Information, Trading Volume and International Stock Market Comovements

Louis Gagnon Associate Professor School of Business Queen’s University Kingston, Ontario Canada, K7L 3N6

G. Andrew Karolyi*

Dean’s Distinguished Research Professor of Finance Fisher College of Business

Ohio State University Columbus, Ohio

USA, 43210-1144

Abstract Using intraday prices for the S&P 500 and Nikkei Stock Average stock indexes and aggregate trading volume for the New York and Tokyo Stock Exchanges, we show how short-run comovements between national stock market returns vary over time in a way related to the trading volume and liquidity in those markets. We frame our analysis in the context of the heterogeneous-agent models of trading developed by Campbell, Grossman and Wang (1993) and Blume, Easley, and O’Hara (1994) and Wang (1994) which predict that trading volume acts as a signal of the information content of a given price move. While we find that there exists significant short-run dependence in returns and volatility among Japan, U.K. and the U.S., we offer new evidence that these return “spillovers” are sensitive to interactions with trading volume in those markets. The cross-market effects with volume are revealed in both close-to-open and open-to-close returns and often exhibit non-linear patterns that are not predicted by theory.

JEL Classification Code: G14, G13

* Contact: Andrew Karolyi, Fisher College of Business, Ohio State University, 2100 Neil Avenue, Columbus, Ohio 43210-1144, (614) 292-0229, (614) 292-2418 fax, karolyi@cob.ohio-state.edu email. L. Gagnon & G.A. Karolyi, 2003.

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Information, Trading Volume and International Stock Market Comovements¤

1. Introduction

The “Asian flu,” the “Russian virus,” the “Tequila effect” and “international

market contagion” are all popular terms that have been coined to explain the 1990s

phenomenon of large comovements of financial asset prices that cannot be easily

explained by economic fundamentals. The attention these events receive from market

participants and financial media attest to the significance of international market

comovements, in general, for corporate risk management strategies and investors’

portfolio allocation strategies in increasingly integrated global financial markets.1 While

most researchers and market-watchers agree that these phenomena are important to study,

there is little agreement on why they arise. Moreover, to date research has been unable to

identify clearly the channels through which financial price changes in one market

transmit to other markets during crisis periods.2

The goal of this empirical study is to examine the short-run correlations in stock

returns and volatility for the two largest international markets - the U.S. and Japan - and

¤ Karolyi received financial support from the Social Sciences and Humanities Research Council of Canada, the Plan for Excellence at the Richard Ivey School of Business of the University of Western Ontario and the Dice Center for Financial Economics at Ohio State University. Gagnon received support from the D.I. McLeod fund at Queen’s School of Business. We thank Warren Bailey, John Campbell, Rob Engle, Steve Foerster, Raymond Kan, Kai Li, René Stulz and participants at the Western Finance Association (San Diego), Northern Finance Association (Winnipeg), and Pacific Basin Financial Management (Shanghai) meetings and University of Toronto Capital Markets Seminar for very helpful comments. The authors are responsible for any remaining errors. 1 Karolyi (2002) documents 2,083 media “hits” on the Lexis-Nexis search engine for “financial contagion” between the years 1994 and 2002. There are significant increases in hits during the Asian financial crisis in 1997, the Russian crisis in 1998 and in late 2001 during the Argentinian currency crisis. 2 Forbes and Rigobon (2002) formally defines contagion as “a significant increase in the cross-market correlation during a period of turmoil” and as a residual of three mechanisms through which shocks propagate internationally. That is, interdependence results from: (1) global shocks, which simultaneously affect the fundamentals of several markets, (2) competitive shocks, in which shocks from one country affect fundamentals in other countries due to trade or policy coordination, and (3) contagion. Other important recent studies on contagion include Connolly and Wang (2003), Bae, Karolyi and Stulz (2003), and a survey by Claessens, Dornbusch and Park (2001).

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to understand how the levels and changes in these correlations relate to market

fundamentals. We are primarily motivated by a substantial literature investigating the

mechanisms through which short-horizon returns and return volatilities in one market are

transmitted across international time zones to other markets. These studies of “spillovers”

employ multiple time-series econometric models for high frequency, intraday stock

returns and include important contributions by Eun and Shim (1989), King and

Wadhwani (1990), Hamao, Masulis, and Ng (1991), Lin, Engle, and Ito (1994).3 While a

number of these studies were able to measure the scope of these short-run international

return correlations and indeed found that they change over time, few have been able to

relate these changes to macroeconomic factors successfully. Von Furstenberg and Jeon

(1989), King, Sentana, and Wadhwani (1994), Longin and Solnik (1995) and Ammer and

Mei (1996) examined time-varying weekly and monthly global return correlations and

found that factors such as aggregate dividend yields, interest rates and exchange rates

were only weakly associated with the changes over time.

We are further motivated by a second strand of literature that has rationalized

short-horizon dependence in stock returns in terms of equilibrium models of trading.

Campbell, Grossman, and Wang (1993) (CGW hereafter) develop a heterogeneous

investor model in which risk-averse market makers interact with liquidity traders. The

role of market makers is to accommodate shifts in supply or demand of liquidity traders

for which they are compensated via price concessions. CGW show that price changes

associated with such shifts in aggregate demand of liquidity traders are associated with

heavy trading volume and, since they are not due to any fundamental revaluation of the

3 See also Neumark, Tinsley and Tosini (1991), Ng, Chang and Chou (1991), Koch and Koch (1991), Chan, Karolyi and Stulz (1992), Engle and Susmel (1993, 1994), Bae and Karolyi (1994), Karolyi (1995), Craig, Dravid and Richardson (1995), Karolyi and Stulz (1996) and Ng (2000).

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stock, will tend to be reversed in the next trading period. As a result, trading volume is a

helpful filter for other market agents to distinguish between price movements associated

with public information and those that reflect liquidity-motivated trading. They find that

this theory is able to explain why serial correlation of daily stock index and individual

stock returns fall (rise) on days following higher (lower) trading volume. Wang (1994)

develops an extended model of competitive stock trading in which the sources of

heterogeneity can stem from not only private investment opportunity sets among agents,

but also information asymmetries. Informed agents can rationally trade for informational

and liquidity reasons and these two motivations can lead to different volume behavior

and return/volume dynamics than that put forward by CGW. Blume, Easley and O’Hara

(1994) (BEO hereafter) develop a different model of trading in which agents learn about

the fundamental value of a security by observing not only past prices but also past trading

volume. In their technical trading model, volume signals the precision or quality of the

information in past prices. Conrad, Hameed and Niden (1994) has found empirical

evidence consistent with the predictions of BEO for weekly returns on Nasdaq stocks;

Llorente, Michaely, Saar, and Wang (2002) provide direct tests of CGW for individual

stocks.4 What is common to each of these theories is that volume plays an important role

in explaining short-horizon predictability in stock returns

This paper contributes to the debate on international financial contagion by

integrating these two strands of the literature. Specifically, we are the first to interpret

observed daily and intradaily correlations in returns across national stock markets in the

context of these equilibrium models of trading. We extend the implications of the CGW,

4 Other important heterogeneous agent trading models of the price formation process include Karpoff (1986), Holthausen and Verrechia (1990), Kim and Verrechia (1991), Harris and Raviv (1993), and Kandel and Pearson (1995). Karpoff (1987) and, more recently, Lo and Wang (2000) provide an extensive survey

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Wang and BEO models to an international setting by allowing trading volume to play the

role of signal filter not only for explaining time-varying serial correlation in market

returns, but also for changing cross-market correlations over time. That is, we

hypothesize that there are two types of price movements in international markets:

liquidity-based and information-based price movements. Liquidity-based price

movements are typically associated with higher trading volume. We predict that they will

not only be more likely to be reversed in the next trading period in the same market, but

will also be less likely to “spill over” to the other market because they do not necessarily

reflect a fundamental revaluation of the market. By contrast, information-based price

movements in one market - which are typically associated with low or normal volume

levels - are less likely to be reversed in their own market and are more likely to be

positively correlated with the price changes in the other market. We test this hypothesis

with intraday opening and closing index values for the Nikkei 225 Stock Average and

Standard & Poor 500 Stock index and New York and Tokyo Stock Exchange (First

Section) trading volume from June, 1988 to August 1997.

We offer several new findings. First, preliminary tests using daily S&P 500

returns are consistent with the predictions and findings of CGW (1993) and Conrad et al.

(1994). That is, the positive serial correlation in daily index returns becomes negative

following days with high NYSE trading volume. But this finding holds only for the pre-

Crash period from 1974 to 1987. During the post-Crash period, the relationship between

trading volume and serial correlation for the S&P 500 and Nikkei 225 is much weaker.

Second, using higher frequency open-to-close and close-to-open returns for the S&P 500

and Nikkei 225 indexes in the post-Crash period, important interactions between lagged

of the theoretical/empirical literature on trading volume and the price formation process. See also

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volume and serial correlation are revealed. Moreover, they are concentrated around the

market openings. Third, and most importantly, while we confirm that there exists

significant short-run dependence in returns and volatility between Japan and the U.S., we

offer new evidence that these “spillovers” are sensitive to interactions with trading

volume in the respective markets. The cross-market correlations open-to-close and close-

to-open returns are significantly lower following high volume days in one market or the

other, but yet often exhibit non-linear patterns in the relationship which are not predicted

by theory.

Section 2 offers some detailed background discussion of the theory and empirical

findings and presents the hypotheses to be tested. Section 3 describes our data and

empirical methodology. Results are presented in section 4 and conclusions follow in

Section 5.

2. Background Literature and Hypotheses

2.1 International stock return comovements

International stock return cross-correlations play a key role in international

finance (Solnik, 1974; Karolyi and Stulz, 2003). Recent studies have examined the

dynamics of these cross-correlations and have focused on high-frequency dependence in

returns and the conditional volatility of returns, commonly referred to as “spillovers.”

These studies often draw on multivariate time series models of conditional

heteroscedasticity (GARCH) based on the work of Engle (1982) and Bollerslev (1986).

Hamao, Masulis, and Ng (1990), for example, observe volatility spillovers from New

York to Tokyo, London to Tokyo, and New York to London but find no evidence of

Campbell, Lo and MacKinlay (1997, Chapter 3).

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volatility spillover effects in other directions. Lin, Engle, and Ito (1994) demonstrate that

spillover effects are much more balanced across markets than previously believed and

show that the early evidence was sensitive to measurement of the opening quotes. Bae

and Karolyi (1994) investigate the asymmetric impact of bad news and good news on

stock market volatility and show that the persistence of spillovers originating either in

Tokyo or New York and transmitting to the other market can be understated if this

asymmetric effect is ignored.

Another line of investigation focuses on the fundamental determinants of

international asset return comovements. Von Furstenberg and Jeon (1989) and King,

Sentana, and Wadhwani (1994) study cross-country comovements and document their

propensity to vary over time in relation to macroeconomic factors. Unfortunately, these

models only manage to explain a small part of the covariance dynamics. Ammer and Mei

(1996) and Longin and Solnik (1995) study monthly excess returns and find that

correlations across countries increase over time and are weakly related to dividends and

interest rates. Karolyi and Stulz (1996) focus on daily stock return comovements between

Japan and the U.S. and show that neither macroeconomic announcements nor interest rate

shocks are successful in explaining the dynamics of high-frequency comovements

between the two countries. However, the authors find that these comovements tend to be

high when contemporaneous returns in both markets are high. These and several other

recent studies (such as, Connolly and Wang, 2003) have met with little success in relating

international stock return comovements to fundamental economic variables.

2.2 The role of trading volume

Several recent articles have examined the relationship between trading volume

and predictable patterns in short-horizon security returns. Kim and Verrechia (1991),

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Harris and Raviv (1993), CGW (1993), BEO (1994), and Kandel and Pearson (1995)

develop heterogeneous investor models of the price formation process that highlight the

role of trading volume as a measure of the quality and precision of information in past

price movements.

CGW (1993) propose an asset pricing model which internalizes the negative

volume-serial correlation property. In their model, prices are set through the interactions

of two groups of investors: one set of traders who exhibit time-varying risk aversion and

a second set whose attitude toward risk is constant over time. In this model, if new

information concerning the expected return on the risky asset reaches the market and

everyone interprets this information in the same way, the risky asset’s price will change

but no trades will take place. If, on the other hand, no new information arrives but the

first set of investors becomes more risk averse due to an exogenous shock to their

preferences, they will shift their wealth from the risky asset to the riskless asset. As a

result, this excess supply of the risky asset will be absorbed by the second group of

investors (acting as market makers in the Grossman and Miller (1988) sense). Prices will

then be pushed down to boost expected returns over the next time interval, and trading

volume will increase substantially. Since no fundamental revaluation takes place, this

price reduction will tend to be reversed in the next trading period. Hence, this model

predicts that return reversals will tend to follow high volume days and that no price

reversals will follow average volume days.

BEO (1994) investigate the informational role of volume and its applicability for

technical analysis. They develop an equilibrium model in which aggregate supply is fixed

and traders receive signals with differing quality. Volume is shown to provide

information on information quality that cannot be deduced from the price statistic.

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Sequences of volume and prices are thus dynamically informative, and technical analysis

arises as a natural component of the agents’ learning process. The distinction between

BEO (1994) and CGW (1993) is that the latter model makes specific predictions about

the relation between volume and return autocorrelations.

2.3 Testable hypotheses

None of these studies on international stock return comovements have rigorously

examined the informational role played by trading volume across markets. As volume

may provide information on the precision of the signal from past returns for future

returns (CGW, 1993; BEO, 1994), it is an empirical question as to whether or not trading

volume in one market can filter the signal from returns in that market as they transmit to

returns in another market. We hypothesize that “liquidity-based price movements” -

which will be defined to be those associated with higher trading volume - will not only be

more likely to reverse itself in the next trading period in the same market, but will also be

less correlated with price changes in the other market because it does not reflect a

fundamental revaluation of the market. Similarly, “information-based price movements”

in one market - which we will associate with low or normal volume levels - are predicted

to be more positively correlated with the price change in the other market. The empirical

methodology below is designed to test this hypothesis.

3. Empirical Strategy

3.1 Data

Our sample period extends from January 4, 1974 through April 24, 1997. Our

main series are daily closing index values on the S&P 500 Stock Index and Nikkei 225

Stock Average and total trading volume (in thousands of shares) on the New York and

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Tokyo Stock Exchanges, all of which are obtained from Datastream International. For

our intraday tests, we obtain opening index values for the Nikkei 225 from the Nihon

Keizai Shimbun, or Japan Economic Journal, (May 31, 1988 to May 29, 1992) and from

Datastream International (June 1, 1992 to April 24, 1997).5 The S&P 500 opening index

values were obtained from the Chicago Mercantile Exchange (May 31, 1988 to May 29,

1992) and from Bloomberg and Datastream International (June 1, 1992 to April 24,

1997).

Daily closing returns were constructed as the log difference of closing index

values for the entire period, and are denoted SPCCt and NKCCt.6 For intraday returns, we

construct open-to-close, or “daytime,” returns as the log difference of closing index value

relative to the opening index value on the same calendar day, and are denoted SPOCt and

NKOCt. Close-to-open, or “overnight” returns, are computed from the opening index

value on calendar day t relative to the closing index value on calendar day t-1, and are

denoted SPCOt and NKCOt. Intraday serial correlations for overnight returns will

condition on the previous calendar day’s daytime returns. However, serial correlations of

daytime returns will condition on previous open-to-open returns on the respective

indexes, and are denoted SPOOt and NKOOt. We need to emphasize the fact that trading

hours for the two markets are perfectly non-synchronous so that Tokyo trading hours run

from 7:00 p.m. to 2:00 a.m. New York time whereas New York runs from 9:30 a.m. to

4:00 p.m. We adopt the timing convention that Tokyo trading hours precede New York

trading hours on a given calendar day (See Figure 1). In our cross-country return

correlations, we will examine contemporaneous returns (overnight returns in one market

5 For missing opening quotes for the Nikkei 225 Stock Average from May 31, 1988 to May 29, 1992, we used Bloomberg as a supplement.

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conditional on daytime returns in the other market) and on a lagged basis (opening-hour

or daytime returns in the foreign market conditional on daytime returns in the domestic

market).

FIGURE 1 ABOUT HERE

Volume data from Datastream International represents thousands of shares traded

on the New York Stock Exchange and the First Section of the Tokyo Stock Exchange.

Other studies have employed different measures, such as aggregate turnover (CGW,

1993) and the total number of transactions (Conrad et al., 1994). In order to work with a

stationary time series of volume, we transform the series into logs and de-trend them

using a time trend variable. Figure 2 illustrates the detrended volume series.

FIGURE 2 ABOUT HERE

Finally, we compute an aggregate stock market volatility series for the S&P 500

and Nikkei 225 using a conditional variance measure from a GARCH model (Engle,

1982; Bollerslev, 1986). We employ a GARCH(1,1) specification and estimate it using

daily closing returns for the full sample from January 1974 through April 1997. Details

on the specification, estimation results and residual diagnostics are available from the

authors upon request.

Summary statistics for daily closing index returns on the S&P 500 and Nikkei 225

are presented in Table 1. While the S&P 500 returns are relatively less volatile, on

average, they exhibit much higher negative skewness and excess kurtosis (Panel A). Box-

Ljung tests for serial correlation in raw returns and squared returns are significant for

both series, suggesting the appropriateness of models of time-varying conditional

6 We need to acknowledge each market has its own holidays and weekend returns may be different because of occasional Saturday trading in Tokyo, before 1988. We adopt the reporting convention in Datastream in which Saturday returns are ignored, but use model specifications that allow weekend returns to differ.

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volatility. Subperiod analysis shows the serial correlation patterns diminish over time.

Panel B presents cross-correlations of the returns, their lagged values and the detrended

volume series. Table 2 presents similar evidence, but for the closing, overnight, daytime

and open-to-open returns available from 1988 to 1997. Cross-correlations presented in

Panel B show that Nikkei 225 daytime returns are more highly correlated with previous

overnight returns than overnight returns with previous daytime returns; the opposite is

the case for the S&P 500. The largest cross-market correlations occur for

contemporaneous returns: SPOCt-1 with NKCOt (equal to 0.329) and NKOCt with SPCOt

(equal to 0.267). These patterns are consistent with Becker et al. (1990), Bae and Karolyi

(1994), Lin et al. (1994) and Connolly and Wang (2003).

TABLE 1 ABOUT HERE

TABLE 2 ABOUT HERE

3.2 Domestic tests

Our empirical strategy consists of two stages. First, we concentrate on the

relationship between trading volume and daily returns, similar to CGW (1993). These

represent our domestic tests though they are applied to not only the U.S. but also

Japanese markets for the first time. The second stage will incorporate cross-

autocorrelations between the U.S. and Japanese returns and the interactions with

aggregate trading volume in both markets, which represents the central hypothesis of our

study. We describe the second stage “international spillover” tests in the next subsection.

For daily closing returns for the full sample, we regress stock index returns on the

previous trading day’s closing return to measure the average autocorrelation:

SPCCt = α + β0 SPCCt-1 + δ1 HOLt + δ2 WKDt + εt (1)

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where HOLt and WKDt represent holiday and weekend dummy variables, respectively. A

similar specification applies to NKCCt. We then extend this specification to allow now

for multiplicative interactions of the lagged index return with lagged detrended volume,

its squared value, and a conditional volatility measure:

SPCCt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPCCt-1 + δ1HOLt + δ2WKDt + εt (2)

where VSP,t-1 is the detrended log volume series for the New York Stock Exchange and

hSP,t-1 is the conditional volatility series from the GARCH model. This extended model

captures the interaction between the return autocorrelation and lagged trading volume

with β1, lagged volume squared with β2, and conditional volatility with β3. CGW predicts

that return autocorrelations will be less positive following high volume days than

following low volume days. That is, β1 is expected to have a negative value. β2 captures

any potential nonlinearity in the autocorrelation-volume relationship. Finally, β3

measures an association between autocorrelations and conditional volatility, uncovered in

earlier studies (LeBaron, 1992). Given that volume and volatility are closely correlated

variables, allowing for an interaction term with conditional volatility presents a more

robust test of the specific role of trading volume in our tests.

We run similar models with intraday returns for the sample period from May

1988 to April 1997. The intraday autocorrelations for overnight returns, SPCOt and

NKCOt, are measured relative to the previous daytime returns and are allowed to interact

with previous day detrended volume and conditional volatility. For the S&P 500, for

example, we propose,

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SPCOt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPOCt-1 + δ1HOLt + δ2WKDt + εt (3)

For daytime returns, SPOCt and NKOCt, the specification is similar except that we

compute intraday autocorrelations relative to the preceding open-to-open index returns,

SPOCt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPOOt + δ1HOLt + δ2WKDt + εt (4)

3.3 International spillover tests

The second stage of our analysis extends the previous tests to allow for returns in

New York or Tokyo to “spill over” to the other market with analogous volume and

volatility interactions specified in equations (2) to (4). Our expanded test equations thus

include the foreign market’s returns and volume/volatility interaction variables in

addition to their domestic counterparts. For daily closing returns, we estimate,

SPCCt = α + β0 SPCCt-1 + γ0 NKCCt + δ1HOLt + δ2WKDt + εt (5)

and its expanded version,

SPCCt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPCCt-1

+ (γ0 +γ1VNK,t + γ2VNK,t2 + γ3hNK,t

1/2) NKCCt

+ δ1HOLt + δ2WKDt + εt (6)

For the intraday return autocorrelations and cross-autocorrelations, we estimate,

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SPCOt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPOCt-1

+ (γ0 +γ1VNK,t + γ2VNK,t2 + γ3hNK,t

1/2) NKOCt

+ δ1HOLt + δ2WKDt + εt (7)

and,

SPOCt = α + (β0 +β1VSP,t-1 + β2VSP,t-12 + β3hSP,t-1

1/2) SPOOt

+ (γ0 +γ1VNK,t + γ2VNK,t2 + γ3hNK,t

1/2) NKOCt

+ δ1HOLt + δ2WKDt + εt (8)

In equations (6) to (8), S&P volume/volatility interactions are captured by the βs while

the γs measure spillover effects from Tokyo. Recall that the purpose of this empirical

investigation is to determine whether volume or volatility interactions observed in one

market, say Tokyo, have any predictive power for returns in the other market, say New

York. On average, we know β0 and γ0 are statistically significantly different from zero

(Hamao et al., 1990, Lin et al., 1994; Bae and Karolyi, 1994). However, if the theories of

CGW (1993) and BEO (1994) can be applied to the international setting, Japanese returns

associated with heavy trading volume will be less informative for traders in New York,

than that those associated with low or normal trading volume. This is the central

hypothesis of our study. We would expect γ0 to be positive, but our foreign volume

interaction parameter, γ1,, to be negative. Possible non-linear effects and volatility

interactions would be captured by γ2 and γ3, respectively.

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4. Results

4.1 Domestic Tests

Table 3 looks at the relationship between trading volume and the autocorrelation

in daily closing stock index returns for the S&P 500 (top panel) and the Nikkei 225

(bottom panel). Each panel reports estimates for equations (1) and (2) for both the pre-

Crash period (January 1974 to September 1987) - which parallels the sample period of

the CGW (1993) study - and the post-Crash period (October 1987 to April 1997). We

present coefficient estimates, robust t-statistics, adjusted R2 and a χ2 test associated with

the null hypothesis that the interaction coefficients -- β1, β2 and β3 in equation (2) – are

jointly equal to zero.

TABLE 3 ABOUT HERE

Regression results for the S&P 500 in the pre-Crash period are virtually identical

to those of CGW (1993). That is, the daily serial correlation for the index (β0) is 0.12 and

statistically significantly different from zero (t-statistic of 6.23). The weekend dummy

coefficient is significantly negative (δ2), consistent with a negative Monday return. The

expanded model that allows for interactions with volume, volume-squared and volatility

shows a statistically significant return reversal (β1 of -0.251 with t-statistic of -3.49)

associated with heavy volume days. No sensitivity to the squared volume or volatility

series is observed, however. These findings are also very similar to the findings of CGW

(1993) and are consistent with the predictions of their model. For the post-Crash period,

daily index serial correlation in the S&P 500 is diminished and evidence of any

significant interactions with volume or volatility is absent. Moreover, the adjusted R2 are

very low. The differences across periods are quite striking.

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Panel B presents the results for the Nikkei 225. While, in the pre-Crash period,

statistically significant positive serial correlation is observed (β0 of 0.065 with t-statistic

of 2.04), interactions with volume and volatility are non-existent. In the post-Crash

period, the results are now consistent with the pre-Crash period for the Nikkei 225,

although now the daily index serial correlation is also absent.

In summary, Table 3 shows that the original findings of CGW (1993) may be

confined to the U.S. market and only for the pre-Crash period and have since

disappeared. One possible explanation for this finding is that the structure of markets has

changed in the U.S. with the advent of new trading practices, like portfolio insurance,

index arbitrage and basket trading (Froot and Perold, 1995). Moreover, the different

results for the Nikkei may be attributable to the distinct behavior of market makers and

differences in market structure between the U.S. and Japan. For example, Hamao and

Hasbrouck (1995) and George and Hwang (1995) have examined the returns and

volatility for stocks traded on the Tokyo Stock Exchange. They show important

differences in daytime and overnight return variances and correlations relative to U.S.-

based evidence, which they suggest may be related to the non-dealer role of the “Saitori”

market-maker on the TSE. In any case, with lower serial correlation in daily index

returns, the power of our regression tests may be significantly diminished. We now turn

to our next set of tests using higher frequency intraday returns.

4.2 Intraday tests

Regression results for open-to-close and close-to-open returns on the S&P 500

and Nikkei 225 are presented in Table 4. We report estimates for equations (3) and (4)

for both indexes which we can contrast with the close-to-close regression results in Table

3. Interestingly, serial correlation in overnight returns on the S&P 500 (relative to the

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previous day’s open-to-close return) is revealed and is statistically significant and

positive (β0 of 0.030 with t-statistic 2.39). For the expanded model, the volume and

volatility interactions are again non-existent. However, we do observe a statistically

significant return reversal associated with the lagged volume-squared variable (β2 of -

0.220 with t-statistic of -1.81), which suggests the possibility of a nonlinearity in the

volume/serial correlation relationship. The serial correlation in open-to-close returns –

which condition on the open-to-open returns during the previous day – is weaker on

average, but is revealed to be significant and positive (β0 of 0.281 with t-statistic of 2.45)

when allowed to interact with conditional volatility (β3 of -0.306 with t-statistic of -2.25).

The adjusted R2 are still low.

TABLE 4 ABOUT HERE

The Nikkei 225 results are quite different. While there was no significant serial

correlation in the daily closing index returns in Table 3, a statistically significant and

positive continuation effect is observed at the open. That is, serial correlation in close-to-

open returns is 0.014 (t-statistic of 2.70). Allowing for the interaction with volume and

volatility, we find that the low average serial correlation results obtains from days with

relatively heavy trading volume and high conditional volatility. The interaction

coefficients with volume and volatility are statistically significant and negative (β1 of -

0.021 with t-statistic of -2.37 and β3 of -0.022 with t-statistic of -2.64). This volume

interaction is consistent with the prediction of CGW (1993). Moreover, for the Nikkei

close-to-open returns, the findings of LeBaron (1992) on the relationship between

conditional volatility and autocorrelation is robust to the existence of volume/serial

correlation interactions. Finally, the serial correlation in open-to-close returns on the

18

Nikkei 225 is weakly significant (β0 of 0.092 with t-statistic of 1.83), but

volume/volatility interactions are non-existent.

Table 4 provides new evidence that the volume/serial correlation relationship in

the S&P 500 and Nikkei index returns is, in fact, observable in the post-Crash period, but

only using finer (intraday) return measurement intervals. In addition, some non-linear

patterns in this relationship are revealed that are not predicted by theory.

4.3 International spillover tests

Hamao et al. (1990), Lin et al. (1994), Engle and Susmel (1993, 1994), Bae and

Karolyi (1994) and Connolly and Wang (2003) have studied how returns that originate in

one market spill over to other markets around the world. Our central hypothesis in this

study is to test whether trading volume represents a signal of the information content of

these returns in the international setting as it does in the domestic setting. The results for

daily closing index returns are presented in Table 5 and for intraday index returns, in

Table 6. In each regression model, we report coefficients associated with domestic serial

correlation and its interactions using βs and the parallel coefficients for the cross-market

effects using γs. We also compute χ2 tests for the domestic and cross-market coefficients.

TABLE 5 ABOUT HERE

Table 5 contrasts the daily index serial correlation and cross-autocorrelation

results for the S&P 500 and Nikkei 225 during the pre- and post-Crash periods. For the

S&P 500 in the pre-Crash period, we see the positive serial correlation, but with the

introduction of significant cross-market effects (γ0 of 0.083 with t-statistic of 2.88) the

negative interaction with volume (in Table 3) surprisingly disappears. During the post-

Crash period, the S&P 500 serial correlation and its interactions with volume and

volatility disappear (as expected in Table 3), but now Nikkei 225 returns are statistically

19

significantly correlated with the S&P 500 (γ0 of 0.085 with t-statistic of 3.76). For the

extended model in the post-Crash period, the volume interactions are negligible, but this

positive “spillover” derives from the conditional volatility of the Nikkei returns (γ3 of

0.105 with t-statistic 4.44) and less so the Nikkei returns themselves (γ0 of -0.077 with t-

statistic of -1.99). This asymmetric response of S&P 500 returns to positive (“good

news”) and negative (“bad news”) Nikkei returns in this returns/volatility interaction are

similar to those uncovered by Bae and Karolyi (1994) and Connolly and Wang (2003).

The lower panel of Table 5 presents results for the Nikkei 225 closing index

returns. In the pre-Crash period, the serial correlation is positive but does not interact

significantly with volume or volatility. As for the S&P 500, the cross-market effects in

the pre-Crash period for the Nikkei are statistically significant. S&P 500 returns

influence Nikkei 225 returns positively (γ0 of 0.224 with t-statistic of 9.59). No

interactions with volume or volatility are observed, however. By contrast, for the post-

Crash period, we find a significant cross-autocorrelation of S&P 500 returns for the

Nikkei 225 (γ0 of 0.443 with t-statistic of 6.28). The most striking finding, however, is

that the volume interactions are statistically significant. We find that the cross-

autocorrelation with the S&P 500 returns are significant and positive (γ0 of 0.316 with t-

statistic of 4.32), but the volume interaction is significantly negative (γ1 of -0.281 with t-

statistic of -2.17) and nonlinear in nature (γ2 of 0.310 with t-statistic of 3.78). That is,

while S&P returns associated with heavy trading volume in New York tend to influence

Nikkei 225 returns more weakly than those returns with normal volume in New York, it

is also true that these S&P 500 returns shocks are larger with unusually high or low

volume. This second-order effect is inconsistent with a direct interpretation of CGW’s

20

(1993) model for the international setting that liquidity-motivated price moves in one

market are likely to be less informative for the other market.

TABLE 6 ABOUT HERE

Table 6 documents the patterns in autocorrelations, cross-autocorrelations and

volume of the S&P 500 and Nikkei 225 for intraday returns. The results for close-to-open

and open-to-close S&P 500 returns suggest that the cross-autocorrelation with Nikkei

225 returns is concentrated around the open. For close-to-open S&P 500 returns, the

sensitivity to a contemporaneous open-to-close Nikkei 225 return is statistically

significantly positive (γ0 of 0.056 with t-statistic of 7.28), and, in the expanded model, the

interactions with volume are significantly negative (γ1 of -0.038 with t-statistic of -3.29)

and nonlinear (γ2 of -0.026 with t-statistic of -1.73). Moreover, the cross-market effects at

the open are also sensitive to interactions with conditional volatility (γ3 of 0.025 with t-

statistic 1.85). For the open-to-close S&P 500 returns, the cross-market effects are

weaker, though statistically significant and positive (γ0 of 0.030 with t-statistic of 1.66).

In addition, the volume interaction with the Nikkei lagged open-to-close return is

significantly negative (γ1 of -0.046 with t-statistic of -1.71). In both cases, the domestic

volume and volatility interactions are negligible and those associated with the Nikkei 225

are significant and mostly consistent with predictions from CGW (1993).

The intraday return autocorrelations and cross-autocorrelations for the Nikkei 225

are surprising. For the closing returns in the post-Crash period, we observed in Table 5

strong cross-autocorrelations with the S&P 500 and significant interactions with volume

and squared volume. For the close-to-open Nikkei 225 returns, the cross-autocorrelations

with the contemporaneous open-to-close S&P 500 returns are statistically significant and

positive (γ0 of 0.139 with t-statistic of 12.56). For the expanded model, the cross-

21

autocorrelation interacts significantly with volume and with positive sign (γ1 of 0.145

with t-statistic of 3.72). It also interacts nonlinearly with volume (γ2 of 0.185 with t-

statistic of 3.69). This finding is unexpected given the predictions of CGW’s (1993)

model; that is, it appears that liquidity-based returns in New York are transmitted more

significantly than otherwise. For the open-to-close Nikkei returns, the lagged S&P 500

open-to-close returns “spill over” significantly with a positive sign (γ0 of 0.225 with t-

statistic of 4.27). In the expanded model, the volume and volatility interactions are not

observed at all. This reinforces our earlier finding that the closing return autocorrelations

and cross-autocorrelations are concentrated around the opening of the markets.

4.4 Robustness tests

In order to evaluate the sensitivity of our findings to various measurement

choices, we investigated three types of robustness tests. The first two tests related to our

measure of volume in each market. Recall that in order to work with a stationary time

series of volume, we transformed the series into logs and detrended using a trend

variable. One supplementary test conditioned the volume series on ex ante economic

variables in addition to the time trend adjustment. Specifically, we allowed trading

volume to depend on changes in U.S. and Japanese daily interest rate and dividend series,

as well as the other market’s past volume. The U.S. interest rate was the daily Federal

Funds rate and the Japanese interest rate was the daily 3-month Gensaki (repurchase

agreement) rate, both available from 1980 with Datastream International. Similarly,

Datastream provided daily dividend yields for the S&P 500 and Nikkei indexes. Several

of these variables were significant predictors of the volume series in each market, yet

most of our findings for the autocorrelations and serial autocorrelations in the market

returns as they interacted with the refined volume series were not changed.

22

Another adjustment to the new volume series was our use of the fitted value from

the new, extended regressions as the interactive variable in the regressions of Tables 3

through 6. Theory offers no guide on whether the predicted or unpredicted component of

the trading volume series is the better filter on information content of price changes.

While many of our findings on the interactions with market returns of the new volume

series were more significant, with some sign changes, our overall inferences about the

importance of volume interactions remained.

A second set of tests concerned the robustness of the volume series as a measure

of the information content of market returns as they “spill over” to the other market. That

is, though large market returns associated with high volume reflect liquidity-based

changes according the CGW (1993) theory, we wanted to test the resilience of such

inferences to interactions that accounted for actual changes in macroeconomic

information. In these tests, therefore, we conditioned all daily and intradaily returns on ex

ante lagged changes in interest rates and dividend yields in the U.S. and Japan and

allowed market returns to interact with not only volume and volatility but also with these

macroeconomic variables. In most cases, these macro variables had predictive power for

the daily and intradaily returns, but the volume and volatility interactions were still

statistically significant. Consider an example of the close-to-open S&P 500 returns, the

strong cross-correlation with the Nikkei open-to-close return persisted (γ0 of 0.026 with t-

statistic of 1.55), but with an even stronger interaction with volume than in Table 6 (γ1 of

-0.039 with t-statistic of -3.41). For Nikkei close-to-open returns, the S&P 500 shocks

were again significant and large (γ0 of 0.131 with t-statistic of 4.71), but the interactive

coefficients on volume and volume-squared were as large as those of Table 6 (γ1 of 0.118

with t-statistic of 3.07; γ2 of 0.185 with t-statistic of 3.92).

23

5. Conclusions

Using intraday prices for the S&P 500 and the Nikkei Stock Average and

aggregate trading volume of the New York and Tokyo Stock Exchanges, we show how

short-run dependence in stock returns and volatility across national markets vary over

time in a way related to the trading volume and liquidity in those markets. We frame our

analysis in the context of equilibrium models of trading developed by Campbell,

Grossman and Wang (1993) and Blume, Easley, and O’Hara (1994). These models

propose an equilibrium relationship between trading volume and stock index return

autocorrelations in which volume represents a signal about the information content of a

given price change. From those models, we hypothesize that liquidity-based price

movements - which are those typically associated with higher trading volume - are more

likely to be reversed in the next trading period and less likely to be transmitted across

markets than those associated with normal trading volume - known as information-based

price changes. Our tests evaluate these theoretical predictions domestically for trading

volume and serial correlation in returns separately for the U.S. and Japanese markets, and

internationally for trading volume and cross-market return correlations between the U.S.

and Japanese markets.

We uncover several new findings. For the domestic market tests, the closing S&P

500 returns during the pre-Crash period are confirmed as consistent with the model

predictions. That is, the positive serial correlation in S&P 500 returns is statistically

significantly lower on days following higher trading volume. However, during the post-

Crash period, the volume/autocorrelation relationship is much weaker. Moreover, we find

no evidence of this relationship for Tokyo’s Nikkei index during the pre- or post-Crash

24

period. Using intraday returns for the S&P 500 and Nikkei 225 indexes in the post-Crash

period, however, important interactions between lagged volume and autocorrelations are

revealed but are concentrated around the open. For the international tests, while we

confirm that there exists significant short-run dependence in returns and volatility

between Japan and the U.S., we offer new evidence that these “spillovers” are sensitive

to interactions with trading volume in both markets. The cross-market effects with

volume are revealed in both close-to-open and open-to-close returns and often exhibit

non-linearities which are not predicted by theory. Moreover, these patterns are robust to

different measures of trading volume and to different conditioning information for market

returns.

Our evidence that large comovements in international markets can be reconciled

with equilibrium models of trading by heterogeneous investors may tempt conclusions

that their existence is not necessarily evidence of international financial contagion.

Unfortunately, it is still too early to make such pronouncements. We do offer, however,

our new evidence as a challenge to existing theories that rationalize trading volume into

the price formation process in markets. In addition, there are a number of limitations in

our work that represent future opportunities for empirical research. First, we use index

returns and, given the work of Miller et al. (1994) and others, important aggregation

biases due to non-synchronous trading of component stocks may affect our results and

interpretations. A useful extension would be to examine whether the volume and

volatility interactions in both domestic and international settings apply to individual

stocks, thus paralleling the recent efforts of Llorente et al. (2002).

Second, we consider only two markets: Japan and the United States. Examining a

broader sample of countries would gauge the sensitivity of our findings to differences in

25

market structures, such as market opening mechanisms, the role of market makers, dealer

versus auction markets, etc. These institutional factors may play an important role in the

relationship between trading volume and short-run persistence in stock prices.

Finally, we examine intraday returns using open and close index values. If these

institutional features of markets are important for the price discovery process,

measurement of price movements over more refined intervals may enable us to

understand their influence better. Comprehensive stock index data across a wide range of

markets at a high frequency, unfortunately, still does not yet exist.

26

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31

Figure 1. Timing Conventions for intraday and overnight returns of Nikkei 225 Stock Average and the Standard and Poor’s 500 stock index, 1/4/74-4/24/97. Daily opening stock index quotes for the Nikkei 225 Stock Average are obtained from the Nihon Keizai Shimbun (The Japan Economic Journal) from May 31, 1988 to May 29, 1992 and from Datastream International from June 1, 1992 to April 24, 1997. Missing opening quotes for the Nikkei 225 index during the May 31, 1988 - May 29, 1992 period were obtained from Bloomberg. For the S&P 500 stock index, daily opening quotes were obtained directly from the Chicago Mercantile Exchange from May 31, 1988 to May 29, 1992, from Bloomberg from June 1, 1992 to July 14, 1992, and from Datastream International from July 15, 1992 to April 24, 1997. Daily closing quotes for both the Nikkei 225 Stock Average and the S&P 500 stock index were obtained from Datastream International for the entire sample period May 31, 1988 - April 24, 1997. Overnight returns (NKCO for Tokyo and SPCO for New York) are computed from each day’s close to next day’s open, daytime returns (NKOC for Tokyo and SPOC for New York) are based on each day’s open-to-close, and open-to-open returns (NKOO for Tokyo and SPOO for New York) are computed from each day’s open to the next day’s open. Timing conventions for a 24-hour period (day t) set the trading day in Tokyo to precede that of New York: Tokyo’s open-close return, NKCOt, is contemporaneous with New York’s overnight return, SPCOt, and both precede Tokyo’s overnight return, NKCOt+1, which is contemporaneous to New York’s open-close return, SPCOt.

Tokyo Trading Hours

S&P 500 Index Open-to-Close Returns

(SPOCt)

S&P 500 Index Close-to-Open Returns

(SPCOt)

Nikkei Stock Average Close-to-Open Returns

(NKCOt+1)

Nikkei Stock Average Open-to-Close Returns

(NKOCt)

Day t

4pm 9:30am

Day t+1 Day t-1

2am 7pm 2am 7pm

New York Trading Hours

32

Figure 2. Detrended Volume Series for the Tokyo Stock Exchange (First Section) and New York Stock Exchange, 1974 to 1997. The raw volume series in number of shares traded is detrended using a regression on a constant and a time trend variable. The regression residuals are plotted.

NYSE Volume

-2-1.5-1

-0.50

0.51

1.52

1988

1990

1992

1994

1996

Tokyo Volume

-2-1.5-1

-0.50

0.51

1.52

1988

1990

1992

1994

1996

33

Table 1: Summary statistics daily closing returns on the Standard and Poor’s 500 Stock Index and the Nikkei 225 Stock Average, 1/4/74-4/24/97. Daily closing stock index values for the Nikkei 225 Stock Average and for the S&P 500 Stock Index as well as daily volume of transactions on the New York and Tokyo Stock Exchanges are obtained from Datastream International Timing conventions for a 24-hour period (day t) set the trading day in Tokyo to precede that of New York: Tokyo’s close-to-close return, NKCCt, precedes New York’s close-to-close return, SPCCt. Log-transformed volume of transactions in New York and Tokyo are denoted as VNK and VSP, respectively. LB(k) is the Portmanteau statistic testing joint significance of the return autocorrelations up to lag k; LB2(k) is the same statistic for the squared returns. ** and * denote significance of the various summary statistics at the 95% and 90% level respectively. 1/4/74-4/24/97 (6080 Observations)

NKCCt SPCCt Mean 0.024 0.034 Variance 1.146 0.878 Skewness -0.170 ** -2.483 ** Kurtosis 17.990 ** 62.770 ** LB(1) 0.510 36.410 ** LB(6) 32.140 ** 47.057 ** LB2(1) 265.063 ** 70.513 ** LB2(6) 559.641 ** 69.028 ** 4/1/74-9/30/87 (3584 Observations) Mean 0.050 0.033 Variance 0.612 0.815 Skewness 0.204 ** 0.115 ** Kurtosis 13.057 ** 1.801 ** LB(1) 4.809 ** 51.502 ** LB(6) 8.420 58.635 ** LB2(1) 0.163 28.953 ** LB2(6) 317.059 ** 258.651 ** 10/1/87-4/24/97 (2496 Observations) Mean -0.013 0.035 Variance 1.912 0.969 Skewness -0.191 ** -5.351 ** Kurtosis 13.013 ** 123.947 ** LB(1) 0.055 1.698 LB(6) 26.420 ** 39.483 ** LB2(1) 126.407 ** 29.485 ** LB2(6) 222.567 ** 151.976 ** Correlation Matrix

NKCCt SPCCt NKCCt-1 SPCC t-1 VNK VSP

1/4/74-4/24/1997 NKCCt 1.000 0.081 0.009 0.241 0.143 -0.002SPCCt 0.081 1.000 -0.035 0.077 0.022 0.043NKCCt-1 0.009 -0.035 1.000 0.082 0.135 -0.012SPCCt-1 0.244 0.077 0.082 1.000 0.060 0.049VNK 0.142 0.022 0.135 0.060 1.000 0.425VSP -0.002 0.043 -0.012 0.049 0.425 1.0001/4/74-9/30/1987 NKCCt 1.000 0.042 0.037 0.164 0.166 0.054SPCCt 0.042 1.000 0.001 0.120 0.039 0.085NKCCt-1 0.032 0.001 1.000 0.043 0.155 0.043SPCCt-1 0.163 0.120 0.043 1.000 0.080 0.103VNK 0.166 0.039 0.155 0.080 1.000 0.649VSP 0.054 0.085 0.043 0.103 0.649 1.00010/1/1987-4/24/97 NKCCt 1.000 0.115 -0.005 0.311 0.155 0.016SPCCt 0.115 1.000 -0.063 0.026 -0.003 0.020NKCCt-1 -0.005 -0.063 1.000 0.115 0.148 -0.019SPCCt-1 0.311 0.026 0.115 1.000 0.037 0.0183VNK 0.155 -0.003 0.148 0.037 1.000 -0.254VSP 0.016 0.020 -0.019 0.018 -0.254 1.000

34

Table 2. Summary statistics for daily closing, overnight, daytime, and daily opening returns for the Standard and Poor’s 500 Stock Index and the Nikkei 225 Stock Average, 5/31/88-4/24/97. Daily opening stock index values for the Nikkei 225 Stock Average are obtained from the Nihon Keizai Shimbun (The Japan Economic Journal) from May 31, 1988 to May 29, 1992 and from Datastream International from June 1, 1992 to April 24, 1997. Missing opening quotes for the Nikkei 225 Stock Average during the May 31, 1988 - May 29, 1992 period were obtained from Bloomberg. For the S&P 500 Stock Index, daily opening quotes were obtained directly from the Chicago Mercantile Exchange from May 31, 1988 to May 29, 1992, from Bloomberg from June 1, 1992 to July 14, 1992, and from Datastream International from July 15, 1992 to April 24, 1997. Daily closing values for both the Nikkei 225 Stock Average and the S&P 500 Stock Index were obtained from Datastream International for the entire sample period May 31, 1988 - April 24, 1997. Overnight returns (NKCO for Tokyo and SPCO for New York) are computed from each day’s close to next day’s open, daytime returns (NKOC for Tokyo and SPOC for New York) are based on each day’s open-to-close, and daily opening returns (NKOO for Tokyo and SPOO for New York) are computed from each day’s open to the next day’s open. Timing conventions for a 24-hour period (day t) set the trading day in Tokyo to precede that of New York: Tokyo’s open-close return, NKCOt, is contemporaneous with New York’s overnight return, SPCOt, and both precede Tokyo’s overnight return, NKCOt+1, which is contemporaneous to New York’s open-close return, SPCOt. LB(k) is the Portmanteau statistic testing joint significance of the return autocorrelations up to lag k; LB2(k) is the same statistic for the squared returns. ** and * denote significance of the various summary statistics at the 95%, and 90% level respectively.

NKCCt NKCOt NKOCt NKOOt SPCCt SPCOt SPOCt SPOOt

Mean -0.016 0.049 -0.066 -0.023 0.048 0.008 0.041 0.056Variance 1.797 0.089 1.663 1.824 0.553 0.087 0.481 0.602Skewness 0.403 ** -0.204 ** 0.562 ** 0.521 ** -0.361 ** -0.224 ** -0.370 ** -0.331 ** Kurtosis 6.209 ** 7.569 ** 7.093 ** 5.978 ** 4.151 ** 11.533 ** 4.483 ** 5.103 ** LB(1) 0.146 1.743 0.092 0.946 2.249 1.509 0.187 1.414LB(6) 11.884 * 64.341 ** 5.880 8.912 11.362 * 22.369 ** 4.878 3.795LB2(1) 46.624 ** 430.995 ** 38.395 ** 38.452 ** 22.289 ** 84.281 ** 60.422 ** 39.080 ** LB2(6) 258.151 ** 1414.502 ** 229.924 ** 225.998 ** 54.437 ** 493.590 ** 72.904 ** 84.124 ** Correlation Matrix

NKCCt NKCOt NKOCt NKOOt SPCCt SPCOt SPOCt SPOOt

NKCCt 1.000 0.387 0.978 0.092 0.122 0.269 0.017 0.276NKCOt 0.387 1.000 0.185 0.274 0.013 0.090 -0.024 0.325NKOCt 0.978 0.185 1.000 0.035 0.127 0.267 0.023 0.221NKOOt 0.092 0.274 0.035 1.000 -0.007 -0.003 -0.006 0.072SPCCt 0.122 0.013 0.127 -0.007 1.000 0.405 0.918 0.173SPCOt 0.269 0.090 0.267 -0.003 0.405 1.000 0.009 0.449SPOCt 0.017 -0.024 0.023 -0.006 0.918 0.009 1.000 -0.005SPOOt 0.276 0.325 0.221 0.072 0.173 0.449 -0.005 1.000NKCCt-1 0.016 0.047 0.006 0.953 -0.021 -0.045 -0.003 -0.009NKCOt-1 0.004 -0.046 0.015 0.171 -0.018 -0.057 0.005 -0.049NKOCt-1 0.016 0.061 0.003 0.976 -0.018 -0.036 -0.004 0.002NKOOt-1 -0.070 -0.082 -0.056 0.024 -0.057 -0.128 -0.007 -0.055SPCCt-1 0.214 0.357 0.147 0.192 0.020 0.050 0.000 0.840SPCOt-1 0.099 0.134 0.075 0.293 0.022 -0.031 0.038 -0.027SPOCt-1 0.189 0.329 0.126 0.082 0.012 0.068 -0.016 0.923SPOOt-1 0.052 0.008 0.053 0.211 -0.015 -0.069 0.014 -0.043

35

Table 3. Test results for trading volume and volatility interactions using daily closing returns for the Standard and Poor’s 500 Stock Index and the Nikkei 225 Stock Average, 1/4/74-4/24/97. We examine the relationship between first order serial correlation in returns and the previous day’s detrended volume for the S&P 500 Stock Index and the Nikkei 225 Stock Average. Daily closing returns on each index are regressed against a constant, the previous trading day’s return on the index, a volume interaction variable based on aggregate trading volume lagged by one period, a second volume interaction based on lagged volume squared, a market volatility interaction variable, a holiday dummy, and a weekend dummy. For instance, using the S&P 500 Stock Index notation, the regression is expressed as follows:

SPCCt = α + (β0 + β1VSP,t-1 + β2VSP,t-12+β3hSP,t-1

1/2) SPCCt-1 +δ1HOLt+δ2WKDt+ε t

VSP represents the detrended volume in Tokyo and is obtained by regressing log-transfomed volume against time. The first volume interaction variable is associated with β1 and measures the influence of the previous trading day’s volume on today’s return autocorrelation. The second volume interaction variable, captured by β2, is used to detect non-linearities in the volume-return autocorrelation relationship while the third interaction variable, which is associated with coefficient β3, measures the impact of the previous day’s conditional market volatility, hSP

1/2, on return autocorrelation. Conditional volatility is modeled as a GARCH(1,1) process following Bollerslev (1986). Regression coefficient t-statistics are based on standard errors robust to serial correlation and heteroscedasticity as in Newey and West (1987). For each regression, the χ2(3) test statistic (with p-value in parenthesis) is for the hypothesis that the interaction parameters, β1, β2, and β3 are jointly equal to zero. ** and * denote significance of the various parameter estimates at the 95% and the 90% level, respectively.

Standard and Poor's 500 Index 1/4/74-9/30/87 α β0 β1 β2 β3 δ1 δ2 Adj. R2

Coefficient 0.049 0.120 0.085 -0.108 0.016t-statistic 2.968** 6.232** 0.983 -2.783** Coefficient 0.059 0.135 -0.251 0.124 0.004 0.082 -0.107 0.020t-statistic 3.464** 1.853* -3.495** 1.003 0.051 0.976 -2.735**

H0: β1=β2=β3 χ2(3) = 13.192 (0.004)** 10/1/87-4/24/97 Coefficient 0.036 0.026 -0.042 -0.004 0.000t-statistic 1.823* 0.324 -1.114 -0.061 Coefficient 0.034* 0.080 0.190 -0.171 -0.014 -0.034 0.006 0.005t-statistic 1.693 0.806 0.463 -0.746 -0.198 -0.653 0.079

H0: β1=β2=β3 χ2(3) = 1.442 (0.696)

Nikkei 225 Index 1/3/80-9/30/87 α β0 β1 β2 β3 δ1 δ2 Adj. R2

Coefficient 0.059 0.065 -0.106 0.0480 0.004t-statistic 3.039** 2.035** -2.390** 0.049 Coefficient 0.052 -0.051 0.078 -0.027 0.003 -0.126 0.042 0.004t-statistic 2.593** -0.458 1.025 -0.332 0.029 -2.551** 0.825

H0: β1=β2=β3 χ2(3) = 1.458 (0.692) 10/1/87-4/24/97 Coefficient 0.033 -0.005 0.045 -0.246 0.004t-statistic 1.082 -0.128 1.354 -3.272** Coefficient 0.032 0.013 0.020 0.042 -0.017 0.064 -0.256 0.004t-statistic 0.948 0.173 0.293 0.469 -0.581 1.734* -3.295**

H0: β1=β2=β3 χ2(3) = 0.842 (0.839)

36

Table 4. Test results for trading volume and volatility interactions using daily closing, overnight, and daytime returns for the Standard and Poor’s 500 Stock Index and the Nikkei 225 Stock Average, 5/31/88-4/24/97. We examine the relationship between first order serial correlation in returns and the previous day’s detrended volume for the S&P 500 Stock Index and the Nikkei 225 Stock Average. Daily closing, overnight, and daytime returns on each index are regressed against a constant, the previous trading day’s return on the index, a volume interaction variable based on aggregate trading volume lagged by one period, a second volume interaction based on lagged volume squared, a market volatility interaction variable, a holiday dummy, and a weekend dummy. For instance, using the S&P 500 Stock Index notation, the three regressions are expressed as follows:

SPCOt = α + (β0 + β1VSP,t-1+ β2VSP,t-12+β3hSP,t-1

1/2) SPOCt-1 +δ1HOLt+δ2WKDt+ε t SPOCt = α + (β0 + β1VSP,t-1+ β2VSP,t-1

2+β3hSP,t-11/2) SPOOt +δ1HOLt+δ2WKDt+ε t

VSP represents the detrended volume in Tokyo and is obtained by regressing log-transfomed volume against time. The first volume interaction variable is associated with β1 and measures the influence of the previous trading day’s volume on today’s return autocorrelation. The second volume interaction variable, captured by β2, is used to detect non-linearities in the volume-return autocorrelation relationship while the third interaction variable, which is associated with coefficient β3, measures the impact of the previous day’s conditional market volatility, hSP

1/2, on return autocorrelation. Conditional volatility is modeled as a GARCH(1,1) process following Bollerslev (1986). Regression coefficient t-statistics are based on standard errors robust to serial correlation and heteroscedasticity as in Newey and West (1987). For each regression, the χ2(3) test statistic (with p-value in parenthesis) is for the hypothesis that the interaction parameters, β1, β2, and β3 are jointly equal to zero. ** and * denote significance of the various parameter estimates at the 95% and the 90% level, respectively. Standard and Poor's 500 Index α β0 β1 β2 β3 δ1 δ2 Adj. R2

SPCO Coefficient 0.020 0.030 -0.055 0.010t-statistic 2.908** 2.388** -3.313** Coefficient 0.021 0.009 0.005 -0.220 0.043 -0.056 0.013t-statistic 3.015** 0.154 0.084 -1.808* 0.522 -3.373**

H0: β1=β2=β3 χ2(3) = 3.404 (0.333) SPOC Coefficient 0.019 -0.001 0.126 0.004t-statistic 1.151 -0.046 3.289** Coefficient 0.015 0.281 0.031 0.015 -0.306 0.126 0.012t-statistic 0.927 2.450** 0.252 0.051 -2.252** 3.362**

H0: β1=β2=β3 χ2(3) = 5.478 (0.140)

Nikkei 225 Index α β0 β1 β2 β3 δ1 δ2 Adj. R2

NKCO Coefficient 0.053 0.014 -0.015 0.003t-statistic 7.582** 2.696** -0.850 Coefficient 0.055 0.044 -0.021 0.004 -0.022 -0.013 0.008t-statistic 7.845** 3.256** -2.365** 0.265 -2.643** -0.767

H0: β1=β2=β3 χ2(3) = 12.776 (0.005)** NKOC Coefficient -0.006 0.030 -0.280 0.008t-statistic -0.208 0.994 -3.536** Coefficient -0.005 0.092 -0.029 -0.040 -0.023 -0.271 0.011t-statistic -0.170 1.830* -0.506 -0.434 -1.568 -3.425**

H0: β1=β2=β3 χ2(3) = 3.191 (0.363)

37

Table 5. Regression results for the international return spillover model for daily closing returns for the Standard and Poor’s 500 Stock Index and the Nikkei Stock Average, 1/3/80-4/24/97. We examine the relationship between first order serial correlation in returns and the previous day’s volume shocks for the S&P 500 Stock Index and the Nikkei 225 Stock Average. Daily closing returns on each index are regressed against a constant, the previous period’s return on the index, a volume interaction variable based on aggregate trading volume lagged by one period, a second volume interaction based on lagged volume squared, a market volatility interaction variable, a holiday dummy, and a weekend dummy. For instance, using the S&P 500 Stock Index notation, the regression is expressed as follows: SPCCt = α +(β0 + β1VSP,t-1+ β2VSP,t-1

2+β3hSP,t-11/2)SPCCt-1 + (γ0 + γ1VNK,t + γ2VNK,t

2+ γ3 hNK,t1/2) NKCCt+δ1HOLt+δ2WKDt + ε t

VSP and VNK represent the detrended volume in New York and Tokyo, respectively, and are obtained by regressing log-transfomed volume against time. The first set of volume interaction variables is associated with β1 and γ1 and measures the influence of the previous trading day’s volume on today’s return autocorrelation in each market. The second set of volume interaction variables, captured by β2 and γ2, is used to detect non-linearities in the volume-return autocorrelation relationship while the third set of interactions, which is associated with coefficients β3 and γ3, measures the impact of the previous day’s conditional market volatility, hSP

1/2 and hNK1/2, on return autocorrelation. Conditional volatility is modeled as a GARCH(1,1) process following Bollerslev (1986).

Regression coefficient t-statistics are based on standard errors robust to serial correlation and heteroscedasticity as in Newey and West (1987). For each regression, the first χ2(3) test statistic (with p-value in parenthesis) is for the hypothesis that the domestic interaction parameters, β1, β2, and β3, are jointly equal to zero while the second χ2(3) test statistic is for the hypothesis that the foreign interactions, γ1, γ2, and γ3, are jointly equal to zero. ** and * denote significance of the various parameter estimates at the 95% and the 90% level respectively. Standard and Poor's 500 Index 1/3/80-9/30/87 α β0 β1 β2 β3 γ0 γ1 γ2 γ3 δ1 δ2 Adj. R2

Coefficient 0.075 0.046 0.083 0.079 -0.151 0.011t-statistic 3.352** 1.904** 2.878** 0.907 -2.820**Coefficient 0.083 0.239 -0.065 0.037 -0.194 0.118 -0.032 -0.032 -0.016 0.098 -0.176 0.011t-statistic 3.535** 2.098** -0.367 0.152 -1.597 1.406 -0.327 -0.386 0.268 1.058 -3.159**

H0: β1=β2=β3 χ2(3) = 3.051 (0.384) H0: γ1=γ2=γ3 χ2(3)= 1.496 (0.683) 10/1/87-4/24/97 Coefficient 0.035 -0.011 0.085 -0.055 0.017 0.012t-statistic 1.757* -0.137 3.762** -1.429 0.261Coefficient 0.021 0.115 0.357 -0.305 -0.058 -0.077 0.001 0.006 0.105 -0.053 0.037 0.052t-statistic 1.053 1.404 0.879 -1.385 -1.141 -1.989* 0.021 0.131 4.439** -0.994 0.500

H0: β1=β2=β3 χ2(3) = 12.471 (0.006)** H0: γ1=γ2=γ3 χ2(3) = 20.091 (0.000)** Nikkei 225 Index 1/3/80-9/30/87 α β0 β1 β2 β3 γ0 γ1 γ2 γ3 δ1 δ2 Adj. R2

Coefficient 0.046 0.044 0.224 -0.081 0.052 0.072t-statistic 2.493** 1.432 9.586** -1.808* 1.020Coefficient 0.027 0.015 0.065 -0.004 0.011 0.169 0.141 0.037 0.007 -0.107 0.045 0.076t-statistic 1.385 0.137 0.912 -0.059 0.124 1.913* 1.107 0.191 0.081 -2.052* 0.940

H0: β1=β2=β3 χ2(3) = 1.664 (0.645) H0: γ1=γ2=γ3 χ2(3) = 5.089 (0.165) 10/1/87-4/24/97 Coefficient 0.016 -0.042 0.443 0.043 -0.240 0.102t-statistic 0.555 -1.185 6.275** 1.010 -3.295**Coefficient 0.030 0.069 0.015 0.009 -0.065 0.316 -0.281 0.310 0.030 0.053 -0.231 0.121t-statistic 0.983 1.219 0.286 0.129 -2.318** 4.321** -2.171** 3.778** 0.464 1.153 -3.037**

H0: β1=β2=β3 χ2(3) = 5.530 (0.137) H0: γ1=γ2=γ3 χ2(3) = 50.538 (0.000)**

38

39

Table 6. Regression results for the international return spillover model for daily closing, overnight, and daytime returns for the Standard and Poor’s 500 Stock Index and the Nikkei Stock Average, 5/31/88-4/24/97. We examine the relationship between first order serial correlation in returns and the previous day’s volume shocks for the S&P 500 Stock Index and the Nikkei 225 Stock Average. Daily closing, overnight, and daytime returns on each index are regressed against a constant, the previous period’s return on the index, a volume interaction variable based on aggregate trading volume lagged by one period, a second volume interaction based on lagged volume squared, a market volatility interaction variable, a holiday dummy, and a weekend dummy. For instance, using the S&P 500 Stock Index notation, the three regressions are expressed as follows: SPCOt = α + (β0 + β1VSP,t-1+ β2VSP,t-1

2+β3hSP,t-11/2) SPOCt-1 + (γ0 + γ1VNK,t + γ2VNK,t

2+ γ3 hNK,t1/2) NKOCt +δ1HOLt+δ2WKDt + ε t

SPOCt = α + (β0 + β1VSP,t-1+ β2VSP,t-12+β3hSP,t-1

1/2) SPOOt + (γ0 + γ1VNK,t + γ2VNK,t2+ γ3 hNK,t

1/2) NKOCt +δ1HOLt+δ2WKDt + ε t

VSP and VNK represent the detrended volume in New York and Tokyo, respectively, and are obtained by regressing log-transfomed volume against time. The first set of volume interaction variables is associated with β1 and γ1 and measures the influence of the previous trading day’s volume on today’s return autocorrelation in each market. The second set of volume interaction variables, captured by β2 and γ2, is used to detect non-linearities in the volume-return autocorrelation relationship while the third set of interactions, which is associated with coefficients β3 and γ3, measures the impact of the previous day’s conditional market volatility, hSP

1/2and hNK1/2., on return autocorrelation. Conditional volatility is modeled as a GARCH(1,1) process following Bollerslev (1986).

Regression coefficient t-statistics are based on standard errors robust to serial correlation and heteroscedasticity as in Newey and West (1987). For each regression, the first χ2(3) test statistic (with p-value in parenthesis) is for the hypothesis that the domestic interaction parameters, β1, β2, and β3, are jointly equal to zero while the second χ2(3) test statistic is for the hypothesis that the foreign interactions, γ1, γ2, and γ3, are jointly equal to zero. ** and * denote significance of the various parameter estimates at the 95% and the 90% level respectively. Standard and Poor's 500 Index α β0 β1 β2 β3 γ0 γ1 γ2 γ3 δ1 δ2 Adj.

R2

SPCO Coefficient 0.020 0.014 0.056 -0.038 0.066t-statistic 2.905** 1.173 7.283** -2.289**Coefficient 0.022 0.046 0.022 -0.161 -0.030 0.025 -0.038 -0.026 0.025 -0.033 0.081t-statistic 3.138** 0.784 0.406 -1.409 -0.374 1.443 -3.291** -1.730* 1.853* -2.003**

H0: β1=β2=β3 χ2(3) = 3.273 (0.351) H0: γ1=γ2=γ3 χ2(3) = 23.724 (0.000)** SPOC Coefficient 0.023 -0.011 0.018 0.122 0.004t-statistic 1.370 -0.355 1.242 3.099**Coefficient 0.023 0.338 0.096 0.059 -0.385 0.030 -0.046 -0.032 -0.034 0.128 0.016t-statistic 1.413 3.136** 0.768 0.198 -2.896** 1.661* -1.709* -0.696 -0.786 3.321**

H0: β1=β2=β3 χ2(3) = 9.329 (0.025)** H0: γ1=γ2=γ3 χ2(3) = 4.491 (0.213) Nikkei 225 Index α β0 β1 β2 β3 γ0 γ1 γ2 γ3 δ1 δ2 Adj.

R2

NKCO Coefficient 0.046 0.013 0.139 0.000 0.108t-statistic 6.758** 2.444** 12.564** -0.016Coefficient 0.047 0.037 -0.017 0.013 -0.019 0.135 0.145 0.185 -0.029 0.000 0.125t-statistic 6.850** 2.644** -1.975** 0.903 -2.245** 5.007** 3.719** 3.691** -0.918 0.005

H0: β1=β2=β3 χ2(3) = 9.457 (0.024)** H0: γ1=γ2=γ3 χ2(3) = 85.976 (0.000)** NKOC Coefficient -0.011 0.022 0.225 -0.259 0.021t-statistic -0.377 0.687 4.272** -3.232**Coefficient -0.011 0.062 -0.030 -0.032 -0.012 -0.145 -0.164 -0.503 0.502 -0.264 0.030t-statistic -0.223 1.147 -0.521 -0.347 -0.810 -0.619 -0.744 -1.269 1.518 -3.296**

H0: β1=β2=β3 χ2(3) = 1.211 (0.750) H0: γ1=γ2=γ3 χ2(3) = 8.870 (0.031)**