NBER WORKING PAPER SERIES FINANCIAL INTEGRATION: A NEW METHODOLOGY AND AN ILLUSTRATION. Robert P. Flood Andrew K. Rose

Transcription

1 NBER WORKING PAPER SERIES FINANCIAL INTEGRATION: A NEW METHODOLOGY AND AN ILLUSTRATION Rober P. Flood Andrew K. Rose Working Paper 9880 hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 050 Massachuses Avenue Cambridge, MA 0238 July 2003 Flood is Senior Economis, Research Deparmen, Inernaional Moneary Fund. Rose is B.T. Rocca Jr. Professor of Inernaional Business, Haas School of Business a he Universiy of California, Berkeley, NBER Research Associae, and CEPR Research Fellow. We hank Pedro Rodriguez for assisance wih he daa, and Ken French, Cam Harvey, Rober Hodrick and seminar paricipans a Darmouh, he Federal Reserve Board, and he IMF for commens. Rose hanks he IMF for hospialiy during he course of his research. The views expressed herein are hose of he auhors and no necessarily hose of he Naional Bureau of Economic Research by Rober P. Flood and Andrew K. Rose. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Financial Inegraion: A New Mehodology and an Illusraion Rober P. Flood and Andrew K. Rose NBER Working Paper No July 2003 JEL No. G4 ABSTRACT This paper develops a simple new mehodology o es for asse inegraion and applies i wihin and beween American sock markes. Our echnique is ighly based on a general ineremporal asse-pricing model, and relies on esimaing and comparing expeced risk-free raes across asses. Expeced risk-free raes are allowed o vary freely over ime, consrained only by he fac ha hey are equal across (risk-adused) asses. Asses are allowed o have general risk characerisics, and are consrained only by a facor model of covariances over shor ime periods. The echnique is undemanding in erms of boh daa and esimaion. We find ha expeced risk-free raes vary dramaically over ime, unlike shor ineres raes. Furher, he S&P 500 marke seems o be well inegraed, and he NASDAQ is generally (bu no always) inegraed. However, he NASDAQ is poorly inegraed wih he S&P 500. Rober P. Flood Research Dep, IMF 700 9h S., NW Washingon, DC 2043 rflood@imf.org Andrew K. Rose Haas School of Business Universiy of California Berkeley, CA and NBER arose@haas.berkeley.edu

3 : Defining he Problem The obecive of his paper is o propose and implemen an inuiive and simple-o-use measure of asse-marke inegraion. Wha does asse-marke inegraion mean? We adop he view ha financial markes are inegraed when asses are priced by he same sochasic discoun rae. More precisely, we define securiy markes o be inegraed if all asses priced on hose markes saisfy he pricing condiion: p + + = E ( m x ) () where: p is he price a ime of asse, E () is he expecaions operaor condiional on informaion available a, m + is he ineremporal marginal rae of subsiuion (MRS), for income accruing in period + (also inerchangeably known as he discoun rae, sochasic discoun facor, marginal uiliy growh, pricing kernel, and zero-bea reurn), and x + is income received a + by owners of asse a ime (he fuure value of he asse plus any dividends or coupons). We rely only on his sandard and general ineremporal model of asse valuaion; o our knowledge his Euler equaion is presen in all equilibrium asse-pricing models. Our obec of ineres in his sudy is m +, he marginal rae of subsiuion, or, more precisely, esimaes of he expeced marginal rae of subsiuion, E m +. The MRS is he unobservable DNA of ineremporal decisions; characerizing is disribuion is a cenral ask of economics and finance. The discoun rae ies pricing in a huge variey of asse markes o peoples saving and invesmen decisions. The hrus of his paper is o use asse prices and payoffs o characerize imporan aspecs of is disribuion.

4 The subsanive poin of equaion () is ha all asses in a marke share he same marginal rae of subsiuion. There is no asse-specific MRS in an inegraed marke, and no markespecific MRS when markes are inegraed wih each oher. Learning more abou he MRS is of inrinsic ineres, and has driven much research (e.g., Hansen and Jagannahan, 99, who focus on second momens). Measures of he expeced MRS also lead naurally o an inuiive es for inegraion. In his paper, we propose and implemen such a simple es for he equaliy of E m + across ses of asses. This is a necessary (bu no sufficien) condiion for marke inegraion. 2: Mehodology We use he fac ha in an inegraed marke, he MRS prices all asses held by he marginal asse holder. Indeed wha we mean by asse marke inegraion is ha he same MRS prices all he asses. In oher words, if we could exrac m + (or raher, is expecaion) independenly from a number of differen asse markes, hey should all be he same if hose markes are inegraed. As Hansen and Jagannahan (99) show, here may be many sochasic discoun facors consisen wih any se of marke prices and payoffs; hence our focus on he expecaion of MRS, which is unique. Consider a generic ideniy relaed o (): p ( = E m x ) = COV ( m, x ) E ( m ) E ( x ). (2) where COV () denoes he condiional covariance operaor. I is useful o rewrie his as x + [ = / E ( m )] COV ( m, x ) + [/ E ( m )] p ε, or 2

5 x+ = ( p COV ( m +, x + )) + ε+ δ (3) where δ / E ( m ) and + ε E x ), a predicion error. + x + ( + We hen impose wo resricions: ) Raional Expecaions: ε is assumed o be whie noise, uncorrelaed wih informaion available a ime, and + 2) Covariance Model: COV ( m, x + ) + = β 0 Σiβi f i, +, for he relevan sample, where: β 0 is an asse-specific inercep, β i is a se of I asse-specific facor coefficiens and f i, a vecor of ime-varying facors. Wih our wo assumpions, equaion (3) becomes a panel esimaing equaion. We exploi cross-secional variaion o esimae {δ }, he coefficiens of ineres ha represen he risk-free reurn and are ime varying bu common o all asses. These esimaes of he MRS are he focus of our sudy. We use ime-series variaion o esimae he asse-specific fixed effecs and facor loadings {β}, coefficiens ha are consan across ime. Inuiively, hese coefficiens are used o accoun for asse-specific sysemaic risk (he covariances). Esimaing (3) for a se of asses =,,J 0 and hen repeaing he analysis for he same period of ime wih a differen se of asses =,,J gives us wo ses of esimaes of {δ }, a ime-series sequence of esimaed discoun raes. These can be compared direcly, using convenional saisical echniques, eiher one by one, or oinly. Under he null hypohesis of marke inegraion, he wo ses of {δ } coefficiens are equal. 3

6 Discussion We make only wo assumpions; boh are convenional in he lieraure, hough we rely on hem less han mos of he lieraure. I seems reasonable o assume ha expecaions are raional for financial markes, a leas in our limied sense ha asse-pricing errors are no ex ane predicable a high frequencies. Our assumpion ha he asse-specific covariances (of payoffs wih he MRS) are eiher consan or depend on a small number of facors is more conroversial, bu sandard pracice. Raher han develop our own facor model, we rely on he well-known hree-facor model famously deployed by Fama and French (996). We defend i on wo grounds. Firs, in applicaions we mainain he covariance model for only wo monhs a a ime (hough we have ried shorer periods wih similar resuls); Fama and French assumed ha he same model worked well for hiry years. Second, our resuls are insensiive o he exac facor model. If our echnique were sensiive o he facors used o model {δ }, hen he measure would be no more useful han any of he individual facor models. Indeed, if he measure were facormodel sensiive, i would be preferable o use he facor model iself as he obec of measuremen. Neverheless we sress ha we mus rely on some model of covariances. While we focus on (3), here are oher momens ha would help characerize he MRS, {δ }; see e.g., Hansen and Jagannahan (99). We concenrae on his one for four reasons. Firs, as he firs momen i is he naural place o check firs. Second, i is simple o esimae. Third, our esimaes and resuls are robus o he facor model ha condiions he measuremens. Finally, he measuremens are discriminaing for marke inegraion, ye hey confirm our prior beliefs and previous research (e.g., Chen and Knez, 995). In he examples below, our measure never reecs inernal marke inegraion for porfolios of S&P socks priced in he NYSE and 4

7 seldom reecs for porfolios priced on he NASDAQ, bu reecs srongly by an order of magniude inegraion beween NYSE and NASDAQ porfolios. Our mehodology has a number of srenghs. Firs, i is based on a general ineremporal heoreical framework, unlike oher measures of asse inegraion such as sock marke correlaions (see he excellen discussion in e.g., Adam e. al. 2002). Second, sandard assepricing models are compleely consisen wih our mehodology, and he exac model does no seem o be imporan in pracice. We use he Fama-French workhorse (which subsumes he CAPM), bu find ha our resuls are insensiive o he exac choice of model. Third, we do no need o model he MRS direcly. The MRS need no be deermined uniquely, so long as is expecaion is unique. Fourh, our sraegy requires only wo assumpions; we need no assume e.g., complee markes, homogeneous invesors, or ha we can model mimicking porfolios well. Fifh, he echnique requires only accessible and reliable daa on asse prices, payoffs, and ime-varying facors. Sixh, he mehodology can be used a very high frequencies and a low frequencies as well. Sevenh, he echnique can be used o compare expeced discoun raes across many differen classes of asses including domesic and foreign socks, bonds, and commodiies. Nex, he echnique is easy o implemen and can be applied wih sandard economeric packages; no specialized sofware is required. Finally, he echnique is focused on an inrinsically ineresing obec, he expeced marginal rae of subsiuion. 3: Relaionship o he Lieraure The lieraure is clear ha asse markes are inegraed when idenical cash flows are priced equally across markes (e.g., Adam e. al., 2002 and Cochrane, 200). This is he assemarke version of economiss rusy Law of One Price. Bu since no wo differen asses have 5

8 idenical cash flows, he inegraion definiion mus be exended o be useful. The sandard holds wo asse markes o be inegraed when risks in hose markes are shared compleely and priced idenically. One way o make his definiion operaional requires idenifying he relevan risks. Roll and Ross (980) recognized he dependence of inegraion measures on risk idenificaion. They esed asse inegraion using he argumen ha wo porfolios are inegraed only if heir implied risk-less reurns are he same; our es is similar o heirs in spiri. This simple observaion is powerful because i invokes he cross-secional dimension where every asse in an inegraed marke implies he same risk-free reurn. The lieraure on asse-marke inegraion has grown along wo branches. The firs branch, based on parameric asse-pricing models, has been surveyed by Adams e. al. (2002), Cochrane (200), and Campbell, Lo, and MacKinlay (997). Along his branch, a parameric discoun-rae models o used o price wo asse porfolios. Pricing errors are compared across porfolios. If he porfolios are inegraed, he pricing errors should no be sysemaically idenifiable wih he porfolios in which hey originae. Roll and Ross (980) esed marke inegraion his way using an arbirage pricing heory model, and a large lieraure has followed. The second branch of lieraure grows from he work of Hansen and Jagannahan (99) and is represened by Chen and Knez (995) and Chabo (2000). Along his branch, daa from each marke are used o characerize he se of sochasic discoun facors ha could have produced he observed daa. Tesing for inegraion across markes involves measuring he disance beween admissible MRS ses, and asking if, and by how much, hey overlap. Our work ress on he firs branch, since we use parameric models o condiion our esimaion. I differs from previous work in four ways. 6

9 Firs, we diverge from he finance profession in reaing {β} as a se of nuisance coefficiens. Raher han being of inrinsic ineres o us, hey are required only o clear he way o produce esimaes of he MRS. Nex, we do no measure inegraion by he cross-secional pricing errors produced by a paricular mode; his approach seems relaively non-specific and model-dependen. Insead we measure inegraion by he implied firs momen of he sochasic discoun rae (MRS). The condiion we sudy, herefore, is a necessary condiion for inegraion. Sudying i will be valuable only if i is a discriminaing condiion; i urns ou o be so. Third, parameric pricing models are ofen esimaed wih long daa spans and are hus sensiive o parameer insabiliy in ime series long enough for precise esimaion (e.g., Fama and French (996); an excellen discussion is provided by Cochrane, 200). We minimize (bu do no avoid compleely) he insabiliy problem by concenraing aenion on a parameer ha is condiionally invarian o ime-series insabiliy. The measure we use is a free parameer, consan across asses bu unconsrained across ime. Our measure is herefore basically crosssecional, ha we esimae precisely using a shor ime-series dimension. Finally, we do no assume ha (3) holds for he bond marke, or ha he bond marke is inegraed wih oher asse markes. When applied o a bond wihou nominal risk (e.g., a reasury bill), equaion () implies = E ( m+ ( + i )) ( ) where: i is a risk-less nominal ineres rae, and m + is a nominal MRS. The radiion inside finance is o assume ha he MRS pricing bonds is he same for all bonds, and idenical o ha 7

10 pricing all socks (and oher asses). If we make his assumpion, / E ( m ) = ( + i ) We do no impose his assumpion; raher we es i (and reec) i. δ. + 4: Empirical Implemenaion We begin by esimaing a model wih asse-specific inerceps and he hree ime-varying facors used by Fama and French (996). In pracice, we divide hrough by lagged prices (and redefine residuals appropriaely): x+ / p = (( p / p ) + β 0 + β f, + β2 f2, + β3 f3, ) + ε+ δ (4) for asses =,,J, periods =,,T. Tha is, we allow { δ } o vary period by period, while we use a hree-facor model and allow { β } varying asse by asse. We normalize he daa by lagged prices since we believe ha COV ( m+, x+ / p ) can be modeled by a simple facor model wih ime-invarian coefficiens more plausibly han COV ( m+, x + ). The hree Fama- French facors are: ) he overall sock marke reurn, less he reasury-bill rae, 2) he performance of small socks relaive o big socks, and 3) he performance of value socks relaive o growh socks. Furher deails and he daa se iself are available a French s websie. For sensiiviy analysis, we also examine wo oher covariance models: one wih only a single ime varying facor, namely he overall marke reurn; and he oher wihou any imevarying facors a all (bu, as always, wih an asse-specific inercep). Equaion (4) can be esimaed direcly wih non-linear leas squares. The degree of nonlineariy is no paricularly high; condiional on { δ } he problem is linear in { β } and vice 8

11 versa. We employ robus (heeroskedasiciy and auocorrelaion consisen Newey Wes ) covariance esimaors. We use a moderaely high frequency approach. In paricular, we use wo-monh spans of daily daa. Using daily daa allows us o esimae he coefficiens of ineres { δ } wihou assuming ha firm-specific coefficiens { β } are consan for implausibly long periods of ime. Our empirical illusraion examines he inegraion of American equiy markes. Large American socks are raded on liquid markes, which we consider a priori o be inegraed. We begin by examining daily daa over a quie wo-monh period, April-May 999 (abou a year before he end of he Clinon bull marke). 2 Two monhs gives us a span of over fory business day observaions; his does no appear o srech our reliance on a facor model of asse covariances excessively, while sill allowing us o es financial marke inegraion for an ineresing span of daa. We see no reason why higher- and/or lower-frequency daa canno be used. 3 Our daa se is drawn from he US Pricing daabase provided by Thomson Analyics. We colleced closing raes for he firs (in erms of icker symbol) one hundred firms from he S&P 500 ha did no go ex-dividend during he monhs in quesion. The absence of dividend paymens allows us o se x + p + = (and does no bias our resuls in any oher obvious way). We group our hundred firms ino weny porfolios of five firms each, arranged simply by icker symbol. We use porfolios raher han individual socks for he sandard reasons of he Finance lieraure. In paricular, as Cochrane (200) poins ou, porfolios beas are measured wih less error han individual beas because of lower residual variance. They also vary less over ime (as size, leverage, and business risk change less for a porfolio of equiies han any individual componen). Porfolio variances are lower han hose of individual securiies, 9

12 enabling more precise covariance relaionships o be esimaed. And of course porfolios are wha invesors end o use (especially hose informed by Finance heory!). Our firs sample period consiss of 4 days. Since we lose he firs and las observaions because of lags p ) and leads ), we are lef wih a oal of 780 observaions in our panel ( ( x + daa se (20 porfolios x 39 days). Our daa has been checked for ranscripion errors, boh visually and wih random crosschecking. There is no reason ha one canno use more daa (longer spans a differen frequencies, for larger number of firms and/or porfolios grouped non-randomly). We choose his sample (only wo monhs of daily price daa for one hundred firms grouped randomly ino weny porfolios) deliberaely o illusrae he power of our mehodology and is undemanding daa requiremens. However, we also check for sensiiviy wih respec o he sample below. 5: Resuls We sar by spliing our 20 porfolios ino wo ses of 0 porfolios each (simply by [ + icker symbol) o esimae discoun raes (i.e., esimaes of δ / E ( m )]). We provide imeseries plos of he esimaed delas from he firs 0 porfolios along wih a plus/minus wo sandard error confidence inerval in Figure. We also include he poin esimaes of dela from he second 0 porfolios, esimaed in precisely he same way bu using daa from he las se of 0 porfolios. There are wo sriking feaures of he graph. Firs, he ime-series variaion in dela is high, consisen wih he spiri of Hansen and Jagannahan (99). As shown in Table, he log likelihood of our equaion esimaed on he firs 0 S&P porfolios is 60. In April-May 999, he US 3-monh Treasury bill rae averaged 4.4%, a daily reurn of.0007 (wih lile ime- 0

13 series variaion). The log likelihood for he defaul equaion esimaed wih.0007 subsiued in place of { δ } is only 059. Under he null hypohesis of delas ha are consan and equal o he T-bill ineres rae, 2*(60-059) is disribued as a chi-square wih 39 degrees of freedom, grossly inconsisen wih he null a any reasonable confidence level. (When we use all 20 porfolios, he analogue is 2*( ), again grossly inconsisen wih he null.) Tha is, he hypohesis ha he MRS is equal o he shor -bill rae is wildly inconsisen wih he daa. The MRS seems much more volaile han shor-erm ineres raes. Second, he esimaes of dela from he wo differen ses of porfolios are similar; he delas from he second se of porfolios almos always lie wihin he +/- 2 sandard error confidence inerval of he firs esimae of dela. Tha is, he wo differen ses of dela are usually saisically indisinguishable on any given day, consisen wih he null hypohesis of inegraion wihin he S&P. Wha abou he wo ses of dela examined oinly? The ocular evidence leads one o believe ha he wo ses of delas are broadly equal. The saisical analogue is conained in he cells a he op lef of Table. The log-likelihood of (4) esimaed from he firs se of 0 porfolios is 60; ha from he second se of 0 porfolios is 66. When (4) is esimaed from all 20 porfolios simulaneously so ha only a single se of { δ } is exraced, he log-likelihood is Under he hypohesis of inegraion (i.e., he same { δ } for boh ses of asses) and normally disribued errors, minus wice he difference in he log-likelihoods is disribued as a chi-square wih 39 degrees of freedom; a likelihood raio (LR) es. The es saisic is 36, consisen wih he hypohesis of inegraion and normal residuals a he.6 confidence level. I is well known ha asse prices are no in fac normally disribued; Campbell, Lo, and MacKinlay (997). Raher, here is srong evidence of fa ails or lepokurosis, and his cerainly

14 characerizes our daa. 4 Accordingly, we use a boosrap procedure o esimae he probabiliy values for our likelihood raio ess. 5 The boosrapped p-value for he es of inegraion is even more consisen wih he null hypohesis of inegraion a he.90 level. To check for sample sensiiviy, we also consider five oher sample periods: July-Augus 999, Ocober-November 999, and he same hree wo-monh samples for he bear marke of Resuls from hese oher sample periods are also included in Table and are also consisen wih he hypohesis of inegraion inside he S&P 500 a sandard confidence levels. Wha abou he NASDAQ marke for smaller socks? We follow exacly he same procedures, bu using daa drawn from he NASDAQ marke. We group (again on he basis of icker symbol) daa from 00 NASDAQ firms ino 20 porfolios of 0 firms each, and es for equaliy of delas (beween he wo differen ses of delas, esimaed from he wo ses of en NASDAQ porfolios) using likelihood raio ess wih boosrapped p-values. The resuls are presened in Table 2, and are generally consisen wih he null hypohesis of inegraion inside he NASDAQ. However, one of our samples (April-May 2002) is inconsisen wih inegraion a he.03 confidence level (his is marked wih an aserisk), while inegraion is overwhelmingly reeced for Oc-Nov 999 (wo aserisks), shorly before he collapse of he NASDAQ. We hink of hese as inuiive, reasonable resuls, possibly consisen wih he exisence of irraional exuberance manifes in he NASDAQ us around he heigh of he inerne bubble. Sill, he mos ineresing quesion o us is: Is he marke for large (S&P 500) socks inegraed wih he NASDAQ? I is easy o ask he quesion by comparing { δ } esimaes when (4) is esimaed wih: a) he weny S&P porfolios; b) he weny NASDAQ porfolios; and c) all fory porfolios pooled ogeher (which is mos efficien if he wo markes are inegraed). Our LR ess (wih boosrapped p-values) for his hypohesis are presened in Table 3 and are grossly 2

15 inconsisen wih he null hypohesis of marke inegraion. The LR es saisics are an order of magniude bigger han hose of Tables and 2. Tha is, while he S&P always seems inegraed and he NASDAQ is generally inegraed, he S&P is never inegraed wih he NASDAQ. This resul is similar o ha of Chen and Knez (995). Time-series plos of { δ } esimaed from all (weny) S&P and NASDAQ porfolios are provided in Figure 2 for all six sample periods, along wih confidence inervals. Figure 3 provides scaerplos of S&P delas agains NASDAQ delas. All hese graphs indicae ha here is no single obvious characerisic difference beween he S&P and NASDAQ delas. 6: Sensiiviy Analysis Thus far we have relied on he Fama-French model of asse covariances. Tha is, he covariance of each asse s reurn wih he MRS is characerized by four parameers: an inercep ( β ) and facor loadings on he marke reurn minus he T-bill rae ( β ), he difference beween 0 small and large sock reurns ( β ), and he difference beween reurns of socks wih high and 2 low book o marke raios ( β ). Are our resuls sensiive o he number of facors used? I urns ou ha he answer is negaive. 3 In Table 4 we provide es saisics (and boosrapped p-values) o examine ess of inegraion wihin he S&P and NASDAQ and beween he wo markes, bu using only he reurn on he marke insead of he hree Fama-French facors (while reaining he porfolio inerceps as well). The es saisics and conclusions are essenially unchanged. Table 5 goes even furher and drops he marke facor from our covariance model, leaving only porfolios-specific inerceps ( β ) bu no ime-varying facors. Again, he resuls 0 3

16 are essenially unchanged. This robusness is encouraging since i demonsraes he insensiiviy of our mehodology o reasonable perurbaions in he exac facor model employed. 7: Summary and Conclusions This paper developed a simple mehod o es for asse inegraion, and hen applied i wihin and beween American equiy markes. I relies on esimaing and comparing he expeced risk-less reurns implied by differen ses of asses. Our echnique has a number of advanages over hose in he lieraure and relies on us wo relaively weak assumpions: ) raional expecaions in financial markes; and 2) covariances beween discoun raes and reurns ha can be modeled wih a small number of facors for a shor period of ime. We illusraed his echnique wih an applicaion o socks drawn from he S&P 500 and he NASDAQ, and found ha a) he ime-series variaion in he Marginal Rae of Subsiuion is high; b) he S&P always seems o be inegraed; c) he NASDAQ is usually (bu no always) inegraed; and d) he S&P and NASDAQ do no seem close o being inegraed. Our resuls seem reasonably insensiive o he exac sample and condiioning model used. If our finding of inegraion wihin bu no across sock markes holds up o furher scruiny, he ineresing quesion is no wheher financial markes wih few apparen fricions are poorly inegraed bu why? We leave ha imporan quesion for fuure research. 4

17 References Adam, Klaus, Tullio Jappelli, Annamaria Menichini, Mario Padula, and Marco Pagano (2002) Analyse, Compare, and Apply Alernaive Indicaors and Monioring Mehodologies o Measure he Evoluion of Capial Marke Inegraion in he European Union Universiy of Salerno manuscrip. Campbell, John Y., Andrew W. Lo, and A. Craig MacKinlay (997) The Economerics of Financial Markes (Princeon: Universiy Press). Chabo, Benamin (2000) A Single Marke? The Sock Exchanges of he Unied Saes and London: Universiy of Michigan working paper. Chen, Zhiwu and Peer J. Knez (995) Measuremen of Marke Inegraion and Arbirage Review of Financial Sudies 8-2, Cochrane, John H. (200) Asse Pricing, Princeon Universiy Press. Fama, Eugene and Kenneh R. French (996) Mulifacor Explanaions of Asse Pricing Anomalies Journal of Finance 5-, Hansen, Lars Peer and Ravi Jagannahan (99) Implicaions of Securiy Marke Daa for Models of Dynamic Economies Journal of Poliical Economy 99-2, Roll, Richard, and Sephen A. Ross (980) An Empirical Invesigaion of he Arbirage Pricing Theory Journal of Finance 35-5,

18 Log Likelihoods April-May 999 July-Aug. 999 Oc.-Nov. 999 Firs 0 porfolios Second 0 porfolios All 20 porfolios Tes (boosrap P-value) 36 (.90) 54 (.37) 5 (.43) April-May 2002 July-Aug Oc.-Nov Firs 0 porfolios Second 0 porfolios All 20 porfolios Tes (boosrap P-value) 75 (.06) 62 (.24) 37 (.90) Table : Inegraion inside he S&P 500, Fama-French-Facor Model Log Likelihoods April-May 999 July-Aug. 999 Oc.-Nov. 999 Firs 0 porfolios Second 0 porfolios All 20 porfolios Tes (boosrap P-value) 42 (.83) 65 (.20) 53** (.00) April-May 2002 July-Aug Oc.-Nov Firs 0 porfolios Second 0 porfolios All 20 porfolios Tes (boosrap P-value) 82* (.03) 58 (.45) 69 (.08) Table 2: Inegraion inside he NASDAQ, Fama-French -Facor Model Log Likelihoods April-May 999 July-Aug. 999 Oc.-Nov S&P Porfolios NASDAQ Porfolios Combined Tes (boosrap P-value) 559** (.00) 403** (.00) 590** (.00) April-May 2002 July-Aug Oc.-Nov S&P Porfolios NASDAQ Porfolios Combined Tes (boosrap P-value) 5** (.00) 46** (.00) 40** (.00) Table 3: Inegraion beween S&P 500 and NASDAQ, Fama-French -Facor Model 6

19 Tes Saisics (boosrap P-value) April-May 999 July-Aug. 999 Oc.-Nov. 999 Wihin S&P 36 (.93) 48 (.75) 30 (.99) Wihin NASDAQ 47 (.79) 65 (.27) 27** (.00) S&P vs. NASDAQ 548** (.00) 388** (.00) 594** (.00) April-May 2002 July-Aug Oc.-Nov Wihin S&P 44 (.88) 55 (.6) 35 (.98) Wihin NASDAQ 80 (.09) 58 (.6) 72 (.3) S&P vs. NASDAQ 497** (.00) 432** (.00) 422** (.00) Table 4: Inegraion wihin and beween S&P 500 and NASDAQ, One-Facor Model Tes Saisics (boosrap P-value) April-May 999 July-Aug. 999 Oc.-Nov. 999 Wihin S&P 33 (.97) 46 (.7) 34 (.94) Wihin NASDAQ 42 (.80) 62 (.28) 4** (.00) S&P vs. NASDAQ 534** (.00) 378** (.00) 59** (.00) April-May 2002 July-Aug Oc.-Nov Wihin S&P 46 (.76) 47 (.77) 36 (.95) Wihin NASDAQ 86* (.03) 52 (.63) 68 (.2) S&P vs. NASDAQ 506** (.00) 46** (.00) 49** (.00) Table 5: Inegraion wihin and beween S&P 500 and NASDAQ, Only Asse Inerceps 7

20 Delas from 2 ses of 0 S&P Porfolios, April May Figure : Esimaes of Marginal Rae of Subsiuion from wo ses of (0) S&P porfolios 8

21 Delas from Differen Markes and Samples April-May 999: S&P Oc-Nov 999: S&P July-Aug 2002: S&P April-May 999: NASDAQ Oc-Nov 999: NASDAQ July-Aug 2002: NASDAQ July-Aug 999: S&P April-May 2002: S&P Oc-Nov 2002: S&P July-Aug 999: NASDAQ April-May 2002: NASDAQ Oc-Nov 2002: NASDAQ Figure 2: Esimaes of Marginal Rae of Subsiuion from ses of (20) porfolios 9

22 Scaerplos of S&P agains NASDAQ Delas April-May July-Aug Oc-Nov naall naall naall April-May July-Aug Oc-Nov naall naall naall Figure 3: Esimaes of Marginal Rae of Subsiuion from ses of (20) porfolios 20

23 Endnoes hp://mba.uck.darmouh.edu/pages/faculy/ken.french/daa_library.hml 2 We choose hese monhs o avoid January (and is effec), February (a shor monh), and March (a quarer-ending monh), bu es for sample sensiiviy exensively below. 3 For insance, we could use daa a five-minue inervals for a day, making our assumpion of consan assespecific effecs even more plausible; bu he quesion of wheher financial markes are inegraed over hours (no weeks) is less ineresing o us. 4 Jarque-Bera ess are inconsisen wih he null hypohesis for {ε} a all reasonable confidence levels. 5 Our boosrap procedure is as follows. We esimae he delas from (say) all 20 porfolios under he null hypohesis of inegraion. This gives us an esimae of {ε}. We hen draw wih randomly wih replacemen from his vecor o creae an arificial vecor of {ε} which we use o consruc an arificial regressand variable {x}. Using his arificial daa we hen generae a likelihood raio es by esimaing he model from he firs se of 0 porfolios, he second se of 0 porfolios, and he combined se of 20. We hen repea his procedure a large number of imes o generae a disribuion for he LR es saisic. 2