European Journal of Economics, Finance and Administrative Sciences

Transcription

1 Tesing world consumpion asse pricing models Auhor Li, Bin Published 2010 Journal Tile European Journal of Economics, Finance and Adminisraive Sciences Copyrigh Saemen 2010 EuroJournals Publishing, Inc. The aached file is reproduced here in accordance wih he copyrigh policy of he publisher. Please refer o he journal's websie for access o he definiive, published version. Downloaded from hp://hdl.handle.ne/10072/34603 Link o published version hp:// Griffih Research Online hps://research-reposiory.griffih.edu.au

2 European Journal of Economics, Finance and Adminisraive Sciences ISSN Issue 22 (2010) EuroJournals, Inc hp:// Tesing World Consumpion Asse Pricing Models Bin Li Griffih Business School, Griffih Universiy, Brisbane, QLD 4111, Ausralia Tel: Absrac Using daa for 17 counries, his sudy empirically examine he performance of four consumpion-based capial asse pricing models (CCAPM): he classic world CCAPM under he assumpion of complee inernaional markes inegraion, he heerogeneous world CCAPM under he framework of Consaninides and Duffie (1996) and wo world habi models. The nonlinear models are esimaed and esed by Hansen s (1982) GMM. The empirical resuls sugges ha a large and economically implausible coefficien of relaive risk aversion is needed o resolve he equiy premium puzzle for he classic world CCAPM; by conras, more sophisicaed consumpion models (he heerogeneous world CCAPM and he world surplus CCAPM) are able o generae an equiy premium a lower coefficiens of relaive risk aversion. The sudy provides anoher piece of evidence supporing consumpion-based models, paricularly he heerogeneous world CCAPM and he world surplus CCAPM, for asse pricing in inernaional markes. Keywords: CCAPM, Consumpion Model, Inernaional Financial Markes, Heerogeneous Consumpion, Habi Formaion JEL Classificaion Codes: G12, G15 1. Inroducion The consumpion-based capial asse pricing model (CCAPM) is he simples and mos inuiive of all asse-pricing models (Cochrane, 2001). Developed by Lucas (1978), Breeden (1979) and ohers, he CCAPM follows from he firs-order condiion for a uiliy-maximising agen s ineremporal consumpion and invesmen choice problem. In equilibrium, he agen invess o he poin where he marginal uiliy los from foregoing curren consumpion is equal o he discouned expeced marginal uiliy gained from ha invesmen in he fuure. Mos ess of he CCAPM are ofen performed in a domesic seing, alhough heory suggess ha he CCAPM is equally applicable across counries. Researchers ofen assume ha here are hree ypes of marke linkage in he inernaional finance lieraure (Bekaer and Harvey, 1995): complee inegraion, complee segmenaion, and mild segmenaion. In a compleely inegraed marke, asse prices are deermined by a world sochasic discoun facor (SDF), which implies ha he SDFs for asse reurns in each counry should be relaed o aggregae world variables raher han counry-specific variables. Under he assumpion of complee segmenaion, asse pricing models are esed using domesic daa only. Under he hypohesis of mild segmenaion, asse reurns are no only relaed o domesic facors bu also o world facors.

3 8 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) The world CAPM, in which he excess reurn on he world marke is a facor, is ypically esed in empirical research on inernaional asse pricing (e.g., Sehle, 1997; Korajczyk and Vialle, 1989; Harvey, 1991; Chan, Karolyis and Sulz, 1992; and De Sanis and Gerard, 1997). Researchers also consider facors from oher models. E.g., Cho, Eun and Senbe (1986) consider facors from he inernaional arbirage pricing heory; Ferson and Harvey (1993) consider global economic facors; Jorion (1991), Dumas and Solnik (1995), and De Sanis and Gerard (1998) consider exchange rae risk. The consumpion-based asse pricing model would be preferred over he world CAPM where differences in consumpion baskes across markes are an imporan facor in deermining he crosssecional variaion in sock reurns (Karolyi and Sulz, 2003). However, research on he consumpion CAPM in he inernaional seing is sill quie limied. Whealey (1988) uses he CCAPM o es inernaional equiy marke inegraion. Cumby (1990) ess a consumpion-based inernaional asse pricing model using he MSCI marke indices daa for he US, he UK, Germany and Japan. Li and Zhong (2005) apply habi-formaion models o invesigae he predicabiliy and cross-secional reurns from inernaional equiy markes. They find ha he surplus consumpion associaed wih a common world SDF can parly explain he reurns on mos developed equiy markes and he habi CCAPM performs well in cross-secional ess. Sarkissian (2003) sudies he CCAPM in foreign exchange markes under he assumpion of imperfec risk sharing across counries and he finds ha he new CCAPM wih he cross-counry consumpion dispersion as a facor can beer explain he currency risk premium han he classic CCAPM. Li and Zhong (2009) incorporae boh habi formaion and uninsurable idiosyncraic risks ino an inernaional CCAPM and hey find ha he model can explain a large fracion of he variaion in he cross secion of currency and equiy premiums in developed counries. In his paper, I sudy he empirical performance of various consumpion models for inernaional equiy markes. I use daa for 17 MSCI counries o examine wheher consumpion variables are relaed o excess reurns on he marke indices in differen counries. The sudy conribues o he lieraure by providing empirical analysis of he incomplee risk sharing in he explanaion of he inernaional sock reurns. I sar wih he classic world CCAPM under he assumpion of complee marke inegraion and complee risk sharing. Under he assumpion ha a represenaive invesor has a power uiliy, world consumpion growh is he only facor ha deermines asse reurns in he classic world CCAPM. However, when here is imperfec consumpion risk sharing across counries, invesors can face persisen consumpion shocks and consequenly he cross-secional variance of consumpion growh can affec asse pricing (Consaninides and Duffie, 1996). Thus in he heerogeneous CCAPM, asse reurns are no only relaed o world consumpion growh, bu also relaed o he cross-counry variaion in consumpion growh. Sarkissian (2003) uses he heerogeneous CCAPM o sudy inernaional currency premiums. As he heerogeneous CCAPM can also be applied o equiy markes, I invesigae wheher his model has explanaory power for he reurn variaion on inernaional equiy markes. Moreover, I exend he Abel (1990) and Campbell and Cochrane (1999) habi models o he inernaional seing o invesigae wheher he more sophisicaed consumpion models have beer performance. Using Hansen s (1982) generalized mehod of momen (GMM), I find ha an economically implausibly large risk aversion is needed o address he equiy premium for he classic world CCAPM. By conras, wih an addiional facor (a cross-counry consumpion dispersion facor), he heerogeneous world CCAPM has significanly lower and economically more plausible coefficien esimaes of consumpion risk aversion. The empirical findings of his sudy provide new evidence for he inernaional asse pricing using consumpion models. The more sophisicaed consumpion models are preferred over he classic CCAPM o reduce he exen of he equiy premium puzzle as hey are able o generae equiy premiums a lower coefficiens of risk aversion. The findings highligh he imporance of cross-counry consumpion dispersion as well as world consumpion growh in deermining he expeced excess reurns on sock markes.

4 9 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) The remainder of his paper is organised as follows. Secion 2 inroduces differen world consumpion models. I sars wih he classic world CCAPM and hen exends o he heerogeneous world CCAPM. For comparison, I also presen he world surplus consumpion model and Abel s habi model. Secion 3 describes he daa and discusses he variables used in asse pricing models. I also provides summary saisics. Secion 4 presens economeric mehod and he empirical resuls from GMM esimaion. Secion 5 concludes. 2. World Consumpion CAPM In his secion, I describe he models employed in he empirical esing. I firs inroduce he classic world CCAPM in which here is a represenaive agen in he complee world marke. Then I describe he heerogeneous world CCAPM under he Consaninides and Duffie (1996) framework in which here is incomplee consumpion risk sharing in he marke and herefore he variaion in idiosyncraic consumpion growh should be priced. For comparison, I also presen wo habi models in he inernaional seing: he Campbell and Cochrane (1999) surplus consumpion model and he Abel (1990) raio habi model Classic World CCAPM Sulz (1981a, b) noes ha asse prices from all counries are deermined by a common sochasic discoun facor under he assumpion of complee inernaional marke inegraion and complee consumpion risk sharing. In erms of he consumpion-based asse pricing model, he expeced reurns of he asses he represenaive invesor holds in he world marke are deermined by heir covariance wih he per capia aggregae world consumpion growh. Wih he assumpion of he power uiliy funcion, he represenaive invesor maximises his life-ime uiliy 1 w C E δw, (1) = 0 1 w where C is he real per capia world consumpion, δ w is he subjecive ime discoun facor, and γ w is he uiliy curvaure parameer, also called he coefficien of relaive risk aversion of he world represenaive invesor. The Euler equaion for he invesor s opimisaion problem is e E Mw, + 1 Ri, + 1 = 0, (2) w e C w, + 1 where R i, + 1is he excess reurn on he asse in counry i from dae o +1, and M w, + 1 = is C w, his sochasic discoun facor. (2) is he SDF represenaion of he classic world CCAPM Heerogeneous World CCAPM The classic world CCAPM is based on he complee marke assumpion. Consaninides and Duffie (1996, hereafer CD) inroduce heerogeneiy effecs ino he CCAPM framework. CD assume an economy where an individual invesor k has his own consumpion level C k,, bu all invesors have he same power uiliy funcion wih he same ime discoun facor δ, and coefficien of relaive risk aversion γ. Under he assumpion of he exisence of permanen income shocks, hey derive he Euler equaion for he heerogeneous CCAPM, which is γ C k, + 1 γ ( γ + 1) 2 e E δ exp d + 1 R k, + 1 = 0, C k, 2 where d + 1is he cross-secional sandard deviaion of consumpion growh (or labelled as crosssecional consumpion dispersion ). Sarkissan (2003) applies he CD model o examine he impac of (3)

5 10 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) he cross-secional consumpion dispersion on he currency risk premium in foreign exchange markes. I follow Sarkissan s approach bu insead I examine he heerogeneous world CCAPM in equiy markes. In he inernaional seing, he Euler equaion can be rewrien as C j, 1 γγ ( 1) + * e E + δ exp dj, + 1 R j, + 1 = 0, C j, 2 (4) * where C j, is he aggregae consumpion in counry k a dae, d j, + 1 = var k ln ( Ckj, + 1 / Ckj, ) is he cross-secional variance of log consumpion growh in counry j, and Ckj, is he consumpion of invesor k in counry j. Assuming here are consumpion heerogeneiies boh wihin and across counries, Sarkissan develops an Euler equaion for counry j: C w, + 1 γ( γ + 1) w * e E δ exp ( d+ 1 + d j, + 1 ) R j, + 1 = 0, C (5) w, 2 w where d+ 1 = var j ln ( Cj, + 1 / Cj, ) is he cross-counry variance of consumpion growh. According o he heerogeneous CCAPM in (5), asse reurns are relaed o world consumpion growh, and he wihin- and cross-counry variance of consumpion growh. Since i is difficul o obain daa o consruc he wihin-counry variance of consumpion growh, I follow Sarkissan o assume * w d j, + 1 = ( η 1) d+ 1, where η is a scale facor represening cross-secional consumpion variaion above and beyond cross-counry dispersion. Then (5) can be rewrien as C w, + 1 γ( γ + 1) w e E δ exp η d+ 1 R j, + 1 = 0, C (6) w, 2 C w, + 1 and he SDF of he heerogeneous world CCAPM is γ( γ + 1) w M + 1 = δ exp η d+ 1. C w, World Surplus CCAPM Campbell and Cochrane (1999) propose a habi model where he invesor s uiliy is a funcion of he difference beween consumpion and habi, and he SDF of his model depends upon he surplus consumpion raio. Hence, I call his model he surplus consumpion model. Accordingly, he model exended o he inernaional seing under he assumpion of complee markes is called he world surplus consumpion model. The SDF of he world surplus CCAPM is w Sw, 1 C + w, + 1 M + 1 = δ, (7) Sw, C w, where Sw, is he world surplus consumpion raio Abel s (1990) Habi World CCAPM Abel (1990) models curren-period uiliy as a funcion of curren-period consumpion, assessed relaive o he prior-period consumpion. Specifically, he relaiviies of curren-o-prior consumpion ake a raio form. In he framework of he world CCAPM, he world represenaive invesor solves he following opimisaion problem:

6 11 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) ( C ) 1 w, + v Xw, + v 1 v max E δ v= 1 1 (8) where X w, capures he impac of pas consumpion on curren uiliy. Abel (1990) adops Xw, = C κ w, 1, such ha habi depends on jus one lag of consumpion and he parameer κ reflecs he degree of ime nonseparabiliy. Under Abel s (1990) model, he firs-order condiion is κ( γ 1) C w, 1 C + w, e E δ R j, + 1 = 0 C w, C (9) w, Daa and Summary Saisics 3.1. Main Variables The es asses in his sudy are he Morgan Sanley Capial Inernaional (MSCI) sock marke indices from 17 counries which are sourced from DaaSream: Ausralia, Ausria, Belgium, Canada, Denmark, France, Germany, Hong Kong, Ialy, Japan, Neherlands, Norway, Spain, Sweden, Swizerland, he UK, and he US. These indices are value-weighed and adjused for dividend reinvesmen. Following Harvey (1991) and Li and Zhong (2005), I calculae excess reurns on he indices as he reurns on he MSCI counry indices in US dollars less he reurns on he risk-free asse, which is proxied by he hree-monh US Treasury bill rae. The US Treasury bill rae is obained from he inernaional financial saisics (IFS). I obain monhly MSCI price indices and Treasury bill rae o calculae quarerly reurns. As he monhly price indices are repored using he prices a he beginning of each monh, he quarerly reurn is calculaed as he log of he price a he firs monh in he following quarer divided by he price a he firs monh in his quarer. 1 The quarerly sample period sars from 1970Q2 hrough 2007Q4. My esing of he world CCAPM requires a world consumpion index, which can be consruced from local consumpion daa. As here is no consumpion daa available for some counries (Belgium, Denmark, HK, and Norway) in he early period of he sample, I use he consumpion daa from he remaining counries o consruc he world consumpion index. Though he heory of he CCAPM requires he use of household non-durables and services consumpion, hese daa are no available for mos counries. Therefore, I use household or privae oal consumpion in each counry insead. The real per-capia consumpion for each 13 counries is consruced as local consumpion in local currency divided by local consumer price index (CPI) and local populaion. The consumpion, populaion and CPI daa are sourced from DaaSream, and heir original source is he IFS. 2 The consumpion daa are seasonally adjused excep for Ausria, Norway, and Sweden. I use he X11 procedure in he RATS sofware o conver hese non-seasonally adjused daa ino seasonally-adjused unis. As he populaion daa is in annual erms for each counry, I use he inerpolaion procedure in 1 For example, he reurn on he firs quarer of 1980 is calculaed as r = ln( P / P ) 1980Q M M1, where P and P 1980M M 1 are he prices in April and January respecively. The reurn on he US Treasury bill rae in 1980Q1 is calculaed as r = ln, ((1 + r ) *(1 + r ) *(1 + r ) f Q f,1980m1 f,1980 M2 f,1980m3 ), and hen he excess reurn in 1980Q1 is calculaed as e r = r r 1980 Q Q1 f,1980q1 2 As consumpion daa for Canada, Japan, and he US are in annual amoun from DaaSream, I conver hem o he quarerly number o be in accord wih consumpion daa for oher counries.

7 12 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) RATS o inerpolae hem ino quarerly numbers. 3 I also conver he non-seasonally adjused CPI daa o seasonally adjused numbers. The real per-capia consumpion growh in each counry is consruced as Δ c = ln( C / C 1). (10) I follow Sarkissan (2003), and Li and Zhong (2005) o consruc a world consumpion index from he gross domesic produc (GDP) weighed average of local real per-capia consumpion growh. The quarerly growh rae of he world consumpion index is a weighed average of he real consumpion growh in each counry wih is GDP weighing in he world GDP, which is he sum of he GDPs of he 13 counries. The weighing for each quarer is deermined by he GDP in US dollars a he beginning of he quarer. The quarerly GDP daa are obained from DaaSream and heir original source is he IFS. 4 I also use he X11 procedure o conver he non-seasonally adjused GDP daa for Ausria, Norway, and Sweden ino seasonally-adjused unis. As he GDP daa are in local currency, I obain he foreign exchange daa from DaaSream o conver hem ino dollar erms. I obain MSCI FC/US$ for Ausralian Dollar, Canadian Dollar, Hong Kong Dollar, Norwegian Krona, Swedish Krona, and Swiss Franc, and UK Serling. The exchange raes for oher currencies are quoed in erms of UK Serling from he world marke. Then he cross rae for oher currencies agains US$ can be derived as he muliplicaion of he FC/UK and UK /US$ Insrumenal Variables The insrumenal variables in he GMM ess include he lagged world consumpion growh, he lagged US consumpion-wealh raio, and he lagged US erm spread. The US consumpion-wealh raio is from he websie of Marin Leau which is consruced as per Leau and Ludvigson (2001a, 2001b). The US erm spread is he 10-year US governmen bond yield minus he US 3-monh Treasury bill rae. The choice of he insrumens is based on previous sudies (e.g., Harvey, 1991; Bekaer and Harvey, 1995; and Li and Zhong, 2005) Summary Saisics Table 1 repors summary saisics for he 17 counries. Mean, median, sandard deviaion, and minimum, maximum and he firs-order auocorrelaion coefficiens are repored. The sample period sars from 1970Q2 hrough 2007Q4 (151 observaions). Panel A repors summary saisics of he quarerly excess reurn on he MSCI counry indices. The excess reurns are calculaed in US dollars in excess of he holding period reurn on he hree-monh US Treasury bill. The 17 counries are: Ausralia, Ausria, Belgium, Canada, Denmark, 3 Li and Zhong (2005) also inerpolae he populaion daa. 4 As GDP daa for Canada, Japan, and he US are in annual amoun from DaaSream, I conver hem o he quarerly number o be in accord wih GDP daa for oher counries.

8 13 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Table 1: Summary Saisics Panel A: Excess reurns on he MSCI counry index Counry Mean (%) Median (%) Sd Dev (%) Min (%) Max (%) ρ (1) Ausralia Ausria Belgium Canada Denmark France Germany Hong Kong Ialy Japan Neherlands Norway Spain Sweden Swizerland UK US World average median Panel B: Consumpion growh in each counry Counry Mean (%) Median (%) Sd Dev (%) Min (%) Max (%) ρ (1) Ausralia Ausria Canada France Germany Ialy Japan Norway Spain Sweden Swizerland UK US average median Panel C: World Consumpion variables Variables Mean Median Sd Dev Min Max ρ (1) Δc w, (%) d w, ( 10 ) s w, Panel D: Insrumenal Variables Term us (%) cay us (%) Noes: This able repors mean, median, sandard deviaion, and minimum, maximum and he firs-order auocorrelaion coefficiens of he variables. The sample period sars from 1970Q2 hrough 2007Q4. Panel A repors summary saisics of he quarerly excess reurn on he MSCI counry indices. The excess reurns are calculaed in US dollars in excess of he holding period reurn on he hree-monh US Treasury bill. There are 17 counries: Ausralia, Ausria, Belgium, Canada, Denmark, France, Germany, Hong Kong, Ialy, Japan, Neherlands, Norway, Spain, Sweden, Swizerland, he UK, and he US. The numbers are in percenage excep for ρ(1). Panel B: repors summary saisics of he real per capia consumpion growh in 13 counries. Panel C: repors summary saisics of world consumpion growh Δcw,, he cross-secional dispersion of consumpion growh dw,, and he log world surplus consumpion raio sw,. Excep for ρ(1), he numbers for he world consumpion growh is in percenage and for he cross-secional dispersion of consumpion growh is muliplied by 104. Panel D: repors summary saisics of insrumenal variables: he US erm spread Termus and he US consumpion-wealh raio cayus. The numbers are in percenage excep for ρ(1).

9 14 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Germany, Hong Kong, Ialy, Japan, Neherlands, Norway, Spain, Sweden, Swizerland, he UK, and he US. The highes mean excess reurn over he sample is 1.45% per quarer from he Hong Kong marke. Hong Kong also has he highes sandard deviaion. The mean excess reurns for he US marke is lower han mos oher markes, and he US has he lowes sandard deviaion. These findings are consisen wih Harvey (1991) whose sample period is he early par of my sample period. The reurns on he Ialian and Spanish markes are negaive, which suggess he reurns on he marke indices in US dollars in hese wo counries are less han he reurn on he US Treasury bill on average. As he MSCI world marke porfolio is a value-weighed average of counry reurns, i achieves a lower sandard deviaion han any of he 17 markes due o marke diversificaion. The firs-order auocorrelaion coefficien is low for each counry. Panel B repors summary saisics of he real per capia consumpion growh in 13 counries. The ime-series average of consumpion growh does no differ much across counries. The firs-order coefficiens are all negaive excep for Ialy and he US, suggesing ha here is mean-reversion in consumpion growh in mos counries. Panel C shows summary saisics for he main variables used in asse pricing ess. These variables are he world consumpion growh, he cross-secional consumpion dispersion, and he world surplus consumpion raio. I shows ha he mean world consumpion growh rae is 0.49%, which is close o he consumpion growh in he US. The sandard deviaion for he world consumpion growh is 0.64%, which is lower han he corresponding figure for he US. The range beween he minimum and he maximum for he world consumpion growh is smaller han he one for he US. This is because he world consumpion growh is consruced as a GDP-weighed average of consumpion growh in 13 counries, and consequenly he series become smooher. The cross-secional dispersion of consumpion growh has a mean of %, and he firs-order auocorrelaion is only Compared o he world consumpion growh and he cross-secional consumpion dispersion, he world surplus consumpion raio has a low sandard deviaion and a high auocorrelaion. Panel D shows summary saisics of insrumenal variables: he US erm spread and he US consumpion-wealh raio. The firs-order auocorrelaions for hese wo variables are close o Economeric Mehod and Empirical Resuls 4.1. Economeric Mehod In his secion, I esimae he coefficiens of relaive risk aversion γ and es he four consumpion models: he world CCAPM, he heerogeneous world CCAPM, he world surplus CCAPM, and he Abel habi model. I firs examine hese models for all he G7 counries (Canada, France, Germany, Ialy, Japan, he UK, and he US) and he world marke simulaneously. Then all markes in 17 counries are considered a he same ime. Hansen s (1982) GMM mehodology is employed o esimae and es he models. Following Sarkissan (2003), I model he mean pricing errors for each asse as he parameers o be esimaed along wih γ. 5 The error erm for he heerogeneous world CCAPM is defined as 6 where C γ( γ + 1) u = exp η d ( R α ), j, + 1 w, + 1 w e 1 j, 1 C + + w, 2 j α j is he mean pricing error for asse j, which is he difference beween he realised excess reurn on asse j and he fied reurn prediced by he asse pricing model. If we se η o zero, (11) collapses o he error erm for he classic world CCAPM. The momen resricions for GMM esimaion are 7 (11) 5 The advanage of his approach is ha i enables us o compare pricing errors across differen models. 6 As my focus is on he esimaions of he coefficiens of relaive risk aversion, I omi he ime discoun facor δ (assuming δ=1) in error erms. 7 The momen resricions for a single asse can be easily obained by seing N=1.

10 15 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) 1 ( e + j, + 1 α j) = 0, = 1,, (12) C w+ γ( γ + 1) w + 1 = exp η d + 1 C w, 2 E M R z i N, 1 where M, and z is an I 1vecor of insrumenal variables known a ime. (12) represens N I momen resricions implied by he Euler equaions for N asse reurns. There are N+1 parameers, γ and α j ( j = 1,, N) o be esimaed. Therefore he Hansen J-es has (N I-N-1) overidenifying resricions. The momen resricions for he world surplus consumpion model and he Abel habi model can be derived accordingly. I use wo-sep GMM o esimae he models wih he ideniy weighing marix in he firs sage. I use he Newey and Wes (1987) heeroskedasiciy and auocorrelaion (HAC) consisen marix wih wo lags lengh o obain -saisics for he esimaes. For model comparison, I use he mean pricing errors generaed by each model. I also repor he Hansen and Jagannahan (1997) disance o compare each model s performance. Hansen and Jagannahan (1997) develop a measure of how badly a general asse pricing model is misspecified using an esimae of is SDF. I can assess he relaive fi of nonnesed models. Hansen and * Jagannahan look a he shores disance beween he esimaed SDF, M + 1, and he rue SDF M + 1, * e HJD = min M+ 1 M+ 1, such ha E M 1R = 0. (13) They show ha HJD can be expressed as 1/ 2 * e e e' 1 * e HJD = E M 1R E R+ 1R + 1 E M+ 1R + 1, (14) and HJD can be inerpreed as he maximum pricing error among he se of asses. Then he lowes HJD implies ha he corresponding SDF is closer o he rue SDF Empirical Resuls Table 2 repors he GMM esimaes for he world CCAPM, he heerogeneous World CCAPM wih he parameer η being se o 0.5, 1, 2, 5, 10, respecively, he world surplus CCAPM, and he Abel habi model wih he parameer κ se o1. The es asses are he MSCI counry indices in he G7 counries (Canada, France, Germany, Ialy, Japan, he UK, and he US) plus he world marke index. GMM sysems use all he es asses simulaneously. The insrumens include a consan, he lagged values of he world consumpion growh, he US erm spread and he US consumpion-wealh raio. The able repors he esimaed coefficien of risk aversion γ, average pricing error for each marke α, and he corresponding -saisic is given in parenheses. I also repor he mean absolue pricing errors (MAE) and mean squared pricing errors (MSE) for each model, he means and sandard deviaions (SD) of he esimaed SDFs, and he Hansen J-es and is associaed p-value in parenheses on he nex righ column. The las row repors he Hansen and Jagannahan (1997) disance (HJD) of he esimaed SDFs. My sample sars from 1970Q3 hrough 2007Q3 (149 observaions).

11 16 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) Table 2: Tess of he Euler Equaions (G7+World) Average Pricing Errors Pricing Kernel World CCAPM Heerogeneous World CCAPM η= World Surplus CCAPM Abel s Habi Model (κ=1) γ 63.06* (2.01) (1.54) (1.30) (0.98) 6.63 (0.55) 3.56 (0.31) 1.97 (1.23) (0.90) α CA 0.39 (0.63) 0.43 (0.74) 0.46 (0.78) 0.48 (0.82) 0.51 (0.86) 0.53 (0.88) 0.57 (0.99) 0.52 (0.56) α FR (-0.81) (-0.21) (-0.01) 0.10 (0.13) 0.18 (0.24) 0.20 (0.27) 0.06 (0.07) (0.86) α DE (-0.78) (-0.20) (-0.01) 0.08 (0.12) 0.14 (0.20) 0.15 (0.22) (-0.14) (0.07) α IT (-1.57) (-1.18) (-1.06) (-0.95) (-0.82) (-0.76) (-0.79) (-0.02) α JP (-0.78) 0.09 (0.11) 0.33 (0.42) 0.50 (0.65) 0.63 (0.84) 0.68 (0.91) 0.21 (0.23) 0.36 (-1.14) α UK 0.06 (0.10) 0.34 (0.57) 0.41 (0.68) 0.44 (0.74) 0.46 (0.76) 0.46 (0.75) 0.36 (0.60) 0.29 (0.41) α US (-0.16) 0.20 (0.39) 0.27 (0.54) 0.32 (0.63) 0.34 (0.69) 0.35 (0.71) 0.28 (0.56) 0.30 (0.58) α WM (-0.43) 0.17 (0.34) 0.28 (0.59) 0.36 (0.76) 0.41 (0.88) 0.43 (0.92) 0.29 (0.57) 0.31 (0.69) MAE MSE J p (0.79) (0.51) (0.41) (0.33) (0.27) (0.25) (0.24) (0.29) Mean SD HJD Noes: This able repors GMM esimaes for he world CCAPM, he heerogeneous World CCAPM wih η=(0.5,1,2,5,10), he world surplus CCAPM, and he Abel habi model (κ=1). Two-sage GMM are used. The es asses are he MSCI counry indices in he G7 counries (Canada (CA), France (FR), Germany (DE), Ialy (IT), Japan (JP), UK, and US) plus he world marke index (WM). All he es asses are used in he GMM sysems. Insrumens used are he lagged values of he world consumpion growh, he US erm spread, and he US consumpion-wealh raio. The able repors he esimaed coefficien of he risk aversion γ, and he average pricing error for each marke α (e.g. α CA is he average pricing error for he Canadian marke). The corresponding - saisics are given in parenheses on he nex righ column. The able also repors mean absolue pricing errors (MAE) and mean squared pricing errors (MSE) for each model, as well as he Hansen J-es wih is associaed p- value below in parenheses. The las hree rows repor summary saisics of he SDF. The means, sandard deviaions (SD) and he Hansen and Jagannahan (1997) disance (HJD) of he esimaed SDFs are repored. The sample sars from 1970Q3 hrough 2007Q3. Significan coefficiens a he 5% (10%) significance level are denoed wih ** and * respecively. Table 2 shows ha for he classic world CCAPM, he esimaed coefficien of relaive risk aversion, γ, is wih a -saisic of This high risk aversion is no unexpeced as he world consumpion growh has a much lower volailiy han he reurns on equiy indices, which can be seen in Table 1. The parameer, γ, measures invesors willingness o subsiue heir consumpion ineremporally. Various sudies sugges ha he coefficien of risk aversion, γ, should be a small number in he range beween zero and wo, wih he upper bound value of 10 (see Mehra and Presco, 1985). Therefore, given he high γ esimae, he classic world CCAPM is unable o resolve he equiy premium puzzle: The hisorical equiy premium, which is he reurn on equiy indices in excess of he risk-free rae, is much greaer han he value explained by he classic CCAPM wih an economically reasonable coefficien of risk aversion, γ. 9 The resuls for he heerogeneous world CCAPM, ino which a cross-counry consumpion dispersion facor is added in addiion o he world consumpion growh, show ha he coefficien esimae of risk aversion drops as we increase he scale facor η from 0.5 o The esimaed coefficiens of risk aversion decrease wih η, bu become more imprecisely esimaed. When η=5, he esimaed γ is 6.63, which is similar o he finding in Sarkissian (2003) on foreign exchange markes. This suggess ha he heerogeneous world CCAPM can reconcile he esimaed equiy premium wih 8 Sarkissian (2003) repors he esimae of γ of 119 for foreign exchange markes, and Yogo (2006) repors he esimae of γ of 191 for he US Fama-French porfolios. 9 See Mehra (2003) for an overview of he equiy premium puzzle issues. 10 The scale facor η represens cross-secional consumpion variaion above and beyond cross-counry dispersion.

12 17 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) lower values of coefficiens of risk aversion. Though he esimaes of he average pricing error for each counry in boh models are saisically insignifican, he heerogeneous world CCAPM has lower mean absolue errors and mean squared errors han he classic world CCAPM. Furhermore, he average pricing errors of he heerogeneous world CCAPM for France, Germany, and Ialy are significanly smaller han of he classic world CCAPM. Based on he lower esimaes of risk aversion and smaller pricing errors, he heerogeneous world CCAPM ouperforms he classic world CCAPM. Table 2 also repors he Hansen J-es saisics and heir associaed p-values. The resuls show ha neiher he classic world CCAPM nor he heerogeneous world CCAPM can be rejeced a convenional significance levels. In oher words, boh models successfully price he 7 marke indices and he world marke indices simulaneously. 11 Neverheless, he fi of he model for he heereogeneous world CCAPM is worse han for he classic CCAPM. This is because he classic CCAPM has a relaively higher volailiy in he SDF, as noed by Sarkissian (2003). As can be seen, he heerogeneous world CCAPMs have higher means of he SDF han he classic world CCAPM, bu lower sandard deviaions. In addiion, he mean increases wih η, and he sandard deviaion decreases wih η, which means ha he volailiy of he SDF decreases wih η in he heerogeneous world CCAPM. The classic world CCAPM has a lower Hansen and Jagannahan disance, which subsaniaes ha he model has a beer fi of he daa han he heerogeneous world CCAPM. Neverheless, he magniude of he differences beween he HJDs for he wo models is small. How do he world surplus CCAPM and he Abel habi model perform? The resuls sugges ha boh models have similar performance as he heerogeneous world CCAPM. Boh models have lower esimaed coefficiens of risk aversion and pricing errors. The esimaed coefficien of risk aversion for he world surplus consumpion model is only 1.97 wih a -saisic of Compared o he classic world CCAPM, i is a large drop. Even hough he coefficien esimae of risk aversion for he Abel habi model does no fall as much as he world surplus consumpion model, i is close o he esimaed value in he heerogeneous world CCAPM when η=1. The Hansen J-es saisics for boh models are larger han he one for he classic CCAPM, bu he p-values sugges ha i fails o rejec boh models a convenional significance levels. Again, boh models have higher HJDs han he classic world CCAPM. Above all, GMM es resuls sugges ha all four models (he classic world CCAPM, he heerogeneous world CCAPM, he world surplus CCAPM, and he Abel habi model) can price he equiy marke indices in he G7 counries and he world marke indices simulaneously. The more sophisicaed models (he heerogeneous world CCAPM, he world surplus CCAPM, and he Abel habi model) have lower and more economically reasonable esimaed coefficiens of risk aversion and lower pricing errors han he classic world CCAPM. However, he overall fi of he model for he more sophisicaed models are worse han he one for he classic world CCAPM based on he Hansen J- saisics and he Hansen-Jagannahan disances. Nex, I exend he analysis o all he 17 counry indices which are from he G7 counries menioned above plus Ausralia, Ausria, Belgium, Denmark, Hong Kong, Neherlands, Norway, Spain, Sweden, and Swizerland. The resuls are repored in Table 3. Similar o he findings in Table 2, Table 3 shows ha he more sophisicaed models have lower and economically more plausible coefficien esimaes of risk aversion han he classic world CCAPM, and he more sophisicaed models perform worse han he classic world CCAPM in erms of he goodness-of-he-fi. However, here are wo excepions. Firs, he esimaes for he coefficien of risk aversion are smaller for all models using he 17 counry index daa han hose only using he G7 counry index daa. Second, he pricing errors for he classic world CCAPM are lower han for he more sophisicaed models. This is because in he single asses GMM sysems, he esimaes for he coefficien of risk aversion in he classic world CCAPM for many non-g7 counries such as Ausralia, Belgium, Denmark, Hong Kong, and Norway are lower (close o 2.0) han he esimaes for he G7 counries. 12 Therefore, including 11 I is also possible ha he resuls are due o he low power of ess. 12 See Appendix A6.1 in Li (2009) for deails.

13 18 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) hese counries in he GMM sysem lowers he risk aversion esimaes, which in urn affecs pricing errors of differen models. 5. Conclusion In his paper, I sudy he empirical performance of various consumpion models for inernaional equiy markes. I use daa for 17 MSCI counry indices o examine wheher consumpion variables are relaed o excess reurns on he marke indices in differen counries. I sar wih he classic world CCAPM, which assumes ha here is a world represenaive invesor and his consumpion growh is he only facor in deermining asse reurns. Then I sudy he heerogeneous world CCAPM under he framework of Consaninides and Duffie (1996) o invesigae wheher incomplee consumpion risk sharing affecs asse pricing. Under he assumpion of incomplee consumpion risk sharing, counry specific facors canno be diversified away, and herefore idiosyncraic consumpion risk mus be relaed o asse reurns. I also exend he world CCAPM o wo world habi models. Table 3: Tess of he Euler Equaions (17 counries) Average Pricing Errors Pricing Kernel World CCAPM Heerogeneous World CCAPM World Surplus Abel s Habi η= CCAPM Model (κ=1) γ 28.18* (1.70) (1.57) (1.51) (1.35) 6.28 (1.09) 4.01 (0.92) 1.70* (1.99) 2.00 (0.21) α AU 0.23 (0.40) 0.29 (0.53) 0.33 (0.63) 0.38 (0.73) 0.42 (0.83) 0.44 (0.87) 0.35 (0.65) 0.49 (0.92) α AT 0.37 (0.67) 0.46 (0.92) 0.52 (1.05) 0.56 (1.17) 0.60 (1.26) 0.61 (1.29) 0.50 (0.97) 0.61 (1.24) α BE 0.35 (0.65) 0.43 (0.85) 0.47 (0.96) 0.51 (1.07) 0.54 (1.16) 0.56 (1.20) 0.33 (0.67) 0.57 (1.20) α CA 0.37 (0.72) 0.40 (0.81) 0.42 (0.85) 0.44 (0.89) 0.45 (0.91) 0.46 (0.92) 0.42 (0.85) 0.46 (0.91) α DK 0.42 (0.65) 0.53 (0.86) 0.59 (1.00) 0.65 (1.13) 0.69 (1.25) 0.71 (1.30) 0.67 (1.12) 0.74 (1.33) α FR 0.25 (0.38) 0.31 (0.48) 0.34 (0.53) 0.37 (0.58) 0.40 (0.61) 0.40 (0.62) 0.25 (0.39) 0.41 (0.62) α DE (-0.10) 0.01 (0.01) 0.05 (0.08) 0.08 (0.13) 0.11 (0.18) 0.12 (0.20) (-0.08) 0.13 (0.20) α HK 1.57 (1.52) 1.59 (1.55) 1.58 (1.56) 1.56 (1.56) 1.54 (1.55) 1.53 (1.54) 1.36 (1.39) 1.50 (1.52) α IT (-1.07) (-1.02) (-0.96) (-0.90) (-0.83) (-0.79) (-0.84) (-0.68) α JP 0.72 (1.01) 0.79 (1.15) 0.84 (1.22) 0.87 (1.28) 0.91 (1.33) 0.92 (1.35) 0.47 (0.70) 0.93 (1.35) α NL 0.55 (1.06) 0.58 (1.16) 0.60 (1.22) 0.62 (1.27) 0.64 (1.32) 0.64 (1.33) 0.53 (1.08) 0.66 (1.36) α NO 1.11 (1.37) 1.13 (1.44) 1.14 (1.49) 1.15 (1.52) 1.16 (1.55) 1.16 (1.56) 1.18 (1.54) 1.19 (1.61) α ES (-0.26) (-0.23) (-0.21) (-0.19) (-0.18) (-0.18) (-0.41) (-0.19) α SE 0.85 (1.03) 0.87 (1.10) 0.89 (1.14) 0.90 (1.18) 0.91 (1.21) 0.92 (1.22) 0.98 (1.25) 0.94 (1.26) α CH 0.66 (1.31) 0.71 (1.48) 0.74 (1.57) 0.77* (1.65) 0.79* (1.71) 0.79* (1.73) 0.64 (1.37) 0.80 (1.73) α UK 0.38 (0.77) 0.42 (0.85) 0.44 (0.89) 0.45 (0.91) 0.46 (0.92) 0.46 (0.92) 0.34 (0.70) 0.44 (0.88) α US 0.34 (0.84) 0.37 (0.94) 0.39 (1.00) 0.41 (1.04) 0.42 (1.07) 0.42 (1.07) 0.38 (0.98) 0.42 (1.06) MAE MSE J p (1.00) (1.00) (0.99) (0.99) (0.99) (0.98) (0.98) (0.98) Mean SD HJD Noes: The es asses are he MSCI counry indices in 17 counries: Ausralia (AU), Ausria (AT), Belgium (BE), Canada (CA), Denmark (DK), France (FR), Germany (DE), Hong Kong (HK), Ialy (IT), Japan (JP), Neherlands (NL), Norway (NO), Spain (ES), Sweden (SE), Swizerland (CH), he UK, and he US. Also see noes o Table 2. The models are esimaed and esed using Hansen s (1982) GMM. I find ha a large risk aversion is needed o explain he equiy premium for he classic world CCAPM. The heerogeneous world CCAPM wih he cross-counry consumpion dispersion as he oher facor in addiion o he world consumpion growh has a lower and economically reasonable esimae for he coefficien of consumpion risk aversion. The esimae for he coefficien of risk aversion for he world surplus consumpion model is also low. However, he overall fi of he model for he more sophisicaed models are worse han he one for he classic world CCAPM based on he Hansen J-saisics and he Hansen-Jagannahan disances.

14 19 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) The empirical findings of his sudy provide new evidence for inernaional asse pricing using consumpion models. Under he world represenaive agen model, which assumes ha he marke is complee, counry-specific consumpion risk is perfecly shared among invesors and consequenly only he aggregae world consumpion risk maers for asse pricing (see Cochrane (2001, Ch.3) for he discussion on risk sharing). The findings ha he heerogeneous consumpion model, relaive o he represenaive agen model, can generae much lower and economically plausible coefficiens of relaive risk aversion, which suggess ha counry-specific consumpion risk is no fully diversified a he global level and herefore here is a relaion beween sock reurns and he idiosyncraic consumpion risk. References 1] Abel, Andrew B., Asse prices under habi formaion and caching up wih he Joneses, American Economic Review Papers and Proceedings 80, pp ] Bekaer, Geer, and Campbell R. Harvey, Time-varying world marke inegraion, Journal of Finance 50, pp ] Breeden, Douglas T., An ineremporal asse pricing model wih sochasic consumpion and invesmen opporuniies, Journal of Financial Economics 7, pp ] Campbell, John Y. and John H. Cochrane, By force of habi: A consumpion-based explanaion of aggregae sock marke behaviour, Journal of Poliical Economy 107, pp ] Chan, K.C., G. Andrew Karolyi, and Rene M. Sulz, Global financial markes and he risk premium on U.S. equiy, Journal of Financial Economics 32, pp ] Cho, D. Chinhyung, Cheol S. Eun, and Lemma W. Senbe, Inernaional arbirage pricing heory: An empirical invesigaion, Journal of Finance 41, pp ] Cochrane, John H., Asse Pricing, Princeon Universiy Press, Princeon, NJ. 8] Consaninides, George M. and Darrel Duffie, Asse pricing wih heerogeneous consumers, Journal of Poliical Economy 104, pp ] Cumby, R.E., Consumpion risk and inernaional equiy reurns: Some empirical evidence, Journal of Inernaional Money and Finance 9, pp ] De Sanis, Giorgio and Bruno Gerard, Inernaional asse pricing and porfolio diversificaion wih ime-varying risk, Journal of Finance 52, pp ] De Sanis, Giorgio and Bruno Gerard, How big is he premium for currency risk?, Journal of Financial Economics 49, pp ] Dumas, Bernard and Bruno H. Solnik, The world price of foreign exchange risk, Journal of Finance 50, pp ] Ferson, Wayne E. and Campbell R. Harvey, The risk and predicabiliy of inernaional equiy reurns, Review of Financial Sudies 6, pp ] Hansen, Lars Peer, Large sample properies of generalized mehod of momens esimaors, Economerica 50, pp ] Hansen Lars Peer and Ravi Jagannahan, Assessing specificaion errors in sochasic discoun facor models, Journal of Finance 52, pp ] Harvey, Campbell R., The world price of covariance risk, Journal of Finance 46, pp ] Jorion, Philippe, The pricing of exchange rae risk in he sock marke, Journal of Financial and Quaniaive Analysis 26, pp ] Karolyi, G. Andrew and Rene M. Sulz, Are financial asses priced locally or globally?, in George M. Consaninides, Milon Harris, and Rene M. Sulz, eds.: The Handbook of he Economics of Finance, Norh-Holland, Amserdam. 19] Korajczyk, Rober A. and Claude J. Vialle, An empirical invesigaion of inernaional asse pricing, Review of Financial Sudies 2, pp

15 20 European Journal of Economics, Finance And Adminisraive Sciences - Issue 22 (2010) 20] Leau, Marin and Sydney Ludvigson, 2001a. Consumpion, aggregae wealh, and expeced sock reurns, The Journal of Finance 56, pp ] Leau, Marin and Sydney Ludvigson, 2001b. Resurrecing he (C)CAPM: A cross-secional es when risk premia are ime varying, Journal of Poliical Economy 109, pp ] Li, Bin, Essays on Consumpion-based Asse Pricing Models, PhD Thesis, he Universiy of Queensland, Ausralia. 23] Li, Yuming and Maosen Zhong, Consumpion habi and inernaional sock reurns, Journal of Banking & Finance 29, pp ] Li, Yuming and Maosen Zhong, Inernaional asse reurns and exchange raes, European Journal of Finance 15, pp ] Lucas, Rober E. Jr., Asse prices in an exchange economy, Economerica 46, pp ] Mehra, Rajnish, The equiy premium: Why is i a puzzle?, Financial Analyss Journal 59, pp ] Mehra, Rajnish and Edward C. Presco, The equiy premium: A puzzle, Journal of Moneary Economics 15, pp ] Newey, Whiney K. and Kenneh D. Wes, A simple, posiive semi-definie, heeroskedasiciy and auocorrelaion consisen covariance marix, Economerica 55, pp ] Sarkissian, Sergei, Incomplee consumpion risk sharing and currency risk premiums, Review of Financial Sudies 16, pp ] Sehle, Richard, An empirical es of he alernaive hypoheses of naional and inernaional pricing of risky asses, Journal of Finance 32, pp ] Sulz, Rene M., 1981a. A model of inernaional asse pricing, Journal of Financial Economics 9, pp ] Sulz, Rene M., 1981b. On he effecs of barriers o inernaional invesmen, Journal of Finance 36, pp ] Whealey, Simon, Some ess of inernaional equiy inegraion, Journal of Financial Economics 21, pp ] Yogo, Moohiro, A consumpion-based explanaion of expeced sock reurns", Journal of Finance 61, pp