nº 55, pp

16 Hrrson, M. nd Kreps, D. (979), Mrtngles nd Arbtrge n Multperod Secutty Mrkets, Journl of Economc Theory, 20, Joron, P. nd Schwrtz, E. (986), Integrton versus Segmentton n the Cndn Stock Mrket, The Journl of Fnnce, Vol. XLI, Nº3, pp Ks, K. (992) Common stochstc trends n nterntonl stocks mrkets, Journl of Monetry Economcs, 29, pp Lelnd, H. (999) Beyond Men-Vrnce: Performnce Mesurement n Nonsymmetrcl World, Fnncl Anlysts Journl, Jn-Feb.pp Mloud, A. (2003), Interdépendnces entre Plces Fnncères Européennes: une Anlyse en terme de Contégrton et de Cuslté, document de recherche, ATER en Fnnce, Unversté de Rennes. Rngvd, J. (200), Incresng convergence mong Europen stock mrkets? A recursve common stochstc trends nlyss, Economcs Letters, 7, pp Rchrds, A. (995), Co movements n ntonl stock mrkets returns: Evdence of predctblty, but not co ntegrton, Journl of Monetry Economcs, 36, pp Stehle, R. (977), An Emprcl Test of the Alterntve Hypothess of Ntonl nd Interntonl Prcng of Rsky Assets, The Journl of Fnnce, Vol. XXXII, Nº2, pp Solnk, B. (974), An Equlbrum Model of Interntonl Cptl Mrket, Journl of Economc Theory, Nº 8, pp Solnk, B. nd Roulet, J. (2000), Dsperson s Cross-Sectonl Correlton, Fnncl Anlysts Journl, Jnury-Februry, pp Whtelw, R. (994), Tme Vrtons nd Covrtons n the Expectton nd Voltlty of Stock Mrket Returns, Journl of Fnnce, 49, pp Whtelw, R. (997), Tme-Vryng Shrpe Rtos Mrket Tmng, Workng Pper Unversty of New York. 5

17 Tble I.: Estmton of the condtonl men return nd condtonl voltlty Austr ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(,) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

18 Tble I.2: Estmton of the condtonl men return nd condtonl voltlty Belgum ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

19 Tble I.3: Estmton of the condtonl men return nd condtonl voltlty Denmrk ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

20 Tble I.4: Estmton of the condtonl men return nd condtonl voltlty Fnlnd )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

21 Tble I.5: Estmton of the condtonl men return nd condtonl voltlty Frnce )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

22 Tble I.6: Estmton of the condtonl men return nd condtonl voltlty Germny )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

23 Tble I.7: Estmton of the condtonl men return nd condtonl voltlty Greece )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

24 Tble I.8: Estmton of the condtonl men return nd condtonl voltlty Hollnd )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b) The Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c) F Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

25 Tble I.9: Estmton of the condtonl men return nd condtonl voltlty Irelnd )Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf 0, , , , , , , , , , , , , , , , , , , , , , , , GARCH(.) ε 0, , , , ,ε 0, , , , ,ε 0, , , , b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) 2, ,72504 LB(8) 5,6380 0,68769 LB(2), ,52652 LB(6),7890 0,76309 LB(20) 9, ,5002 LB(24) 20, ,6546 c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

26 Tble I.0: Estmton of the condtonl men return nd condtonl voltlty Itly ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c) F Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

27 Tble I.: Estmton of the condtonl men return nd condtonl voltlty Norwy ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf 0, , , , , , , , , , , , , , , , , , , , , , , , GARCH(.) ε 0, , , , ,ε 0, , , , ,ε 0, , , , b)the Ljung-Box Qu- Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4),7220 0,88265 LB(8) 4, ,78547 LB(2) 5, ,94007 LB(6) 8,260 0,94544 LB(20) 3, ,842 LB(24) 6, ,87284 c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

28 Tble I.2: Estmton of the condtonl men return nd condtonl voltlty Portugl ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c) F Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

29 Tble I.3: Estmton of the condtonl men return nd condtonl voltlty Spn ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

30 Tble I.4: Estmton of the condtonl men return nd condtonl voltlty Sweden ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf , , GARCH(.) ε ,ε ,ε b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c) F Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

31 Tble I.5: Estmton of the condtonl men return nd condtonl voltlty Swtzerlnd ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf 0, , , , , , , , , , , , , , , , , , , , , , , , GARCH(.) ε 0, , , , ,ε 0, , , , ,ε 0, , , , b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) 7,0595 0,3278 LB(8) 2,9620 0,37 LB(2) 6,2472 0,807 LB(6) 20,970 0,7966 LB(20) 23,3852 0,27028 LB(24) 26,00 0,353 c)f-test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

32 Tble I.6: Estmton of the condtonl men return nd condtonl voltlty Unted Kngdom ) Coeffcents of the condtonl men nd condtonl voltlty Coeff Estmte Std Error T-Stt Sgnf GARCH(.) ε ,ε ,ε b) The Ljung Box Qu Squred Test for Serl Correlton n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level LB(4) LB(8) LB(2) LB(6) LB(20) LB(24) c) F Test of no ARCH vs. ARCH n Normlzed Resduls (number of lgs wthn prenthess) Test Sttstc Sgnfcnce Level ARCH(4) ARCH(8) ARCH(2) ARCH(6) ARCH(20) ARCH(24)

33 Tble II Sttstcs on the Shrpe rtos Sttstcs on the Condtonl Shrpe Rto AUSTRIA SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level BELGIUM SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level DENMARK SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level FINLAND SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level FRANCE SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level GERMANY SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level GREECE SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level Ex Post Shrpe Rto

34 Tble II (Cont.) Sttstcs on the Condtonl Shrpe Rto HOLLAND SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level IRELAND SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level ITALY SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level NORWAY SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level PORTUGAL SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level SPAIN SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level SWEDEN SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level Ex Post Shrpe Rto

35 Tble II (Cont.) Sttstcs on the Condtonl Shrpe Rto SWITZERLAND SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level UNITED KINGDOM SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level Ex Post Shrpe Rto

36 Tble III Sttstcs on the Cross Secton Dsperson Mesure between the Condtonl Shrpe Rtos of the 6 stock ndexes SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level Tble IV Sttstcs on the Cross Secton Dsperson Mesure between the Condtonl Shrpe Rtos of the EMU members stock ndexes SUB-SAMPLE MEAN STD ERROR SIG LEVEL Test for equlty cross the subsmples: Ch-Squred(4)= wth Sgnfcnce Level

37 36

38 37

39 38

40 ESTUDOS DO G.E.M.F. (Avlble on-lne t The performnce of the Europen Stock Mrkets: tme-vryng Shrpe rto pproch - José A. Sores d Fonsec Exchnge Rte Men Reverson wthn Trget Zone: Evdence from Country on the Perphery of the ERM - Antóno Portugl Durte, João Sous Andrde & Adelde Durte The Extent of Collectve Brgnng nd Workplce Representton: Trnstons between Sttes nd ther Determnnts. A Comprtve Anlyss of Germny nd Gret Brtn - John T. Addson, Alex Bryson, Pulno Texer, André Phnke & Lutz Bellmnn How well the blnce-of- pyments constrnt pproch explns the Portuguese growth performnce. Emprcl evdence for the perod - Mcel Antunes & Els Soukzs Atypcl Work: Who Gets It, nd Where Does It Led? Some U.S. Evdence Usng the NLSY79 - John T. Addson, Chd Cott & Chrstopher J. Surfeld The PIGS, does the Group Exst? An emprcl mcroeconomc nlyss bsed on the Okun Lw - João Sous Andrde A Polítc Monetár do BCE. Um estrtég orgnl pr estbldde nomnl - João Sous Andrde Wge Dsperson n Prtlly Unonzed Lbor Force - John T. Addson, Rlph W. Bley & W. Stnley Sebert Employment nd exchnge rtes: the role of openness nd technology - Fernndo Alexndre, Pedro Bção, João Cerejer & Mguel Portel Chnnels of trnsmsson of nequlty to growth: A survey of the theory nd evdence from Portuguese perspectve - Adelde Durte & Mrt Smões No Deep Pockets: Some stylzed results on frms' fnncl constrnts - Flpe Slv & Crlos Crrer Aggregte nd sector-specfc exchnge rte ndexes for the Portuguese economy - Fernndo Alexndre, Pedro Bção, João Cerejer & Mguel Portel Rent Seekng t Plnt Level: An Applcton of the Crd-De L Rc Tenure Model to Workers n Germn Works Councls - John T. Addson, Pulno Texer & Thoms Zwck Unobserved Worker Ablty, Frm Heterogenety, nd the Returns to Schoolng nd Trnng - An Sof Lopes & Pulno Texer Worker Drectors: A Germn Product tht Ddn t Export? - John T. Addson & Clus Schnbel Fscl nd Monetry Polces n Keynesn Stock-flow Consstent Model - Edwn Le Heron Unform Prce Mrket nd Behvour Pttern: Wht does the Ibern Electrcty Mrket Pont Out - Vítor Mrques, Isbel Sores & Adelno Fortunto The prtl djustment fctors of FTSE 00 stock ndex nd stock ndex futures: The nformtonl mpct of electronc trdng systems - Helder M. C. V. Sebstão Wter Losses nd Hydrogrphcl Regons Influence on the Cost Structure of the Portuguese Wter Industry - Rt Mrtns, Fernndo Coelho& Adelno Fortunto

41 Estudos do GEMF The Shdow of Deth: Anlysng the Pre-Ext Productvty of Portuguese Mnufcturng Frms - Crlos Crrer & Pulno Texer A Note on the Determnnts nd Consequences of Outsourcng Usng Germn Dt - John T. Addson, Lutz Bellmnn, André Phnke & Pulno Texer Exchnge Rte nd Interest Rte Voltlty n Trget Zone: The Portuguese Cse - Antóno Portugl Durte, João Sous Andrde & Adelde Durte Tylor-type rules versus optml polcy n Mrkov-swtchng economy - Fernndo Alexndre, Pedro Bção & Vsco Gbrel Entry nd ext s source of ggregte productvty growth n two lterntve technologcl regmes - Crlos Crrer & Pulno Texer Optml monetry polcy wth regme-swtchng exchnge rte n forwrd-lookng model - Fernndo Alexndre, Pedro Bção & John Drffll Estrutur económc, ntensdde energétc e emssões de CO 2 : Um bordgem Input-Output - Luís Cruz & Edurdo Brt The Stblty nd Growth Pct, Fscl Polcy Insttutons, nd Stblzton n Europe - Crlos Fonsec Mrnhero The Consumpton-Welth Rto Under Asymmetrc Adjustment - Vsco J. Gbrel, Fernndo Alexndre & Pedro Bção Europen Integrton nd Externl Sustnblty of the Europen Unon An pplcton of the thess of Feldsten-Horok - João Sous Andrde Um Aplcção d Le de Okun em Portugl - João Sous Andrde Educton nd growth: n ndustry-level nlyss of the Portuguese mnufcturng sector - Mrt Smões & Adelde Durte Levels of educton, growth nd polcy complementrtes - Mrt Smões & Adelde Durte Internl nd Externl Restructurng over the Cycle: A Frm-Bsed Anlyss of Gross Flows nd Productvty Growth n Portugl - Crlos Crrer & Pulno Texer Cost Structure of the Portuguese Wter Industry: Cubc Cost Functon Applcton - Rt Mrtns, Adelno Fortunto & Fernndo Coelho The Impct of Works Councls on Wges - John T. Addson, Pulno Texer & Thoms Zwck Rcrdn Equvlence, Twn Defcts, nd the Feldsten-Horok puzzle n Egypt - Crlos Fonsec Mrnhero L ntégrton des mrchés fnncers - José Sores d Fonsec The Integrton of Europen Stock Mrkets nd Mrket Tmng - José Sores d Fonsec Mobldde do Cptl e Sustentbldde Extern um plcção d tese de F-H Portugl ( ) - João Sous Andrde Works Councls, Lbor Productvty nd Plnt Heterogenety: Frst Evdence from Quntle Regressons - Jochm Wgner, Thorsten Schnk, Clus Schnbel & John T. Addson Does the Qulty of Industrl Reltons Mtter for the Mcroeconomy? A Cross-Country Anlyss Usng Strkes Dt - John T. Addson & Pulno Texer