Time-Series and Cross-Sectional ExcessComovement in Stock Indexes

Jarl Kallberg and Paolo Pasquariello1

March 7, 2004

1Associate Professor of Finance at the Stern School of Business and AssistantProfessor of Finance at the University of Michigan Business School, respectively.Please address comments to the authors at the University of Michigan BusinessSchool, 701 Tappan Street, Suite 5210, Ann Arbor, MI 48109-1234, or via email atjkallber@stern.nyu.edu or ppasquar@bus.umich.edu. We would like to thank theF. Conrad Fisher Fund at the University of Michigan Business School for financialsupport. We are grateful to Antell Jan, Joseph Chen, Paulo Gama, Anna Pavlova,Roberto Rigobon, Robert Whitelaw, and participants in seminars at the Universityof Michigan, the 2003 EFMA Meetings, and the 2004 AFA Meetings for helpfulcomments. The usual disclaimer applies.

Abstract

This paper is an empirical investigation of the excess comovement of industryindexes in the U.S. stock market between January 8, 1973 and December 31,2001. We define excess comovement as the correlation between two assetsbeyond what can be explained by fundamental factors. In our analysis, thefundamental factors are sector groupings and the three Fama-French factors.We then estimate excess comovement as the mean absolute unconditionalcorrelation of residuals of univariate (OLS) or joint (FGLS) regressions ofthese fundamentals on industry returns. We show that excess comovement issurprisingly high (a lower bound of 0.138 and an upper bound of 0.263) andrepresents between 32% and 60% of the average raw absolute correlation. Ex-cess comovement is also uniformly significant across industries and over timeand symmetric, i.e., not significantly different in rising or falling markets. Weexplain approximately 25% of this excess correlation by its positive relationto proxies for information asymmetry, information heterogeneity, and U.S.monetary and real conditions, and its negative relation to the level of theshort-term interest rate. This evidence is consistent with the implications ofportfolio rebalancing and product market theories of financial contagion, butoffers little or no support for the correlated liquidity shock channel.

JEL classification: D82; G14; G15

Keywords: Contagion; Excess Comovement; Correlation

1 Introduction

The study of the correlations between different classes of securities is crucialto asset pricing. The recent economic literature has examined the issue ofwhether or not the observed degree of comovement is “excessive.” Whilethe roots of this debate trace back to the early research in portfolio theory,precise notions of excess comovement are more recent.This debate has been especially relevant in the extensive literature deal-

ing with financial crises and the propagation of shocks within and acrossmarkets.1 Many of these papers use observed increases in correlation as ameasure of financial contagion, and analyze whether those increases are dueto the irrational propagation of shocks or merely to the surge in the varianceof a common source of risk driving returns in the affected markets. Thisapproach, however, does not easily reconcile with the definition of financialcontagion as a pervasive feature of capital markets during both tranquil anduncertain times. Indeed, the prevailing view among researchers asserts thatcomovement among asset prices is excessive just when beyond the degreejustified by economic fundamentals, i.e., by factors affecting assets’ payoffsat liquidation.In response to the evidence stemming from this growing body of empiri-

cal studies, the theoretical analysis of financial contagion (which we surveyin the next section) has also gained momentum. Excess comovement hasalternatively been interpreted as due to pure information transmission (Kingand Wadhwani, 1990), wealth effects (Kyle and Xiong, 2001), financial con-straints (Calvo, 1999; Yuan, 2000), sunspot equilibria (Masson, 1998), thefragility of financial markets (Allen and Gale, 2000), the rebalancing activ-ity of risk-averse agents (Fleming et al., 1998; Kodres and Pritsker, 2002),strategic trading by heterogeneous insiders (Pasquariello, 2002), relative realoutput shocks (Pavlova and Rigobon, 2003), or investors’ trading patterns(Barberis et al., 2002). Nevertheless, in spite of this abundance of expla-nations, no “horse race” among these competing (albeit seldom mutuallyexclusive) theories has yet emerged to ascertain their relevance in the data.In this paper we empirically address both these issues by analyzing the

1A partial list of recent contributions includes Shiller (1989), King and Wadhwani(1990), Pindyck and Rotemberg (1990, 1993), King et al. (1994), Karolyi and Stulz (1996),Baig and Goldfajn (1999), Bekaert and Harvey (2000), Connolly and Wang (2000), Forbesand Rigobon (2001, 2002), Barberis et al. (2002), Boyer et al. (2002), Corsetti et al.(2002), and Kallberg et al. (2002).

1

time series of industry index returns in the U.S. stock market over the period1973 to 2001. Rather than employing current and past values of macroeco-nomic variables (as is done, for example, in Pindyck and Rotemberg, 1993and Bekaert et al., 2002), we utilize the factor portfolios suggested by Famaand French (1993) and a set of sector groupings to account for the correlationbetween these indexes due to “common factors,” i.e., to existing interdepen-dence. We then use the term contagion to refer to covariation above thislevel. More specifically, we define excess correlation as the correlation of theestimated residuals from univariate (OLS) and joint (FGLS) regressions ofindustry returns on these common factors. While Pindyck and Rotemberg(1993) only analyze industries ex ante characterized as unrelated, we analyzeall major industry groups for which data are available over the selected sam-ple period (82 in total). The industry correlations are estimated on a rollingannual basis to mitigate problems with the non-stationarity of our data overthis long time interval. Finally, we explore the relation between the level ofexcess correlation and market (and sector) returns and volatility, the disper-sion of analysts’ earnings forecasts, market momentum, market (and sector)trends, fluctuations in interest rates, the state of the U.S. economy, andseasonality effects.Briefly stated, our key findings are as follows. The average excess co-

movement across our entire sample, measured by the absolute correlation ofregression residuals, is very high (a lower bound of 0.138 and an upper boundof 0.263) and represents a significant portion (between 32% and 60%) of theabsolute correlation estimated from the raw return series. Furthermore, thisexcess comovement is highly pervasive: the average excess correlation is sig-nificantly different from zero across all of our industry groups. Our measuresof excess absolute unconditional correlation are also generally symmetric, i.e.,associated with both bull and bear markets, and do not display any signifi-cant relation with levels of market returns or proxies for market momentum.Excess comovement is, however, positively related to market volatility,

information heterogeneity, and U.S. monetary and real output developments,and, when computed using OLS residuals, negatively related to the levelof the short-term interest rate. This evidence offers little or no supportfor liquidity-based theories of financial contagion (Calvo, 1999; Yuan, 2000;Kyle and Xiong, 2001), but is consistent with models interpreting excesscomovement as a symmetric phenomenon due to the portfolio rebalancingactivity of investors (e.g., Kodres and Pritsker, 2002; Pasquariello, 2002) orto product market shocks (Pavlova and Rigobon, 2003).

2

The remainder of the paper is organized in the following way. Section2 presents a brief overview of the relevant economic literature on excess co-movement. Section 3 develops our econometric approach to estimating excesscomovement. Section 4 describes the dataset employed in the analysis. Sec-tion 5 summarizes our estimation results. Section 6 tests for the significanceof many of the proposed explanations for excess comovement mentioned inSection 2. Section 7 contains our conclusions.

2 Literature background

There are two basic strands of literature that are relevant to our paper. Thefirst deals with the excess comovement hypothesis (ECH), which is the notionthat there is comovement in asset prices beyond what could be explainedby common factors such as inflation, aggregate demand, foreign exchange,or interest rates. This excess comovement is often attributed to herdingbehavior on the part of market participants.Studying seven “largely unrelated” commodities, Pindyck and Rotem-

berg (1990) demonstrate that there is excess comovement among them evenafter correcting for forecasts of aggregate production and inflation.2 Theysuggest that the excess comovement in commodity prices could arise fromtwo sources. The first is liquidity constraints: Falling prices in one com-modity lead to declines in others because investors who are long in severalcommodities have to liquidate their positions. This argument, known in theliterature as the “correlated liquidity shock channel,” has been employed byCalvo (1999), Yuan (2000), and Kyle and Xiong (2001) to explain events ofinternational financial contagion. The alternative is some form of irrationalherding behavior or sunspot equilibria, as in Masson (1998). This failure toreject the ECH has been somewhat controversial. For example, Deb et al.(1996), noting that commodity prices have time-varying second moments,suggest the adoption of multivariate GARCH specifications of commodityprice changes. Using a slightly different set of commodities and a more re-cent time-frame,3 they find no evidence of excess comovement when using

2Commodities are there defined as fundamentally unrelated when their cross-price elas-ticities of demand and supply are insignificant. The commodities studied by Pindyck andRotemberg (1990) are not substitutes nor complements of each other and are not grownin similar climates.

3Pindyck and Rotemberg (1990) employ data from 1960 to 1985, while the database of

3

multivariate GARCH models, but some support for the ECH when using aunivariate GARCH specification.Closer in spirit to our work is the paper by Pindyck and Rotemberg

(1993), which tests for excess comovement among unrelated industry groups.This study builds on the factor analysis of Meyers (1973). Meyers (1973)showed that there are components in the correlation structure beyond indus-try factors and noted:

“If these components represent some persistent significant sourceof interdependence among stock prices, then they, rather than in-dustry factors, represent a limitation of the validity of the marketmodel.”

Pindyck and Rotemberg (1993) classified two industry groups as unre-lated if they operate in different business lines and if their earnings (nor-malized by nominal GNP to capture macro effects) are uncorrelated. Co-movement thus arises from shocks to current and expected macroeconomicfactors (as later argued by Pavlova and Rigobon, 2003). They use a multiple-indicator, multiple-cause model, to regress industry returns on contempora-neous, lagged, and forecast values of macroeconomic variables, and estimatethe correlations of the resulting residuals.4 As in their previous study ofcommodity prices, Pindyck and Rotemberg (1993) found evidence of excesscorrelation, but attributed it to herding and market segmentation, in partic-ular to patterns in the holdings of stocks by institutions.The other major strand of the debate on excess comovement has analyzed

financial crises and contagion. Forbes and Rigobon (2002) took significantincreases in cross-market correlations as their definition of contagion. Theyshowed that the standard tests of cross-market correlations are biased andinaccurate. Based on this argument, they then claimed that the Asian crisiswas largely a manifestation of natural dependencies among these marketsrather than a contagion story. A contrary argument is developed in Corsettiet al. (2002), who suggested that the results of Forbes and Rigobon arehighly dependent on their specification of idiosyncratic shocks. When theseshocks are accounted for, Corsetti et al. (2002) found significant evidence ofcontagion during the Asian crisis.

Deb et al. (1996) ranges from 1974 to 1992.4Latent variables are employed in these regressions to model future GNP growth and

inflation.

4

Information asymmetries among traders and portfolio rebalancing by in-siders have also been related to financial contagion. King and Wadhwani(1990) were the first to observe that information asymmetry may lead un-informed investors to incorrect revision of their beliefs about the liquidationvalue of many assets following idiosyncratic shocks to a single asset. Consis-tent with the intuition of Fleming et al. (1998), Kodres and Pritsker (2002)proved that cross-market rebalancing motivated by risk aversion may induceexcess comovement in a classic mean-variance competitive setting with infor-mation asymmetry à la Grossman and Stiglitz (1980). A different approachis presented in Pasquariello (2002). This paper developed a Kyle (1985)-typemodel of financial markets in which the heterogeneity of beliefs of imperfectlycompetitive investors is sufficient to induce comovement of “fundamentallyunrelated” assets (i.e., whose payoffs at liquidation are independent), evenwhen those investors are risk neutral and financially unconstrained. Hence,his model suggests that, regardless of risk aversion and liquidity trading, in-creasing diversity in private information can lead to greater likelihood andintensity of financial contagion.A recent paper that presents a further alternative viewpoint is Barberis

et al. (2002). Rather than attribute comovement only to fluctuations in theunderlying fundamental factors, the authors analyzed the degree to which in-vestor trading patterns cause groups of securities to comove. They attributedthis comovement either to the propensity of investors to group assets into dif-fering categories treated more or less as homogeneous groups (similarly tothe argument presented in Pindyck and Rotemberg, 1993), or to the fact thatcertain investors elect to trade only in a subset of all available investments,i.e., into a specific habitat. Using S&P 500 index realignments, they foundsignificant evidence that these trading theories can help explain shifts in betacoefficients, hence stock comovements.A final view of comovement comes from analyzing the dynamics of related

assets trading in different countries, as in Hardouvelis et al. (1994) andBodurtha et al. (1995). These papers presented significant empirical evidencethat closed-end country funds trading in countries different from the countryof the asset holdings are as correlated with the trading country’s equity indexas with the equity index of the traded asset’s country.5

5Consistent results are found by Froot and Dabora (1999) in their analysis of Siamese-twin equities.

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3 Measuring excess covariance

3.1 The basic estimation strategy

An intense debate in the literature centers on the problem of identifyingand measuring international financial contagion. Nonetheless, a consensushas appeared among researchers that not only periods of uncertainty butalso more tranquil times are generally accompanied by excess comovementamong asset prices within and across both developed and emerging financialmarkets. We define such excess comovement as comovement beyond thedegree that is justified by economic fundamentals, i.e., by factors affectingpayoffs at liquidation, and financial contagion as the circumstance of itsoccurrence.In this section we propose a simple measure of the degree of intertemporal

excess comovement among a set of K asset prices. The starting point of theanalysis is the specification of a multi-factor model of each asset’s return withtime-varying sensitivities. Let rkt be a N × 1 vector of returns for asset kover the interval [t−∆, t], with N = ∆+ 1. We assume that, for each assetk = 1, . . . ,K, the return rkt is characterized by the following linear factorstructure:

rkt = ubtβkt + ftγkt + ekt, (1)

where ubt is a N ×Nu matrix of systematic sources of risk affecting specificsubsets, or blocks of assets (i.e., k ∈ b), ft is a N ×Nf vector of systematicshocks affecting all assets, ekt is a N×1 vector of idiosyncratic sources of risk(hence, independent from any other ent), and βkt and γkt are (Nu × 1 andNf × 1, respectively) vectors of factor loadings. In this setting, comovementbetween any pairs of returns rk and rn is deemed excessive if, even aftercontrolling for u and f , those returns are still correlated.Measurement of such degree of comovement, if any, at each point in time

t requires the estimation of Eq. (1), using sample data for the period [0, T ].The first estimation strategy we adopt in this paper is to regress the availabletime series of returns on a chosen set of block-common and systematic factorsby ordinary least squares (OLS) and to use the resulting estimated residualsbeOLSkt , where

beOLSkt = rkt − bαOLSkt − ubtbβOLSkt − ftbγOLSkt , (2)

6

to compute, for each k 6= n, excess correlation coefficients

bρOLSknt =cov

¡beOLSkt ,beOLSnt

¢[var (beOLSkt ) var (beOLSnt )]

12

. (3)

Forbes and Rigobon (2002) have shown that correlation coefficients likethose in Eq. (3) are conditional on asset volatility. Hence, in the presenceof heteroskedasticity, tests for contagion based on such coefficients may bebiased toward rejection of the null hypothesis of excessive comovement amongasset returns. The bias can however be corrected, Forbes and Rigobon (2002)argued, and an unconditional correlation measure can be computed for anypair of return variables under the assumption of no omitted variables orendogeneity. The measure of excess comovement between rkt and rnt that weadopt in this paper is based on their proposed adjustment and is given by

bρOLS∗knt =bρOLSkntn

1 + bδOLSkt

h1− ¡bρOLSknt

¢2io12

, (4)

where the ratio bδOLSkt =var(beOLSkt )var(beOLSkt )LT

−1, when different from zero, corrects theshort-term, conditional correlation bρOLSknt for the relative difference betweenshort-term volatility (var

¡beOLSkt

¢) and long-term volatility (var

¡beOLSkt

¢LT) of

rkt, for each k, n = 1, . . . ,K and k 6= n. Because we do not make any exante conjecture on the direction of propagation of shocks from one asset toanother, we alternatively assume that the source of these shocks is asset k(in bρOLS∗knt ) or asset n (bρOLS∗nkt ). This implies that bρOLS∗knt may be different frombρOLS∗nkt .We then compute arithmetic means of pairwise adjusted correlation co-

efficients for each asset k, along the lines of King et al. (1994). Much of theliterature on financial contagion explores the circumstances in which correla-tion among asset prices becomes more positive (or less negative) during crisisperiods. However, as is clear from Eq. (1), there is no reason to restrict theconcept of excess comovement to a specific directional move in the correlationcoefficients. In other words, both bρOLS∗knt 6= 0 and bρOLS∗nkt 6= 0 represent evi-dence of comovement between assets k and n beyond what is implied by theirfundamentals, regardless of their sign. Consequently, to prevent such coeffi-cients, if of different sign, from cancelling each other out in the aggregation,

7

we focus on the following means of excess absolute comovement measures:

bρOLS∗kt =1

K − 1XK

n=1n6=k

¯̄bρOLS∗knt

¯̄, (5)

for any k = 1, . . . ,K. Eq. (5) implies that there is excess comovement forasset k at time t if bρOLS∗kt is different from zero. We also compute a market-wide measure of financial contagion as a mean of means of excess correlationcoefficients across all the traded assets, i.e.,

bρOLS∗t =1

K

XK

k=1bρOLS∗kt . (6)

Finally, we want to evaluate the evolution of such measures over timewhile accounting for the dynamics of the fundamental interdependence amongasset returns and of their variances. Ignoring time-varying factor loadingsand nonstationary variances in Eq. (1) may in fact bias the inference onnon-fundamental comovement from Eqs. (5) and (6). Parametric ARCH andstochastic volatility models, as well as their generalizations to multivariatesettings, are frequently employed to describe such dynamics.6 Nonetheless,these models are in general very difficult to estimate and do not offer a clearadvantage over simpler, nonparametric approaches, especially when used tomeasure covariance, rather than forecast it. Indeed, Campbell et al. (1997)observe that rolling filters, like the rolling standard deviation measure usedby Officer (1973), usually provide very accurate descriptions of historicalvariation (or comovement), in particular (as shown in Nelson, 1992) whenvolatility (or covariance) changes are not too gradual.In light of these considerations, in this paper we treat the covariance

matrix of return residuals as observable and construct time series of rollingrealized excess correlations for each asset k. To that purpose, we estimatebeOLSkt , bδOLSkt , and bρOLS∗knt over rolling short-term and long-term intervals of thedata of fixed length ∆ and g∆ (with g > 1), respectively, according to thefollowing scheme:

6See Campbell et al. (1997) for a review of the literature on parameric models ofchanging volatility.

8

beOLSkt , var¡beOLSkt

¢z }| {

| | |t− g∆+ 1 t−∆+ 1 t

| {z }¡beOLSkt

¢LT, var

¡beOLSkt

¢LT

(7)

In other terms, at each point in time t and for each asset k, the modelof Eq. (1) is estimated twice, once over the short-term interval [t−∆+ 1, t]to compute bρOLSknt as in Eq. (3) for each n 6= k, and once over the long-terminterval [t− g∆+ 1, t] to compute the adjustment ratio bδOLSkt and, eventu-ally, bρOLS∗knt as in Eq. (4) for each n 6= k. This rolling procedure generatestime series of aggregate excess comovement measures

©bρOLS∗t

ªTt=g∆

, whichwe use in our analysis, without resorting to parametric specifications for theintertemporal dynamics of the covariance matrix of asset returns. OLS esti-mation of the model of Eq. (1) for each asset separately may however leadto underestimating the degree of excess covariance across those assets. Toovercome this difficulty, a more involved model may be needed. This is thetopic of the next subsection.

3.2 Latent comovement

In the estimation approach just described, return residuals ekt are estimatedseparately for each of the available assets via OLS. Therefore, this approachoperates under the implicit null hypothesis that the returns rkt, after control-ling for block-common and systematic sources of risk, are indeed independent.This strategy may however lead to underestimating the extent of excess co-movement among those ekt. In this subsection, we propose an alternativeestimation strategy that instead uses as its starting point the hypothesisthat return residuals do comove beyond what is justified by the economicfundamentals ub and f , rather than ignoring that possibility.The basic intuition of this strategy is to estimate the residuals for each

asset k jointly, rather than separately. We start by specifying the following

9

stacked version of the model of Eq. (1) over the interval [t−∆+ 1, t]:r1tr2t...rKt

=

F1t O · · · OO F2t · · · O

...O O · · · FKt

B1tB2t...BKt

+e1te2t...eKt

(8)

= FtBt + et, (9)

where Fkt = [ubt, ft] is a N ×M matrix of block-common and systematicfactors affecting rkt (with M = Nu +Nf), Bkt = [β

0kt, γ

0kt]0 is a M × 1 vector

of factor loadings, and O is a zero matrix. We further assume that theidiosyncratic shocks ekt are uncorrelated across assets, i.e., that E [ekte0ns] =σkntI (where I is a N × N identity matrix) if t = s and E [ekte0ns] = Ootherwise. This implies that

E [ete0t] = Vt =

σ11t σ12t · · · σ1Ktσ21t σ22t · · · σ2Kt

...σK1t σK2t · · · σKKt

⊗ I (10)

= Σt ⊗ I. (11)

The above disturbance formulation therefore allows for the parameterscontrolling for the subsample covariance across assets to vary over time. Ef-ficient estimation of the seemingly unrelated regressions model of Eq. (9)is achieved via the feasible generalized least squares (FGLS) procedure de-scribed, for example, in Greene (1997, pp. 676-688). Because the matrixΣt is unknown, OLS residuals can be used to estimate each of its elementsconsistently as:

bσOLSknt =

¡beOLSkt

¢0 beOLSnt

N. (12)

The FGLS estimator of Bt is then given by

bBFGLSt =

·F 0t³bV OLSt

´−1Ft

¸−1F 0t³bV OLSt

´−1rt (13)

=

½F 0t

·³bΣOLSt

´−1⊗ I¸Ft

¾−1F 0t

·³bΣOLSt

´−1⊗ I¸rt, (14)

10

where rt = [r1t, r2,t, . . . , rKt]0. The resulting FGLS residuals beFGLSt = rt −

Ft bBFGLSt are then used to produce an efficient estimate of each element ofthe matrix Σt,

bσFGLSknt =

¡beFGLSkt

¢0 beFGLSnt

N. (15)

Finally, the matrix bΣFGLSt is employed to estimate our measure of market-wide excess comovement

bρFGLS∗t =1

K (K − 1)XK

k=1

XK

n=1n6=k

¡¯̄bρOLS∗knt

¯̄¢, (16)

where

bρFGLS∗knt =bσFGLSknt¡bσFGLSkkt bσFGLSnnt

¢ 12

½1 + bδFGLSkt

·1− (bσFGLSknt )

2

bσFGLSkkt bσFGLSnnt

¸¾12

, (17)

bδFGLSkt = bσFGLSkkt

(bσFGLSkkt )LT

− 1, and ¡bσFGLSkkt

¢LTis obtained from the estimation of

Σt over the interval [t− g∆+ 1, t]. Estimation of bρFGLS∗knt is repeated for allk = 1, . . . ,K and for each t = g∆, . . . , T , as in the rolling approach ofEq. (7), to generate alternative time series of excess comovement measures©bρFGLS∗t

ªTt=g∆

.

4 Data

The basic dataset we use in this paper consists of weekly, continuously com-pounded, dividend-adjusted returns for k = 1, . . . , 96 value-weighted U.S.industry indexes (rkt), over the time period January 8, 1973 to December 31,2001, from Datastream. Datastream classifies approximately 1, 000 represen-tative companies whose common stocks are traded on the AMEX, NASDAQ,or NYSE by industry based uniquely on their primary activity. Equities withsimilar industrial classification are then grouped into i = 1, . . . , 10 sectors(rit). Finally, Datastream also computes returns for s = 1, 2, 3 macro-sectorindexes rst (Resources, Non Financials excluding Resources, and Financials)and for a broad market index of all sectors (rmt). Industry and sector clas-sifications are performed according to definitions provided by the FinancialTimes Stock Exchange (FTSE) Actuaries.

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The choice of the weekly frequency for our database arises from a balancebetween the different properties of accessible time series. The use of dailyequity data in fact raises concerns related to the possibility of biases inducedby infrequent and/or nonsynchronous trading, or short-term noise on theresulting statistical inference. Vice versa, monthly observations may lead usto ignore the relatively more rapid cycles of propagation of shocks acrossfundamentally unrelated assets that appear to characterize the U.S. stockmarket.The companies entering each index are selected on the basis of their mar-

ket capitalization and data availability considerations. Factors like liquidityor cross-holdings are therefore ignored. Datastream also excludes from thoseindexes such securities as unit trusts, mutual and investment funds, and for-eign listings (including ADRs). Index constituents are currently reviewed onan annual basis (in January of each year) to account for declines in marketvalue, takeovers, delistings, changes in the primary business activity, etc.7

We further eliminate from our dataset 14 industry indexes for which pricedata were available only for subsets of the sample period. Our final datasetis then made up of 82 industry, 10 sector, 3 macro-sector, and one marketreturn time series of 1, 512 observations each, which we use in the analysisthat follows.Table 1 presents summary statistics for rmt, for each rst, and for each rit.

Not surprisingly, given the growth experienced by the U.S. stock market inthe past three decades, most mean weekly returns are positive and significant.The variables are also characterized by little or no skewness and strong andsignificant leptokurtosis. Index aggregation seems to induce negative returnautocorrelation; indeed, the estimated first order autocorrelation coefficientsbρ1 are not significantly different from zero for many of the sector returns,and the corresponding value for the Ljung-Box portmanteau test for up tothe fifth-order serial correlation, LB (5), cannot reject the null hypothesisthat those rit are white noise. Similar conclusions can be drawn from theautocorrelation analysis of each of the 82 industry return time series rkt (notreported here). Both bρ1 and LB (5) are instead statistically significant forthe market and for all but the Financials macro-sector returns.

7Prior to May 1995, indices were instead reviewed every three months.

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5 Empirical analysis

5.1 Factor selection

Estimation of Eq. (1) and the seemingly unrelated regressions model of Eq.(9) requires the selection of block-common and systematic factors for industryreturns. This is a crucial step in our analysis. Indeed, the test for excesscomovement is unavoidably also a test of the validity of the specificationwe use to control for fundamental comovement, i.e., to compute bρOLS∗knt andbρFGLS∗knt at each point in time t. The challenge is therefore to design a modelthat is both comprehensive in its scope and general in its structure.We start from the variables entering the matrix ft in Eq. (1). Fama and

French (1992, 1993) find that three systematic factors explain a significantportion of the cross-sectional difference in average stock returns. These fac-tors are market risk, book-to-market risk, and small-firm risk. We use thesebenchmark factors in our regressions. We employ the all-inclusive time seriesof returns for the market designed by Datastream, rmt, to proxy for mar-ket risk. Fama and French (1993) create mimicking portfolios whose returnsproxy for book-to-market risk and small-firm risk. A time series for the for-mer is generated by subtracting the average return of two growth portfolios(consisting of firms with low book-to-market ratios) from the average returnof two value portfolios (consisting of firms with high book-to-market ratios).A time series for the latter is generated by subtracting the average returnof three “big” portfolios (consisting of firms with high market capitaliza-tion) from the average return of three “small” portfolios (consisting of firmswith low market capitalization). Fama and French (1995) show that bothvariables are related to economic fundamentals controlling for common riskfactors in returns. More specifically, the book-to-market ratio is negativelyrelated with current earnings and positively related to their persistence. Sizeappears instead to be negatively related to short and long-term profitability.In the analysis that follows, we use the time series for book-to-market bench-mark returns (rBMt) and small-firm benchmark returns (rSFt) available onFrench’s research website.8

Sector or macro-sector-specific factors may also explain some of the cor-relation between our indexes. This correlation may in fact be due not only tomarket-level, but also to sector-level sources of risk in cash flow innovations.9

8Http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html.9Indeed, Corsetti et al. (2002) observe that ignoring fluctuations in asset-specific factors

13

In addition, stocks (and industry indexes) may be traded together when theyare perceived to belong to the same category or subset, as maintained, for ex-ample, by Barberis et al. (2002). This argument is especially relevant whenwe consider that the performance of many mutual fund managers is evaluatedby comparison with broad sector indexes. It is not surprising therefore thatsuch benchmarks explain at least part of their portfolio allocation decisionsacross assets. Hence, the inclusion of an industry index in a specific sectorgroup may affect the comovement of that index with the rest of the market.We account for these effects by specifying a set of block-common factors foreach return series rkt. More specifically, for each of the 82 available indexes,we identify two benchmark sector and macro-sector-portfolios, according tothe Datastream industrial classification levels, and use their correspondingweighted average returns, rit and rst, respectively, in each of the matrices ub.For example, returns for the broad category portfolios General Industrials(rit) and Non-Financials (rst) are used for the Aerospace industry index k,since k ∈ i and k ∈ s.The final specification of Eq. (1), which we use to control for return

covariance driven by fundamentals, is therefore given by

rkt = αkt + βkitrit + βkstrst + γkmtrmt + γkBMtrBMt + γkSFtrSFt + ekt, (18)

for each k = 1, . . . ,K. Testing for excess comovement and explaining theintertemporal and cross-sectional features of the resulting measures describedin Section 3,

©bρOLS∗t

ªTt=g∆

and©bρFGLS∗t

ªTt=g∆

, and other such aggregates iswhat we do next.

5.2 OLS and FGLS comovement

We start by estimating the model of Eq. (18) over the sample interval Jan-uary 8, 1973 to December 31, 2001 for all indexes in our database using boththe OLS and FGLS procedures. We then use the corresponding estimatedresiduals to compute the unconditional measures of excess comovement de-scribed in Section 3.1 across rolling intervals of about one year (∆ = 50).The correction suggested by Forbes and Rigobon (2002) (reported in Eq.(4)) is implemented by estimating long-term variances for the corresponding

may make tests for contagion biased toward rejection.

14

variables over a two-year interval (g = 2).10 Therefore, the initial t = g∆ cor-responds to December 9, 1974. We plot the resulting time series

©bρOLS∗t

ªTt=g∆

and©bρFGLS∗t

ªTt=g∆

in Figure 1a, together with a benchmark measure of ab-

solute correlation,©bρBASE∗t

ªTt=g∆

, computed using the raw return series rkt,instead of OLS (beOLSkt ) or FGLS (beFGLSkt ) residuals, in Eqs. (3) to (7). Table2 reports summary statistics for bρOLS∗t , bρFGLS∗t , and bρBASE∗t .As previously mentioned, underlying the OLS procedure is the null hy-

pothesis that index returns rkt, after controlling for sector and systematicsources of risk, are independent, since return residuals are estimated sepa-rately (via OLS) for each k. Vice versa, underlying the FGLS procedure isthe null hypothesis that index returns rkt do comove beyond the degree jus-tified by sector and systematic factors, since return residuals are estimatedjointly (via FGLS) for all k. Because the OLS strategy ignores the possibilitythat return disturbances ekt are correlated across securities, the time seriesbρOLS∗t may underestimate the intensity of comovement beyond fundamen-tals. The FGLS strategy obviates this problem. This approach, however,may also capture latent comovement induced by missing common fundamen-tal factors, if the model of Eq. (18) is misspecified. The resulting measurebρFGLS∗t could then overestimate the degree of financial contagion among assetreturns. Therefore, in the analysis that follows, we interpret OLS correlationsbρOLS∗t as a lower bound, and FGLS correlations bρFGLS∗t as an upper boundon the true extent of excess comovement.Our evidence suggests that there is comovement beyond what can be ex-

plained by the fundamental model of Eq. (18) in the U.S. stock market.Indeed, the lower and upper bounds on excess absolute correlation averageabout 0.138 and 0.263, respectively, and are both statistically different fromzero over the entire sample and cross-sectionally at each point in time t.These measures are economically significant as well, for they constitute be-tween 32% and 60% of the benchmark correlation bρBASE∗t . That bρOLS∗t is not

10The adjustment for heteroskedasticity in Eq. (4) may be incorrect in the presence ofomitted variables or endogeneity between assets. Unfortunately, no procedure is currentlyavailable to control for their impact on ρ∗knt. Nonetheless, according to Forbes and Rigobon(2002), the proposed estimates for unconditional correlation are fairly accurate when assetsare closely connected, which is the case in our sample (e.g., the average bρBASE∗t = 0.436 inTable 2). Moreover, bρ∗knt systematically underestimates the true unconditional correlationwhen there is feedback from asset n to asset k, biasing the inference toward rejection,rather than acceptance, of the null hypothesis of excess comovement.

15

simply a rescaling of its benchmark is proven by bρBASE∗t and bρOLS∗t beingalmost uncorrelated: Their correlation is in fact 0.12 in Table 2. The upperbound bρFGLS∗t instead mimics more closely the behavior of bρBASE∗t , as is clearfrom both Figure 1a and their correlation of 0.51 (in Table 2).Excess comovement also fluctuates over time, especially bρFGLS∗t , which

ranges between a minimum of 0.122 and a maximum of 0.412 along rela-tively long cycles of peaks and troughs. However, the estimated lower boundon excess absolute correlation, bρOLS∗t , tends to follow the swings in the FGLSbound with an often sizeable delay: Their contemporaneous correlation isactually only 0.31. Both measures grow and decline after the first oil crisisof 1973 and 1974, but remain relatively stable for almost ten years after-wards; bρOLS∗t and bρFGLS∗t again increase during the spring and summer of1987, well before the Black Monday of October 19, 1987, and subsequentlydecline, although not simultaneously: Indeed, bρOLS∗t first reaches a high of0.165 in early April 1989. Another cycle of excess comovement is centeredduring the Internet bubble, between 1998 and 1999. Upper and lower abso-lute correlations steadily decline in the first half of 2000, but then bρFGLS∗t ,experiencing a “decoupling” from bρBASE∗t , increases in the second half of theyear, peaks following the events of September 11, 2001 (as does the lowerbound measure), but eventually drops to near-historical lows by the end ofthe sample period.Similar conclusions are reached when we examine arithmetic averages

of both measures bρOLS∗kt and bρFGLS∗kt (and their corresponding benchmarksbρBASE∗kt ) across each of the sector aggregations listed in Table 1. We displaythese measures in Figures 2a to 2j and report summary statistics in the lowerpanels of Table 2. There is little cross-sectional variability in our estimatesfor the lower bound on excess absolute correlation. Greater sector variationinstead characterizes the upper bound estimates. The sector with the highestmean excess correlation is Cyclical Services (from Retailers Soft Goods toShipping & Ports), with an average bρFGLS∗it of 0.289. Utilities (Electricity,Gas Distribution, and Water) is the index characterized by the lowest excesscomovement (0.178). Excess absolute correlation bρFGLS∗it was highest between1987 and 1988 for each sector grouping, while most lower bounds on sector-wide excess comovement peak or increase substantially only by the end of thesample, with the exception of Utilities and the Information Technology index(Computer Hardware and Service, Semiconductors, and Telecom Equipment)indexes. Those two sectors, together with Non-Cyclical Services (Food andDrug Retailers, Telecom Fixed Line, and Telecom Wireless), also display the

16

widest intertemporal fluctuations for both bρOLS∗kt and bρFGLS∗kt .There is much greater cross-sectional variation in the ratios between eitherbρOLS∗i or bρFGLS∗i and bρBASE∗i , which we interpret as a proxy for the percentage

of raw absolute correlation unexplained by the model of Eq. (18). Indeed,lower bound ratios range between 29% for the General Industrials index (fromAerospace to Engineering General) and 45% for the Resources aggregation(from Gold Mining to Oil Integrated); FGLS excess comovement explainsfrom 41% (in the case of Non-Cyclical Services) to almost 72% (in the caseof Cyclical Services) of the indexes’ benchmark absolute correlation. Non-fundamental comovement appears to be especially relevant from the Fall of1998 onward, as suggested by Figure 1b. This trend is led by Resources, Non-Cyclical Services, and Utilities, whose measures bρOLS∗it and bρFGLS∗it beganto significantly depart from their corresponding bρBASE∗it in the late 1990s.Nevertheless, the ratios for all sectors experienced a significant increase in1999, 2000, and 2001.

6 Explaining excess comovement

The evidence presented in the previous section indicates that a significantportion of return comovement among industry indexes in the U.S. stockmarket in the past three decades cannot be explained by sector or system-atic factors. We also found that our measures of excess absolute correlationdisplay significant intertemporal, but little cross-sectional variation, exceptwhen relative to their benchmarks. Perhaps more interestingly, Figure 1afurther shows that absolute raw correlation is lower in the past decade thanin the previous twenty years (a statistically significant difference in meansof almost eleven basis points, i.e., 0.375 versus an average of 0.484 for the1970s and the 1980s), while our lower bound estimate of excess comovementis relatively stable (0.136 versus 0.139) and the upper bound measure dropsby roughly three basis points by the end of the sample (0.245 versus 0.277).Campbell et al. (2001) have argued that this decline in raw correlations maybe due to a general decline in the correlation of stock fundamentals. Figure1b suggests that non-fundamental comovement played a crucial role in af-fecting levels and fluctuations of the correlations among stock indexes duringthe 1990s and the early 2000s, ranging between 39% and 68% of bρBASE∗t .Understanding these phenomena represents therefore one of the priorities forresearch in financial economics.

17

In Section 2 we have briefly overviewed the major explanations proposedby the literature. In the remainder of the paper, we tackle the task of as-certaining the empirical relevance of some of those explanations using ourmeasures of excess absolute correlation bρOLS∗t and bρFGLS∗t . To that purpose,we first develop proxies for information asymmetry and heterogeneity, mo-mentum trading, liquidity shocks, and product market shocks. Then, wediscuss the resulting inference at the aggregate and industry level.

6.1 Information asymmetry and heterogeneity

Information asymmetry has long been suggested as a cause of comovementamong asset prices beyond what would be justified by their fundamentals(King andWadhwani, 1990; Fleming et al., 1998; Kodres and Pritsker, 2002).In this branch of the literature, the inability to distinguish between idiosyn-cratic and systematic shocks to those fundamentals leads prices to movetogether regardless of the underlying structure of the economy. Pasquar-iello (2002) added a new dimension to this issue by arguing that greaterheterogeneity of information endowments among insiders may increase theintensity of excess comovement among returns. The intuition for his resultis that market-makers fail to learn with sufficient accuracy about signalsand trades of insiders sharing information asymmetrically. Incorrect cross-inference about fundamentals and contagion then ensue.We use market (sector) return volatility σmt (or σit) computed over the

interval [t− g∆+ 1, t] as a proxy for both the level of confusion and uncer-tainty existing in a market (or sector) and the degree of disagreement amonginvestors with respect to the value of the traded assets at time t. Indeed,in Pasquariello (2002), greater information heterogeneity makes equilibriumasset prices more volatile as well. The dispersion in analysts’ earnings fore-casts represents another proxy for information heterogeneity (e.g., Diether etal., 2002). We construct this proxy from the I/B/E/S database containingall analysts’ annual earnings forecasts between January 1976 and December2001. For each public firm in the I/B/E/S “US Only” universe, we definediversity of opinion in week t of any given month as the standard deviationof earnings forecasts made during that month for that firm’s fiscal year onescaled by the absolute value of the corresponding mean earnings forecast.11

11Each stocks must therefore be followed by two or more analysts during that month tobe included in the sample.

18

According to Pasquariello (2002), more heterogeneously informed insiderscan more easily disguise their strategic trading activity, increasing equilib-rium excess comovement. Thus, we further multiply the ratio above by thenumber of analysts covering the firm in that month. We finally compute itscross-sectional mean and Winsorize it at two standard deviations to obtaina market-wide estimate of information heterogeneity Ht.

6.2 Momentum trading

Momentum trading (De Bondt and Thaler, 1985, 1987; Jegadeesh and Tit-man, 1993) is another potential explanation for excess comovement. Gen-eralized purchases or sales of assets across sectors or industries, motivatedeither by imitation, injections and redemptions of cash in mutual funds, theactivity of momentum fund managers, or by rational or irrational bubbles,may indeed link prices of assets otherwise sharing very little in common witheach other.We test for the validity of this argument by regressing our measures of

aggregate and sector-wide excess absolute correlation on a proxy for monthlymarket momentum,Mt, provided by French in his research website. The timeseriesMt is constructed by first forming six value-weighted portfolios on sizeand prior returns and then computing the difference between the averagereturn on the two high prior return portfolios and the average return on thetwo low prior return portfolios. Because Mt is available only at a monthlyfrequency, we consider two additional proxies for momentum. The first issimply the sequence of contemporaneous and lagged returns rmt−l (or rti−l),for l = 0, 1, 2. We also construct momentum dummy variables dmt and dit.These variables are equal to one when the sign of the corresponding returnrmt or rit is the same for the current and each of the previous two weeks,and equal to zero otherwise. In other words, these dummies are positivewhen either the broad stock market index or the corresponding sector indexis experiencing a positive or negative run of length of (at least) three weeks.12

6.3 Liquidity shocks

Financial contagion has long been related to the dynamics of interest rates.In his empirical analysis of comovement between real stock prices in the U.S.12According to this criterion, the market experienced (positive or negative) runs for 322

weeks over our sample.

19

and the U.K., Shiller (1989) found that a relevant portion of excess pricecovariance can be explained by positively correlated, extremely time-varyinginterest rates affecting the values of the traded assets. According to the “cor-related liquidity shock channel,” excess comovement among asset returns isthe result of the trading activity of financially constrained investors. In-deed, Calvo (1999), Yuan (2000), and Kyle and Xiong (2001) have arguedthat short-selling, borrowing, and wealth constraints induce rational specula-tors to liquidate fundamentally unrelated assets in response to idiosyncraticshocks. The main implication of these arguments is that the intensity of fi-nancial contagion within and across markets should be greater when interestrates are high or during a bear market or a correction, i.e., when those finan-cial constraints tend to become more binding for traders and speculators.Alternatively, Fleming et al. (1998), Kodres and Pritsker (2002), and

Pasquariello (2002) emphasized how portfolio rebalancing activity by insid-ers, motivated either by risk considerations or strategic motives, may eventu-ally lead equilibrium asset prices to move together beyond the degree justifiedby underlying systematic factors, but in a symmetric fashion. Along theselines, any variable affecting the costs of rebalancing (transaction fees, bid-askspreads, and interest rates) should have an impact on the intensity of finan-cial contagion, insofar as it affects the intensity of such rebalancing activity.Higher interest rates increase the opportunity cost of trading in risky assets,the cost of borrowing and shorting, so should reduce the scope of portfoliorebalancing for investors and of the resulting excess comovement.In this paper we employ rFt, a weekly time series of three-month Treasury

Bill rates, as a proxy for the time-varying risk-free rate. These rates arecomputed as averages of bid rates quoted by primary dealers in the secondarymarket and reported to the Federal Reserve Bank of New York at the officialclose of the U.S. government securities market every business day, and areavailable on the website of the Federal Reserve Board.13 To test directly forasymmetric contagion, we also devise two additional sets of dummy measuresd+mt and d

−mt (and d

+it and d

−it , for each i = 1, . . . , 10), equal to one if the sign

of rmt (rit) over the current and each of the previous two weeks is positive ornegative, respectively, and equal to zero otherwise.14

13http://www.federalreserve.gov/releases/h15/data/b/tbsm3m.txt.14According to this criterion, there are 100 weeks of down markets and 222 weeks of up

markets in our sample.

20

6.4 Product market shocks

In a recent paper, Pavlova and Rigobon (2003) showed that output (or pro-ductivity) shocks, when resulting in fluctuations of relative output prices,may induce contagion among fundamentally unrelated markets. The intu-ition of their model is that an output shock to one asset alters consumers’ rel-ative demand for other assets, hence the prices of the corresponding financialclaims.15 Albeit symmetric in principle, such contagion should nonethelessbe more intense in states of the world when those shocks are more likely tooccur, i.e., during either recessions or expansions. We define U.S. economicstates using the business cycle dates provided by the National Bureau of Eco-nomic Research (NBER).16 NBER expansions (recessions) begin at the peak(trough) of the cycles and end at the trough (peak). We then construct adummy dRt equal to one if week t falls into a month of recession, and equal tozero otherwise. In our sample, economic contractions have shorter durationthan expansions, and dRt = 1 for just 187 of the 1413 weeks for which bρOLS∗t

and bρFGLS∗t have been estimated.Excess comovement may also be related to the monetary policy of the

Federal Reserve. Many studies report direct and indirect evidence of a linkbetween monetary policy and economic activity.17 Therefore, changes in themonetary stance of a Central Bank can be regarded as signaling (or eveninducing) present and future real output shocks to the economy or to thesectors most sensitive to it. Furthermore, financial constraints are more likelyto affect the portfolio choices of investors during restrictive monetary regimes.As in Jensen et al. (1996), we measure the stringency of U.S. monetarypolicy by using changes in the discount rate. More specifically, we defineexpansionary monetary environments as periods of declining Federal Reservediscount rates and tight monetary environments as those characterized byrising discount rates. Finally, we construct a dummy dTt equal to one ifweek t falls into a month of restrictive monetary policy, and equal to zerootherwise. Monetary contractions are more frequent than recessions over thesample period, since they occur for 569 weeks between December 9, 1974 andDecember 31, 2001.

15Pavlova and Rigobon (2003) use this intuition to explain excess comovement amonginternational financial markets.16Thise dates are reported in the NBER’s website, www.nber.org/cycles.html.17See Jensen et al. (1996) for a review.

21

6.5 Aggregate time-series results

To determine the relevance of these considerations at the aggregate level,we regress our measures of excess absolute correlation within the U.S. stockmarket (bρOLS∗t and bρFGLS∗t ) on each of the above proxies, first separately(models (1) to (8) in Tables 3 and 5) and then on all of them jointly (models(9) and (10) in Tables 3 and 5). Regressions are estimated via OLS, but weevaluate the statistical significance of the coefficients’ estimates with Newey-West standard errors to correct for heteroskedasticity and autocorrelation.18

Information asymmetry among traders is the single most relevant sourceof excess comovement in our sample. Indeed, market return volatility ex-plains a significant portion of variability in excess absolute unconditionalcorrelation, whether measured with OLS or FGLS residuals. The coefficientsfor the variable σmt are positive (hence in the direction suggested by theliterature) and strongly significant, generating an adjusted R2 of about 10%for bρOLS∗t and 24% for bρFGLS∗t . Interestingly, even after accounting for σmt,greater information heterogeneity has a positive, statistically significant im-pact on the upper bound for excess comovement (models (8) to (10) in Table5). Coefficients for Ht in regressions for the lower bounds (models (8) to (10)in Table 3) are instead negative, but have much less economic significance.Overall, these results provide support for the role of the portfolio rebalanc-ing activity of investors and speculators, either motivated by risk or strategicconsiderations, in explaining pervasive intra-market contagion.Consistent with this assertion, excess absolute comovement in our sample

turns out to be a symmetric phenomenon. When dummy variables d+mt andd−mt are included in the regressions of Tables 3 and 5 (in models (3) and (10)),we find that the corresponding coefficients are in fact not statistically differentfrom zero. The lack of asymmetry in our measures of excess comovementis unfavorable to theories of contagion relying on the role of financial andwealth constraints, which are seemingly tighter during market downturns.A further test for liquidity-based theories of financial contagion comes fromthe inclusion of short-term interest rates in the analysis. The correlatedliquidity shock channel implies that excess correlation should be greater whenrF is higher. The resulting evidence is again unconvincing. Estimates fromthese regressions are reported in models (5), (9), and (10) of Tables 3 and 5.

18Our proxy for information heterogeneity, Ht, is available only from January 15, 1976onward. Therefore, all models including Ht (models (8) to (10)) are estimated over thisshorter sample period.

22

The coefficient for rFt on bρOLS∗t is negative and strongly significant, and theadjusted R2 for model (5) is about 7%. Moreover, both sign and statisticalsignificance are preserved even after including all the other proxies. Hence,higher interest rates tend to reduce the lower bound on the degree of excesscomovement in the U.S. stock market. Yet, interest rates are unrelated tobρFGLS∗t , at least at the 10% significance level, and alone can explain lessthan 0.3% of its variability. Finally, the coefficient for rFt is not statisticallysignificant in the aggregate regressions of models (9) and (10). Therefore,liquidity shocks appear to have no explanatory power on our measures ofexcess absolute comovement.Market momentum is equally insignificant, as are contemporaneous and

lagged returns, unless after controlling for positive and negative market runsfor bρFGLS∗t (model (10) in Table 5). In addition, the coefficient for the dummyfor existing market trend (dmt) is never statistically significant in the regres-sions for both bρOLS∗t and bρFGLS∗t (model (3) in Tables 3 and 5). Thus, excessabsolute correlation neither increases nor decreases during prolonged marketswings. The upper bound on non-fundamental comovement is instead sensi-tive to fluctuations in the U.S. economy. In particular, according to models(9) and (10) in Table 5, bρFGLS∗t declines by 0.9 basis points when dRt = 1and increases by about one basis point when dTt = 1. Therefore, even aftercontrolling for fluctuations in interest rates, excess comovement is (almostsymmetrically) greater during expansions and during the monetary contrac-tions generally accompanying them. We interpret these findings as consistentwith the notion that both positive and negative real output shocks inducefinancial contagion among unrelated industries in our sample.

6.6 Turn-of-the-year effect and excess comovement

We also test for the possibility that the turn-of-the-year effect of Banz (1981),Blume and Stambaugh (1983), Keim (1983), and Roll (1983) may contributeto the excess comovement observed among equity indexes. There is strongevidence that stocks with small market capitalization tend to outperformstocks with large market capitalization between the end of December andthe beginning of January, with the excess return progressively decreasing bythe end of that month. Keim (1989) argued that closing prices recorded atthe bid in December and at the ask in January may represent a partial expla-nation of such phenomenon. Yet, its most popular interpretations rely on theactivity of investors attempting to realize a fiscal gain by selling stocks that

23

have already declined during the year, before buying them back in January(Roll, 1983) or parking the proceeds of such sales that were not immediatelyreinvested (Ritter, 1988).In any case, the resulting trading activity of individual and institutional

investors selling first and buying later according to their portfolio composi-tions may drive upward the return comovement of the stocks sold and bought.If that is the case, we should expect our correlation measures to be signif-icantly higher either in December or in January (or in both months) thanduring the rest of the year. In Table 7 we test this hypothesis by computingt-statistics for the paired differences between lower and upper bounds on theexcess comovement measures (in Panels A and B, respectively) from Februaryto November and those in either December or January, under the assump-tions that the paired differences are independent and normally distributed,with the same mean and either equal or unequal variance. The same analysisis repeated for the benchmark bρBASE∗t , in Panel C. The results reported inTable 7 reject the hypothesis that the turn-of-the-year effect has any impacton excess and raw comovement: In each case, none of the correspondingt-statistics is statistically different from zero.

6.7 Industry Time-Series Results

We lastly investigate the ability of information, momentum, liquidity, andproduct market shocks to explain excess comovement at the industry level.We regress the upper and lower bounds for excess absolute correlation foreach of the ten sectors in Table 1 (displayed in Figure 2) on all the proxiesdescribed in Sections 6.1 to 6.4 and report estimated coefficients in Tables 4and 6, respectively.Consistent with the aggregate results, information asymmetry, informa-

tion heterogeneity, and real output shocks uniformly explain a significant por-tion of bρOLS∗it and bρFGLS∗it , for i = 1, . . . , 10, and have the correct signs. How-ever, the explanatory power of those regressions varies considerably acrosssectors, ranging from the lows of Non-Cyclical Services and Information Tech-nology to the highs of Basic Industries (from Chemical Commodity to Steel),Non-Cyclical Consumer Goods (fromBrewers to Retailers-Department Stores),and Financials (from Banks to Other Financials). Greater sector volatilityand asymmetric sharing of information among analysts are less relevant onlyfor the non-fundamental comovement of companies within the Utilities andInformation Technology groupings. The lower bound for excess sector cor-

24

relation is generally independent of the state of the U.S. economy, while itsupper bound is lower during recessions or more expansive monetary condi-tions, especially for Basic Industries and Financials.Momentum Mt is never significant in the regressions of Table 4, and

is associated with greater bρFGLS∗it only for the Resources and Non-CyclicalServices indexes. Consistently, contemporaneous and lagged returns againplay little or no role in the dynamics of bρOLS∗it and bρFGLS∗it . A dichotomybetween OLS and FGLS excess comovement nonetheless arises for sectorperformance dummies. Indeed, the coefficients for dit, d+it , and d

−it are rarely

significant in the upper bound regressions of Table 6. There instead appearsto be a generally positive (negative), and in some cases statistically significantrelationship between bρOLS∗it and short-term upward (downward) trends in thecorresponding indexes. However, coefficients for dit for bρFGLS∗it are in mostcases negative and of greater absolute magnitude than for bρOLS∗it . Theseestimates suggest that protracted runs in sector returns tend to affect thedegree of sector-wide excess comovement, contrary to the market-wide resultsreported in Tables 3 and 5. Once more, we find no evidence that excesscomovement in our sample is related to liquidity shocks: Most of the lowerand upper bounds to it are symmetric and negatively related to the level ofshort-term interest rates. Additionally, Table 6 reveals that there is positivedependence of bρFGLS∗mt on rFt for just four sectors, Non-Cyclical ConsumerGoods, Cyclical Services, Utilities, and Financials.Overall, and despite some strong cross-sectional variation, market (and

sector) volatility, dispersion of analysts’ earnings forecasts, and monetaryand real output developments contribute to about 24% and 27% of the fluc-tuations in our measures for the lower and upper bounds on excess absolutecorrelation, respectively. Nevertheless, the positive and strongly significantconstant terms in all of the above regressions of Tables 3 to 6 and the disap-pointing results of momentum, contemporaneous and lagged returns, markettrends, and the turn-of-the-year effect suggest that much more of the excesscomovement we find in the U.S. stock market remains to be explained.

7 Conclusions

This study investigates one of the most fundamental aspects of asset pricing,the comovement of security prices, focusing on the degree to which observedcorrelations cannot be explained by fundamental factors. It has presented an

25

empirical analysis of excess comovement in a sample of 82 industry indexesfor the U.S. equity market over the interval January 8, 1973 to December 31,2001. Excess correlation is defined here as the unconditional correlation of theestimated residuals from univariate (OLS) and joint (FGLS) regressions ofindustry returns on fundamental sources of risk, specifically sector groupingsand the three Fama-French factors.Our analysis showed that lower and upper bounds on the degree of ex-

cess absolute correlation are surprisingly high, averaging 0.138 and 0.263,respectively, over our entire sample, representing between 32% and 60% ofthe average raw absolute correlation. Excess comovement is also uniformlysignificant across all industries over the entire time interval. Furthermore,our results suggest that non-fundamental comovement has been playing anincreasingly important role in affecting the covariance among stock indexes,especially during the 1990s and the early 2000s.We also analyzed the determinants of this excess comovement. We found

that lower and upper bounds on excess absolute correlation are positivelyrelated to market volatility, the dispersion of analysts’ earnings forecasts,and the state of the U.S. economy, and that lower bound measures are neg-atively related to the level of the short-term interest rate. These variablesexplain about 24% of the fluctuations in excess comovement estimated viaOLS and more than 27% of the absolute correlation estimated using FGLSresiduals. In addition, most estimated indicators of excess comovement aresymmetric, i.e., not significantly different in rising or falling markets. Thisevidence supports the theoretical literature attributing financial contagionto the portfolio rebalancing decisions of investors, to the heterogeneity oftheir information endowments, or to product market shocks, but also sug-gests that excess comovement in the U.S. stock market does not stem fromliquidity shocks.

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30

Table1.Descriptivestatistics

Thistablereportssummarystatisticsforthetimeseriesofweeklyreturnsforthemarket(rmt),the3macro-sectorindexes

( rst),andthe10sectorindexes(rit)definedinSection4,overtheintervalJanuary8,1973-December31,2001(i.e.,1,512

observations).Nisthenumberofsub-categoryconstituentsforeachindex.µisthemeanandσisthestandarddeviationof

eachtimeseriesofweeklyindexreturns.Skew

isthecoefficientofskewness,whileKurtistheexcesskurtosis.Thestandard

errorsofthesestatisticsintheirasymptoticnormaldistributionsarecomputedas¡ 6 T¢1 2 an

d¡ 24 T¢1 2 ,re

spectively.bρ 1is

the

estimatedfirst-orderautocorrelation.LB(5)isthevalueoftheLjung-Boxtestofrandomnessforuptothefifth-orderserial

correlation.A“*”indicatesthatthestatisticisequaltozeroatanyconventionalsignificancelevel.

Index

Nµ

σSkew

Kurt

bρ 1LB(5)

Market

30.152%

2.40%

-1.32

17.05

-0.070

13.64

Macro-sectors

Resources

10.132%

2.92%

-0.81

8.71

-0.114

29.89

Non-Financials

80.148%

2.48%

-1.26

16.25

-0.069

12.12

Financials

10.184%

2.72%

-0.59

5.99

0.020∗

8.74∗

Sectors

Resources

40.132%

2.92%

-0.81

8.71

-0.114

29.89

BasicIndustries

90.122%

∗3.00%

-0.66

11.47

0.012∗

5.39∗

GeneralIndustrials

80.178%

2.76%

-1.09

12.21

-0.025∗

4.39∗

CyclicalConsumerGoods

70.080%

∗2.90%

-0.96

12.01

-0.001∗

6.17∗

Non-CyclicalConsumerGoods

140.192%

2.62%

-1.06

12.72

-0.085

17.71

CyclicalServices

170.151%

2.97%

-1.17

13.89

-0.022∗

6.54∗

Non-CyclicalServices

30.133%

2.40%

-0.96

12.48

-0.101

19.34

Utilities

30.063%

∗2.01%

-0.09∗

7.86

-0.013∗

0.93∗

InformationTechnology

40.163%

3.80%

-0.58

6.40

-0.070

10.15

Financials

130.184%

2.72%

-0.59

5.99

0.020∗

8.74∗

31

Table2.Descriptivestatistics:OLSandFGLScomovement

ThistablereportssummarystatisticsfortheweeklytimeseriesofexcessabsolutecorrelationinEq.(6),estimatedusing

OLSandFGLSresiduals,andofbenchmarkcorrelationofgrossreturns,forthemarket( bρOLS

∗t

,bρFGL

S∗

t,andbρBAS

E∗

t),for

the3macro-sectorindexes( bρOLS

∗st

,bρFGLS∗

st,andbρBAS

E∗

st)andthe10sectorindexes(bρOLS

∗it

,bρFGLS∗

it,andbρBAS

E∗

it)defined

inSection4,overtheintervalDecember9,1974-December31,2001(i.e.,1,413observations).ρisthecorrelationbetweenthe

pairbρ∗ tan

dbρBAS

E∗

t.Rρistheratiobetweenthepairbρ∗ tan

dbρBAS

E∗

t.A“*”indicatesthatthet-statisticfortheone-sided

testofthenullhypothesisthatbρ∗ t=

0againstthealternativehypothesisthatbρ∗ t>

0issignificantatthe10%level.

bρOLS∗

tbρFGL

S∗

tbρBAS

E∗

t

Index

µσ

ρRρ

µσ

ρRρ

µσ

Market

0.138∗

0.010

0.12

32%

0.263∗

0.050

0.51

60%

0.436∗

0.102

Macro-sectors

Resources

0.140∗

0.013

-0.22

45%

0.195∗

0.082

0.25

62%

0.313∗

0.121

Non-Financials

0.140∗

0.010

0.13

32%

0.248∗

0.044

0.51

57%

0.437∗

0.106

Financials

0.136∗

0.012

-0.34

29%

0.270∗

0.070

0.57

58%

0.468∗

0.090

Sectors

Resources

0.140∗

0.013

-0.22

45%

0.195∗

0.082

0.25

62%

0.313∗

0.121

BasicIndustries

0.138∗

0.014

0.13

30%

0.277∗

0.061

0.57

60%

0.459∗

0.113

GeneralIndustrials

0.139∗

0.011

-0.07

29%

0.255∗

0.055

0.28

52%

0.490∗

0.110

CyclicalConsumerGoods

0.139∗

0.012

-0.16

32%

0.277∗

0.058

0.43

62%

0.445∗

0.104

Non-CyclicalConsumerGoods

0.138∗

0.012

-0.04

32%

0.268∗

0.054

0.49

61%

0.438∗

0.120

CyclicalServices

0.135∗

0.011

0.08

34%

0.289∗

0.066

0.58

72%

0.402∗

0.094

Non-CyclicalServices

0.141∗

0.018

0.07

32%

0.179∗

0.060

-0.02

41%

0.440∗

0.112

Utilities

0.143∗

0.018

0.36

42%

0.178∗

0.059

0.23

52%

0.345∗

0.113

InformationTechnology

0.143∗

0.017

0.46

30%

0.264∗

0.065

0.28

56%

0.475∗

0.118

Financials

0.136∗

0.012

-0.34

29%

0.270∗

0.070

0.57

58%

0.468∗

0.090

32

Table3.Market:basicregressionsforOLScomovement

ThistablereportsOLSestimatesforthecoefficientsoftheregressionofbρOLS

∗t

onvariousexplanatoryvariables.σmtis

marketreturnvolatilityovertheinterval[t−g∆,t].MtisaproxyformarketmomentumprovidedbyFrenchinhisresearch

website.r m

t−laremarketreturnslaggedbylweeks.dmtisadummyvariableequaltooneifsign(rmt)=sign(rmt−1)=

sign(rmt−2)andzerootherwise.r Ftisthethree-monthTreasuryBillrate,whiled+ mt(d− mt)isadummyvariableequaltoone

ifsign(rmt)=sign(rmt−1)=sign(rmt−2)=+(−)andzerootherwise.dR tisadummyvariableequaltooneifthe

U.S.economywasinrecessioninweekt(accordingtotheNBER),andequaltozerootherwise,whiledT tisadummyvariable

equalto1iftheFederalReserve’smonetarystancewasrestrictiveinweekt,accordingtothemethodologyofJensenetal.

(1996),andequaltozerootherwise.Finally,thevariableHtisaproxyforthedegreeofinformationheterogeneityintheU.S.

stockmarket.Htisconstructedasthemarket-wide,cross-sectionalmeanofthestandarddeviationsofanalysts’one-yearEPS

forecastsinweekt’smonthandyear(asreportedbyI/B/E/S),multipliedbythenumberofanalystscoveringeachcompany

attimetanddividedbythecorrespondingmeanEPSforecasts,forallcompaniesintheU.S.stockmarketuniverse.The

resultingseriesisWinsorizedattwostandarddeviationsfrom

itsmeantoobtainHt.Thisvariableisavailableonlyfrom

January5,1976onward:A“ˆ”indicatesthatthecorrespondingmodelisestimatedoverthisshortersampleperiod.R2 ais

theadjustedR2.StatisticalsignificanceisevaluatedusingNewey-Weststandarderrorsandtheensuingt-statisticsareshown

inparentheses.A“∗”indicatessignificanceatthe10%level. 33

Table3(Continued).

Regressionmodels

Variables

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)ˆ

(9)ˆ

(10)ˆ

Constant

0.1286∗

(100.3)

0.1380∗

(296.8)

0.1378∗

(289.1)

0.1378∗

(289.1)

0.1441∗

(133.7)

0.1381∗

(298.7)

0.1380∗

(293.9)

0.1413∗

(126.9)

0.1372∗

(81.92)

0.1372∗

(81.91)

σmt

0.4121∗

(6.85)

0.5404∗

(7.88)

0.5403∗

(7.87)

Mt

0.0055

(0.54)

0.0073

(0.67)

0.0072

(0.66)

r mt

-0.0026

(-0.27)

-0.0016

(-0.16)

0.0010

(0.10)

r mt−1

-0.0051

(-0.50)

-0.0037

(-0.37)

-0.0008

(-0.08)

r mt−2

-0.0068

(-0.68)

-0.0043

(-0.44)

-0.0015

(-0.14)

dmt

0.0009

(1.22)

0.0010

(1.38)

d+ mt

0.0007

(0.69)

0.0007

(0.72)

d− mt

0.0015

(1.32)

0.0015

(1.30)

r Ft

-0.0922∗

(-6.99)

-0.1044∗

(-7.06)

-0.1046∗

(-7.08)

dR t

-0.0012

(-0.73)

0.0010

(0.69)

0.0010

(0.66)

dT t

0.0001

(0.08)

-0.0001

(-0.11)

-0.0001

(-0.10)

Ht

-0.0023∗

(-3.70)

-0.0032∗

(-4.52)

-0.0032∗

(-4.51)

N1413

1413

1413

1413

1413

1413

1413

1357

1357

1357

R2 a

9.52%

-0.19%

0.09%

0.05%

6.71%

-0.09%

-0.07%

2.33%

23.93%

23.89%

34

Table4.Sectors:basicregressionsforOLScomovement

ThistablereportsOLSestimatesforthecoefficientsoftheregressionsofbρOLS

∗it

onvariousexplanatoryvariablesforeach

ofthe10sectorslistedinTable1.

σitissectorireturnvolatilityovertheinterval[t−g∆,t].Mtisaproxyformarket

momentumprovidedbyFrenchinhisresearchwebsite.r it−laresectorireturnslaggedbylweeks.ditisadummyvariable

equaltooneifsign(rit)=sign(rit−1)=sign(rit−2)andzerootherwise.r Ftisthethree-monthTreasuryBillrate,

whiled+ it(d− it)isadummyvariableequaltooneifsign(rit)=sign(rit−1)=sign(rit−2)=+(−)andzerootherwise.

dR tisadummyvariableequaltooneiftheU.S.economywasinrecessioninweekt(accordingtotheNBER),andequalto

zerootherwise,whiledT tisadummyvariableequalto1iftheFederalReserve’smonetarystancewasrestrictiveinweekt,

accordingtothemethodologyofJensenetal.(1996),andequaltozerootherwise.Finally,thevariableHtisaproxyforthe

degreeofinformationheterogeneityintheU.S.stockmarket.Htisconstructedasthemarket-wide,cross-sectionalmeanof

thestandarddeviationsofanalysts’one-yearEPSforecastsinweekt’smonthandyear(asreportedbyI/B/E/S),multiplied

bythenumberofanalystscoveringeachcompanyattimetanddividedbythecorrespondingmeanEPSforecasts,forall

companiesintheU.S.stockmarketuniverse.TheresultingseriesisWinsorizedattwostandarddeviationsfrom

itsmean

toobtainHt.Thisvariableisavailableonlyfrom

January5,1976onward:A“ˆ”indicatesthatthecorrespondingmodel

isestimatedoverthisshortersampleperiod.R2 aistheadjustedR2.StatisticalsignificanceisevaluatedusingNewey-West

standarderrorsandtheensuingt-statisticsareshowninparentheses.A“∗”indicatessignificanceatthe10%level.

35

Table4(Continued).

Sectors

Variables

Resources

Basic

Industries

General

Industrials

Cyclical

ConsumerGoods

Non-Cyclical

ConsumerGoods

Constant

0.1406∗

(53.39)

0.1405∗

(53.43)

0.1279∗

(39.10)

0.1279∗

(38.97)

0.1319∗

(72.82)

0.1318∗

(73.12)

0.1409∗

(54.66)

0.1409∗

(54.63)

0.1301∗

(52.90)

0.1301∗

(52.70)

σit

0.2294∗

(2.31)

0.2316∗

(2.34)

0.7238∗

(6.77)

0.7240∗

(6.77)

0.6643∗

(10.22)

0.6691∗

(10.28)

0.5396∗

(6.78)

0.5398∗

(6.78)

0.7936∗

(9.30)

0.7933∗

(9.29)

Mt

0.0035

(0.35)

0.0033

(0.33)

0.0204

(1.39)

0.0205

(1.40)

-0.0068

(-0.66)

-0.0061

(-0.59)

-0.0082

(-0.74)

-0.0082

(-0.75)

0.0094

(0.72)

0.0091

(0.71)

r it

-0.0017

(-0.16)

-0.0081

(-0.70)

-0.0044

(-0.37)

-0.0063

(-0.43)

-0.0028

(-0.26)

-0.0156

(-1.31)

-0.0168

(-1.63)

-0.0202∗

(-1.72)

-0.0037

(-0.36)

0.0043

(0.38)

r it−1

-0.0024

(-0.22)

-0.0090

(-0.76)

-0.0002

(-0.01)

-0.0019

(-0.13)

-0.0027

(-0.25)

-0.0160

(-1.30)

-0.0133

(-1.27)

-0.0167

(-1.38)

-0.0024

(-0.23)

0.0062

(0.52)

r it−2

-0.0068

(-0.65)

-0.0134

(-1.14)

-0.0007

(-0.05)

-0.0025

(-0.16)

-0.0019

(-0.18)

-0.0153

(-1.30)

-0.0111

(-1.05)

-0.0142

(-1.18)

-0.0010

(-0.09)

0.0074

(0.63)

dit

0.0015

(1.50)

0.0008

(0.89)

0.0002

(0.26)

-0.0016∗

(-1.87)

0.0009

(1.23)

d+ it

0.0025

(1.53)

0.0010

(0.71)

0.0018∗

(1.81)

-0.0011

(-0.87)

-0.0001

(-0.05)

d− it

0.0002

(0.14)

0.0005

(0.33)

-0.0025∗

(-1.86)

-0.0022

(-1.60)

0.0023∗

(2.10)

r Ft

-0.1791∗

(-8.76)

-0.1788∗

(-8.73)

-0.0655∗

(-3.35)

-0.0653∗

(-3.34)

-0.0786∗

(-3.73)

-0.0788∗

(-3.78)

-0.1362∗

(-6.82)

-0.1367∗

(-6.82)

-0.1194∗

(-5.18)

-0.1204∗

(-5.22)

dR t

-0.0006

(0.38)

-0.0006

(0.38)

-0.0001

(-0.05)

-0.0001

(-0.04)

0.0001

(0.06)

0.0004

(0.19)

0.0045∗

(2.25)

0.0046∗

(2.28)

0.0056∗

(2.29)

0.0056∗

(2.23)

dT t

0.0043∗

(2.67)

0.0043∗

(2.64)

0.0025∗

(1.84)

0.0025∗

(1.84)

-0.0024∗

(-2.31)

-0.0025∗

(-2.34)

0.0002

(0.13)

0.0001

(0.11)

0.0005

(0.42)

0.0006

(0.46)

Ht

0.0022∗

(2.20)

0.0022∗

(2.21)

-0.0050∗

(-5.50)

-0.0050∗

(-5.49)

-0.0027∗

(-3.77)

-0.0027∗

(-3.82)

-0.0053∗

(-6.47)

-0.0053∗

(-6.46)

-0.0030∗

(-4.10)

-0.0030∗

(-4.08)

N1357

1357

1357

1357

1357

1357

1357

1357

1357

1357

R2 a

11.20%

11.23%

23.50%

23.45%

21.53%

21.96%

19.57%

19.54%

28.20%

28.29%

36

Table4(Continued).

Sectors

Variables

Cyclical

Services

Non-Cyclical

Services

Utilities

Information

Technology

Financials

Constant

0.1311∗

(69.74)

0.1311∗

(69.75)

0.1610∗

(51.75)

0.1609∗

(51.63)

0.1178∗

(30.64)

0.1179∗

(30.76)

0.1472∗

(33.96)

0.1474∗

(34.05)

0.1467∗

(64.30)

0.1467∗

(64.28)

σit

0.5190∗

(8.01)

0.5182∗

(8.02)

-0.5798∗

(-4.85)

-0.5796∗

(-4.83)

1.3964∗

(7.08)

1.3889∗

(7.08)

0.0059

(0.07)

0.0054

(0.07)

0.2557∗

(3.86)

0.2560∗

(3.86)

Mt

0.0186

(1.50)

0.0187

(1.51)

0.0176

(1.07)

0.0176

(1.07)

0.0064

(0.33)

0.0074

(0.39)

-0.0071

(-0.40)

-0.0069

(-0.39)

0.0047

(0.46)

0.0047

(0.46)

r it

0.0007

(0.08)

-0.0043

(-0.49)

-0.0028

(-0.14)

-0.0033

(-0.15)

0.0416∗

(1.75)

0.0253

(0.87)

0.0064

(0.55)

0.0122

(0.92)

-0.0067

(-0.66)

-0.0080

(-0.71)

r it−1

-0.0044

(-0.52)

-0.0099

(-1.09)

-0.0035

(-0.17)

-0.0040

(-0.17)

0.0342

(1.45)

0.0188

(0.67)

0.0055

(0.42)

0.0116

(0.79)

-0.0090

(-0.90)

-0.0104

(-0.91)

r it−2

-0.0039

(-0.47)

-0.0091

(-1.01)

0.0003

(0.01

-0.0003

(-0.01)

0.0263

(1.15)

0.0109

(0.41)

0.0022

(0.17)

0.0086

(0.58)

-0.0122

(-1.19)

-0.0135

(-1.17)

dit

-0.0012

(-1.45)

0.0030∗

(2.39)

-0.0018

(-1.56)

-0.0014

(-1.13)

0.0009

(1.07)

d+ it

-0.0005

(-0.53)

0.0031∗

(1.79)

-0.0003

(-0.19)

-0.0026

(-1.43)

0.0010

(0.90)

d− it

-0.0022

(-1.41)

0.0029

(1.37)

-0.0036∗

(-2.39)

0.00004

(0.02)

0.0006

(0.46)

r Ft

-0.0559∗

(-3.69)

-0.0558∗

(-3.68)

-0.1120∗

(-4.02)

-0.1120∗

(-4.01)

-0.0024

(-0.09)

-0.0025

(-0.10)

-0.0214

(-0.80)

-0.0238

(-0.87)

-0.1790∗

(-10.46)

-0.1790∗

(-10.46)

dR t

0.0027∗

(2.04)

0.0028∗

(2.09)

-0.0030

(-1.11)

-0.0030

(-1.11)

-0.0130∗

(-7.85)

-0.0129∗

(-7.77)

-0.0052∗

(-2.68)

-0.0053∗

(-2.70)

0.00001

(0.00)

0.00003

(0.02)

dT t

-0.0030∗

(-2.56)

-0.0031∗

(-2.60)

0.0009

(0.39)

0.0009

(0.38)

0.0002

(0.08)

0.0002

(0.08)

0.0052∗

(2.47)

0.0053∗

(2.49)

-0.0003

(-0.24)

-0.0003

(-0.24)

Ht

-0.0040∗

(-4.87)

-0.0040∗

(-4.90)

-0.0006

(-0.38)

-0.0006

(-0.38)

0.0014

(1.17)

0.0013

(1.13)

-0.0023∗

(-1.65)

-0.0023∗

(-1.66)

-0.0033∗

(-4.31)

-0.0033∗

(-4.31)

N1357

1357

1357

1357

1357

1357

1357

1357

1357

1357

R2 a

20.00%

20.03%

7.96%

7.89%

18.66%

18.73%

4.62%

4.63%

25.68%

25.63%

37

Table5.Market:basicregressionsforFGLScomovement

ThistablereportsOLSestimatesforthecoefficientsoftheregressionofbρFGL

S∗

tonvariousexplanatoryvariables.σmtis

marketreturnvolatilityovertheinterval[t−g∆,t].MtisaproxyformarketmomentumprovidedbyFrenchinhisresearch

website.r m

t−laremarketreturnslaggedbylweeks.dmtisadummyvariableequaltooneifsign(rmt)=sign(rmt−1)=

sign(rmt−2)andzerootherwise.r Ftisthethree-monthTreasuryBillrate,whiled+ mt(d− mt)isadummyvariableequaltoone

ifsign(rmt)=sign(rmt−1)=sign(rmt−2)=+(−)andzerootherwise.dR tisadummyvariableequaltooneifthe

U.S.economywasinrecessioninweekt(accordingtotheNBER),andequaltozerootherwise,whiledT tisadummyvariable

equalto1iftheFederalReserve’smonetarystancewasrestrictiveinweekt,accordingtothemethodologyofJensenetal.

(1996),andequaltozerootherwise.Finally,thevariableHtisaproxyforthedegreeofinformationheterogeneityintheU.S.

stockmarket.Htisconstructedasthemarket-wide,cross-sectionalmeanofthestandarddeviationsofanalysts’one-yearEPS

forecastsinweekt’smonthandyear(asreportedbyI/B/E/S),multipliedbythenumberofanalystscoveringeachcompany

attimetanddividedbythecorrespondingmeanEPSforecasts,forallcompaniesintheU.S.stockmarketuniverse.The

resultingseriesisWinsorizedattwostandarddeviationsfrom

itsmeantoobtainHt.Thisvariableisavailableonlyfrom

January5,1976onward:A“ˆ”indicatesthatthecorrespondingmodelisestimatedoverthisshortersampleperiod.R2 ais

theadjustedR2.StatisticalsignificanceisevaluatedusingNewey-Weststandarderrorsandtheensuingt-statisticsareshown

inparentheses.A“∗”indicatessignificanceatthe10%level. 38

Table5(Continued).

Regressionmodels

Variables

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)ˆ

(9)ˆ

(10)ˆ

Constant

0.1878∗

(30.04)

0.2633∗

(117.1)

0.2630∗

(111.2)

0.2630∗

(111.2)

0.2562∗

(46.11)

0.2631∗

(109.4)

0.2568∗

(108.9)

0.2515∗

(54.33)

0.1761∗

(22.35)

0.1762∗

(22.35)

σmt

3.3116∗

(12.52)

3.4742∗

(12.88)

3.4744∗

(12.90)

Mt

0.0100

(0.26)

0.0418

(0.98)

0.0427

(1.01)

r mt

-0.0682

(-1.14)

-0.0541

(-1.15)

-0.0837

(-1.63)

r mt−1

-0.0455

(-0.77)

-0.0260

(-0.53)

-0.0583

(-1.06)

r mt−2

-0.0940

(-1.52)

-0.0721

(-1.48)

-0.1033∗

(-1.95)

dmt

-0.0002

(-0.04)

0.0001

(0.05)

d+ mt

-0.0002

(-0.05)

0.0033

(0.80)

d− mt

-0.00003

(-0.01)

-0.0057

(-1.04)

r Ft

0.1016

(1.34)

-0.0209

(-0.27)

-0.0194

(-0.25)

dR t

-0.0015

(-0.29)

-0.0090∗

(-1.82)

-0.0085∗

(-1.72)

dT t

0.0153∗

(3.31)

0.0103∗

(2.05)

0.0101∗

(2.03)

Ht

0.0079∗

(2.85)

0.0053∗

(1.71)

0.0052∗

(1.68)

N1413

1413

1413

1413

1413

1413

1413

1357

1357

1357

R2 a

23.84%

0.03%

-0.14%

-0.12%

0.25%

-0.06%

2.19%

1.00%

27.13%

27.17%

39

Table6.Sectors:basicregressionsforFGLScomovement

ThistablereportsOLSestimatesforthecoefficientsoftheregressionsofbρFGL

S∗

itonvariousexplanatoryvariablesfor

eachofthe10sectorslistedinTable1.

σitissectorireturnvolatilityovertheinterval[t−g∆,t].Mtisaproxyformarket

momentumprovidedbyFrenchinhisresearchwebsite.r it−laresectorireturnslaggedbylweeks.ditisadummyvariable

equaltooneifsign(rit)=sign(rit−1)=sign(rit−2)andzerootherwise.r Ftisthethree-monthTreasuryBillrate,

whiled+ it(d− it)isadummyvariableequaltooneifsign(rit)=sign(rit−1)=sign(rit−2)=+(−)andzerootherwise.

dR tisadummyvariableequaltooneiftheU.S.economywasinrecessioninweekt(accordingtotheNBER),andequalto

zerootherwise,whiledT tisadummyvariableequalto1iftheFederalReserve’smonetarystancewasrestrictiveinweekt,

accordingtothemethodologyofJensenetal.(1996),andequaltozerootherwise.Finally,thevariableHtisaproxyforthe

degreeofinformationheterogeneityintheU.S.stockmarket.Htisconstructedasthemarket-wide,cross-sectionalmeanof

thestandarddeviationsofanalysts’one-yearEPSforecastsinweekt’smonthandyear(asreportedbyI/B/E/S),multiplied

bythenumberofanalystscoveringeachcompanyattimetanddividedbythecorrespondingmeanEPSforecasts,forall

companiesintheU.S.stockmarketuniverse.TheresultingseriesisWinsorizedattwostandarddeviationsfrom

itsmean

toobtainHt.Thisvariableisavailableonlyfrom

January5,1976onward:A“ˆ”indicatesthatthecorrespondingmodel

isestimatedoverthisshortersampleperiod.R2 aistheadjustedR2.StatisticalsignificanceisevaluatedusingNewey-West

standarderrorsandtheensuingt-statisticsareshowninparentheses.A“∗”indicatessignificanceatthe10%level.

40

Table6(Continued).

Sectors

Variables

Resources

Basic

Industries

General

Industrials

CyclicalConsu-

merGoods

Non-Cyclical

ConsumerGoods

Constant

0.1038∗

(8.52)

0.1036∗

(8.52)

0.1755∗

(17.06)

0.1744∗

(17.18)

0.2019∗

(21.21)

0.2020∗

(21.20)

0.2080∗

(18.55)

0.2081∗

(18.56)

0.1687∗

(17.39)

0.1688∗

(17.40)

σit

3.9367∗

(9.98)

3.9450∗

(10.00)

3.3084∗

(11.28)

3.3227∗

(11.43)

3.2599∗

(11.07)

3.2585∗

(11.04)

1.8624∗

(5.11)

1.8627∗

(5.11)

2.9399∗

(9.82)

2.9412∗

(9.82)

Mt

0.1086∗

(1.92)

0.1080∗

(1.92)

0.0461

(1.00)

0.0530

(1.17)

0.0448

(1.06)

0.0446

(1.05)

0.0084

(0.16)

0.0082

(0.16)

0.0737

(1.54)

0.0747

(1.57)

r it

-0.0927

(-1.43)

-0.1175

(-1.62)

-0.1048∗

(-2.05)

-0.2016∗

(-4.05)

-0.1069∗

(-2.32)

-0.1032∗

(-1.98)

-0.0459

(-0.90)

-0.0537

(-0.96)

-0.0312

(-0.66)

-0.0663

(-1.23)

r it−1

-0.0043

(-0.06)

-0.0299

(-0.39)

-0.0565

(-1.16)

-0.1487∗

(-3.04)

-0.0324

(-0.69)

-0.0285

(-0.53)

-0.0738

(-1.39)

-0.0818

(-1.39)

0.0372

(0.73)

-0.0004

(-0.01)

r it−2

-0.0333

(-0.50)

-0.0590

(-0.78)

-0.0734

(-1.61)

-0.1700∗

(-3.37)

-0.0649

(-1.34)

-0.0610

(-1.12)

-0.0532

(-0.92)

-0.0605

(-0.95)

-0.0152

(-0.28)

-0.0517

(-0.85)

dit

-0.0036

(-0.70)

-0.0053

(-1.41)

-0.0027

(-0.79)

-0.0042

(-1.08)

-0.0045

(-1.26)

d+ it

0.0002

(0.03)

0.0073

(1.44)

-0.0032

(-0.66)

-0.0031

(-0.54)

-0.0002

(-0.04)

d− it

-0.0086

(-1.09)

-0.0226∗

(-3.76)

-0.0019

(-0.34)

-0.0055

(-0.91)

-0.0107∗

(-1.82)

r Ft

-0.9636∗

(-9.32)

-0.9625∗

(-9.32)

-0.1300

(-1.46)

-0.1194

(-1.36)

-0.2065∗

(-2.67)

-0.2065∗

(-2.67)

0.0815

(0.79)

0.0818

(0.79)

0.1826∗

(1.99)

0.1869∗

(2.04)

dR t

-0.0073

(-0.78)

-0.0073

(-0.78)

-0.0217∗

(-3.49)

-0.0211∗

(-3.35)

0.0028

(0.49)

0.0028

(0.47)

-0.0071

(-1.03)

-0.0069

(-1.00)

0.0031

(0.44)

0.0037

(0.52)

dT t

0.0313∗

(4.27)

0.0312∗

(4.25)

0.0225∗

(3.99)

0.0225∗

(4.00)

-0.0058

(1.14)

-0.0058

(-1.13)

0.0085

(1.43)

0.0084

(1.42)

0.0105∗

(1.98)

0.0103∗

(1.92)

Ht

0.0250∗

(4.91)

0.0250∗

(4.91)

0.0090∗

(2.67)

0.0091∗

(2.75)

0.0104∗

(-3.14)

-0.0104∗

(-3.13)

0.0070∗

(1.81)

0.0070∗

(1.81)

0.0078∗

(2.36)

0.0077∗

(2.32)

N1357

1357

1357

1357

1357

1357

1357

1357

1357

1357

R2 a

21.38%

21.37%

26.86%

27.71%

18.12%

18.06%

6.89%

6.83%

16.54%

16.61%

41

Table6(Continued).

Sectors

Variables

Cyclical

Services

Non-Cyclical

Services

Utilities

Information

Technology

Financials

Constant

0.1729∗

(16.10)

0.1734∗

(16.13)

0.1427∗

(14.64)

0.1429∗

(14.60)

0.0880∗

(8.84)

0.0885∗

(8.92)

0.2309∗

(17.86)

0.2306∗

(17.76)

0.1744∗

(10.23)

0.1741∗

(10.23)

σit

3.7497∗

(11.25)

3.7438∗

(11.23)

2.8766∗

(8.40)

2.8699∗

(8.39)

3.3155∗

(7.43)

3.2973∗

(7.39)

1.2502∗

(5.04)

1.2513∗

(5.04)

2.0595∗

(4.03)

2.0730∗

(4.07)

Mt

0.0487

(0.87)

0.0498

(0.89)

0.1019∗

(2.10)

0.1014∗

(2.09)

0.0144

(0.29)

0.0170

(0.35)

0.0607

(1.22)

0.0602

(1.21)

-0.0185

(-0.28)

-0.0187

(-0.28)

r it

-0.0095

(-0.17)

-0.0489

(-0.83)

-0.1484∗

(-2.38)

-0.1358∗

(-1.88)

0.0426

(0.51)

0.0031

(0.03)

0.0036

(0.08)

-0.0103

(-0.21)

-0.0984

(-1.50)

-0.1529∗

(-2.05)

r it−1

0.0023

(0.04)

-0.0408

(-0.68)

-0.1103

(-1.47)

-0.0976

(-1.16)

0.0093

(0.10)

-0.0282

(-0.28)

0.0245

(0.53)

0.0095

(0.19)

-0.0145

(-0.22)

-0.0715

(-0.92)

r it−2

-0.0310

(-0.55)

-0.0725

(-1.17)

-0.1068

(-1.62)

-0.0951

(-1.29)

0.0562

(0.60)

0.0189

(0.18)

-0.0124

(-0.28)

-0.0280

(-0.55)

-0.0343

(-0.52)

-0.0895

(-1.19)

dit

-0.0122∗

(-2.77)

-0.0022

(-0.53)

-0.0004

(-0.11)

-0.0043

(-1.02)

0.0001

(0.01)

d+ it

-0.0070

(-1.19)

-0.0036

(-0.62)

0.0031

(0.51)

-0.0016

(-0.28)

0.0066

(1.00)

d− it

-0.0205∗

(-2.63)

-0.0003

(-0.04)

-0.0049

(-0.88)

-0.0079

(-1.12)

-0.0104

(-1.22)

r Ft

0.1893∗

(1.80)

0.1905∗

(1.81)

-0.2735∗

(-3.03)

-0.2739∗

(-3.03)

0.2980∗

(3.87)

0.2977∗

(3.89)

-0.5155∗

(-5.23)

-0.5106∗

(-5.14)

0.1872∗

(1.66)

0.1893∗

(1.68)

dR t

-0.0136∗

(-1.95)

-0.0131∗

(-1.89)

0.0078

(0.98)

0.0077

(0.97)

0.0069

(1.28)

0.0073

(1.35)

0.0048

(0.64)

0.0049

(0.66)

-0.0263∗

(-4.28)

-0.0251∗

(-4.06)

dT t

-0.0025

(-0.36)

-0.0028

(-0.40)

0.0061

(1.05)

0.0061

(1.06)

0.0162∗

(2.97)

0.0162∗

(2.98)

0.0381∗

(6.03)

0.0380∗

(6.01)

0.0244∗

(2.96)

0.0245∗

(2.98)

Ht

0.0035

(0.77)

0.0033

(0.74)

-0.0095∗

(-2.65)

-0.0095∗

(-2.65)

0.0029

(0.83)

0.0028

(0.81)

0.0062∗

(1.69)

0.0063∗

(1.70)

0.0162∗

(3.15)

0.0161∗

(3.14)

N1357

1357

1357

1357

1357

1357

1357

1357

1357

1357

R2 a

22.43%

22.51%

13.87%

13.81%

12.65%

12.65%

13.39%

13.36%

9.58%

9.70%

42

Table7.Testfortheturn-of-the-yeareffect:OLSandFGLScomovement

Thistablereportsparametrict-testsofthenullhypothesisthatthepaireddifferencesbetweeneachoftheexcessco-

movementmeasuresbρOLS

∗t

(PanelA),bρFGL

S∗

t(PanelB),andbρBAS

E∗

t(PanelC)inthemonthsofFebruarytoNovember

andineitherDecemberorJanuaryareequaltozero,undertheassumptionthatthepaireddifferencesareindependentand

normallydistributed,withthesamemeanandeitherequalorunequalvariance.Inthelattercase,thet-statisticiscomputed

ast=(x−y)³ S2 x mS

2 y n

´ −1 2 .A“∗”indicatessignificanceatthe10%level.

t-statistic

DataRange

NMean

Stdev

EqualVariance

UnequalVariance

PanelA:bρOLS

∗t

December

123

0.138

0.011

0.560

0.503

January

120

0.138

0.009

-0.432

-0.483

February-November

1,170

0.138

0.010

PanelB:bρFGL

S∗

t

December

123

0.267

0.051

0.868

0.856

January

120

0.264

0.050

0.234

0.235

February-November

1,170

0.262

0.050

PanelC:bρBAS

E∗

t

December

123

0.434

0.100

-0.166

-0.093

January

120

0.435

0.108

-0.098

-0.168

February-November

1,170

0.436

0.101

43

Figure 1. Mean excess correlation: OLS and FGLS procedures

Figure 1a plots the time series of mean excess absolute correlations bρOLS∗t (com-

puted according to the OLS procedure described in Section 3.1 of the text) and bρFGLS∗t

(computed according to the FGLS procedure described in Section 3.2 of the text), and a

measure of absolute correlation, bρBASE∗t , computed using the raw return series rkt in Eq.(3) instead of the estimated residuals beOLSkt or beFGLSkt . Figure 1b plots the ratios between

both bρOLS∗t and bρFGLS∗t and bρBASE∗t in percentage terms (defined in Table 2 as Rρ).

a) bρ∗t

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

OLS

BASE

FGLS

b) bρ∗t / bρBASE∗t (in %)

0%

20%

40%

60%

80%

100%

120%

140%

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

/ m

ean

_rh

o*_B

ASE

(%

)

OLS / BASE

FGLS / BASE

44

Figure 2. Mean excess correlation for sectors: OLS and FGLS procedures

Figures 2a to 2j plot the time series of mean excess absolute correlation bρOLS∗it andbρFGLS∗it for each of the 10 sectors listed in Table 1. Each measure is computed as an

arithmetic average of the corresponding correlations bρOLS∗kt and bρFGLS∗kt (using all k ∈i), estimated according to the procedures described in Sections 3.1 and 3.2 of the text,respectively. In each figure, we also plot a measure of absolute correlation, bρBASE∗it ,

computed as an arithmetic average of the corresponding correlations bρBASE∗kt (using all

k ∈ i), estimated using the raw return series rkt in Eq. (3), instead of the estimatedresiduals beOLSkt and beFGLSkt .

a) Resources b) Basic Industries

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

OLS

BASEFGLS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

OLS

BASE

FGLS

c) General Industrials d) Cyclical Consumer Goods

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_rh

o*

BASE

OLS

FGLS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

45

Figure 2 (Continued).

e) Non-Cyclical Consumer Goods f) Cyclical Services

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

g) Non-Cyclical Services h) Utilities

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

i) Information Technology j) Financials

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

12/9/1974 5/8/1980 10/6/1985 3/6/1991 8/3/1996 1/1/2002

Time

mea

n_r

ho*

BASE

OLS

FGLS

46