Order Imbalance, Liquidity, and Market ReturnsTarun ChordiaRichard RollAvanidhar SubrahmanyamApril 12, 2001ContactsChordiaRollSubrahmanyamVoice:1-404-727-16201-310-825-61181-310-825-5355Fax:1-404-727-52381-310-206-84041-310-206-5455E-mail:Tarun_Chordia@@@:Goizueta Business SchoolAnderson SchoolAnderson SchoolEmory UniversityUCLAUCLAAtlanta, GA 30322Los Angeles, CA 90095-1481Los Angeles, CA 90095-1481This paper owes a significant debt to Charles Lee and Mark Ready for developing thetrade signing algorithm. For helpful comments, we owe a debt of gratitude to ananonymous referee, Hank Bessembinder, Jeff Busee, Clifton Green, Paul Irvine, JonathanKarpoff, Olivier Ledoit, Ross Valkanov, and Sunil Wahal.
Order Imbalance, Liquidity, and Market ReturnsAbstractTraditionally, volume has provided the link between trading activity and returns. Wefocus on a hitherto unexplored but intuitive measure of trading activity: the aggregatedaily order imbalance on the New York Stock Exchange. Signed order imbalancesincrease (decrease) following market declines (rises), which reveals that investors arecontrarians on aggregate. Order imbalances in either direction, either excess buy or sellorders, reduce liquidity. Market-wide returns are strongly affected by contemporaneousand lagged order imbalances. Market-wide returns reverse themselves after high negativeimbalance, large negative return days; the magnitude of this reversal is partiallypredictable from the level of the imbalance and return. Even after controlling foraggregate market volume and liquidity, market returns are affected by order Imbalance, Liquidity, and Market Returns, April 12, 2001
large literature has studied the association between trading activity and stock market returns;(., see Benston and Hagerman, 1974; Gallant, Rossi, and Tauchen, 1992; Hiemstra and Jones,1994; Lo and Wang, 2000; and also the studies summarized in Karpoff, 1987). Stock tradingvolume is also linked inextricably to liquidity (Benston and Hagerman, 1974; Stoll, 1978b). Ouraim here is to shed further light on the tri-partite association among trading activity, liquidity,and stock market returns using a lengthy and recent set of high frequency most existing studies, trading activity is measured by volume. But volume alone is absolutelyguaranteed to conceal some important aspects of trading. Consider, for example, a reportedvolume of one million shares. At one extreme, this might be a million shares sold to the marketmaker while at the other extreme it could be a million shares purchased. Perhaps more typically,it would be roughly split, about 500,000 shares sold to and 500,000 shares bought from themarket maker. Clearly, each possibility has its own unique implications for prices and suggests that prices and liquidity should be more strongly affected by more extremeorder imbalances, regardless of volume, for two reasons. First, order imbalances sometimessignal private information, which should reduce liquidity at least temporarily and could alsomove the market price permanently, as also suggested by the well-known Kyle (1985) theory ofprice formation. Second, even a random large order imbalance exacerbates the inventoryproblem faced by the market maker, who can be expected to respond by changing bid-askspreads and revising price quotations. Hence, order imbalances should be important influenceson stock returns and liquidity, conceivably even more important than volume. Indeed, theOrder Imbalance, Liquidity, and Market Returns, April 12, 20011
inventory models of Stoll (1978a), Ho and Stoll (1981), and Spiegel and Subrahmanyam (1995)involve market makers accommodating buying and selling by outside investors, and liquidity aswell as returns are influenced by inventory concerns in this existing studies analyze order imbalances around specific events or over short periods oftime. Thus, Sias (1997) analyzes order imbalances in the context of institutional buying andselling of closed-end funds; Lauterbach and Ben-Zion (1993) and Blume, MacKinlay, andTerker, (1989) analyze order imbalances around the October 1987 crash; and Lee (1992) doesthe same around earnings announcements. Chan and Fong (2000) analyze how order imbalancechanges the contemporaneous relation between stock volatility and volume using data for aboutsix months. Hasbrouck and Seppi (2001) and Brown, Walsh, and Yuen (1997) study orderimbalances for thirty and twenty stocks, over one and two years, long-term study using order imbalances for a broad cross-section has not been performedprimarily because transactions databases do not identify buyers and sellers. Thus, theinvestigator is obliged to undertake an arduous task: assigning hundreds of millions oftransactions to either the buyer-initiated or seller-initiated categories. Happily, assignmentalgorithms are available for this first contribution is to construct a database of estimated market-wide order imbalances for acomprehensive sample of NYSE stocks during the period 1988-1998 inclusive. Using data fromthe Institute for the Study of Security Markets (1988-1992) and the TAQ database provided bythe NYSE, every transaction is assigned using the Lee/Ready (1991) Of course, 1 The Lee/Ready algorithm is basically quite simple; a trade is classified as buyer (seller) initiated if it is closer tothe ask (bid) of the prevailing quote. The quote must be at least five seconds old. If the trade is exactly at the mid-Order Imbalance, Liquidity, and Market Returns, April 12, 20012
there is inevitably some assignment error, so the resulting order imbalances are estimates. Yet,as shown in Lee and Radhakrishna (2000), and Odders-White (2000), the Lee/Ready algorithm isaccurate enough as to not pose serious problems in our large sample empirical study focuses in sequence on (1) characterizing properties and determinants ofmarket-wide daily order imbalances (2) investigating the relation between order imbalance andan aggregate measure of liquidity,2 and (3) investigating the extent to which daily stock marketreturns are related to order imbalances after controlling for the effects of market liquidity. Toour knowledge, this is the first paper to consider daily order imbalances for a comprehensivesample of stocks over a long sample the aggregate market, asymmetric information is not likely to be an issue, and we expect theinventory paradigm to be more relevant in the interplay between imbalances, liquidity, andreturns. For example, in this paradigm, after a large inventory imbalance, market makersposition their quotes to encourage trading on the other side of the market in order to stabilizetheir inventory. This strategy, if successful, will cause a direct relation between past returns andfuture order imbalances. Further, in this paradigm, imbalances cause price pressures that have adirect effect on returns. Finally, increased return fluctuations cause a widening of the bid-askspread due to an increase in inventory risk. While the intention of our study is mainly toexamine the relation between imbalances, spreads, and returns from a purely empiricalstandpoint, the inventory paradigm serves as the theoretical underpinning of our analysis. As point of the quote, a “tick test” is used whereby the trade is classified as buyer (seller) initiated if the last pricechange prior to the trade is positive (negative.)2 Liquidity is measured by the daily value-weighted quoted spread associated with each transaction during the weights are proportional to market capitalization of each stock at the beginning of the calendar Imbalance, Liquidity, and Market Returns, April 12, 20013
we describe below, our results are broadly supportive of the central implications of this paradigmof price find that the daily levels of order imbalances are persistent, though their first differences arenegatively autocorrelated. In addition, there is evidence that aggregate order imbalance iscontrarian; buying activity is more pronounced following market crashes, and selling activity ismore pronounced following market rises. This evidence is consistent with the notion thattemporary inventory imbalances and consequent price pressures are countervailed effectively byastute analysis also indicates that order imbalances are significantly associated with daily changesin liquidity and with contemporaneous market returns, after controlling for the level of unsignedtrading activity. The latter result underscores the role of excess buying and selling activity, asopposed to just trading volume, as a determinant of fluctuations in market contrast to market returns, we find liquidity is highly predictable not only by its own pastvalues, but also by past market returns. This result is consistent with the notion that increasedasset price fluctuations cause a decrease in liquidity owing to an increase in inventory the daily serial dependence in both order imbalances and liquidity, there is noevidence they can predict one-day ahead stock market returns. Thus, the aggregate market isresilient to market microstructure effects; in general, there is no evidence that the effects ofilliquidity and order imbalance on market returns persist beyond a single day. (The S&P 500 3 Harris and Gurel (1986) and Shleifer (1986) document price pressures when stocks are added to the S&P500 Imbalance, Liquidity, and Market Returns, April 12, 20014
return series was selected as the object to be predicted because its unconditional daily serialcorrelation was virtually zero during the 1988-1998 sample period and we wanted a difficultobjective.) However, there is evidence that large negative order imbalance, large negativereturn days are accompanied by strong reversals, consistent with the block trading literature forindividual stocks (., Kraus and Stoll, 1972), which suggests that large block sells areaccompanied by reversals in stock prices. Our results underscore the point that price pressurescaused by imbalances in inventory are an issue not just for individual stocks, but for theaggregate market as well. This finding has direct implications for agents wishing to trade adiversified market decision to analyze liquidity, order imbalances, and returns over daily intervals is to someextent arbitrary (one could have chosen hourly intervals, or for that matter, monthly intervals).Our justification is, first, the inventory paradigm that motivates our interplay between liquidity,order imbalances, and returns is most likely to be manifest itself over rather short horizons, .,daily as opposed to weekly or monthly; and second, higher than daily frequency poses problemsof inter-asset synchronicity which could make it more difficult to detect market-wide paper is organized as follows. Section 2 describes the data. Section 3 discusses thedeterminants of order imbalance. Section 4 discusses the relation between liquidity and orderimbalances while Section 5 discusses the relation between returns and order imbalances. Section6 S&P500 is our representative stock market index. It was selected because the serialcorrelation in its return series is close to zero (its first-order autocorrelation coefficient wasOrder Imbalance, Liquidity, and Market Returns, April 12, 20015
, p-value=; higher-order coefficients are also close to zero), and we wanted a difficultobject to be The transactions data sources are the Institute for the Study of SecuritiesMarkets (ISSM) and the New York Stock Exchange TAQ (trades and automated quotations).The ISSM data cover 1988-1992 inclusive while the TAQ data are for Inclusion RequirementsStocks are included or excluded during a calendar year depending on the following criteria:• To be included, a stock had to be present at the beginning and at the end of the year in boththe CRSP and the intraday databases, and in the S&P 500 at the beginning of the year.• To keep the size of our sample manageable, and also because signing trades for Nasdaqstocks is problematic (see, ., Christie and Schultz, 1999), and also, we include only NYSEstocks in the calculation of aggregate order imbalance.• If the firm changed exchanges from Nasdaq to NYSE during the year (no firms switchedfrom the NYSE to the Nasdaq during our sample period), it was dropped from the sample forthat year.• Because their trading characteristics might differ from ordinary equities, assets in thefollowing categories were also expunged: certificates, ADRs, shares of beneficial interest,units, companies incorporated outside the ., Americus Trust components, closed-endfunds, preferred stocks and REITs.• To avoid the influence of unduly high-priced stocks, if the price at any month-end during theyear was greater than $999, the stock was deleted from the sample for the year. 4 We also performed regressions using value-weighted and equally-weighted order imbalances for all NYSE stocks,and value-weighted imbalances for NYSE stocks in the top size decile. The results were broadly consistent withthose reported in this paper for the S&P500 index, and are available upon request from the Imbalance, Liquidity, and Market Returns, April 12, 20016
Given that a stock is included in the sample, its transaction data are included or excludedaccording to the following criteria:• A trade is excluded if it is out of sequence, recorded before the open or after the closing time,or has special settlement conditions (because it might then be subject to distinct liquidityconsiderations).• Quotes established before the opening of the market or after the close are excluded.• Negative bid-ask spreads are discarded.• Only BBO (best bid or offer)-eligible primary market (NYSE) quotes are retained (Chordia,Roll, and Subrahmanyam, 2001, provide a justification for using only NYSE quotes).• Following Lee and Ready (1991), any quote less than five seconds prior to the trade isignored and the first one at least five seconds prior to the trade is Order Imbalance VariablesEach transaction is designated as either buyer-initiated or seller-initiated according to the Leeand Ready (1991) algorithm. For each stock-day we compute• OIBNUMt: the number of buyer-initiated less the number of seller-initiated trades on day t.• OIBSHt: the buyer-initiated shares purchased less the seller-initiated shares sold on day t.• OIBDOLt: the buyer-initiated dollars paid less the seller-initiated dollars received on day addition to the order imbalance measures, we also computed the following measures oftrading activity and liquidity:• QSPRt: the quoted bid-ask spread averaged across all trades on day t.• NUMTRANSt: the total number of transactions on day t• $VOLt: the total dollar volume for day tOrder Imbalance, Liquidity, and Market Returns, April 12, 20017
From this point, our analysis focuses on the order imbalance, liquidity, and trading activitymeasures aggregated in a value-weighted manner over all stocks in our sample each day. (Thevalue-weights were computed based on market capitalization as of the end of the previous year.) Summary StatisticsTable 1, Panel A presents descriptive statistics for market-wide order imbalance measures, andother measures of liquidity and trading activity used in this study. The mean/standard deviationratios are of similar magnitude for all three measures of order imbalance. The average quotedspread is about 18 cents, and the average number of transactions is about 658. Interestingly, theorder imbalance measures have positive means and medians. This finding relates to the fact thatwe sign market orders in our analysis, which suggests that the excess of buy market orders oversell market orders is accommodated by the limit order book, provided specialists succeed inmaintaining zero inventory levels on average. Since returns have been overwhelmingly positiveover our sample period, this suggests that limit orders have generally been on the wrong side ofthe trades in the B gives correlations among the three measures of the order imbalance, the concurrent dailyreturn on the S&P500 index, dollar volume, and the total number of transactions. All variablesare strongly positively correlated, with the exception of the correlations between the S&P500return and NUMTRANS, and the S&P500 return and $VOL, which are virtually zero. Thispoints to the notion that the variable which relates trading activity to returns is order imbalance,rather than aggregate trading Imbalance, Liquidity, and Market Returns, April 12, 20018
Panel C reports autocorrelations. Market order imbalances are persistent up to five daily lags butthe S&P500 return has no autocorrelation of any significance. Thus, the market appears to takeimmediate account of the forecastable portion of the persistence in Changes in thequoted spread are significantly negatively autocorrelated at lags of one and two days and arepositively autocorrelated at a lag of five days; the latter reveals a weekly seasonal in the we will report regression results measuring order imbalance in transactions only. Wemade this choice for the following reasons. First, the share measure of order imbalance isinfluenced by stock splits and reverse splits, whereas the number of transactions is not directlyinfluenced by these events. Further, the dollar measure of order imbalance includes the pricelevel, and return and liquidity forecasts using a variable that includes the past price level maylead to misleading conclusions. Thus, given the high correlations among different measures oforder imbalance, and based on the work of Jones et al. (1994) mentioned earlier, we perform ourregressions using OIBNUM; all three measures yield qualitatively similar . What Causes Order Imbalance?On a given day, market-wide order imbalance could conceivably be caused by many returns and changes in macroeconomic variables such as interest rates immediately cometo mind. There is also some reason to expect weekly regularities in order imbalance, given theregularities in daily returns (see, ., Gibbons and Hess, 1981) and the weekly regularities inmarket liquidity documented by Chordia, Roll, and Subrahmanyam (2001). Finally, if temporary 5 An interesting feature of the OIBNUM series is that its first differences exhibit strong negative autocorrelationwhich decays Imbalance, Liquidity, and Market Returns, April 12, 20019
price pressures caused by imbalance are reversed by other traders, one would expect this tomanifest itself in the order imbalance on the above arguments, in this section we ask whether order imbalance can be predictedusing past market returns after controlling for weekly regularities and past lagged values of orderimbalance. Thus, the daily order imbalance in number of transactions (OIBNUM) is regressedon day-of-the-week dummies and variables designed to capture past up-market and down-marketmoves, and on past values of order Regression ResultsThe time-series regression described above is reported in Table 2. The results show that, inaggregate, investors act as contrarians. They buy after market declines and sell after marketadvances. This behavior is particularly significant for market declines. For both marketadvances and declines, the behavior persists for up to three order imbalances are highly predictable, returns on the S&P500 index are virtuallyuncorrelated. During our sample period, the first-order autocorrelation coefficient of theS&P500 daily return is (p-value=), and higher-order coefficients are also close to , order imbalances respond to past market moves in a manner that makes the S&P500close to a random walk. The order imbalance pattern is consistent with price pressure caused byinventory imbalances on a given day which is corrected by some investors taking the oppositeside of the market on the succeeding day. This phenomenon will be examined further in Imbalance, Liquidity, and Market Returns, April 12, 200110
As Table 2 also reveals, there appears to be a significant Wednesday regularity in orderimbalance. However, from Chordia et al. (2001), trading activity itself tends to be higher duringmid-week. To ascertain whether the above results are driven by trading activity per se, we scaledthe dependent variable OIBNUM by the total number of transactions (see Panel B of Table 2).There remains strong evidence of a contrarian pattern in investor trading. The weekly seasonalsare now insignificant, suggesting that there is no significant seasonality in order imbalance aftercontrolling for the overall level of trading Summary of ResultsThe central results in this section are consistent with the inventory paradigm. In particular, theparadigm suggests that after an event that causes a large inventory imbalance on one side of themarket, market makers set quotes to elicit trading on the other side of the market. Our evidencethat investors are contrarians on aggregate, ., they are net sellers after market rises, and viceversa, indicates that they are successful in this endeavor and that temporary price pressures are,in general countervailed effectively by financial market . The Relation Between Liquidity and Order ImbalanceTheoretical paradigms of price formation predict that liquidity is influenced by inventoryconcerns caused by an imbalance between buyer- and seller-initiated trades. For an individualstock, a large order imbalance could be random or induced by either public or privateinformation. Regardless of the cause, market makers can be expected to respond by worseningtheir offered terms of trade. At the market level, it seems unlikely that asymmetric informationis behind aggregate order imbalances, yet market maker inventories still experience periodicOrder Imbalance, Liquidity, and Market Returns, April 12, 200111
strain. Such inventory problems could persist beyond a trading day and thus have extendedeffects on liquidity. The next sub-sections provide empirical evidence about these Order Imbalance and Contemporaneous Changes in LiquidityTo measure liquidity, we first average each individual stock’s quoted spread over all dailytransactions, and then value-weight across stocks (as explained in Section 2 above). The dailypercentage change in the resulting market-average quoted spread is regressed on (1) a non-linearfunction of the contemporaneous daily change in the absolute order imbalance between thenumber of buyer- and seller-initiated trades, (2) the simultaneous daily percentage change in thenumber of transactions, (3) concurrent return, and (4) concurrent market volatility (measured bythe absolute return on the S&P 500). Both the order imbalance and the number of transactionsare value-weight averaged over NYSE stocks in the S&P500 controls (2)-(4) are inserted to account for aggregate trading activity and market imbalance itself could be associated with greater trading activity as well as with largemarket movements; however, our aim is untangle the incremental effect, if any, of orderimbalance on liquidity above and beyond its association with trading and price is no theoretical guide to the functional form of the relation between liquidity and orderimbalance, so the extent of non-linearity was estimated empirically by employing a Box/Coxtransformation, F(x)=(xλ-1)/λ; (see Judge, et. al., 1985, ch. 20.) Since the absolute value of orderimbalance is taken prior to the non-linear transformation, the results (Table 3, second column)indicate that higher spreads occur when orders are more unbalanced in either direction. TheOrder Imbalance, Liquidity, and Market Returns, April 12, 200112
effect turns out to be highly significant and non-linear, with a t-statistic of about 12 and acurvature between cubic and quartic; the maximum likelihood estimate of λ being change in the number of transactions has a separate and very significant positive impact onspreads. This is a bit surprising in that order imbalance has already been taken into possible explanation is measurement error in the order imbalance variable thereby leavingsome explanatory scope for the number of trades. Another possibility is that changes in the sheervolume of trading, without any imbalance in orders, makes it more difficult for market makers tocontrol inventory and induces them to respond by increasing quoted spreads. An alternativeexplanation is that during periods of increased trading volume, the inside limit orders are pickedoff, widening the difference between posted bid and ask quotes. In addition, market volatility asmeasure by the absolute value of the contemporaneous market return, is positively associatedwith changes in spreads, and, as in Chordia et al. (2001), market returns are negatively associatedwith changes in spreads. As reported in the second column of Table 3, approximately 26% ofthe average daily variation in quoted spreads is explained by these overall implication is that contemporaneous changes in liquidity are strongly and non-linearly associated with order imbalances , after controlling for both trading activity and for thesign and magnitude of the market return. To some extent, the contemporaneous associationbetween the quoted spread and order imbalance could arise because of the inability of specialiststo adjust quotes on both sides of the market during periods of large imbalances. In particular, iforders tend to occur on one side of the market during a period, then the specialist has to rapidlyadjust quotes or clear the limit order book on that side of the market. If the book on the other sideOrder Imbalance, Liquidity, and Market Returns, April 12, 200113
is not adjusted quickly enough, the spread will widen. Nevertheless, the widening of the spreaddoes reflect an increase in trading costs when order imbalances are The Predictability of LiquidityWe use the same variables as in the previous subsection to predict the next day’s percentagechange in the market-wide quoted spread. The ensuing results are reported in the third columnof Table 3. While order imbalance appears to have no forecasting ability, there is evidence thatboth the number of trades and the market return can predict future changes in for the market return, the predictive power of volatility is only marginal. To furtherdisentangle the role of market moves, instead of the return and its absolute value, separatevariables for up and down market moves are used in the regression reported in the last column ofTable 3. We find that liquidity persistently follows previous market moves. A down marketpredicts low liquidity (higher spreads) the next day. An up-market also predicts higher liquiditythe next day though the magnitude of the effect is much smaller than for a previous 3 shows also that an increase in transactions is associated with a spread increase on thefollowing day (as well as on the same day). The R2 of this forecasting regression is about 13%which, not surprisingly, is lower than that for the contemporaneous spread regression reported inthe second column of the Table. These results are consistent with inventory models of the spread(., Stoll, 1978a). In such models, imbalances cause a shift in quotes but do not affectliquidity. However, market movements do affect liquidity, and our results show that it is downmarkets where the effects of index movements exert the strongest effects on liquidity. AOrder Imbalance, Liquidity, and Market Returns, April 12, 200114
plausible explanation for this finding is that inventory financing constraints are more binding infalling markets where specialist inventory levels might become very Summary of ResultsThe data reveal a very strong contemporaneous association between changes in the absolute levelof market-wide order imbalance and market-wide liquidity. There is also strong evidence thatchanges in liquidity can be predicted using market returns. In particular, liquidity falls followingmarket declines. For academics, these results are consistent with the notion that inventory riskincreases during periods of large price fluctuations. From a practical standpoint, they haveimportant implications for the design of trading strategies. For example, it would seem unwiseto trade on days immediately following a down-market if waiting costs are not very , portfolio managers would do well to avoid trading on days when the preponderance oftrades is on one side of the . Daily Market Returns, Order Imbalance, and LiquidityInventory concerns could influence risk premia and thus alter required returns (Stoll, 1978a, andSpiegel and Subrahmanyam, 1995). Empirical studies of block trading dating back to Kraus andStoll (1972) find that large trades induce price pressures. In either case, there is reason to expectthat aggregate market order imbalances can exert pressure on market returns; so this sectionprovides information on the phenomenon by estimating the directional impact of orderimbalances on contemporaneous and future market such an empirical investigation one would ideally use a market index unaffected by non-synchronous trading and the concomitant nuisance of spurious serial dependence. The S&P500Order Imbalance, Liquidity, and Market Returns, April 12, 200115
is actually quite appropriate. As mentioned in Section 3, during our January 1988 throughDecember 1998 sample period, it displayed virtually no unconditional serial dependence (seeTable 1, Panel C). Returns on the S&P500 appear to be unpredictable by their own past Returns, Order Imbalance, and LiquidityTo examine the relation between S&P500 returns and order imbalances, a signed measure oforder imbalance is desirable (in contrast to the absolute value used in the liquidity regression ofTable 3). So, order imbalance is split into positive and negative parts and included as separateregressors. This allows for a differential impact of excess buy and sell second column of Table 4, Panel A shows that contemporaneous order imbalance (asmeasured by OIBNUM) exerts an extremely significant impact on market returns in the expecteddirection; the positive coefficients imply that excess buy (sell) orders drive up (down) , lagged order imbalance exert a significant negative effect on the current day'sreturn after controlling for the contemporaneous order imbalance. This is consistent withinventory stabilization, wherein the previous day's imbalance is reversed and hence exerts anegative effect on the contemporaneous return. Given the well-known noise in daily returns, theexplanatory power is good: an adjusted R-square of 28%. A significant portion of daily stockmarket movement can be explained by the buying and selling activity of the general results reveal that microstructure effects are not restricted to the level of the individualstocks; they influence the price process at the aggregate market Imbalance, Liquidity, and Market Returns, April 12, 200116
The third column of Table 4, Panel A adds lagged negative and positive market , even though the S&P500 has virtually zero unconditional serial correlation, theselagged returns are highly significant. Controlling for order imbalances, both positive returns andnegative returns exhibit continuation. The explanatory power is impressive: 33%. However, itseems unlikely that these results reveal a profit opportunity because only specialists know orderimbalances in real time for individual stocks and no specialist knows it for all stocks check whether predictability is present without contemporaneous order imbalanceknowledge, we estimated the regression reported in the fourth column of Table 4. Lagged orderimbalances become insignificant when not accompanied by their contemporaneous lagged market returns also fall in magnitude, but remain significant. However, given thedifficulty of procuring aggregate order imbalance data even with a one-day lag, there might besome doubt that these results represent a profit opportunity based on publicly this point, the reader may wonder whether any of our results in this section are driven by therelation between returns and unsigned trading volume. We did not include unsigned volume asan explanatory variable in Table 4, Panel A because there is no strong a priori reason for volumeto be related to signed returns. However, inclusion of trading volume (dollar volume or numberof transactions) does not alter any of the results of Panel A. The regressions including unsignedvolume are available from the authors upon Imbalance, Liquidity, and Market Returns, April 12, 200117
The fifth column of Table 4, Panel A reports a forecasting model for the next day’s market indexreturn using past returns alone, which would of course be publicly available information. Asmight have been expected, the predictive power is minimal (adjusted R-square: .)However, the signed lagged market returns have surprisingly large significance levels. Despitethe virtual complete absence of ordinary serial dependence for the S&P500 index, the signedlagged returns are both significant. A positive return tends to be followed by a continuation (asrevealed by the positive coefficient) while a negative return tends to be reversed. We thoughtthis surprising result, to our knowledge never before noticed, deserved mention and the results of Atkins and Dyl (1990) and Cox and Peterson (1994), who find reversals inindividual stocks following large stock price declines, there is ample reason to believe thatmarket-wide reversals genuinely follow market crashes and that the phenomenon is not anartifact of the data. To investigate further, we calculated the correlation corr(Rt, Rt-1|Rt-1<-1%)and corr(Rt, Rt-1|Rt-1<%). The values for the two correlations respectively are (126observations - p-value<) and (1087 observations - p-value<). Thus, thereversal effect is most pronounced after larger market declines. We also calculated thecorresponding correlations for up-markets, corr(Rt, Rt-1|Rt-1>+1%) and corr(Rt, Rt-1|Rt-1>+%).The values for the two correlations respectively are (296 observations - p-value ) and+ (1313 observations - p-value ). Evidently, the continuation in up-markets is notdependent on the size of the studies of block trading find that large block sales are followed by price reversals whilelarge buys are not (see Kraus and Stoll, 1972). To relate this empirical finding for individualOrder Imbalance, Liquidity, and Market Returns, April 12, 200118
stocks to our market-wide data, we sorted all days by order imbalance and S&P500 return. Wethen calculated the serial correlation for those days t (a) that fell into the top quintiles of both theorder imbalance and return sorts and (b) that fell into the bottom top quintiles of both the orderimbalance and return sorts. The serial correlation for days falling into category (b) was (sample size=235) whereas that for those falling in category (a) was only (samplesize=233). Hence, there is evidence of strong reversals following large negative return, largenegative imbalance days, but only weak reversals following large positive return, positiveimbalance Panel B of Table 4 reports a predictive regression using observations belonging to categories(a) and (b). There is significant evidence that returns are predictable using past imbalances andpast returns following large negative order imbalance, large negative return days, but there is nopredictive power following high positive order imbalance, high positive return days. Two of thefour regressions reported in Panel B also control for aggregate trading volume, to ensure that thepredictability for high negative imbalance, large negative return days is not driven by the level ofunsigned trading volume. As can be seen, inclusion of dollar trading volume does not materiallyalter the results,6 underscoring the importance of imbalance in the predictive Volatility, Volume, and ImbalancePrevious literature has focused extensively on the relation between volume and volatility (see,., Gallant, Rossi, and Tauchen, 1992). However, daily imbalances could provide informationabout stock price movements in addition that provided by aggregate daily volume. For example,if aggregate daily volume is driven by equal amounts of buying and selling activity, the impact 6 Trading volume measured in number of transactions does not change the qualitative results of Panel B Imbalance, Liquidity, and Market Returns, April 12, 200119
of volume on price movements may be minimal, while if volume is driven by a large imbalance,it could have a large impact. Note that the exercise of disentangling the role of volume vis a visimbalance in explaining stock price fluctuations is best done using volatility as the dependentvariable. This is because, as we mentioned in the previous subsection, there is no a priori reasonto believe that unsigned volume would have an effect on signed returns. We therefore explorethe role of unsigned order imbalances in explaining return volatility over and above the influenceof trading 5 provides some information about this issue. The first regression, reported in the secondcolumn, regresses the absolute value of the S&P500 contemporaneous return on dollar volume,the positive and negative parts of order imbalance, the average quoted spread, and the laggedabsolute market return. The quoted spread is included to control for any liquidity effect onvolatility while the lagged absolute return is included to account for the well-documentedpersistence in enough, order imbalance is significant. The effect is asymmetric; excess sell orders have animpact four times that of excess buy orders; this result is consistent with that in Table 4, Panel B,wherein large sell orders have a greater price impact. Both volume and quoted spreads are alsosignificant. Thus, considerable improvement in explanatory power for contemporaneous dailyvolatility can be obtained by accounting for the joint and several influences of all these that the lagged absolute market return has a negative coefficient. Its persistence is,therefore, fully offset by the other Imbalance, Liquidity, and Market Returns, April 12, 200120
In the third column of Table 5, the same variables are used to predict volatility on the followingday. Here, order imbalance disappears as a significant explanatory factor while dollar volumeand the lagged quoted spread retain their significance. The lagged volatility proxy |Rt| now has asignificant positive impact on |Rt+1|, thereby verifying the usual finding. Evidently, thepersistence in volatility is induced partly by persistent levels of volume and liquidity. Incontrast, but perhaps not surprisingly, order imbalance has only a fleeting influence on the effect of imbalance on future volatility is subsumed by the influences of lagged liquidityand past Summary of ResultsThere is a strong contemporaneous association between stock returns and order is evidence that market prices tend to reverse following declines and continue followingprevious up-moves. Reversal effects are particularly pronounced after large down-market, largenegative imbalance days. Our results are consistent with the inventory paradigm, which suggeststhat imbalances cause price pressures, and with the block trading literature for individual stocks,which indicates that price pressures caused by large sell orders are greater than those for buyorders. Order imbalance also has an impact on contemporaneous volatility above and beyond thewell-known influence of trading volume. Our results underscore the point that price pressurescaused by imbalances are not an artifact of price formation at the individual stock level; they alsomanifest themselves at the aggregate market level. This finding has direct implications foragents wishing to trade the aggregate market . ConclusionOrder Imbalance, Liquidity, and Market Returns, April 12, 200121
The relations between trading activity and liquidity and between trading activity and marketreturns have been explored extensively. Trading activity has usually been measured by volume,but the inventory paradigm, (developed, for example, in Stoll, 1978a, and Spiegel andSubrahmanyam, 1995) suggests that the imbalance between buyer- and seller-initiated orderscould be a powerful determinant of liquidity and price movements beyond trading volume per turns out to be empirically upheld by a daily index of aggregate market order imbalance forNYSE analysis of the determinants and properties of market-wide order imbalances, and of therelation between order imbalances, liquidity, and daily stock market returns is generallyconsistent with the inventory paradigm and yields the following empirical stylized facts:• Order imbalances are strongly related to past market returns. There is evidence of aggregatecontrarian behavior; signed order imbalances are high following market crashes and lowfollowing market increases. Since returns on the S&P500 are virtually uncorrelated, this isevidence that price pressures and inventory imbalances are countervailed efficiently by themarket participants.• Liquidity is predictable from market returns, but not from past imbalances. In particular,down market days tend to be followed by days of decreased liquidity. These findings areconsistent with inventory models of liquidity such as Stoll (1978a), where imbalance affectsthe placement of quotes but not the size of the bid-ask spread, and with the notion thatspreads depend on the costs of holding inventory, which arise from risk and financingconstraints. Our results indicate that such costs are particularly high in down Imbalance, Liquidity, and Market Returns, April 12, 200122
• There is some evidence that reversals tend to follow negative market returns while positivereturns tend to be continued. Returns following large negative order imbalance, largenegative return days are partially predictable using order imbalance and return, but the sameis not true for large positive imbalance, large positive return days. This result is consistentwith the block trading literature for individual stocks dating back to Kraus and Stoll (1972),wherein large block sells are followed by reversals but large block buys are not. Our resultsindicate that price pressure effects of large trades are not restricted to individual stocks butalso influence returns at the aggregate market level; this has implications for agents wishingto trade large dollar amounts of a diversified market portfolio.• Order imbalances are strongly related to contemporaneous absolute returns after controllingfor market volume and market liquidity. This underscores the importance of accounting fororder imbalance, in addition to volume, as a determinant of return our knowledge, this is the first study to analyze daily order imbalances for a comprehensivesample of stocks over a long sample period. Our results generally indicate that imbalances affectliquidity and returns not just at the individual stock level but at the aggregate market level aswell. Since private information is not likely to be an issue at the aggregate market level, theresults generally support the notion that the inventory paradigm, wherein market makersaccommodate uninformed imbalances from outside agents, plays an important role in priceformation in the stock for order imbalance open arenas of research beyond those in this paper. For example,analyzing order imbalances over longer horizons could shed light on growth/value effects inreturns and how they relate to investor trading patterns. In addition, order imbalances aroundOrder Imbalance, Liquidity, and Market Returns, April 12, 200123
major macroeconomic announcements could help shed additional light on the informationparadigm by ascertaining whether agents are able to predict the sign of the impendingannouncement. These and other possible topics are left for future Imbalance, Liquidity, and Market Returns, April 12, 200124
ReferencesAtkins, A., and E. Dyl, 1990, Price reversals, bid-ask spreads, and market efficiency, Journal ofFinancial and Quantitative Analysis 25, , G., and R. Hagerman, 1974, Determinants of bid-asked spreads in the over-the-countermarket, Journal of Financial Economics 1, , M., A. MacKinlay, and B. Terker, 1989, Order imbalances and stock price movementson October 19 and 20, 1987, Journal of Finance 44, , George G., W. E. Griffiths, R. Carter Hill, Helmut Lütkepohl, and Tsoung-Chao Lee,1985, The Theory and Practice of Econometrics, (New York: Wiley).Brown, P., D., Walsh, and A. Yuen, 1997, The interaction between order imbalance and stockprice, Pacific-Basin Finance Journal 5, , K., and W. Fong, 2000, Trade size, order imbalance, and the volatility-volume relation,Journal Of Financial Economics 57, , W., and Schultz, P., 1999, The initiation and withdrawal of odd-eighth quotes amongNasdaq stocks: An empirical analysis, Journal of Financial Economics 52, , T., R. Roll, and A. Subrahmanyam, 2001, Market liquidity and trading activity, Journalof Finance, , D., and D. Peterson, 1994, Stock returns following large one-day declines: Evidence onshort-term reversals and longer-term performance, Journal of Finance 49, , A., P. Rossi, and G. Tauchen, 1992, Stock prices and volume, Review of FinancialStudies 5, Imbalance, Liquidity, and Market Returns, April 12, 200125
Gibbons, M., and P. Hess, 1981, Day of the week effects and asset returns, Journal of Business54, , L.., and E. Gurel, 1986, Price and volume effects associated with changes in the S&P 500list: New evidence for the existence of price pressures, Journal of Finance 41, , J., and D. Seppi, 2001, Common factors in prices, order flows and liquidity, Journalof Financial Economics 59, , C., and J. Jones, 1994, Testing for linear and nonlinear Granger causality in the stockprice-volume relation, Journal of Finance 49, , T., and H. Stoll, 1983, The dynamics of dealer markets under competition, Journal ofFinance 38, , C., G. Kaul, and M. Lipson, 1994, Transactions, volume, and volatility, Review ofFinancial Studies 7, , J., 1987, The relation between price changes and trading volume: A survey, Journal ofFinancial and Quantitative Analysis 22, , A., and H. Stoll, 1972, Parallel trading by institutional investors, Journal of Financial andQuantitative Analysis 7, , A., 1985, Continuous auctions and insider trading, Econometrica 53, , B., and U. Ben-Zion, 1993, Stock market crashes and the performance of circuitbreakers: Empirical evidence, Journal of Finance 48, , C., 1992, Earnings news and small traders: An intraday analysis, Journal of Accounting andEconomics 15, Imbalance, Liquidity, and Market Returns, April 12, 200126
Lee, C., and B. Radhakrishna, 2000, Inferring investor behavior: Evidence from TORQ data,Journal of Financial Markets 3, , C., and M. Ready, 1991, Inferring trade direction from intraday data, Journal of Finance 46, A., and J. Wang, 2000, Trading volume: definitions, data analysis, and implications ofportfolio theory, Review of Financial Studies 13, -White, Elizabeth R., 2000, On the occurrence and consequences of inaccurate tradeclassification, Journal of Financial Markets 3, , A., 1986, Do demand curves for stocks slope down?, Journal of Finance 41, , R., 1997, Price pressure and the role of institutional investors in closed-end funds, Journalof Financial Research 20, , M., and A. Subrahmanyam, 1995, On intraday risk premia, Journal of Finance 50, , H., 1978a, The supply of dealer services in securities markets, Journal of Finance 33,, H., 1978b, The pricing of security dealer services: An empirical study of NASDAQ stocks,Journal of Finance 33, Imbalance, Liquidity, and Market Returns, April 12, 200127
Table 1Market-wide Order Imbalance – Summary statistics and correlationsDescriptive statistics are given for average daily order imbalance measures from NYSE stocks belongingto the S&P 500 over 1988-1998 inclusive, 2,779 observations. Trades are signed using the Lee andReady (1991) algorithm. OIBNUM, OIBSH, and OIBDOL measure the value-weighted7 orderimbalance in number of transactions, shares, and dollars, respectively. $VOL, NUMTRANS, and QSPRare the value-weighted averages of dollar volume (in millions of dollars), number of transactions, and theaverage daily quoted spread, respectively. The variables DQSPR and DOIBNUM denote the dailypercentages and the daily first differences in QSPR and OIBNUM, respectively. S&P500 is the dailyreturn on the Standard & Poor’s 500 A: Summary x x |OIBNUM||OIBSH|/1 x |OIBDOL|/1 x $(%) B: CorrelationsOIBNUMOIBSHOIBDOLNUMTRANS$$& C. Autocorrelations8Lag(Days)OIBNUMOIBSHOIBDOLS& 7 The value weights are proportional to market capitalization at the end of the previous calendar Values in bold face are significantly non-zero with an asymptotic p-value less than Imbalance, Liquidity, and Market Returns, April 12, 200128
Table 2What causes Market-wide Order Imbalance?The dependent variable is the daily order imbalance measured in number of transactions(OIBNUMt) on trading day t. It is regressed on day-of-the-week dummies and past positive andnegative parts of S&P500 returns; Rt denotes the S&P500 index return on day t. TheCochrane/Orcutt procedure was applied to correct for first-order serial dependence in theresiduals. In Panel A, the dependent variable is the value-weighted order imbalance for NYSE-listed stocks in the S&P 500 index. In Panel B the dependent variable isOIBNUMt/NUMTRANSt, where NUMTRANS is total number of transactions (again value-weighted for NYSE stocks in the S&P500). 1988-98 inclusive, 2779 observations. T-statisticsare in Imbalance, Liquidity, and Market Returns, April 12, 200129
Panel A: Dependent variable is the value-weighted order imbalance for NYSEstocks in the S&P 500Explanatory variableCoefficient(t-statistic)()()()()()Min(0, -1)()Min(0, -2)()Min(0, -3)()Min(0, -4)()Min(0, -5)()Max(0, -1)()Max(0, -2)()Max(0, -3)()Max(0, -4)()Max(0, -5)()-1()-2()-3()-4()-5()Durbin -Orcutt Imbalance, Liquidity, and Market Returns, April 12, 200130
Panel B: Dependent variable is OIBNUM/NUMTRANSExplanatory variableCoefficient(t-statistic)()()()()()Min(0, -1)()Min(0, -2)()Min(0, -3)()Min(0, -4)()Min(0, -5)()Max(0, -1)()Max(0, -2)()Max(0, -3)()Max(0, -4)()Max(0, -5)()-1()-2()-3()-4()-5()Durbin -Orcutt Imbalance, Liquidity, and Market Returns, April 12, 200131
Table 3Changes in Market Liquidity, Contemporaneous Changes in Order Imbalance and theNumber of Transactions, and Market Up and Down MovesThe dependent variables are the contemporaneous and next-day’s daily percentage change in thevalue-weighted9 quoted spread for NYSE-listed stocks in the S&P500. Explanatory variablesinclude the daily first difference in a Box/Cox transformation of the absolute value of the value-weighted order imbalance for NYSE stocks in the S&P500 measured in number of shares(OIBNUM), the daily percentage change in the number of transactions for NYSE stocks in theS&P 500, the S&P 500 return if it is positive, and zero otherwise (S&P500+), and the S&P 500return if it is negative, and zero otherwise (S&P500-). The Cochrane/Orcutt procedure wasapplied to correct for first-order serial dependence in the residuals. The Box/Coxtransformation’s λ is estimated by maximizing the explanatory power of the contemporaneousregression using the original variables and the Cochrane/Orcutt coefficient estimates. 2778observations, 1988-98 inclusive. T-statistics are in parenthesesPercentage changePercentagePercentagein value-weightedchange inchange inquoted spreadvalue-weightedvalue-weighted(contemporaneous)quoted spreadquoted spread(next day)(next day)Explanatory variableCoefficientCoefficientCoefficient(t-statistic)(t-statistic)(t-statistic)(|OIBNUMλλ|-|-1|)/λ()()()% Change in Number of ()()()S&()()|S&P500|()()S&P500+()S&()Lagged (one-day)()()()()()Adjusted λ 9 The value weights are proportional to market capitalization at the end of the previous calendar Imbalance, Liquidity, and Market Returns, April 12, 200132
Table 4Returns on the S&P500 Stock Market Index,Contemporaneous and Lagged Order Imbalancesand Lagged ReturnsThe dependent variable is the daily return on the S&P500 index, denoted Rt. Explanatoryvariables include contemporaneous and lagged positive and negative daily order imbalancesmeasured in number of trades and lagged positive and negative index returns. Order imbalancesare value-weighted averages for NYSE stocks in the S&P500. For Panel B, days are sortedseparately by OIBNUM and by the S&P500 return. Then a predictive regression is fit usingobservations that are common to the top 20% of days with high imbalance as well as the top 20%of days with high returns. Another predictive regression is run for high sell order imbalance,large negative return days (., days that are common to the bottom 20% of both variables). Theresults for these two regressions are reported respectively in the second and third columns ofPanel B. Data cover 1988-98 inclusive. T-statistics are in A: Dependent variable: RtExcess Buy Orders,[0,OIBNUMt]()()Excess Sell Orders,-Min[0,OIBNUM(1t])()Excess Buy Orders,[0,OIBNUMt-1]()()()Excess Sell Orders,-Min[0,OIBNUMt-1]()()()Lagged , max[0,Rt-1]()()()Lagged , min[0,Rt-1]()()()()()()()Adjusted of Observations2778277827782778Order Imbalance, Liquidity, and Market Returns, April 12, 200133
Panel B: Dependent variable: Rt+1Days with OIBNUMDays with OIBNUMt int in topbottom quintile and Rquintile t inand Rt in top quintilebottom quintileLagged order (OIBNUMt)()()()() return (Rt)()()()()Lagged volume ($)()()()()()()Adjusted of Observations233233235235Order Imbalance, Liquidity, and Market Returns, April 12, 200134
Table 5Absolute Returns on the S&P500 Stock Market Index,Order Imbalance, Volume and LiquidityThe dependent variable is the absolute value of the daily return on the S&P500 index, denoted|Rt|. Explanatory variables include contemporaneous and lagged positive and negative dailyorder imbalances measured in number of trades, dollar volume, and quoted spreads. Orderimbalances, volume, and spreads are value-weighted averages for NYSE stocks in the S& cover 1988-98 inclusive. T-statistics are in Variable|Rt||Rt+1|Explanatory VariableCoefficient(t-statistic)Excess Buy Orders,[0,OIBNUMt]()()Excess Sell Orders,Min[0,OIBNUMt]()()Dollar ($VOLt/100)()()Quoted ()()One-day lagged |R|()()()()Adjusted of Observations27782778Order Imbalance, Liquidity, and Market Returns, April 12, 200135
