An empirical examination of information, differences of opinion, and trading activity

ELsrnIER

s’ournal of Financial Economics 40 (19%) iO5 iI4

An empirical examination of inhnation, difirrences of’ opinion, and trading activity Hendrik BessembindeP”, Kalok Cl-tan”, Paul J. Seguin?*.” 3Co!!ege of &csiness, Arizona Slate ihitersi~: Tempe. AZ S.5.?87.USA bUni~ersi~ of Michigan Business %hool, Ann Arbor. M 48109. L!SA

(Received November 1994 final version received May 1995)

Abstract We investigate the relations between trading volumes and our proxies for information flows and divergences in opinions. We view S&P 500 Index futures’ open interest as a useful proxy for divergences of traders’opinions, and find that volumes are higher on days when open interest increases than on days with declines. Volume in individual equities is more dosely related to firm-specific information plows, while equity basket volume is more closely associated with market information. This differential impact is greatest for small capitalization stocks where market-wide news has no explanatory power. Key words: Volume; Volatility; Information flows: FL&uresmarkets; Open interest JEL classification: D82: G19

1. Introduction

‘The literature on asset markets has, to a great extent, focused on explaining asset prices with only peripheral attention to trading volume’ conclude Harris and Raviv (1993, p. 475). This statement is particularly pertinent for empirical

*Corresponding author. We thank seminar participants at Arizona State University, University of California- Riverside, Case Western ReserveUniversity, City Polytechnic of Hong Kong, University of Iowa, University of Michigan, University of Missouri, Ohio State University, Pennsylvania State University, the 1995 Annual Meetings of the Western Finance Association, and Mason Gerety, Gautam Kaul. Ananth Madhavan, Steve Slezak, Richard Smith, Bill Schwert (the editor), and Kenneth French (the referee) for their comments and suggestions. 0304~405X/96/il5.00 0 1996 Elsevier Science S.A. All rights reserved SSDI 0304405X9500839

7

work: Despire the importance of the topic, surprisingly little empirical research has addressed the determinants of trading volume. The objective of this study is to address this deficiency by empirically evaluating the determinants of trading activity in individual securities, irading for individual equities stratified by firm size, and trading in a stock ‘basket”, the S&P 500 futures contract. Our investigations uncover several new empirical patterns. Perhaps our mcst intriguing set of findings concerns relations between trading activity and cross-sectional differences of opinion. We assert that the open interest in the S&P 500 Index futures contract, like short interest, represents a useful empirical proxy for the cross-sectional dispersion of traders’ opinions regarding underlying values. Consistent with this assertion, we find that trading volumes are significantly related to this proxy. However, the relation is asymmetric; trading volume on days when open interest increases significantly exceeds volume on days when open interest decreases. Increases in open interest, which we interpret as evidence of diverging opinions, are associated with significantly larger volumes. In contrast, decreases in open interest have no discernible effect on volumes. These relations are robust and arise for aggregate NYSE volume, for each size-ranked portfolio volume, and for index futures volume. The absence of a statistical relation between open interest decreases and futures volum: is particularly striking. With the exception of contract expirations, contracts must be traded for open interest to decline. Thus, the lack of a statistical relation between open interest decreases and futures volume indicates that reductions in open interest must be correlated with some unobservable variable that is itself associated wiih decreases in volume. Following the intuition of Varian (1986), Harris and Raviv (1993), and Shalen [ i93.3), we believe that the most plausible candidate is the cross-sectional vari;;&m in opinions, which is a determinant of both trading activity and or,en interest. We believe these conclusions are important, since they focus atteption on, and provide the first empirical evidence of, the role of variation in agents’ interpretations of common information as a determinant of trading strategies and, therefore, price formation. It has been well documented that volume, volatility, and information flows are all highly contemporaneously correlated.’ However, we document substantial cross-sectional variation in the relations between trading volume and volatility measures, which we view as proxies for information flows. We find that the magnitude of the volume-volatility relation depends on both the type of

‘See Karpoff (1987) for a review. and Gerety and Mulhcrin (1992) and Bessembinder and Seguin (1993) for more recent evidence on the positive relation between trading volume and price volatility, and Mitchell and Mulherin (1994) for evidence on the relation between trading volume and measures of public information flows.

information and the nature of tile security inwIved. We construct separate empirical proxies for f%-m-specific and common or market-wide infu~mation flows. We find that trading volume for individual stocks is more ciosclg related :o our proxy for !;rm-specific information. while trading in the stock bask& is more closely associated with our proxy for market-wide information. The asymmetry is least pronounced for those firms that are in the largest capitalization portfolio and are components of the S&P 500 Index. The asymmetry is most pronounced for portfolios of smail-capitalization equities. where trading volume varies closely with security-specific information flows, but is entirely unrelated to market-wide information. Finding that volumes of both large and small stocks are related to proxies for firm-specific information flows is consistent with the class of Kyle (1985) models, which predict that information is incorporated in prices through agents’ trades. Our evidence indica?es that firm-specific information is incorporated into both small and large stock prices through trading. In contrast, the absence of a relation between proxies for market-wide information flows and small-firm volume indicates that trading activity is not always required for price formation. Small fums’ share prices are known to be sensitive to market information, as evidenced by their large beta coefficients. However, our evidence suggests that these price moves occur without associated trading volume. Perhaps market-makers ascertain the effect of market-wide information on small stocks by simply observing price changes in large firms. Finally, we ailow for day-of-the-week effects in trading volumes. We document inverted U-shaped patterns in both equity and basket volume; across the trading week. We also find that relative to individual equity volumes, basket volumes are higher earlier in the week and lower at the end of the week. Our results are robust to several specification checks, including the use of equalversus value-weighted indices, subperiods, log transformations of volumes. and adjustments of cross-sectiona! dispersion measures to accommodate differences in systematic risk. In the next section, we review the theoretic literature on the determinants of volume. In Section 3, we introduce our empirical methods and data. We perform our empirical results and specification tests in Section 4. In the final section, we provide some conclusions and suggestions for further work.

2. Theoretic determinants of trading volume Several theoretic analyses of volume have emerged recently in the literature. Briefly, these theories suggest that trading volumes in financial markets are determined by (i) traders’ exogenous liquidity needs; (ii) information flows, both public and private; (iii) cross-sectional differences in agents’opinions or assessments of intrinsic value; and (iv) the strategic interactions between informed and

liquidity traders. In this section. we review these themes with the intention of deriving empirically verifiable implications. Trade in any asset occurs because of cross-sectional variation in tr;:der-s’net demand for it. One key determinant of variation in demand for fi~a~acralassets is cross-sectionai di$erences in the information possessed by traders. However., diflerences in information alone do not guarantee that trading will occur. Grossmar? (!976) and Milgrom and Stokey (1982) ncte that each agent may realize ;. counterparty’s willingness to trade can indicate that the counterparty has superior private information. This can lead to a ‘no-Lrade’ equi!Ibrium. Since volume is, indeed, observed in financial markets, theoreticians have sought to identify sets of sufficient conditions that circumvent the no-trade equilibrium. Verrecchia (1981.) shows that heterogeneity in traders’ tastes or endowments can lead to trading, but only one ‘round’ of trading is required. Foster and Viswanathan (1993) show that such heterogeneity can also lead to trading in response to public information announcements, as agents rebalance their portfolios. Kyle (i985), Admati and Pfleiderer (1988), and Foster and Viswanathan (1990) circumvent the no-trade equilibrium by introducing ‘liquidity’ traders, uninformed agents who transact solely to meet exogenous liquidity needs. With liquidity traders in the market, other agents htirlt: incentives to invest in information acquisition. informed trading can occur in these models because prospective counterparties cannot perfectly distinguish informed from liquidity traders. Trading can also occur when no one agent has superior information, but all agents differ in their assessment of common information. For example, in Varian (1986) traders differ in their prior beliefs regarding value, while in Harris and Raviv (1993) and Shalen (1993) traders differ in their interpretation of common signals. Each of these models predicts that trading volume increases with the dispersion of traders’ private valuations. An additional branch of theoretic literature that we addrr.ss concerns the trading behavior of agents who can trade either individual secL.I’+s or a diversified ‘basket’ of securities, such as an index or a futures contract based on an index. Agents with information specific to individual or small grouns of companies (e.g., earnings announcements, dividend changes, merger proposals, and industry-specific news) will trade individual securities. However, Subrahmanyam (1991) and Gorton and Pennacchi (1993) suggest that agents endowed with information relevant for valuing large numbers of’equities (e.g., interest rates or anticipated macroeconomic activity) will prefer to trade the basket, rather than a portfolio of component stocks, for at least two reasons. First, explicit transaction costs for the basket can be substantially lower than those incurred by trading the portfolio of individual securities. Second, adverse selection costs are higher when trading individual securities, since there is a greater chance that the counterparty has superior firm-specific information. Thus, the choice of trading individual securities versus the basket depends crucially on

whether the information held by agents is firm-specific or ccmmofi across secxities. Despite :he intuitive appeal of these mod.els and their predictions, we arc aware of little empirical validation of models that link volume to info~matio~n f?ows, beyond documentation of a positive volume-volatility relation. SLKAI validation is the objective of the empiricai work that follows.

3. Data a.nd empirical methods Investigating relations between information flows and trading activity requires measures of information arrivals. Because traders can choose between trading individual securities or diversified baskets of equities, we construct separate measures of market-wide and company-specific information fio:irs Testing the veracity of differences-of-opinion models also requires a proxy for cross-sectional dispersion of beliefs. Finaliy, we employ control variables that accommodate previously identified regularities in volume, such as the systematic changes in volume associated with futures contract expirations and the da) of the week. In this section, we describe the empirical proxies ana control variables used in our investigation. 3.1. Information flows Ross (1989) shows that in a frictionless market characterized by an absence ot arbitrage opportunities, the rate of information flow is revealed by the degree of price volatiIity. Based on this intuition, we use measures of price votati!ity as proxies for information flows. We do not distinguish pub;ic!y announced information from private information revealed through the trading process. We do, however, distinguish between common and security-specific information flows and construct separate measures of each. We use the volatility of returns to a diversified equity portfolio as our proxy for the arrival rate of common or market information. We then construct a measure of the cross-sectional dispersion of individual security returns that is similar to the one created in Christie and Huang (1991), and use this cross-sectional measure as ;1proxy for the arrival rate of firm-specific information. 3. I. 1. Common irljormation We use lipzyl, the absolute value of the Center for Research in Security Prices (CRSP) value-weighted market return including dividends, to proxy for common information flows. One potential problem with this index is that the CRSP index includes all stocks listed on both the NYSE and AMEX, while our stock ‘bundle’, the S&P 500 Index futures contract, is based on a portfolio of 500 stocks that comprise the S&P index. However, during our sample period the

correlation between CRSP va!ue-weighted market returns and percentage changes in the S&P 500 Index exceeded 0.99. suggesiing that each proxy extracts essentialEy the same infxmetion.

We use absolute deviations of individuai firm returns from market-model cxpccted returns as measures of firm-specific information flows. Capturing all firm-specific information can require as many variables as firms. For tractability, we use the cross-sectional average of these absoiute deviations, computed across all NYSE/AMEX firms on the CRSP file. In the absence of a theoretical reason to prefer one? we construct and investigate two aggregate measures of firm-specific information: MADE” is the equal-weighted average of the betaadjusted differences between firm returns and the equal-weighted market return, or:

while MAD”” IS ’ the value-weighted analog. In each case, betas are estimated using the previous year’s daily data. We note that MAD variables that were not beta-adjusted yielded the same conclusions. One alternative to mean-absolute-deviation statistics is the cross-sectional standard deviation of market-model residuals. We prefer the mean-absolutedeviation metrics for econometric reasons, though below we demonstrate that our results are generally robust to the use of equal- and value-weighted crosssectional standard deviations. The primary reason for preferring a MAD variable is that previous research has demonstrated that the nonnormality of returns in general, and the fat-tans of return distributions in particular, affect standard deviation metrics more than they affect absolute deviation measures.’ 3.2. DiJ-erences OJ opinion

Diamond and Verrscchia (1987) develop a model in which insiders possessing negative information take short positions in individual equities. By implication, short interest represents the sum of such inside information. Recent studies that have empirically investigated links between short interest and equity returns include Woolridge and Dickinson (1994) who find no significant relation between short interest and returns, and Senchack and Starks (1993), Choie and Hwang (1994), and Asquith and Meulbroek (1995) all of whom report a significant negative relation between short interest and equity returns.

%X Davidian and Carroll (1987). Schwert and Seguin (1990), and Granger and Ding (1993).

Though short interest may represent a useful proxy for dilferences in opiniont short-interest data is, unfortunately, not reported on a daily basis. IIowever, open interest III the equity-index f~ltures markets. which is the erdogenously determined number of futures contracts in existence, is available daily. Since open interest equals both the total net long position and total net short position of agents, it is directly analogous to short interest. Open interest reflects the cross-sectional variation in agents” net demand for positions in the equity basket, including the variation attributable to differences of opinion. Of course, open interest is an imperfect proxy fbr differences in opinion, since it can also reflect variation in net demand due to differing endowments or tastes. 3.3. Control

t~ariahles

In assessing relations between information flows and volume, we control for two previously identified determinants of volume. First, to accommodate the empirical regularity that volumes vary by the day of the week, we include indicator variables for each trading day other than Wednesday. The regression intercept thus represents Wednesdays. while the daily indicators measure differences in volume relative to the Wednesday benchmark. We also control for variations in trading activity associated with the S&P 500 futures contract life cycle, since it has been well documented that the period around contract expiration is associated with unusual volume and open interest. 3.4. Data sources and descriptice statistics We use daily trading volumes and open interests for all outstanding S&P 500 Index futures contracts for the period May 1982 to December 1991. We obtain these data from the Columbia University Futures Center and from Data Resources, Inc. We also use composite daily NYSE trading volume for the same period. These data are from Schwert (1990) and from Data Resources, Inc.” Finally, we employ daily return and volume data for individual firms from the CRSP files. Table 1 reports overall and selected annual means of daily futures volume, open interest, and NYSE volume. Fig. 1 displays annual means for NYSE volume, and S&P 500 Index futures volume and open interest. We construct the Index futures’ open-interest and volume series by adding across all active contracts. We also report mean daily share volumes for each of live portfolios formed on the basis of market capitalization. We state futures volume and open interest in terms of total contracts, though similar summary statements can be made for contract dollar values. The levels depicted in Fig. 1 demonstrate the

‘We thank G. William Schwert for these data.

Table 1

Daily means for S&P futures volume, open interest, and equity market volumes, May 1982 to December !99l This table contains daily averages of SRtF 500 Index futures vohune. S&P SC0!ndcx futures open interest. aggregate NYSE trading volume, and the volumes of five size-ranked portfolios. S&P 500 Index futures vclumc and open interest are stated in numbers of contracts, and arc constructed by adding across all active contracts, using data from the Columbia University Futures Center and Data Resources Inc. NYSE volume reflects composite daily trading volume stated in numbers of shares, from Schwcrt (1990) and Data Resources Inc. Portfolio volumes, also stated in numbers of shares. are averaged across firms within five size-ranked portfolios. Portfolio 1 is comprised of the 20% of firms with the smallest market capitalization at the end of the prior year. while portfolio 5 contains the 20% of firms with the larges? market capitalization. --CVC.ia!l 1982 1987 1991 dally daily daily daily mean mean mean mean -_._ S&P 501)Index futures volume (contracts) 50,389 17.080 75,249 48,541 S&P 500 Index futures open interest 124,214 (contracts) 92.402 12.025 152,841 Aggregate NYSE volume 188.96 179.65 (mil!ions of shares) 137.22 71.24 Size-ranked portjXo

1 (smallest) 2 3 4 5 (largest)

drtme

(shares prr firm)

6,326 10,739 22,606 56,585 218,665

2,167 5,456 11,402 28,844 I 12,103 .-.

8,900

15,869 30.319 82,953 309.866

10,380 15,473 32,749 70,161 258,408

tremendous growth in futures trading activity experienced over the first half of our sample: Daily futures volume, in terms of contracts traded, experience year-on-year growth rates of 87.7%, 52.3%, 21.7%, and 29.6%, respectively, in the first four years we examine. Open interest grew similarly, with the dollar values of daily open interest more than doubling in three of the first four years. In comparison, growth rates for NYSE volume during the same period are substantial, but more modest. Following the stock market crash in 1987, both spot and futures volumes suffered setbacks. From the 1987 peak to the end of our sample period, S&P futures and NYSE spot volumes actually declined, while S&P futures’ open interest increased, but at a slower rate than in the first half of the sample. ‘Thesedescriptive statistics illustrate that the volume and open-interest series are not stationary, and that a substantial portion of the time-series variation in trading activity is attributable to secular growth. Fig. 2 displays annual means of our measure of common information flow and both the equal- and

8OuOO-!

I

2ooO0 0 ’ 1982 ’ 1983 ’ 1984 ’ 1985 ’ 1986 ’ 1987 ’ 1988 ’ 1989 ’ 1990 ’ 1991 ’ Average Daily S&P 500 Contract Trading Volume ryI0 q Average Daily S&P 500 Contract Open Interest

n

Average Daily NYSE Share Trading Volume

Fig. 1. Mean daily trading volume and open interest by year. This figure plots average daily values of NYSE share volume, S&P 500 Index futures contract trading volume, and S&P 500 index futures contract open interest. For each day, total tradmg volume across all NYSE stocks deflated by a factor of IO,000 (from Schwert, 1990. and Data Resources, inc.), and total volumes and open interests aggregated across ail active contracts (from the Columbia University Futures Center and Data Resources.Inc.) are collected. Averages across all trading days in a given calendar year are the!; calculated.

value-weighted measures of security-specific information flow. Notably, these measures of information flow do not display trend growth similar to that of trading volume. Accordingly, we do not attempt to explain the trend growth in trading activity, rathz we seek to explain deviations around the trend. To do so, we detrend each volume and open-interest variable and use the detrended variables in subsequent analysis. We report results obtained by calculating the trend as a 40-day moving average, which does not require the trend to be a linear function of time. We then detrend each time series by subtracting its respective moving average. Below, we investigate the robustness of our results to the use of log-transformed activity series, which we detrend by subtracting the moving average of the log-transformed series. Table 2 reports contemporaneous correlations among detrended volumes and open interest, as well as some of our control variables and measures of information flows. Results indicate that both futures and spot volumes are positively and significantly correlated with open interest and changes to it. This correlation provides initial support for the existence of an economic relation between

0 1982 - 1983 - 1984

1985

1986

1987

1988 - 1989

H

Equally-weighted Mear! Absolute Deviation

q n

Value. weighted Mean Absolute Daviation

1990

Average Absolute Return to the Value Weighted CRSP Index

1991 -

I

Fig. 2. Mean daily market-wide and cross-sectional volatili!y. This figure plots average daily values of three mcasurcs of equity-market volatility. The equalweighted mean absolute deviation is the cross-sectional average of the absolute values of betaadjusted differences between firm returns and the equal-weighted market return, computed across all NYSE/AMEX firms on the CRSP file. The value-weighted mean absolute deviation is the weighted average of these differences with the market value of equity used as weights. In each case, betas are estimated using the previous year’s daily data. We also plot the average absolute value of the CRSP value-weighted market return including dividends. Averages across all trading days in a siven calendar year are calculated in percent.

open interest and trading activity. The correlation coeflicient between futures trading volume and MADE” (0.079) is roughly half the correlation between futures trading volume and the absolute market return (0.217). This finding indicates that futures trading activity is more closely related to market volatility, our proxy for the flow of common information, than it is to cross-sectional volatility, our proxy for the flow of firm-specific information. In contrast, the correlation coefficient of NYSE volume with MADEW (0.432) is larger than the correlation with absolute market return (O-397), suggesting that spot trading activity is more closely related to our proxy for firm-specific information flows than it is to flows of market-wide information. Correlations associated with the number of days until a futures contract expires support the need to control for the contract life cycle: All three activity variables are significantly and negatively related to the days until expiration, with futures activity the most highly correlated. However, each of these correlations is simple, not partial. Since severai of the explanatory variables are correlated with each ether, we use

Conlemporancou~ correlations among daily S&P 5tij Index futures volume. oprn interest. NYSE iiading voiume, c!ays untrl nearest inde:r futures contract expiration. and mean absolute return deviation S&P 5G8 Index futures voiumc. and open interest series are constructed by addtnp across all act~vc contidcts, and each series is detrendcd by subtracting its own 4i)-day moving dvcrape. NYSE volume reflects composite daily trading ?lumc. and is also detrendcd by subtracting its S&day moving average. Absolute change in open interest dcnotcs the absolute vaiue of the change in fdetrendcdj futures open interest. Days to contract expiration is the number of tradmg days untii the nearest futures expiration d?y. Mean absctutc return deviation is the cross-sectional average of the absofure values of beta-adjusted differences between firm returns and the equal-weighted market return, computed across all NYSE;AMEX firms on the CRSP file. Absolute market return is the absolute value of the return to the CRSP value-weighted NYSE!AMEX index with dividends. An asterisk (‘“j denotes an estimate whose magnitude is at least two approximate standard errors from zero. --_______--. -----__------.-.-Absolute LIean Futures change in Days to absolute Absolute ::YSE open OpCtl COl7tiaCt return market vo!ume interest interest expiration deviation return __ -__---.-___-.-____ -__--.-_-.-_--~ 0.4tz* 0.393* 0.024 - 0.413* 0.079* O.Z!I’ Futures volume o.t91* 0.432* 0.;95* NYSE volume 0.121* - 0.034 - 0.147* - 0.6i7* Futures open interest 0.114* o.ow* Absoiutr change in open interest 0.104* 0.107* 0.010 Days to contract expiration - o.oca 0.030 Mean absolute return deviation 0.545* ---___~____-__----

a multiple-regression framework to estimate the marginal impacts of these variables eta futures and NYSE volumes. 3.5. Model speciJicatiott To estimate reiations between our set of crt,planatory variables and trading activity in individual stocks and stock baskets we estirnate the following two regression equations:

DTSpot Volume = x, + fisl MADEW + fis2 IRL”j

DTP’utnres b*o!tme is d&trended +?<,ading volume in contracts for the S&F 500 futures market, DTSpot Vohtv is &~-en&xl trading volume in shares on the NYSE, and /LiQpin/ is the unsigned change in futures open interest. To ease comparison of coefkient estimates, w=L multiply each voiume series and the open-in&zest series by a multiple of each series’ mean price so that units represent order flows of $1 million. We 21~0 include six variables that control for futures contract expiration and the day-of-the-week effects, Cj. Subscripts denoting time are omitted throughout. The hypothesis that a change in an explanatory variable is associated with equal doilar trading volumes in the spot and the futures markets can be assessed by comparing estimated coefficients across Eqs. (2) and (3).

3.6. Empirical predictions in thi; subsection, we derive empirical predictions for two sets of variables, prosies for information flows and proxies for differences of opinion.

3.6. I. ITformation flows The arrival of common information should be reflected in an increase in iRzWI, which, based on the theories reviewed above, implies increased futures trading volume and a positive estimate for Prz. However, ;: ‘: also anticipate a positive estimate associated with IRIWI for spot volume for two reasons. First, the effects of innovations in common factors need not be homogeneous across firms. If traders project that a macroeconomic innovation will affect individual firms differentially, they can exploit deviations by taking appropriate positions in individual stocks. Second, futures trading based on common informatron may generate temporary price discrepancies that trigger index arbitrage activity, which requires trades on both the spot and futures markets. The arrival of firm-specific information should be reflected in an increase in M ADEW, the cross-sectional dispersion in prices, which, again relying on the theories reviewed above, implies increased spot trading and, hence, a positive estimate for /Is,. However, increases in firm-specific information may also result in increased futures activity if agents use futures contracts to hedge the systematic component of a spot position established to exploit firm-specific information.

3.6.2. DiJerences of opinion The models of Varian (1986), Harris and Raviv (1993), and Shalen (1993) imply that increased divergences of opinion are associated with increased

trading volume. If so, we expecr to observe a positive relation te~weer! dwngtx in open interest and v~1umes. However, changes in open interest can arise for reasons other than d.ifferences of opinion. For examp!e, endowment changes can lead to changing hedging requirements which in tu.rn leacl ;o changes in open interest. It is also crucial to recognize the existence of meckanicaI Iinks bermen futures trading volume and open interest. Although futures contracts can be traded with no change in open interest, with the exception of ccvttract exri. ration, increases arrll decreases in open interest require contracts tc be traded. implying that any open-interest change is automaticaliy accompanied by futures trading volume. However, such mechanical hnks imply a symmetric reIation between volume and open interest increases and decreases. For open-inreresi changes due to endowment changes or other nocinformacional motiva”riorrr;. a decrease in open-interest would be expected to increase volume a; much as an increase in open interest. In contrast. if a rise (decline) in open interest is due 13 divergence (convergence) of opinion, then a rise in open interest ~,i;l be accomparried by greater volume than wiil a decline in open interest. Thus, the key implication in testing the hypothesis on differences of opinion is not whether futures volume varies with absolute changes in open interest, but. whether the effects of open-interest increases on trading volume are greater than the effects of open interest decreases. To investigate potential Esymmetries in volume respoxei to increases and decreases in open interest, we multiply the unsigned change in open interest by three separate open-interest indicator variables. The first indicator variable equais one if open interest increases, zero otherwise. The second indicator variable equals one if open interest declines, zero otherwise. On contrac: expiration days, the third indictor is set to one and the first two are set to zero. Thus, the coefficient on the first indicator estimates the volume associated ~4th open-interest increases, while the coefficient on the second estimates volume associated with open-interest decreases. The third coefficient accommodates the unique relation between open interest and volume on expiration .%ys. 3.7. Estimatim

We obtain coefficient and standard error estimates using Generalized Method of Moments (GMM). Becztusethe set of instruments kvc use is Zen&al to the set of regressors, coefhcient estimates are identical to those obtained by Ordinary Least Squares (OLS) estimation. However, standard errors, and therefore inferences, differ from those obtained using OLS because we employ the covariance matrix specified by Newey and West (1987a), using ten lags. ‘This procedure yields a covariance matrix that is consistent in the presence of conditional heteroskedasticity and autocorrelation. We use the Wald statistic described by Newey and West (1987b) for testing joint hypotheses, including our cross-equation tests of the equality of coefficient

Tahlc 3 Determinants of daily S&P 500 Index futures and NYSE ir,rding voluncs This table reports coefhcients obtained from repressions of S&P 503 fndex futures and NYSE trading volumes on information-flow proxies and control variables. Each voiume series is detrcnded by subtractmg its own 4%day moving average. and is scaied by a multipie of its associated mean price so that units are order flows of S I million. Absolute market return is the absoluie value of the rriurn (r the CRSP vaiue-weighted index. The absolute cihangc in onen interest is multiplied by three separate indicator variables: (i) a nonexpiration increase indicator that equals 1 on those nonexpiration days when open interest increased and 0 otherwise. (ii) a nonexpiration decrease indicator that cquais 1 on those nonexpiration days when open interest declined and 0 otherwise, and (iii) an S&P 500 contract expiration indicator, which equals I on contrast expiration days and 0 otherwise Cays to contract expiration is the number oi’trading days until the nearest futures expiration day. Panel A reports regression resutls obtained when the mean absolute return deviation (IMAD) is computed as the cross-sectional average ot the absolute values of beta-adjusted diiferences between firm returns and the equal-weighted market return, computed across ail NYSE!‘AMEX firms on the CRSP file. Panel B reports regression results where the &IAD variable is computed as the value-weighted average of the beta-adjusted deviations be:ween individual-firm returns and returns to the value-weighted CRSP index. Coefficient estimaies for the open interest and control variables are not meaningfully altered relative to those reported on panel A, and are not reported. The residual AR(I) coefficient is the simple correlation between regression residuals at one lag. Standard errors based on the Newey- West procedure are in parentheses.An asterisk (*) denotes an estimate whose magnitude is at least two standard errors from 0. We use the Wald statistic from Newey and West (1987b) for hypothesis tests. This statistic is asymptotically distributed z2 with degreesof freedom equal to N, the number oirrsirictions imposed under the null. P-values rcprcscnt the areas to the right of the test statistic under a xi distribution. -

-___--

S&P futures volume

NYSE volume

Test coefficients equal: x2 Cp-value]

1692.23* (457.23)

- 1542.08* (361.84)

49.39

- 259.12 (259.63)

8!9.98* (201.88)

17.81

453.22* (111.41)

282.62* (44.34)

2.77 [0.096]

Parcel A: Equal-weighted MAD

Intercept

CO.~l

Itlforrnaiionpon~ variables Mean absolute cross-sectional return deviation (MAD) Absolute market return

ww

Ahsoiute change ill open interest

(0.321)

1.077* (0.175)

23.13 lY.~l

Nonexpiration decrease

0.102 (0.106)

0.038 (0.044)

0.30 [0.585]

S&P contract expiration

-o-319* (0.139)

0.462* (0.115)

23.77

Nonexpiratioa increase

Test increase = decrease: ,y2 b-value]

2.j.d*

57.81 ro.ow

34.69

I?.~1

W.~l

Table 3 (conrinucd)

- 44.42* (2.91)

0.03 (1.76)

‘67.94 [O.OOO]

Expiratiosi indicator

- 68S.16” (299.99)

632.83” (225.69)

12.53 [O.OOO]

Monday indicator

- f545.22* (74.74)

- 704.e4* (4574j

0.81 [0.368]

Tuesday indicator

25.51 (68.03)

- 169.60* (41.57)

13.16 [O.OOO]

Thursday indicator

- 263.94, (69.72)

- 35.08 (39.74)

Friday indicator

-- 830.34* (79.84)

- 208.35* (47.04)

Test all daily indicators = 0: x2 Cp-value] Regression RZ Residual AR(I) coefiicient Panel B: Fake-weighted

173.80

ww 0.323 0.561

I3.9G WW 89.89

~0.~1

266.04

L-o.ow 0.321 0.542

MAD

Mean absolute cross-sectional return deviation (h4AD) Absolute market return

486.36 (378SS)

1684.95* (158.81)

9.91 [0.002]

244.01* (loo.SO)

33.46* (36.98)

2.71 [0.0993

estimates. We let k denote the number of parameters estimated for each of the two equations, B denote the 2k x 1 vector of coefficient estimates, and R the appropriate !V x 2k restriction matrix for an N-dimensional test of RB = 0. The Wald test statistic for the joint hypothesis is computed as Q = (RB)’ (RWR)-’ x RB, where W is the 2k x 2k covariance matrix of the parameter estimates as described by Newey and West (1987a). The test statistic Q is asymptotically distributed x2 with ATdegrees of freedom.

4. Results The first two columns of Table 3 report the results of estimating our spot and futures volume specifications, respectively. The third column reports x2 test

statistics for the hypotheses that corresponding coe!Ecients are equal across equations. Panel A reports estimates ob tained using the equai-weighted mean of absolute cross-sectionid return deviations, MAi>‘“‘. Panel B report5 selected results when a vatr:a-weighted fi4AD is employed. We alw reporl adjusred .R2’s and the estimated frrstmorder autocorrelations for each specification. The large estimates of residual autacorre*eIation substantiates rmr USC of Newey-.West standard errors th~o@o~!.. 4.1. Comrnorz ir!fomalion

As predicted, the estimated effects of our proxy for common information, [RI”/, on trading volume In both the individual equity and equity basket markets are positive and significant. However, the impact of market information on volume is not symmetric across markets: The estimated effect of a 1% absolute market return on futures volume substantially exceeds that for spot volume ($453 million to $283 million), and the x2 test statistic indicates that this difference is significant at the 10% level. These results are consistent with the reasoning that common information flows are associated with increased trading in both spot and futures markets, but that the security basket is the preferred asset. 4.2. SecuriQvpec$c

information

We also observe a positive and highly significant relation between our prcxy for security-specific information, MADEW, and spot market trading volume. However, in contrast to results for market-wide informarion, the estimated coefhcient linking firm-specific information and trading volume for the basket is negative and statistical!y insignificant. The test statistics for the difference between the two estimates is significant at any standard significance level @-value < 0.001). These findings are consistent with the reasoning that agents with firm-specific information choose to trade exclusively in indivtdual securities rather than trading in a basket. 4.3. Differences of opinion

As discussed above, we view changes in futures open interest as a proxy for changes in the dispersion of traders’ beliefs or opinions. For futures volume, the point estimate on (dOpin for days with declines in open interest is 0.1, implying that when futures’ open interest decreases by ten contracts, futures volume increases by only one contract, on average. The absence of a significant relation between futures volume and decreases in open interest is striking because on

nunexpiratior; days, contracts must be (radsd if open i~?teresfis to dec!inc4 WC view this absence of a relation as evidence thzt reductions in open intcresr must also proxy for some uncbscrvable iariable that is itseif associated with cl,creased volume. such as a convergence of spiiGo77. In contrast. for days thaF experience increases in open intcr~5F. a oncunit change in open interesF is associated with a 2.53~unit increase in basket trading volume. This asymmetry in the reaction of equity baskeF volume to open-interest increases versus deciines is verified by a formal test of the hypothesis that coefficients for increases and decreases are equal (‘Test Increase = Decrease’) The null of equality is rejected with a p-value less than 0.001. Combined, these results are consistent with the joint hypothesis that (i) changes in open interest proxy for changes in the divergence of opinion across traders and (ii) this divergence is a determinant of trading volume. Finally, unsigned changes in open interest on S&P SO0 futures contract expiration days are associated with a statistically significant decline in volume. This reflects the fact that expiration reduces the number of contracts in existence without requiring trading volume. and the fact (discus& belo=w)that expiration days are characterized by relatively light futures trading volume. For NYSE volume. the estimated coefficient for ldOpi~/ for days with increases in open interest is 1.077, while the ctieficient for tdOpirlj for days with declines in open interest is 0.038. Again, the x2 test statistic rejects the hypothesis that the two coefficients are equal at a 0.001 level. The positive relation between open-interesr i<-I.rea.jes and spot-trading volume supports the joint hypothesis that an increase in open interest signals more divergent be!iefs across traders, and that such differences in beliefs are reflected in trading activity for individual equities. Mowever. a decrease in futures open interest, which proxies for a decline in the dispersion of investors beliefs, does not appreciably affect NYSE volume. Unsigned changes in open interest on S&P 500 futtlres contract expiration days are significantly and positively related to spot-market volume. This can be attributed to the previously documented empirical regularities of large reductions in open interest and large ircreases in spot-market trading on contract expiration days (see Bessembinder and Seguin, 1992), although the results here suggest that spot volumes are greater still when a greater number of futures positions are unwound.

%ince, with the exception of contract expirations, a unit change in open interest requires a unit of trading volume, it is tempting to compare the estimated effect of a change in open intertit on iutures volume of a benchmark of one. However, detrended unit; are no ionger directly comparable. Thk results in a benchmark that varies over time, and that can be shown to be generally gwaier than one.

The EStillialCd cffccls of both ixniract lilt?-cycle variatf!es (d~;4,s-ru-ez;pira~ion arid an cspirntiotl-day dummyj on fu!uiw ~dhmle arc” ncgativc and sigaificani. The ilcgatjbil rtrcificior:t cstimalt 011 the c!~rgit;-ii?-esypiraiini~ I;arial-ilc int.kn!cs Flci~rs. The cxpiratiorlthcri f’uttms %dumc increases as contrnct expiration

day indicvtrtr is associated wilf; 3 negstive corffic;ent. indicating that futures !;0lL:IllCS 011 expiration days, When S(i?TkC rcmai!;ing COtliiXti; 2K LlrlWGUTld ~vitho~~ttrading. art: rough!> Sri85 million Iess ~.ht~nwouId be cxpcctcd. For NYSE volumes, the point estimate on day s-to-expiration is insignificant, while the point estimate on the expiration-day indicator is statistically significant and, consistent with Stolf and Whaley (1987). indicates volume on expi:?tion days that is approximately $633 million above normal. These results: which are confirmed by the assoclatcd 2’ test statistics, imply that the futw-es contract life cycle affects baskr;t trading volume throughout the life cyctc, while cffccts on spot-market voiumc are confined to expiration days. Though not reported. these results arc- robust to a!tcrnativc specifications, including use of the square root of days-to-expiration or in(O.5 + days-toexpiration).

in Fig. 3. we piot estimates of daily indicators from both the spot and futures markets specifications as reported in Table 3: except that each coefficient has been divided by the sample-wide average dollar volume for the corresponding market. Consistent with the findings of Jain and Joh (198Q the coefficients indicate an inverted U-shaped pattern for volumes in both markets across the five trading days of the week, with trading activity in each market highest on Wednesdays and lower on Mondays and Fridays. There arc, however, systcmatic difierences in the weekly trading pattern across the futures and spot markets. Rclativc to the volume of individual equities, basket volumes are higher early in the week and lower later in the week. The cross-equation x2 test statistics indicate that these cross-equation differences are statistically significant on Tuesdays, Thursdays, and Fridays. In this specification, the diperences in Monday dollar volume are not statistically significant, though below we observe that the difference on Mondays is statistically significant when stated in percentage terms. Although our original motivation for including day-of-the-week indicators was to control for previously identified patterns in trading volumes, we believe that the cross-market differences in these indicators can be interpreted in the framework of recent models in which liquidity traders behave strategically. For example, Admati and Pfleiderer (1988) and Foster and Viswanathan (1990) assert that the lack of trading opport.unities over the weekend prevents traders

from acting on the hformation they accumulate. Thus, an! information advantage of informed traders relative to liquidity traders is greatest at the resumption of trading. Liquidity :raders who have discretion over the iiming of their trades have incentives to defer their trades until later in the week, by which time an; private information is already reflected in prices. These theoretic models predicts lower trading volumes on Mondays. a prediction rhat they. and we. empirically verify. We extend the intuition of these models and argue that if privaie information accumulated over the weekend nontrading period regarding the overall market is less valuable or more perishable than the private firm-specific information accumulated over the weekend. then discretionary equity-basket traders have a relatively smaller incentive to defer their trades compared to discretionary spot traders. This implication is consistent with our finding that futures volume is higher relative to spot volumeearly in the week, but declines through the week as more discretionary traders with firm-specific information defer their trades. Finally, we note that estimates of first-order residual autocorrelation are large and positive. underscoring the need to use the Newey-West methodology for statistical inference. Further, because autocorrelation remains even though

Absent theoretic guidelines, we chose ;I measure OFfirm-specific information that weights eacil: firm equally. As a :es? of the rotwstness of this decision. we rc-estimate Eqs. (2) and (3) using the vaiue-weighted average oF unsigned deviaticrns of individual returns from the value-weighted market return as our measure of firm-specific information flow. As most point estimates are not meaningfully altered by this adjustment, in panel B of Table 3 we report only the coeiifcients associated. with MAD and the absolute value ol the market return. As in panel A, our proxy for firm-specific information flow is significantly related to the combined volume of individual securities, but not to basket volume. Again, our proxy for the flow of common information is significantly related to volume in both markets. Consistent with the results reported in Section 4.1, the effect on basket volume is greater at a 10% significance ievel. We also re-estimate the specifications reported in Table 3, but replace the &IAD bariabie with a value-weighted cross-sectional standard deviation. Results remain robust. For completeness, we estimate our equations usir.g an equal-weighted cross-sectional standard deviation. A few of our conclusions are sensitive to this specification. However. as Granger and Ding ilti93) note. standard deviations are inherently more sensitive to outliers than are mean absolute deviations. As a result, the signal-to-noise ratio of this measure is lower and the crrorin-variables problem is exacerbated. In our sample, we find that a single large return to a single penny stock can meaningfully affect estimated equal-weighted cross-sectional standard deviations. When the four largest daily returns to individual penny stocks (each in excessof 100%) are purged, all conclusions obtained using equal-weighted cross-sectionai standard deviations are consistent. 4.6.2.

Nonnormality of volume and the et-ask of ‘875

In Table 4. we report estimates of specifications that accommodate two potential criticisms of our previous specifications. First, Ajinkya and Jain (1989)

sWe thank the participants at the Ohio Stale University suggesting some of the robustness tes:s performed.

for outlining

these potential

concerns

and

repoi-2ihat mding vnittme is not norrllally distkt?uti:ci,.t,u?,tti;lr foE-tr~i?:;f(J~~:~~f volwne adheres more doscly to the propci-ties of the nnrmj1: distrit-tutionl. Spccificatlon tests (not reported) confim this regularity in our sampie. Mcnce. in Table ,4, WC report results obraincd when we USC:og-tr;lnsfornlcd v:71i:ines.Fo! this analysis. we &trend volumes by subtracting from each fog serif3 the 40-&t:,) moving average of the log series. Our conclusions arc identical if we instead divide each raw volume number by its 40-day moving average and then take the log of the LJUO~!~“FI~. Though COIIC~US~OIIS are unchanged, point estimates do differ between the two specifications. In the specification used in Table 4, we subtract the average of the log series, which is the sample counterpart of E{ln(s)f, while in the alternative. we subtract the log of the moving average, which is the sample counterpart of ln(E(x:). Using the moments of the lognorma) distribution, E fln(s)l = ln(E{~)) - 4 var{In(x)]~. The results using log-transformed voiume series, which appear in panel A of Table 4. indicate that our results are robust to the monn~rmality of volume. As above, our proxy for the flow of common informa:ion is significantly related to trading activity of individual securities and the security basket. though the significantly larger coefficient associated with basket volume suggests that the basket is the preferred security for trading on common information. Again. our proxy for firm-specific information is statistically unrelated to basket trading activity, but it is positively and significantly related to ?he vo!ume of individual securities. In each market. we observe that increases in open interest are associated with greater volume than are declines in open interest. Each difference is statisticaily significant. This is again consistent ivith the joint hypothesis that open interest proxies for the degree of diflerences of opinion, and that these differences are related to trading activity. Finally, WCagain observe that basket volume is high early in the week and low later in the week, compared to individual equity volumes. with statistically significant differences on each day. As above, we interpret this finding as being consistent with the joint hypothesis that liquidity traders defer trades until the value of private information is dissipated. and that common information is either iess valuable or mere perishable than firmspecific information. The second potential criticism we address stems from the market break in October ‘87. In reaction to the crash, several regulatory initiatives were introduced that affected market trading mechanisms, including regulations that affected the linkage between the spot and futures markets. Thus, it could be argued that the market structure differed significantly in the post-crash period. To address this possibility, we partition our sample as of November i. 1987 and obtain parameter estimates for each subsample. Panel B reports results based on data from the pre-crash subperiod and the week of the market break itself, while the post-crash data are used for results reported in panel C.

of daily s&P 500 futures and NYSE trading volumes measured in logs of contra&

and logs of share

-

~wiahks

----_-

Absolute market return

Mean absolute cross-sectional return deviation IMAD)

Injifrmariorr-jhv

Intercept

0.070’ (0.0191

- 0.013 (0.039)

0.249* (0.072)

Futures volume

0.0371 mw

0.145* (0.019)

0.242* (0.033)

NYSE volume

7.32 [0.007]

P.fJw

27.73

lY*~l

78.16

Test x2 Cp-value] ---

Panel A: May 1982 to December 1991 ---_-

0.035+ (0.014)

0.028 (0.036)

0.165, (0.063)

Futures volume

o.ooo (0.007)

0.249. (0.043)

0.361+ (0.070)

NYSE volume

Panel B: May 1982 to October -

--

6.12 [0.0131

50.83 [0.ooo]

109.63 [wooJ

Test x” Cp-value] -_---

1987

0.118* (0.016)

-- 0.036 (0.039)

0.310* (0.079)

Futures volume

Panel C: November ----.-__.-..-

0.057’ (0.0 12)

00X3* (0.030)

.- 0.199* (0.058)

VdUitlC

NYSE

ww

24.2’1 WJW 25.4X

x1.64 [O.oooJ

Test %” [p-valucJ

19x7 to December 1991 _-._ ._ - -_-_.

This table reportscoeficient estimates from regressions ofdaily log S&P 500 Index futures and NYSE trading voiumcs on information Row vari;lblcs and control variables. Each log-volume series is de&ended by subtracting its own &day moving average. Mean absolute return deviation (MAD) is computed as the cross-sectional average of the absolute values of beta-adjusted differences between firm returns and the equal-weighted market return. computed across all NYSE/AMEX firms on the CRSP file. Absolute market return is the absolute value of the return to the CRSP value-weighted index. The absolute change in open interest is multiplied by the same three indicator variables described in Table 3. Days to contract expiration is the number of trading days until the nearest futures expiration day. The expiration indicator equals 1 on futures expiration dates and 0 othcrwiw. Standard errors. based on the Newey-West covariance matrix, are in parentheses. An asterisk (*) denotes an estimate whose magnitude is al least two approxim;ite slandard errors from 0. The x2 test reported in the third column of each panel is a test of the hypothesis that the associated coefficient is equal across future and NYSE volume. We use the Wald statistic frem hlewcy and West (1987b) for hypothesis tests. This slatistic is asymptotically distnbured x’ with dcgrces of freedom equal to N. the number of rcstrictlons i.mpi -& under the null. P-values represent the arcas to the right ol the lest statistic under a ,j, distribution. -----------...__.~__

Table 4 Determinants

g

2! $ 2. N_ a 2 $ 2. G I= 2 Leo E 5

9 3I w ‘Z:

G 0 -3 s5 < ;k

3 2

-. g

0.006 (0.01 L) - 0.042* (0.012: - 0.155*

Tuesday indicator

Test all daily indicators = 0: X2 [p-valucJ Regression f?’ Residual AK(i) coeficient -... __----.--.-

Friday indicator

Thursday indicator

0.28.7 0.576 --.. . . ..-

ww

517.87

((i.0 I ‘i)

- 0.108* (0.013)

Monday indicator

Expiration indicatol-

- 0.769* lO.OS6) - 0. I46* (0.051I

- 0.298 (0.204) 66.14, [O.Ooo]

3.564* (0.354) 0.670* (0.194)

Days to expiration ( x IO- “)

Control variables

Test increase = decrease: x2 [p-value]

S&P contract expiration

Nonexpiration decrease

Nonexpiration increase

Absolutr! change in rtperr interrsr

23.83 ro.ow 2.43 [0.119] 0.19 CO.6661

231.73 - 0.033 (0.035) W.~l 0.250* 39.74 (0.037) [0.ooo] - 0.163* 26.81 ~0.009) NW - 0.037* 25.75 (0.008) ro.0f-u - 9.009 12.09 IO.i.08) lO.f)oll -- 0.056* 76.14 (0.0 IO) [O.OOO] 394.I6 [O.OOO] 0.261 0.54J

2.173* (0.279) 0.406* (C.117) - 0.163 (0.233) 41.42 ww

1.718* (0.294) 0.221 (O.ll3) -- 0.391 10.211) 27.16 [O.OOO]

- 0.036 (0.044) O.Ibl* 0.036 (0.043) (0.059) - 0. I 16’ - 0.167* (0.01I) (0.01h) - 0.037* 0.004 (0.010) (0.0 14) -- 0.013 - 0.046* (0.010) (0.0 I 6) - 0.070* - q.203* (0.013) (0.018) 274.34 ZOO.6I [0.ooo] [O.OOO] 0.350 0.250 0.5G8 0.59X - 0.576* (0.071)

3.038* (0.342) 0.459* (0.206) - 0.552’ (0.224) 52.05 ~0.~1 95.96 P.ow 5.04 [0.025] 16.49 [ROOO] 16.77 [OSNO] 6.7s [O.OoY] 100.66 [O.CUlo.]

27.05 ww 1.70 CO.1923 0.42 CO.5181

0.56U

c-h.177

~O.WO~

((‘.022) 63.74

.- 0.10~4’

(0.017)

- 0.049*

0.006 (0.017)

(0.071) -- 0.101* (0.019)

- 0.362*

.-- 1.030* jU.083)

39.1 1 CO.~l

(0.386)

- 0.050

6.522” (0.877) 1.412* (0.297)

0.2x* (0.039)

(it.050)

- O.O?

0.04s (0.x%’ - O.fj46” 10.241;) 12.35 [o.rxto]

2.61t’ (0.742,

LJp to this point. we l13ve treated individual firms as fungible. However, as has been well documented, firms that differ by the m ;:,‘cet value of oulstanding equity, or ‘si7e’, vary along a number of important microstructure dimensions, including risk, transaction costs, or --- as suggested by Conrad, Giiitekin, and Kaul (1991) - relevant information sets. To investigate whether the results for the NYSE as a whole are robust across firms of varying market capitalization, we create five annually rebalanced, size-ranked portfolios, and calculate share volume aggregated across all component securities for each of the five portfolios. Wc again use log t;ansfOrined share volume and detrend each volume series. In panel A of Table 5, we report the results obtained when we regress each portfolio volume on the same control variables and information proxies employed earlier. Again, our proxy for the Row of firm-specific information is positively and significantly related to the trading volume for each of the five portfolios. However, this coefficient declines monotonically as firm size iycreases, indicating that firm-specific information has a larger proportional effect on the volume of small firms. Surprisingly,, our proxy for the flow of market-wide information is positive and significant only for the portfolio of the largest firms. Coefficients for the remaining firms arc either insignificant or negative. Though not reported, this result also holds when we use the absolute value of the equal-weighted market return as the proxy for market-wide information flows. It is well established that the prices of small firms do respond to market-wide information - as demonstrated by their large beta coefficients. However, our evidence suggests that price reactions to market-wide information can occur without detectable trading volume. This result is consistent with the reasoning presented by Brennan, Jegadeesh, and Swaminathan (19931, Chan (1193), Jones, Jcaul, and Lipson (19943, and Mech (1993). These studies argue that prices can change in the absence of trading volume, when market-makers or specialists alter their quotes upon observing stock price changes for individual firms or an equity basket. There are at least two potential explanations for the cross-sectional variation in the effect of market information on individual firm volumes. First,

arbitrageurs will trade on the valuation efTectsof markel-wide informHim. but only in those stocks f‘ir which the CO-~ c+sof transacting are sul%cicntly lo\;-. since large stocks generally have lower Iransaction COSTS. Lwch arbitrage activity may be concenbrated in those issues. Second, we doc:ment ;hat the ha&et is the preferr*ed venue for trading bassd on ma&t-wide inf~~riTMtioi~ flow5. !Scwt:ctw. this futures activity may trigger program trades, eilher fdr arbitrage o!* pc~tfolio insurance. both of which typical!y involve spot-market orders for individual components of the S&P 500 Index. We next evaluate the relative importance o f size. per se. relative to c1crri5ership in the basket in expiaining differenti relations between market-wide information and volume. To do so. ive partition the largest-firm portfolio (5) into two subportfolios. one consisting of constituen:c qf the S&P 500 index and one consisting of the remaining firms. 6 We obtained yuarter’ry reports of changes in the S&P 500 from the Compustat tapes, and altered the composition of the two subportfolios at the end of each quarter. On average. our iargc-firm portfolio contains 339 S&P 500 firms and 172 non-S&P 500 firms. WC then repeat the cmpirica! anaty& regressing detrended log volumes for each subport folio on the set of explanatory variables used above. Empirical results for each of these subportfolios and cross-equation test statistics are reported in panel B of Table 5. The estimates indicate that the relation between market-wide informaiiori and volume depends on both firm size and S&P 500 membership. The coefficient linking market-wide information to volume for the large firms that are not members of the S&f‘ 500 is larger than the estimates for the first four size portfolios. This suggests that firm size, and perhaps its attendant liquidity. affects the magnitude of the link between voiume and market information. However, the coefficient on the market-information proxy for the portfolio of large firms included in the S&P 500 is larger than the coefficient for the nonmember subportfolio (0.050 versus 0.03 1, p-value = 0.03 1). Note also that the coefficient measuring volume shifts on S&P 500 contract expiration days is significant only for the subportfolio of firms included in the index. These results are consistent with the hypothesis that, due to differing levels of index arbitrage activity, the relations between volume, market information, and futures contract expiration are dependent on whether a firm is a member of the S&P 500. We note that two of the empirical regularities reported are pervasive across the five portfolios. The inverted U-shape in volume occurs in all five portfolios, although the weekly pattern is not significant for the smallest firms’ portfolio. Finally, we note that the relation between open-interest changes and volume is pervasive; for all five portfolios, increases in open interest are associated with larger volume than are decreases.

‘We thank our referee for this suggestion.

wriohlrs

Absolute market return

Mean absolute cross-sectional return deviation (MAD)

Infimnatinn-jlow

Intercept

-____

0.212” (0.022)

- 0.017* (0.008)

0.222*

- 0.027* (0.01I)

-0.321* (0.038)

2

__

(0.029)

-0.311* (0.054)

1

Size portfoho ___-..

0.011 (0.007)

(0.006)

(0.018)

0.166*

--0.257* (0.032)

4

-.-.-..

- 0.003

(0.012)

0.195*

-0.312* (0.032)

3

.

0.124* (0.02I ) 0.047* (0.01I)

19.82 W.~l.l 26.19 ww

il.39 [0.023]

~. Test cocflcients equal: z2 [-~-value]

-0.213” (0.036)

s

.--..-...

(C.012)

0.050*

(0.020)

0.i25*

- 2.1 t* (0.035)

(0.008)

0.03 1*

(0.0 I81

0. ! 26”

- 0.224’ (O.OXJ

Portfolio 5 firms ..-.. -.----. . S&P Non-S&P SO0firms 500 firms

fp’aluc]

co.03 11

4.65

[0.9;7:j

O.Ohh

0.37 [.0.543_1

2:

fcs1 cnc!Lxnl~ c.~u,tl:

This table reports coefficients obtained from regrpssirns ofdaily log-share volume for size-ranked portfolios on information-Row variabtcs and controi variables. Portfolio I is comprised of the 20% of firms with the smallest market capitalization as of the end of the prior year. Portfoiio 5 contains the 2O?, of firms wi\h the largest captilization. Portfolio 5 firms are further dichotomized based on inclusion in the S&P SO0Index. Each !og-volume series is dctrended by subtr;ictir\g it,, own 40-day moving average. Mean absolute return deviation (MAD) is computed as the cross-sectional average of the absolute va!ucs of beta-adjusicd diKcr;:nces between firm returns and the equal-weighted market return. computed across ail NYSE/AMEX firms on the CRSP file. .Eh~dute market return IS the ;Ihsoiurc value of the return to the CRSP value-weighted index. The absolute change in open in&rest is multiplied by the sa:nc three indicator variables descrihcd in T;tblt: 3. Days to contract expiration is the number of trading days lmtil the nearest futures expiration day. The expiration indicator equals I on futures expiratio;) dates and 0 otherwise. Standard errors, based on the Newey-West covariance matrix, are in parentheses.An asterisk (*) dcnotcs an cstimatc whose mapni?udc i\ at lcasr two approximate standard errors from 0. The x2 test reported in the sixth commn tests whether the coefficients arc equal gross all live portfolios, whiic thL x’-$cst reported in the right-most column tests whether the coetlieicnts for the S&P 500 firms equal those for the non-S&P 500 firms. WC USCtnc Wald statistic frc,m Newey and West t1987b) for hypothesis tests. This statistic is asymptotically distributed $ with dcprecs of freedom equal lo IV. the number ofrcstrrctions imposed under the null. p-values represent the areas to the right of the test statistic under a ;(‘, distribution. _--.--. .._...-.--..------------ .--~ -.- .-....._ ..--~.--______----_.. Panel A: Panel B:

Table 5 Determinants of daily log-share volume for size-ranLed portfolios

.f

II

5. Conshsion We document several empirical reguiarities regarding the relations between information flow and trading volume. Consistent with the implications of Foster and Viswanathan (1993), Kyle (1985), and Ross (1988!, we find that trading volume in both the spot and futures markets varies positively with proxies for information flows. Also, consistent with Gorton and Pennacchi (1993) and Subrahmanyam (1991), we find that the choice of trading venue depends on the nature of the information: Those with firm-specific information trade primarily on the spot equity market. In contrast, those with market-wide information trade in both the spot and a basket with lower transactions costs, but the effect on the volume of the basket is larger. We investigate trading volume for portfolios of firms based on market capitalization and find a reliably positive volume reaction to increased flows of common or market-wide information for large firms only. For smaller firms, our evidence indicates that price reactions to common information shocks are accomplished without detectable effects on trading. in contrast, while firmspecific information affects volumes for all firms, firm-specific information has the largest proportional effect on volumes of small firms. We explore the relations between trading volume and our proxy for the cross-sectional divergences of opinion: The open interest of the S&P 500 Index futures contract. We find that trading volumes in both the spot and futures markets rise as a function of our proxy for differences of opinion, while decreases in open interest have no discernible effect on volumes. These relations occur for aggregate NYSE volume, for each size-ranked portfolio volume, and for index futures volume. Because contracts must be traded for open interest to decline prior to expiration, the lack of a statistical relation between open-interest decreasesand futures volume is striking. It indicates that open-interest decreases proxy for some unobservable variable that is associated with volume declines. Finally, we find evidence consistent with models of strategic behavior by liquidity or uninformed traders. Consistent with previous studies, we find that trading volumes in both the spot market and the basket tend to be relatively low early and late in the week. However, we also document that day-of-the-week effects are asymmetric across markets, with lower futures volume relative to spot volume late in the week. If common information is less valuable or more perishable than firm-specific irrormation, then this result is consistent with the strategic behavior predictions of Foster and Viswanathan (1990). While we document several empirical regularities, we believe that two are particularly important. In our view, the most plausible explanation for our findings linking volume and open interest is that open interest proxies for differences of opinions. Consistent with the models of Varian (1986), Harris and Raviv (1993), and Shalen (1993), these differences of opinion are a determinant of both trading activity and open interest. Our results suggest that a better

understanding of the determinants of trading activity and, by extension, price formation? hinges on improving our understanding of the determinants of cross-sectional variation In traders’ assessments of intrinsic value. Second, our evidence on large-firm and basket a:oiumcs is consistent with the model of Kyle (1985). who predicts that prices change in rehponse to order flows. However, we find no reiation between proxies for market-wide information flows and small-firm volume. This finding affirms that price movements can occur without trading. Brennan, Jegadeesh, and Swaminathan (1993) Chan (1993), Lipson, Kaul, and Jones (1994), and Mech (1993) predict that marketmakers in small stocks need not depend solely on order flows to determine the valuation effects of market-wide information flows. Instead, they can update their quotes based on observed large-firm price changes. We believe that additional research is warranted on identifying those circumstances under which price formation will depend primarily on order flow or on the observation of public information. References Ajinh;a, B. and P. Jam, 1989, The behavior of daily stock market trading volume. Journal of Accounting and Economics 1 I, 331-359. Admati, A. and P. Pfleiderer, 1988, A theory of intraday patterns: Volume and price variability, Review of Financial Studies 1, 3-40. Asquith, P. and L. Meulbroek, 1995, An empirical investigation of short interest. Unpublished working paper (MIT. and Harvard University, Cambridge, MA). Bessembinder, H. and P.J. Seguin, 1992, Futures-trading activity and stock price volatility, Journal of Finance 47, 2015 - 2034. Bessembinder, H. and P.J. Seguin. 1993, Price volatility, trading volume, and market depth: Evidence from futures markets, Journal of Financial and Quantitative Analysis 28. 21. 39. Brennan, M.J., N. Jegadeesh,and B. Swaminathan, 1993, Investment analysis and the adjustment of stock prices to common information, Review of Financial Studies 6, 799 -824. Chan, K., 1993, Imperfect information and cross-autocorrelation among stock prices. Journal of Finance 48, 1211~ 1230. Choie, K.S.N. and S.J. Hwang, 1994, Profitability of short-selling and exploitation of short information, Journal of Portfolio Management 20, 33-38. Christie, W.G. and R.D. Huang, 1991, Equity return dispersions, Unpublished working paper (Vanderbilt University, Nashville, TN). Conrad, J., M.N. Gilltekin, and G. Kaul, 1991, Asymmetric predictability of conditional variances, Review of Financial Studies 4, 5977622. Davidian, M. and R.J. Carroll, 1987, Variance function estimation, Journal of the American Statistical Association 82, 1079- 1091. Diamond, D.W. and R.E. Verrecchia, 1987, Constraints on short-seliing and asset price adjustment to private information, Journal of Financial Economics 18, 277-312. Foster, F.D. and S. Viswanathan, 1990, A theory of interday variations in volumes. variances, and trading costs in securities markets. Review of Financial Studies 3, 593-624. Foster, F.D. and S. Viswanathan, 1993,The effects of public information and competition on trading volume and price volatility, Review of Financial Studies 6, 23-56.

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