International Market Risk and Cross-section of Greek Average Returns

In e empo al Ma ke Risks and he C oss-Sec ion o G eek A e age Re u ns1 Michail Koubou os2 Uni e si y o Peloponnese & Uni e si y o Pi aeus Eka e ini Panopoulou3 Na ional Uni e si y o I eland, Maynoo h & Uni e si y o Pi aeus This d a : Feb ua y 20, 2006 1We a e in eb ed o Gikas Ha dou elis, Dimi ios Mallia opulos, Jack Meye and an anonymous e e ee o hei sugges ions. We would also like o hank he semina pa icipan s a he Uni e - si y o Peloponnese, he Uni e si y o Pi aeus, he Na ional Uni e si y o I eland and he 4 h HFAA Con e ence (Pi aeus, 2005) o hei help ul commen s. We acknowledge nancial suppo om he G eek Minis y o Na ional Educa ion and Religious A ai s and he Eu opean Union unde he “PYTHAGORAS: Funding o easea ch g oups in he Uni e si y o Pi aeus” g an . The usual dis- claime applies. 2Co esponding au ho : Uni e si y o Peloponnese, Depa men o Economics, Te ma Ka aiskaki, 221 00 T ipolis, G eece. Phone: (+30) 2710 230129, ax: (+30) 2710 230139, e-mail: [email p o ec ed]. 3Depa men o Banking and Financial Managemen , Uni e si y o Pi aeus, G eece and Depa - men o Economics, Na ional Uni e si y o I eland Maynoo h, email: [email p o ec ed]. Abs ac This pape examines whe he he o e all ma ke isk along wi h isks eec ing unce ain y ela ed o he long un dynamics o ma ke cash ows (di idends) and discoun a es ( e- u ns) p ice a e age e u ns on single-so ed po olios o he G eek s ock ma ke . Ou e- sul s sugges ha a wo-be a in e empo al p icing model explains hal o he c oss-sec ional a ia ion in a e age e u ns and deli e s an economically and s a is ically accep able es i- ma e o he coe cien o ela i e isk a e sion. Despi e he ela i e impo ance o ma ke discoun - a e isk, i is ma ke di idend-g ow h isk ha u ns ou o be a mo e signican in de e mining a e age e u ns on G eek po olios. JEL: G11, G12, G14 Keywo ds: CAPM, be a, cash ow isk, discoun a e isk, isk a e sion. 1 In oduc ion Nume ous s udies ha e shown ha he single be a CAPM, a leas in i s uncondi ional o m, pe o ms poo ly since he c oss-sec ional a ia ion in uncondi ional ma ke be as canno ma ch he obse ed sp ead in a e age excess e u ns.1Recen ly, Campbell and Vuol eenaho (2004) and Campbell, Polk and Vuol eenaho (2005) show ha he ma ke be a can be decomposed in o a ela i ely bad cash-ow be a, eec ing news abou he ma ke 's u u e cash ows (di idend g ow h a es), and a ela i ely good discoun - a e be a, eec ing news abou he ma ke 's u u e discoun a es ( e u ns). Acco ding o hei model he wo pa s o o al ma ke isk ha e di e en implica ions in asse p icing. Specically, since ma - ke cash-ow shocks and discoun - a e shocks ep esen pe manen and empo a y shocks o o e all weal h espec i ely, a ional conse a i e in es o s a e pa icula ly a e se o he o me and equi e a highe p emium. Mo e impo an ly, his cash-ow isk p emium should be a mul iple o hei a i ude owa d isk. Empi ically, Campbell and Vuol eenaho (2004) nd ha hei decomposi ion could sol e he small- alue puzzle ound in US da a. In his pape we s udy he c oss-sec ional beha io o cash-ow and discoun - a e isks along wi h hei abili y o p ice e u ns o a se o 25 single so ed po olios o he G eek s ock ma ke (A hens S ock Exchange, A.S.E.) o he pe iod om 1991 o 2003. Using he empi ical me hodology o Campbell (1991), Campbell and Mei (1993), Campbell and Vuol eenaho (2004) and Campbell, Polk and Vuol eenaho (2005), we  s es ima e ma - ke cash-ow and discoun - a e news and be as and hen check whe he he sensi i i ies o po olio e u ns o hese o al ma ke isk componen s can se e as su cien isk measu es which a e p iced in A.S.E. e u ns. Al hough some ecen s udies examine he p ope ies o he wo componen s o agg ega e ma ke e u n in se e al eme ging ma ke s (e.g. Phylak is and Ra azzolo, 2002), he e is no o he s udy, o he bes o ou knowledge, which exam- ines he asse p icing implica ions o his decomposi ion using A.S.E. da a. In his espec , ou s udy comes as a di ec complemen o hese empi ical ndings since i p o ides some 1Fo a ecen e iew on he CAPM li e a u e see, among o he s, Fama and F ench (2004). 1 new insigh s, in e ms o a small and eme ging ma ke , on he independen ole o economic undamen als in p icing he c oss-sec ion o a e age s ock e u ns. Ou esul s indica e ha he wo-be a decomposi ion o he o al ma ke isk inc eases he abili y o he s a ic, single ac o , CAPM o p ice G eek s ock e u ns. Mo e in de ail, all po olios exhibi conside able sp ead in isk exposu e o ma ke cash-ow and discoun - a e isk and bo h ypes o isk a e c oss-sec ionally p iced. Fu he mo e, by employing a disc e e- ime in e empo al asse p icing model, we nd ha cash-ow isk is mo e impo - an o he c oss-sec ion o a e age A.S.E. e u ns since i embodies a be a- isk p emium ha is much highe han he one embodied in discoun - a e isk. Specically, he wo-be a model cap u es almos hal o he a ia ion in po olio mean e u ns, pe o ms sligh ly be e han he popula Fama-F ench (1993) model and deli e s meaning ul and highly sig- nican alues o isk a e sion. O e all, and in line wi h he US ndings o Campbell and Vuol eenaho (2004) and Campbell, Polk and Vuol eenaho (2005), he wo-be a model ex- plains he sp ead in e u ns ound ac oss alue and size po olios and hus p o ides aluable insigh s o he small-o e -la ge and alue-o e -g ow h puzzles. The emainde o he pape is o ganized as ollows: Sec ion 2 p o ides he heo e ical decomposi ion o o al ma ke isk in o wo pa s; e u n isks associa ed wi h ma ke 's cash- ow and discoun - a e dynamics. I also de elops he in e empo al asse p icing amewo k ha will be used o he asse p icing es ima ion. The da ase and he econome ic me hod- ology employed o ex ac he news componen s o ma ke unexpec ed e u ns a e gi en in Sec ion 3. Sec ion 4 p esen s he empi ical esul s and, nally, Sec ion 5 o e s some concluding ema ks. 2 The Model Agen s a e assumed o choose hei op imal consump ion and po olio posi ions using he ecu si e u ili y amewo k p o ided by Eps ein and Zin (1989, 1991) and Weil (1989). 2 The li e ime u ili y unc ion o he in es o is gi en by he ecu si e u ili y unc ion U ; dened o e cu en eal consump ion, C , and expec ed u ili y o u u e eal consump ion, E [U C1]: U .C ;E [U C1]/D.1/C 1  CE [U1 C1]1  1 (1) whe e 0 <  < 1 is he subjec i e discoun ac o ,  > 0 is he cons an , unde his specica ion, coe cien o ela i e isk a e sion (CRRA), is a pa ame e dened as D .1 /=.11/; and  > 0 is he elas ici y o in e empo al subs i u ion (EIS) be ween cu en and expec ed u u e consump ion. Equa ion (1) has he ad an age o b eaking he igh link be ween CRRA and EIS gi en by powe u ili y (D1 ), hus, disconnec ing in es o s' isk a i ude ac oss s a es o na u e (desc ibed by ) and ac oss ime (desc ibed by ). The consume is assumed o nance all he consump ion plan en i ely om he o al eal weal h W ;gi en he ollowing dynamic budge cons ain : W C1D.1CRW; C1/.W C /(2) whe e RW; C1is he ne eal e u n on o al weal h. Eps ein and Zin (1989) sol e o he op imal po olio and consump ion policies and show ha he ollowing se o condi ional momen es ic ions hold o each asse iand he o al-weal h po olio W: E [G R1 W; C1Ri; C1]D1I o iD1; :::; N(3) whe e G C1 de DC C1 C is he op imally chosen g oss g ow h a e o eal consump ion be ween and C1. The abo e se o non-linea momen es ic ions can be linea ized using he assump ion o join condi ional log-no mali y o asse e u ns and consump ion in he spi i o Hansen and Single on (1983). Using hese s ong assump ions along wi h he dynamic budge cons ain in (2), Campbell (1993, 1996) de i es he ollowing c oss-sec ional linea 3 es ic ions on asse s' isk p emia ha places no ole in consump ion as a p iced isk ac o : E [Re i; C1]Dco . i; C1; W; C1E [ W; C1]/C.1/co . i; C1;NDR W; C1/; (4) whe e E [Re i; C1]de DE [Ri; C1]R ; C1, and R ; C1is he simple e u n on he isk- ee asse . The abo e equa ion can be iewed as a disc e e- ime e sion o Me on's (1973) I- CAPM whe e changes in he u u e in es men oppo uni y se s (cap u ed by news abou u u e o al weal h po olio e u ns, NDR W; C1) a e also p iced in addi ion o he con empo a- neous ma ke isk ( he  s co a iance e m). Campbell and Vuol eenaho (2004) go one s ep u he and, using he unexpec ed e- u n decomposi ion de eloped by Campbell and Shille (1988a) and u he ex ended by Campbell (1991), b eak he  s ac o (ma ke e u n inno a ion) in o news abou u u e di idend (cash-ows) g ow h a es and news abou u u e o al e u ns (discoun - a es). Fo - mally, Campbell (1991) has de i ed he ollowing app oxima e log linea decomposi ion o e u ns in o ime C1 e ision in expec a ions (news) abou he p esen alue o all u u e o al-weal h di idend g ow h a es (cash-ow news, NC F W) and he ime C1 e ision in expec a ions abou he p esen alue o all u u e o al-weal h e u ns (discoun - a e news, NDR W): W; C1E C1[ W; C1]DNC F W; C1NDR W; C1;(5) whe e NC F W; C1DE C1[P1 jD0j1dW; C1Cj]E [P1 jD0j1dW; C1Cj] and NDR m; C1D E C1[P1 jD1j W; C1Cj]E [P1 jD1j W; C1Cj], PW; C1is he eal agg ega e (ma ke ) s ock p ice measu ed a he end o pe iod C1 (ex-di idend), dW; C1Dlog.DW; C1/is he log o he eal di idend paymen o o al weal h du ing his pe iod, W; C1Dlog.PW; C1CDW; C1 PW; / is he one-pe iod holding log eal g oss e u n on he o al weal h po olio, WD1=[1 C exp.W/] and WDE[log.dW; pW; /] is he uncondi ional mean o he log agg ega e di idend-p ice a io. The  s e m in (5) is he ime C1 e ision in di idend g ow h expec a ions and ep esen s a pe manen posi i e e ec on o al weal h since i is ne e e- e sed subsequen ly, whe eas he second one is he ime C1 e ision in expec a ions abou 4 u u e e u ns on o al weal h and hus can be iewed as a empo a y shock o he o al weal h since he unexpec ed capi al gain oday  W; C1E C1[ W; C1]>0is a a cos o lowe u u e in es men oppo uni ies, i.e. E C1[P1 jD1j W; C1Cj]E [P1 jD1j W; C1Cj]<0. Using he abo e decomposi ion o he o al weal h unexpec ed e u n and he wo ac o asse p icing es ic ion in (4) we ge he ollowing asse p icing model ha assigns di e en oles o agg ega e di idend g ow h a es' news and e u ns' news in de e mining asse isk p emia: E [Re i; C1]Dco . i; C1;NC F W; C1/Cco . i; C1;NDR W; C1/; (6) The co a iance isk p emium ep esen a ion in (6) can ha e an equi alen be a-like p emium ep esen a ion (Coch ane, 2001). Mul iplying and di iding by he a iance o o al-weal h e u n inno a ions, a . W; C1E  W; C1/, we ge : E [Re i; C1]DC F; i;C F; CDR; i;DR; (7) wi h C F; D a . W; C1E [ W; C1]/,DR; D a . W; C1E [ W; C1]/and: i;W; Dco . i; C1;NC F W; C1/ a . W; C1E [ W; C1]/Cco . i; C1;NDR W; C1/ a . W; C1E [ W; C1]/ Di;C F; Ci;DR; (8) Equa ion (8) s a es ha he equi ed isk p emium on asse iis join ly de e mined by he be as o i s e u n wi h he co esponding decomposed componen s o he o al ma ke isk; cash-ow and discoun - a e be a ha add o he ull o al weal h, CAPM, be a. A conse a i e isk-a e se in es o ( > 1) demands a highe isk p ice o isks associa ed wi h o al-weal h cash-ow (di idend g ow h) unce ain y (i;C F ) a he han o isks linked o shocks o o al weal h po olio e u ns (i;DR), since any posi i e (nega i e) shock o weal h discoun a es is a a bene (cos ) o wo se u u e in es men oppo uni ies, whe eas 5 he in es o is ne e compensa ed la e o e e y posi i e (nega i e) shock o di idends. Hence, he be a p ice o ma ke cash-ow isk C F is a mul iple o he be a isk p ices o ma ke discoun - a e isk DR. Thus, o a conse a i e in es o i mus be C F > DR >0. In o de o ge compa able esul s o he empi ical li e a u e o he uncondi ional CAPM and, mo e impo an ly, o he empi ical ndings o he wo-be a model o Campbell and Vuol eenaho (2004) ha places a ela i ely mo e impo an ole in cash-ow isk, we condi- ion down equa ion (7) and p oceed wi h i s uncondi ional e sion. 3 Da a and Empi ical Me hodology Ou s udy is based on mon hly G eek asse and mac oeconomic da a o he pe iod om June 1991 o May 2003 (133 mon hly obse a ions) ob ained om he Da as eam In e - na ional da abase. Specically, ou da a consis o (a) di e en se s o common s ock es po olios so ed on a ious  m specic cha ac e is ics such as book- o-ma ke , di idend yield, ma ke capi aliza ion, p ice-ea nings a io and 3-mon h momen um, and (b) a se o economy-wide a iables ha se e as ins umen s. The so ing cha ac e is ics whe e cho- sen in o de o gene a e clea sp eads in a e age e u ns ha will challenge he empi ical alidi y o he wo-be a asse p icing model. On he o he hand, and ollowing he common p ac ice, he s a e a iables ha e been selec ed unde he assump ion ha hey exhibi some o ecas ing abili y o e u u e po olio e u ns. Las ly, we assume ha he o al ma ke alue-weigh ed po olio is a good p oxy o he o al-weal h po olio in he G eek econ- omy, so ha RWDRM. We employ a a ian o he Fama and F ench (1993) me hodology o cons uc alue- weigh ed e u ns on 25  m-cha ac e is ic po olios so ed on he abo e cha ac e is ics, and e u ns on he wo Fama and F ench (1993) agg ega e size and book- o-ma ke ac- o mimicking po olios, Small-Minus-Big (SM B) and High-Minus-Low (H M L), espec- i ely. The la e ac o -mimicking po olios will be used as benchma ks in ou asse p icing 6 es s. The po olio cons uc ion p ocedu e has as ollows. In June, e e y yea , we b eak he ull menu o A.S.E. common s ocks a ailable in o 5 g oups based (once a a ime) on las - mon h book- o-ma ke , di idend yield, ma ke capi aliza ion, p ice-ea nings a io and 3- mon h momen um, so ha each g oup con ains an equal numbe o s ocks. We  s collec mon hly closing p ices o each s ock and since he heo e ical decomposi ion in (5) equi es con inuous da a on di idends we di ide he annual di idend paymen by 12 and add i o he mon hly closing p ice.2Then, we compu e he alue-weigh ed mon hly holding pe iod simple po olio e u n by weigh ing each s ock by i s ela i e con ibu ion o he po olio's o al capi aliza ion. The p ocedu e is epea ed e e y yea and we end up wi h ime-se ies da a o simple e u ns on each cha ac e is ics-so ed po olio. Finally, and al hough he model in (7) is w i en in eal log e u ns, we assume ha o he mon hly es in e al we employ, ina ion a es a e almos ully o ecas able, and hus we p oxy eal log e u ns wi h nominal log e u ns. Fo he cons uc ion o he e u ns on he agg ega e alue ac o -mimicking ze o-cos po olio (High Minus Low, H M L) we used he 30-40-30 ule employed by Fama and F ench (1993). Howe e , o he agg ega e size ac o -mimicking ze o-cos po olio (Small Minus Big, SM B) we adjus he o ma ion p ocedu e o accoun o he cha ac e is ics o he G eek da a. We use he 70 h quan ile o he o al ma ke alue ins ead o he median ha was used by Fama and F ench. Gi en, ha ew la ge s ocks domina e he G eek s ock ma ke , a 50% so ing would gene a e a small-cap po olio ha would ep esen only a e y small p opo ion o he o al ma ke alue. In his espec , using a la ge b eakpoin we can c ea e a dis ibu ion o agg ega e ma ke alue ac oss po olios ha is ela i ely simila o he dis ibu ion in Fama and F ench(1993), while he small capi aliza ion po olio ep esen s on a e age he 8% o he o al A.S.E. ma ke capi aliza ion.3A he end o June 2Al hough his echnique o sp eading he di idends o e he yea on he closing p ice assumes s ong o m e ciency o he ma ke , i is common p ac ice when cons uc ing o al ma ke indexes ha assume ein es men o di idends o e he nex pe iod. We hank an anonymous e e ee o poin ing his ou . 3Fo a simila cons uc ion p ocedu e using da a om he UK ma ke , see Dimson, Nagel and Quigley (2003). 7 he uncondi ional e sion o he asse p icing model in (7). Howe e , and gi en he low quali y o isk- ee a e da a o ou sample pe iod we p oceed wi h he ze o-be a e sions o ou asse p icing es s. So, he cons an e m 0in he linea specica ions below is no longe he a e age p icing e o as i would be in (4), (6) and (7), and hus, i can (o be e should, unde he hypo hesis o he exis ence o a ze o-be a asse in A.S.E.) be di e en om ze o. The model is es ed agains he s a ic CAPM and he Fama-F ench (1993) h ee- ac o . Mo e specically, we conside he ollowing c oss-sec ional specica ion o he wo be a (cash-ow and discoun - a e) model: ET[Ri]D0CC Fb i;C F CDRb i;DR;(13) and we es his wo-be a specica ion agains he popula s a ic single-be a CAPM ha imposes he same isk p ices in cash-ow and discoun - a e isk and hus p ices agg ega e ma ke isk, i;M: ET[Ri]D0CMb i;M;(14) and he popula h ee- ac o Fama-F ench (1993) model ha adds agg ega e alue (H M L) and size (SM B) ac o mimicking po olios as compe ing ac o s o he agg ega e ma ke e u n: ET[Ri]D0CMb i;MCH M Lb i;H M L CSM Bb i;SM B;(15) In all equa ions ET[Ri] deno es a e age (sample mean) po olio e u ns and b i;kdeno e he es ima ed be as on he k h ac o as dened in (11) and (12). We es ima e he uncondi ional un es ic ed p ices o be a isks (b s) o he a o emen ioned models as well as he ollowing es ic ed e sion o he wo-be a model in (16): ET[Ri]D0C b i;C F Cb i;C F (16) This las e sion enables o es ima e he coe cien o ela i e isk a e sion and he isk p emium on he discoun - a e ac o . The model p edic s ha he p emium associa ed 14 wi h ma ke cash-ow isk mus be a mul iple o he p emium associa ed wi h discoun - a e isk. Fo a conse a i e isk-a e se in es o ( > 1 in (1)); C F mus be g ea e han DR;i.e. C F > DR. Table 6 p esen s he empi ical ndings o he c oss-sec ional asse p icing es s. The able epo s he mean and s anda d e o o each es ima e, as well as he a e age adj.-R2o he eg ession. Figu e 1 gi es a isual illus a ion o he empi ical abili y o he al e na i e models by plo ing he ealized and  ed a e age e u ns. The be e he model pe o ms he closes o he 45-deg ee line he poin s all. A pe ec ma ch (R2D100%) is achie ed when all poin s all on he 45-deg ee line. Con a y o many US s udies (e.g. Fama and F ench, 1992, Campbell, Polk and Vuol eenaho, 2004), he adi ional s a ic CAPM pe o ms qui e well and explains almos hal o he c oss- sec ional a ia ion in a e age e u ns. Howe e , i ails o p oduce a signican es ima e o he ze o-be a coe cien (b 0D 0:005 wi h s:e:D0:0048). Nex , we check whe he he wo-be a decomposi ion in (13) wi h un es ic ed p ices o be a isk can imp o e he empi ical alidi y o he s anda d s a ic CAPM and whe he he e a e di e en oles in ma ke cash-ow and discoun - a e isks. The model pe o ms qui e well and gene a es s a is ically signican p emia and explains 46.6% o he obse ed c oss- sec ional a ia ion in A.S.E. po olio e u ns. Mo e impo an ly, i gene a es signican isk p emia o bo h ypes o isk wi h he p emium associa ed wi h ma ke cash-ow isk being much highe han ha associa ed wi h ma ke 's discoun - a e isk (b C F D0:0274 and b DR D0:0096). These esul s a e in line wi h Campbell and Vuol eenaho (2004) and in a o o he o al ma ke isk decomposi ion in (7) and (8). Fu he , when we es ima e he es ic ed e sion o he model in (16) he ac o o p opo ionali y, which is es ic ed o be equal o he coe cien o ela i e isk a e sion,  ; is bo h economically and s a is ically signican . Specically, he es ima e o bD2:8572 (s:e:D0:1612) is in he ange hypo he- sized by Meh a and P esco (1985) ha could sol e he well known equi y p emium puzzle. We also es ed o uncons ained isk p emia using cash-ow and discoun - a e isk once a a 15 ime (see, columns labelled CF and DR). Again, ou esul s indica e ha , al hough bo h ypes o in e empo al ma ke isks a e needed o desc ibe he c oss-sec ion o e u ns, cash-ow isk is much mo e impo an wi h a isk p emium h ee imes highe han he one o discoun - a e isk. The espec i e es ima es a e b C F D0:0320 and b DR D0:0107. The wo Fama- F ench (1993) ac o s, H M L and SM B;pe o m ela i ely well by explaining he same p opo ion o c oss-sec ional ola ili y as he wo-be a model, bu ail o deli e posi i e and s a is ically signican p emium o he o e all ma ke isk (b MD 0:0015;s:e:D0:0064). Wha is mo e, none o he agg ega e alue and size p emia (H M L and SM B) a e signi- can a he 1% le el. Las ly, and o expe imen al pu poses we use all ac o s in an ex ended model. Ou esul s sugges ha he ela i e impo ance o cash-ow isk is clea bu we a e inconclusi e on he one o he discoun - a e isk, especially when he signican size isk is included. 5 Conclusions This pape builds on he decomposi ion o he o e all ma ke , o CAPM, isk in o pa s eec ing ime a ia ion ela ed o he dynamics o agg ega e ma ke cash ows and discoun a es using da a om he small and eme ging G eek s ock ma ke (A hens S ock Exchange). Employing he me hodology o Campbell (1991), Campbell and Mei (1993) and Campbell and Vuol eenaho (2004) we decompose ma ke be as in o wo sub-be as, associa ed wi h e isions in expec a ions abou u u e ma ke di idend g ow h a es and u u e e u ns. Using a VAR(1) app oach and a disc e e ime e sion o Me on's I-CAPM, we es whe he hese componen s o o e all ma ke isk a e a ionally p iced and hus explain he alue, size and momen um p emia obse ed in ou mon hly 1991-2003 sample. The heo e ical model p edic s ha al hough bo h ypes o isk a e impo an o he c oss-sec ion, ma ke cash- ow isk (cap u ed by he sensi i i y o e u ns o ma ke cash-ow news) should ea n a highe be a- isk p emium han ma ke discoun - a e isk. 16 The wo-be a model pe o ms qui e well in p icing a e age e u ns on single-so ed po - olios acco ding o book- o-ma ke , di idend-yield, ma ke capi aliza ion, p ice-ea nings and 3-mon h momen um. Consis en wi h heo y, he model deli e s an economically and s a is ically signican es ima e o he coe cien o ela i e isk a e sion (close o 3), ex- plains almos hal o he c oss-sec ional a ia ion in A.S.E. po olio e u ns and gene ally pe o ms a leas as good as he popula h ee- ac o Fama-F ench (1993) model. We nd ha he exposu e o G eek s ock po olios o isks associa ed wi h pe manen shocks o agg ega e ma ke alue (cap u ed by ma ke cash-ow isk) is compensa ed wi h highe uncondi ional isk p ices han he exposu e o isks associa ed wi h u u e ma ke e u ns. Ou esul s a e in a o o a a ional isk I-CAPM- ype s o y whe e economic agen s ha e a long- e m op imizing beha io , do no beha e myopically and alue s ocks acco ding o hei long- un iskiness. 17 Re e ences B ennan, M., A. Wang and Y. Xia, 2004, “Es ima ion and Tes o a Simple Model o In- e empo al Asse P icing,” Jou nal o Finance, 59, 1743-1775. Campbell, J. 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VAR es ima es o ma ke po olio and diagnos ic es s Panel A: VAR Es ima es M; C11log .L I C1/p C1e C1V S C1 cons an 0:033 .0:021/ 0:023 .0:009/0:055 .0:029/ 0:032 .0:041/ M; 0:147 .0:086/ 0:056 .0:039/ 0:043 .0:119/ 0:185 .0:165/ 1log .L I /0:194 .0:160/0:528 .0:073/ 0:077 .0:223/ 0:405 .0:308/ p e 0:007 .0:001/ 0:011 .0:007/ 0:969 .0:021/0:044 .0:028/ V S 0:036 .0:006/ 0:003 .0:006/ 0:034 .0:018/ 0:967 .0:025/ R29:5% 32:9% 94:7% 91:9% F-s a . 3:530 16:499 598:4 384:70 Panel B: Uni Roo Tes s M1log .L I/pe V S ADF 10:199 6:391 1:722 1:746 ADF-GLS 10:200 6:088 1:7401:759 PP 10:259 6:388 1:944 2:046 KPSS 0:229 0:095 0:180 0:137 Panel C: LM Tes o He e oscedas ici y (ARCH Tes : lag D4/ Ou MOu1log.L I /OupeOuV S F-s a . 0:327 1:081 2:134 0:709 p- alue [0:859] [0:369] [0:080] [0:593] No e: Panel A. p esen s es ima es o he VAR(1) sys em in (9). M;is he alue-weigh ed ma ke e u n, 1log .L I/is he change in he loga i hm o he OECD leading indica o , peis he ma ke log p ice-ea nings a io and V S is he alue-sp ead dened as he di - e ence be ween he log(B/M) o he small high-B/M po olio and he log(B/M) o he small low-BE/ME po olio. S anda d e o s o he es ima es a e in pa en heses. Panel B. p esen s he uni - oo es s o he s a e a iables used in he VAR(1). ADF, ADF-GLS, PP and KPSS s and o he alues o he Dickey-Fulle , Dickey-Fulle wi h GLS de ending, Phillips-Pe on and Kwia kowski-Phillips-Schmid -Shin es s, espec i ely. *, ** and *** deno e signicance a 10%, 5% and 1%, espec i ely. Panel C. epo s he alues o ARCH he e oscedas ici y es s on he es ima ed VAR(1) esiduals. The sample pe iod spans om June 1991 o May 2003. 22 Table 2. Ma ke po olio cash-ow and discoun - a e news Co a iance ma ix o news News co /s d.de . NC F MNDR MNC F MNDR M NC F M0:0081 0:0034 NC M0:091 0:563 NDR M0:0034 0:0046 ND M0:563 0:215 Co ela ions o inno a ions wi h news Func ions Inno a ions/News NC F mNDR mNC F MNDR M M0:679 0:225 Mshock 1:052 0:052 1log .L I/0:277 0:295 1log .L I /shock 0:683 0:683 pe0:224 0:398 peshock 0:273 0:273 V S 0:603 0:855 V S shock 0:399 0:399 No e: The able epo s he es ima ed co a iance ma ix (uppe -le ) and he co ela ion ma ix wi h s anda d de ia ions (uppe - igh ) o he es ima ed ma ke po olio cash-ow and discoun a e news using equa ions (9) o (10), he co ela ions o inno a ions o s a e a iables wi h ma ke news (lowe -le ) and he mapping unc ions dened in (10). The sample pe iod spans om June 1991 o May 2003. 23