Information Diffusion and Asymmetric Cross-Autocorrelations in Stock Returns

Transcription

1 Dissertation and Job Market Paper Information Diffusion and Asymmetric Cross-Autocorrelations in Stock eturns Kewei Hou 1 Abstract This paper investigates whether the lead-lag effect in short horizon stock returns is due to slow diffusion of common information between firms. After controlling for both portfolio autocorrelations and underreaction to information in market returns, I find that the leadlag effect is mainly caused by stock prices sluggish adjustment to negative information. Furthermore, this effect is shown to be a predominantly intra-industry phenomenon that drives not only the lead-lag effect, but the industry momentum anomaly as well. eturns on industry leaders lead returns on other firms in the industry, and returns on distressed firms lead returns on their non-distressed industry peers, controlling for firm size and trading volume. The intra-industry lead-lag effect is more pronounced in less competitive, value and small industries. Consistent with lagged information diffusion, I also find past earnings surprise to be related to intra-industry lead-lag effect. 1 PhD candidate, the Graduate School of Business, University of Chicago (kewei.hou@gsb.uchicago.edu, ). I would like to thank Jonathan Arnold, Nicholas Barberis, Xia Chen, George Constantinides, Douglas Diamond, Eugene Fama, Kathleen Fitzgerald, Milton Harris, Owen Lamont, ichard Leftwich, Lubos Pastor, David obinson, Andrew Wong, and especially Tobias Moskowitz, as well as seminar participants at the University of Chicago for helpful comments and suggestions. All errors remain my responsibility. 1

2 1. Introduction Lo and MacKinlay (1990) document an asymmetry in the weekly cross-autocorrelations between big firms and small firms (this is also known as the lead-lag effect ). They find that lagged returns on big firms are correlated with current returns on small firms, but not vice versa. Subsequently, asymmetric cross-autocorrelations have been identified between firms with different levels of analyst coverage (Brennan et al. (1993)), different levels of institutional ownership (Badrinath et al. (1995)), and different levels of trading volume (Chordia and Swaminathan (2000)). Although academics have agreed on the magnitude and statistical significance of the lead-lag effect, its source has been subject to debate. The explanations fall into three principle categories. The first explanation attributes the lead-lag effect to either nonsynchronous trading or market frictions such as transaction and information cost. The second explanation posits that the lead-lag effect is the manifestation of the differences in the level of time variation in expected returns across firms. The third explanation is that the lead-lag effect is due to some firms stock prices underreacting to common market information. This paper largely focuses on the view that the lead-lag effect arises because information cost and investment restrictions cause some firms stock prices to react sluggishly to information produced on other firms, following the theoretical work in Badrinath et al. (1995) and Chan (1993), among others. The mechanism of this lagged information diffusion process can be summarized as follows. The information set-up cost (as postulated by Merton (1987)) causes a larger amount of information to be produced by informed investors on a subset of firms (for example, large firms) where the added value of information gathering is greater relative to the fixed cost. Part of the information is idiosyncratic. But because the return generating processes of different securities are not totally independent of each other, part of the information produced on large firms has value implications for small firms by 2

3 signaling the changes (usually market-wide or industry-wide) in the economic environment. If the informed investors face substantial investment cost (information setup cost or some sort of investment restrictions such as the short sale constraint or the prudence restriction) which prevents them from investing in small firms, then the common information will only be impounded by the (uninformed) investors of small firms into their stock prices with a lag after they observe past price changes of the large firms. Thus a lead-lag relation between the returns on large firms and small firms emerges. I explore the above information diffusion hypothesis through several channels. First, if market frictions are responsible for the lagged adjustment of stock prices to new information, then one would expect an asymmetry in the price adjustment process as certain market imperfections become more pronounced when bad news arrives (for example, as the short sale constraint becomes more and more distortionary). My results confirm this. I find that the lead-lag effect is almost entirely driven by slow diffusion of bad news between firms. A negative return on the portfolio of big firms predicts a negative return on the portfolio of small firms next week, whereas a positive return on the portfolio of big firms does not necessarily lead to a positive return on the portfolio of small firms next week. Also consistent with investors facing larger investment cost when times are bad, I find that the lead-lag effect is more pronounced when the market goes down or when the economy is going through a contraction. The above results are robust when I use trading volume instead of size to measure the rate of information flow. Second, the information diffusion story might be more relevant for firms within the same industry. Firms tend to move with their industry peers, since they operate in the same business and legal environment and face the same supply and demand shocks. They react similarly to changing economic conditions. Their growth opportunities, as well as investment and financing policies tend to be correlated. So it is more likely for shocks to big firms (and firms with high trading volumes) to convey information about future prospects of small firms (and firms with low trading volumes) in the same industry. Therefore I predict a significant portion of the lead-lag effect should come from firms 3

4 within the same industry. Indeed, when I decompose the unconditional lead-lag effect into intra-industry and inter-industry components, I find the intra-industry component drives the results and there is little evidence of cross-predictability between industry portfolios. eturns on big firms (and firms with high trading volumes) tend to lead returns on small firms (and firms with low trading volumes) within the same industry. More interestingly, it appears that the role that firm size plays in the information diffusion process hinges on its correlation with industry leadership. I find that returns on industry leaders (big sales share or large &D spending) lead returns on other firms in the industry, controlling for size and trading volume. On the other hand, the size-based intra-industry lead-lag effect disappears once I control for sales. Consistent with the hypothesis that firms in distress are subjected to higher scrutiny by (informed) investors, I find returns on distressed firms (high earning-to-price ratio or high book-to-market ratio) lead returns on their non-distressed industry peers, controlling for size and trading volume. The strength of the intra-industry lead-lag effect is related to the characteristics of the industry in question. It is more pronounced in concentrated industries than in competitive industries, more pronounced in value industries than in growth industries, and more pronounced in small industries than in big industries. Moskowitz and Grinblatt (1999) conclude that the individual stock momentum is largely driven by the momentum in industry portfolio returns. They argue that industry momentum has to be due to a lead-lag effect within industries, since there is little evidence of intra-industry individual stock momentum. To test it, I interact the lead-lag effect with the industry momentum effect. The evidence is consistent with the Moskowitz and Grinblatt prediction. I find that the intra-industry lead-lag effect between small and big firms explains virtually all of the industry momentum effect. This result suggests that slow diffusion of common information between firms is important for understanding the profitability of the momentum strategies. Finally, I link the lead-lag effect to the adjustment of stock prices to news in earnings announcements. Consistent with a lagged information diffusion process between big 4

5 firms and small firms, I find that the stock prices of small firms react positively (negatively) to positive (negative) earnings surprises to the big firms within the same industry, even after controlling for the effects of their own earnings surprises. However, this effect is really nothing more than the lead-lag effect in operation: Once I account for the lagged returns on big firms, the positive relation between returns on small firms and earnings surprises to big firms becomes statistically insignificant, suggesting that the past price movements on big firms convey less noisy signals about the future prospects of small firms. There are certainly other plausible explanations of the data. For example, nonsynchronous trading could induce spurious autocorrelations and crossautocorrelations in stock returns (see Boudoukh et al. (1994), among others). Lo and MacKinlay (1990) conclude that unrealistically high levels of nontrading are needed to explain the lead-lag effect between small and big firms. Mech (1992) tests for asymmetric cross-autocorrelations using data that has been adjusted for nontrading and concludes that only a small portion of the return autocorrelation (cross-autocorrelation) can be attributed to nontrading. 2 Kadlec and Patterson (1999) study the nonsynchronous trading problem by sampling stock returns from transaction data where the actual trade times can be obtained. They estimate that the proportion of autocorrelation (and crossautocorrelation) that is due to nonsynchronous trading is roughly 25 percent. Different levels of time variation in expected returns between small firms and big firms can also be responsible for the lead-lag effect (Conrad and Kaul (1988 and 1989), Conrad et al. (1991), Hameed (1997), and Boudoukh et al. (1994)). Specifically, they argue that the asymmetric cross-autocorrelations between the portfolio of small firms and the portfolio of big firms can be better explained by the autocorrelation of the small firm portfolio coupled with the high contemporaneous correlation between the two portfolios. In other words, once we control for the autocorrelations of the small firm portfolio, the two portfolios should no longer be cross-autocorrelated. I test this hypothesis by 2 See also Chordia and Swaminathan (2000) for similar conclusions. 5

6 including the lagged returns on the portfolio of small firms in the vector-auto regression test of the lead-lag effect. The results in this paper are inconsistent with the above prediction. I find that the lagged returns on large firms can reliably predict current returns on small firms above and beyond the predictive power of lagged returns on small firms. Another alternative explanation attributes the lead-lag effect to underreaction (delayed reaction) of some firms stock prices to common information arriving to the market (Brennan, Jegadeesh and Swaminathan (1993) and Chordia and Swaminathan (2000)). For example, a lead-lag effect could arise if small firms underreact to common information in market returns, whereas big firms adjust more quickly. I address this hypothesis by testing whether returns on large firms continue to lead returns on small firms using returns pre-adjusted for potential delayed reaction to market returns. I find that the lead-lag effect persists, indicating that underreaction (delayed reaction) to market information can explain little, if any, of the observed cross-autocorrelation patterns in stock returns. Understanding the source of the lead-lag effect has important implications for market efficiency and asset pricing, as it can strengthen our understanding of the mechanism by which information is disseminated between firms and impounded into stock prices. Besides presenting evidence consistent with a lagged information diffusion process between firms (especially between firms within the same industry), this paper contributes to the literature in several other ways. First, the empirical results in this paper can shed light on some of the puzzling issues in stock return dynamics. For example, since the autocovariance of a portfolio is merely the sum of the autocovariances of the individual stocks in the portfolio and the crossautocovariances between them, the positive cross-autocorrelation patterns described in this paper can serve to reconcile the seemingly contradictory fact that portfolio returns 6

7 are significantly positively autocorrelated whereas individual stock returns are on average negatively autocorrelated. Second, my findings can also help to determine the validity of different theories that have been proposed for the momentum anomaly in stock returns. Insofar as the lead-lag effects are driven by slow diffusion of negative information between firms, my results is consistent with the explanation that attributes the momentum effect to gradual diffusion of bad news (Hong and Stein (1999), and Hong et al. (2000)). Third, understanding the source of the lead-lag effect is important for policy considerations. To the extent that information frictions and investment restrictions are responsible for introducing the lags in the price adjustment process, my results suggest that increased disclosure and improvement in the information communication as well as market mechanisms can help stock prices become informationally more efficient. The rest of the paper is organized as follows. In section 2, I introduce the data and the vector-auto regression test of the lead-lag effect, showing that the lead-lag effect persists after controlling for own autocorrelations and underreaction to market returns. In section 3, I explore the information diffusion hypothesis in more detail and explain why the slow diffusion of bad news is responsible for the lead-lag effect. In section 4, I decompose the unconditional lead-lag effect into inter- and intra-industry components and show that the intra-industry component drives much of the effect. In section 5, I address additional determinants of the intra-industry lead-lag effect and study the cross-industry differences in the lead-lag effect. In section 6, I show how the intra-industry lead-lag effect explains the industry momentum anomaly. In section 7, I relate the intra-industry lead-lag effect to stock prices response to news in earning announcements. Section 8 contains my conclusions and points out future areas of research. 2. Data and VA test of the Lead-Lag Effect 7

8 I obtain daily stock price and trading volume data for all publicly listed firms on the NYSE, AMEX and NASDAQ daily tapes maintained by the Center for esearch in Security Prices (CSP) for the period beginning in July 1963 and ending in June I then match the CSP stock data with the balance sheet and income statement data from the merged COMPUSTAT industrial annual and quarterly files. I follow the procedure in Fama and French (1992) to make sure the accounting data is known before the return series it is measured against. For each year from 1963 through 1996, the return series between July of year t and June of year t+1 is matched with the accounting information for fiscal yearends in year t-1. 3 I calculate the weekly returns from Wednesday close to the following Wednesday close. 4 This way of measuring weekly returns is a common practice in the literature. 5 For a return year t (from July of calendar year t to June of calendar year t+1), I measure trading volume of a firm using (a) the average number of shares traded per week, (b) the average dollar value of shares traded per week, and (c) the average turnover per week, defined as the ratio of the number of shares traded in a week to the number of shares outstanding at the end of the week, averaging from July of calendar year t-1 to June of calendar year t. I multiply the number of shares outstanding by the per share price at the end of June of year t to measure a firm s size, and I use the market value of equity at the end of December of year t-1 to calculate the fundamental accounting ratios (book-to-market equity and earnings-to-price ratio) for year t-1. Book equity is defined as the sum of COMPUSTAT (1) stockholders equity, (2) investment tax credit and (3) balance sheet deferred tax (when available), minus the book value of preferred stock (redemption, liquidation, or par value). Earnings is defined as the sum of COMPUSTAT (1) income 3 See Fama and French (1992) for the rationale behind this minimum 6-month gap between the fiscal yearend and return series. 4 I choose to measure the lead-lag effect at a weekly frequency to avoid the substantial bias introduced by nonsynchronous trading at daily level, but to have a large number of time series observations at the same time. Forester and Keim (1998) estimate the likelihood for a typical stock going untraded for five consecutive days to be 0.42 percent. 5 Keim and Stambaugh (1984), Bessembinder and Hertzel (1993), Boudoukh et al. (1994), and Chordia and Swaminathan (2000) document seasonal patterns in weekly autocorrelations of stock returns. Autocorrelations calculated using Friday close to Friday close are too high and autocorrelations based on Tuesday closes are too low, with autocorrelations of weekly returns ending on Wednesdays in the middle. 8

9 before extraordinary items, and (2) income statement deferred tax, minus preferred dividends. Sales is net sales, as reported by COMPUSTAT; &D is research and development expense, as reported by COMPUSTAT. At the beginning of July of each year between 1963 and 1996, I assign all firms on the CSP NYSE/AMEX/NASDAQ tape into three portfolios (top 30 percent, middle 40 percent and bottom 30 percent) according to their end-of-june market value of equity. Portfolio 1 contains the smallest 30 percent stocks and portfolio 3 contains the largest 30 percent stocks. 6 Equal-weighted weekly returns are calculated for each portfolio with its composition kept fixed until the end of June of next year. Panel A of Table I presents summary statistics of the three size portfolios. Not surprisingly, the weekly mean return is negatively correlated with firm size, with portfolio 1 ( P1 ) having the highest average return almost 44 basis points per week. The first order autocorrelation decreases with size (0.429 for P1, for P2 and for P3). Higher order autocorrelations also decline with size and decay over time. The Ljung-Box Q statistics reject the null that the first eight autocorrelations are zeros at all conventional significance levels for the three size portfolios. Panel B of Table I reports the autocorrelation matrices for the three size portfolios, with the contemporaneous correlation matrix and the first- through fourth-order autocorrelation matrices presented from left to right. eturns on the size portfolios are highly temporally correlated, as evidenced by the magnitude of the correlation coefficients in the leftmost matrix. Consistent with the findings of Lo and MacKinlay (1990), the coefficients in the autocorrelation matrices that are above the diagonals are greater than those below the diagonals. Put differently, the cross-autocorrelations between lagged returns on big firms and current returns on small firms are always bigger 6 Since I am using all firms to determine the size breakpoints here, the portfolio for small firms (P1) is likely to be dominated after 1973 by the small stocks from NASDAQ, which probably are most subject to nosynchronrous trading and other microstructure biases. Also, one might argue that institutional differences between NYSE/AMEX and NASDAQ (specialist market vs. dealer market) could affect the way information is diffused into stock prices. To address this issue, and more importantly to ensure that those 9

10 than the cross-autocorrelations between lagged returns on small firms and current returns on big firms. What has emerged from Panel B is interesting, but it alone does not prove whether lagged returns on big firms contain any information about contemporaneous returns on small firms that is independent from that in lagged returns on small firms. In other words, the evidence in Panel B is perfectly consistent with the alternative hypothesis that lagged returns on big firms are noisy proxies for lagged returns on small firms and, once it is accounted for, the lead-lag effect between small and big firms should disappear (Conrad and Kaul (1988 and 1989), Conrad et al. (1991), Hameed (1997), and Boudoukh et al. (1994)). To determine the validity of the above argument and formally examine the lead-lag effect between size portfolios, I implement the VA test procedure in Brennan et al. (1993). Specifically, to test whether returns on portfolio P3 lead returns on portfolio P1, I estimate the following two-equation system: 1, t = a 0 + K k = 1 a k 1, t k + K k = 1 b k 3, t k + u 1, t, (1) 3, t = c 0 + K k = 1 c k 1, t k + K k= 1 d k 3, t k + u 3, t. (2) Estimations are conducted with 1 lag (K=1) and 4 lags (K=4). The advantage of using only one lag is that it is easy to interpret, but it does not allow for time-series dependency beyond one week in weekly returns. VA test with four lags eliminates this problem to a large extent, but at the expense of possibly adding noise to the estimation procedure. If returns on P1 and P3 are serially and cross-sectionally independently distributed, the regression coefficients on the lagged returns in equation (1) and (2) should be zero. I include lagged returns on P1 as explanatory variables in the VA test. If the asymmetric cross-autocorrelations between P1 and P3 are merely a restatement of P1 s own small firms on NASDAQ do not drive my findings, I rerun all the tests in this section and the rest of the 10

11 autocorrelations coupled with high contemporaneous correlations between P1 and P3, then once I control for the explanatory power of lagged returns on P1, the lead-lag effect between P1 and P3 should disappear. In the context of the VA test, it predicts b k = c k =0 for all k. On the contrary, if lagged returns on big firms do contain information about current returns on small firms that is independent from the information in lagged returns on small firms, the lead-lag effect should remain significant even after controlling for own autocorrelations of small firms. In other words, lagged returns on P3 should continue to predict current returns on P1, and this ability is better than that of lagged returns on P1 to predict current returns on P3, i.e. K k= 1 b k c > K k= 1 k. 7 The VA estimation results are reported in Table I.C. For the 4-lag VA, the sum of the regression coefficients on lagged returns of P3 in equation (1) is bigger than the sum of the coefficients on lagged returns of P1 in equation (2) ( vs ), with the Wald test statistic for the cross-equation restriction easily rejecting the null of K k= 1 b k c = K k= 1 k at the 1 percent significance level. The bigger adjusted -squared for equation (1) (20.8 percent) also indicates that weekly return on small firms is more predictable than that on big firms. The 4-lag VA result clearly shows a significant leadlag relation between P1 and P3. It suggests that cross-autocorrelations do contain information that is independent from that in own autocorrelations, as the sum of the regression coefficients on lagged returns of P3 in equation (1) is statistically different from zero. The 1-lag VA result is very similar to that of the 4-lag VA. Next, I examine the extent to which the lead-lag effect between small firms and big firms can be attributed to the stock prices of small firms underreacting to common information paper using firms from NYSE/AMEX alone, and obtain similar results. 7 See the appendix in Brennan et al. (1993) for the derivation of this cross-equation restriction based on a simple model of lagged price adjustment. They also show that the sum of the c k s in equation (2) can be negative, if variance of the residual terms in (1) and (2) is sufficiently small. 11

12 imbedded in market returns (see Brennan, Jegadeesh and Swaminathan (1993) and Chordia and Swaminathan (2000)). To do that, I first regress the weekly returns of P1 and P3 on the contemporaneous and past four weeks market returns to account for the alleged delayed reaction to market information. 8 Then I rerun the 4-lag VA using the market-adjusted returns (the residuals from the previous market model regressions). If the lead-lag effect between big firms and small firms is caused by underreaction of small firms stock prices to common information in market returns, then lagged returns on big firms should no longer predict current return on small firms once I use market-adjusted returns. Panel D of Table I reports the results. When current returns of P1 are regressed on lagged returns of both P1 and P3, the sum of the regression coefficients on lagged returns of P3 turns out to be and is statistically significant at the 5 percent level, indicating lagged returns on big firms still reliably predict contemporaneous returns on small firms, after controlling for delayed reaction to market returns. 9 So it does not look like small firms underreacting to common market information is causing the lead-lag effect between size portfolios Lagged Information Diffusion and Lead-Lag Effect: Does Bad News Travel Slowly? In this section, I explore the information diffusion hypothesis that information cost and investment restrictions cause the information produced on big firms to be impounded into the prices of small firms with a lag. Specifically, I study whether there is an asymmetry in the lagged adjustment of small firm prices to news on big firms, as there are reasons to 8 I use the value-weighted index on NYSE/AMEX/NASDAQ as the proxy for the market. 9 The converse is not true, the sum of coefficients on lagged market-adjusted returns of P1 in equation (2) is only and remains statistically insignificant. 10 As another way to account for the delayed reaction to market returns, I add lagged market returns from week t-4 to week t-1 to the 4-lag VA. I obtain the same result. 12

13 believe that the impact of certain market frictions is more pronounced when bad news arrives. 11 I augment lagged returns on P1 and P3 in the 1-lag VA using dummy variables for the direction of lagged price movements: 1, t = a 0 + a 1 1, t 1 D 1, t 1 + a 2 1, t 1 + b 1 3, t 1 D 3, t 1 + b 2 3, t 1 + u 1, t, (3) 3, t = c 0 + c 1 1, t 1 D 1, t 1 + c 2 1, t 1 + d 1 3, t 1 D 3, t 1 + d 2 3, t 1 + u 3, t, (4) where D 1,t-1 (D 3,t-1 ) take the value of 1 if 1,t-1 ( 3,t-1 ) is positive and 0 otherwise. Panel E of Table I presents the estimation results which confirm my conjecture. Sum of the slope coefficients b 1 and b 2 is not statistically different from zero, which suggests that, conditioning on returns on the big firms last week being positive, lagged returns on big firms can not predict contemporaneous returns on small firms. This is not true if the big firms experienced price declines last week. The b 2 being statistically significant means lagged returns on big firms can still reliably predict contemporaneous returns on small firms, if the returns on big firms were negative last week. Therefore good news is diffused rather quickly between small and big firms, while it is mainly the sluggish adjustment of small firm prices to bad news on big firms that is causing the observed lead-lag relation. In panels F and G, I interact lagged returns on P1 and P3 with a dummy variable for the direction of lagged market movement, as well as the stage of business cycle that the economy is in (expansion vs. contraction, defined by the NBE). I find, for both cases, b 2 in equation (3) is statistically significant while b 1 +b 2 is not, indicating that the lead-lag effect is more pronounced when the market goes down or when the economy is going through a contraction. This is consistent with casual observations that investors face larger investment cost when times are bad, resulting in a longer delay in the price adjustment process. 11 Diamond and Verrecchia (1987) argue that short sale constraints can slow down the response of stock prices to bad news. See also Hong and Stein (1999). 13

14 So far my results on the lead-lag effect are obtained between the two portfolios of different size (P1 and P3). 12 To ensure robustness, I re-examine those findings using another measure of the lagged information diffusion process trading volume. 13 I measure a firm s trading volume using its average weekly dollar trading volume (product of the number of shares traded in a week and the price per share at the end of the week) over the past year. 14 The problem of using the dollar trading volume is that it is highly correlated with firm size. To better focus on the role of trading volume in the information diffusion process, I sort firms into portfolios based on trading volume while keeping size relatively constant, following the procedure in einganum (1981), Basu (1983), Cook and ozeff (1984), and Badrinath et al. (1995). Specifically, I first group all firms on NYSE/AMEX into three portfolios (top 30 percent, middle 40 percent and bottom 30 percent) according to their market value of equity. 15 Stocks within each size portfolio are then divided into three portfolios (top 30 percent, middle 40 percent and bottom 30 percent) based on their average trading volume. Finally, firms from the lowest trading volume portfolio in each of the three size portfolios are grouped into portfolio 1, firms from the middle trading volume portfolio in each of the three size portfolios are grouped into portfolio 2, and firms from the highest trading volume portfolio in each of the three size portfolios are grouped into portfolio 3. This way, portfolio 1 will have lower trading volume than portfolios 2 and 3 do, but the average firm size of the three portfolios does not differ by much. 12 I also analyze the lead-lag relation between size portfolios P1 and P2. The results are similar. For brevity, they are not reported here. 13 Chordia and Swaminathan (2000) document a volume-based lead-lag effect in stock returns. 14 I also measure the trading volume using raw trading volume (the number of shares traded in a week) and weekly turnover (the number of shares traded in a week divided by the number of shares outstanding at the end of the week). Sorting firms based on dollar trading volume provides the sharpest results. 15 Because of the institutional difference between NYSE/AMEX and NASDAQ (specialist market vs. dealer market), the recorded trading volume is not directly compatible between them. Also the trading volume data is not available on the NASDAQ tape prior to I thus focus on the NYSE/AMEX market to study the volume based lead-lag effect. esults form the NASDAQ market can be obtained from the author upon request. I find little, if any, evidence for the volume-based lead-lag effect on NASDAQ. I suspect the institutional difference and data measurement error are partially responsible. Further investigation is warranted. 14

15 esults based on the above three size-volume portfolios are presented in Table II, and are very similar to those in Table I. eturns on firms with high trading volumes lead returns on firms with lower trading volumes, keeping size fixed. The lead-lag effect persists after controlling for own autocorrelations of low volume firms and underreaction of low volume firms to common information in market returns. I find this lead-lag effect is almost entirely driven by sluggish adjustment of low volume firms to bad news on high volume firms. I also find a more pronounced volume-based lead-lag effect when the market goes down or when the economy is undergoing a contraction. 4. Inter- versus Intra-Industry Lead-Lag Effects: the Intra-Industry Component Matters I have presented evidence that stock prices of small firms (and firms with low trading volumes) adjust sluggishly to information, especially negative information, produced on large firms (and firms with high trading volumes). Since it is natural to think that the lagged information diffusion hypothesis might be more relevant for firms within the same industry, I decompose the unconditional lead-lag effect into inter-industry and intraindustry components. Firms in the same industry move with each other, since they operate in the same business and legal environment and face the same supply and demand shocks. They react similarly to changing economic conditions. Their growth opportunities, as well as investment and financing policies, tend to be correlated. So it is more likely for shocks to big firms (and firms with high trading volumes) to convey information about future prospects of the small firms (and firms with low trading volumes) in the same industry. Therefore I predict that a significant portion of the sizeand volume-based lead-lag effects should come from firms within the same industry. I assign all firms listed on NYSE/AMEX/NASDAQ 16 between 1963 and 1997 into 48 industries according to their 4-digit Standard Industrial Classification (SIC) codes, following the industry grouping procedure in Fama and French (1997). 15

16 To study the contribution of cross-industry information diffusion to the unconditional size-based lead-lag effect, I first calculate industry returns by value-weighting all firms in an industry according to their market value of equity. Then I group the 48 industries into three portfolios (top 30 percent, middle 40 percent, and bottom 30 percent) according to their median firm size. Equal-weighted returns are calculated for the three portfolios. Panel A of Table III reports the 1-lag VA results estimated between P1 and P3. I find no evidence of a lead-lag relation between big industries and small industries. The regression coefficients on the cross terms are small and statistically insignificant for both portfolios, indicating that lagged returns on big industries can not predict current returns on small industries, and vice versa. If the size-based lead-lag effect does not exist inter-industry, then it has to have a strong intra-industry component (this follows from the significance of the unconditional sizebased lead-lag effect we know there is an effect, so it must come from either the interindustry component or the intra-industry component). To show that the intra-industry component is indeed what is operating, I first sort firms within each industry into three size portfolios (top 30 percent, middle 40 percent, and bottom 30 percent). Then I place firms from the smallest size portfolio from different industries into one portfolio (P1), firms from the middle size portfolio from different industries into portfolio P2, and firms from the largest size portfolio from different industries into portfolio P3. I refer to the three portfolios as intra-industry size portfolios and use them to test the intra-industry size-based lead-lag effect. 17 Panel A of Table IV presents the results. Both 4-lag and 1- lag VA tests confirm my prediction that there exists a strong intra-industry size-based lead-lag effect. 18 The ability of lagged returns on big firms to predict contemporaneous returns on small firms within the same industry is greater than the ability of lagged returns on small firms to predict current returns on big firms in the same industry. 16 NYSE/AMEX when we study the lead-lag effect related to trading volume. 17 This is equivalent to conducting the lead-lag analysis for each industry separately and then averaging across industries. 18 I also estimate the VA for each industry separately, and find confirming evidence. esults can be obtained from the author per request. 16

17 Similarly, when I decompose the unconditional lead-lag effect related to trading volume into inter- and intra-industry components (Table III.B and IV.B), I find the volume-based lead-lag effect does not exist inter-industry, but has a strong intra-industry component. Weekly returns on high volume firms lead weekly returns on low volume firms within the same industry. 5. More on Intra-Industry Lead-Lag Effect: A Closer Look Previously, I showed that the unconditional size- and volume-based lead-lag effects are primarily driven by their intra-industry component. It suggested that industries are important for understanding the information diffusion process between firms. In this section, I further explore the intra-industry lead-lag effect from three angles. First, I examine whether and to what extent firm size affect the price adjustment process through its effect on other firm characteristics that are relevant for information transmission between firms. I find that the size-based lead-lag effect disappears once we control for sales. Second, I examine whether there is a lead-lag relation between distressed firms and their non-distressed industry peers, and find that indeed returns on distressed firms lead returns on non-distressed firms, controlling for size and trading volume. Third, I examine whether different industries exhibit different levels of intra-industry lead-lag effect, and find more pronounced lead-lag effect in less competitive, value and small industries Industry Leaders and Followers A number of researchers have argued that firm size affects the speed of price adjustment through its correlation with other firm characteristics and thereby proxies for the amount of information being produced on a firm (Admati and Pfleiderer (1998), Badrinth et al. (1995) and Brennan et al. (1993)). I explore this hypothesis in the context of the intraindustry lead-lag effect. 17

18 For example, size could be related to industry leadership, as there might exist a lead-lag relation between industry leaders and other firms within the industry. A new piece of information usually hits the industry leaders (big industry sales share, big &D spending) first. However, this new information will be impounded into the prices of other firms in the industry with a lag because of information cost and investment restrictions. As investors take time to reevaluate those firms by extracting information from past price movements of the industry leaders, a lead-lag relation between industry leaders and other firms in the industry arises. Similar to the procedure used to test the intra-industry size-based lead-lag effect, I first divide all firms in an industry into three sales-ranked portfolios (top 30 percent, middle 40 percent, and bottom 30 percent). Then firms from the lowest sales-ranked portfolio from different industries are grouped into portfolio P1, firms from the highest salesranked portfolio from different industries are grouped into portfolio P3, and everything else goes into P2. I use these three portfolios to test the intra-industry sales-based lead-lag effect. Panel C in Table IV reports the VA results. I find returns on firms with big industry sales share lead returns on firms with small industry sales share. Lagged returns on industry sales leaders can significantly predict current returns on low sales firms, even after controlling for lagged returns of low sales firms. However, lagged returns on low sales firms have no power to predict contemporaneous returns on firms with high sales. Do sales data contain information about lagged information diffusion within an industry that is independent from that in firm size and trading volume? I re-examine the intraindustry sales-based lead-lag effect by controlling for firm size and trading volume. Within each industry, I first sort firms into three size portfolios and within each size portfolio into three sales portfolios. As a result of this two-way sorting, I have nine sizesales portfolios in each industry. Then firms from the same sales-ranked portfolio from each of the three size portfolios from different industries are grouped into one portfolio. I end up with three intra-industry sales-ranked portfolios holding size fixed. The same procedure is used to form intra-industry sales-ranked portfolios controlling for trading volume. 18

19 Panels D and E of Table IV present results of the lead-lag tests. The intra-industry salesbased lead-lag effect remains significant after controlling for firm size and trading volume. Actually it becomes stronger, suggesting that controlling for size and trading volume helps us filter out the noise contained in sales data that is unrelated to intraindustry lagged information diffusion. On the other hand, I find the intra-industry sizebased lead-lag effect disappears, once sales is controlled for (Table IV, Panel F), consistent with my conjecture that the role that firm size plays in the information diffusion process hinges on its relation with industry leadership. The intra-industry leadlag effect that is related to trading volume remains significant after controlling for sales (Table V, Panel G). I also measure industry leadership using the &D-to-sales ratio of a firm. Panel H of Table IV shows that returns on firms with high level of research and development spending lead returns on firms with low level of &D spending in the same industry. This lead-lag effect remains significant after sales is controlled for (Table IV, Panel I) Distressed and Non-Distressed Firms Fama and French (1995), among others, argue that firms with high earnings-to-price ratio or high book-to-market ratio are in relative distress as evidenced by their persistent poor earnings in the past. Since I found earlier that the lead-lag effect is about bad news, it might make sense to investigate whether there is a lead-lag relation between distressed firms and non-distressed firms. Also, when a firm becomes distressed (all else being equal), it is usually subjected to higher scrutiny by (informed) investors, resulting in a larger amount of information being produced on it. Then according to the lagged information diffusion hypothesis, returns on distressed firms would lead returns on their non-distressed industry peers, keeping size and trading volume fixed. Table IV, Panel J presents 4-lag and 1-lag VA results for intra-industry portfolios based on earnings-to-price ratio while keeping size fixed, with one week skipped between 19

20 lagged returns on P1 and P3 and the returns they are explaining. 19 esults from these two VAs are consistent with returns on high E/P firms leading returns on low E/P firms. Panel K of Table IV reports the skipping-week VA tests for E/P portfolios when I control for trading volume instead of size. The results are the same. When I change the measure of relative distress from earnings-to-price ratio to book-tomarket ratio, the inferences do not change (Panels L and M in Table IV). I find returns on high BE/ME firms lead returns on low BE/ME firms in the same industry after controlling for size and trading volume Cross-Industry Differences in Lead-Lag Effect Findings on the intra-industry lead-lag effect I have presented so far are obtained by grouping firms from different industries into one portfolio according to their characteristics. They tell us what happens in an average industry, but cannot provide clear inferences on whether different industries exhibit different levels of intra-industry leadlag effect. In this subsection, I explore how the differences across industries in the speed of information transmission are related to their differences in the product market and financial market characteristics, as well as growth opportunities. I construct two variables to measure the strength of the intra-industry lead-lag effect. The first one is the difference between the ability of lagged returns on big firms to predict current returns on small firms and the ability of lagged returns on small firms to predict current returns on big firms. Specifically, within each of the 48 industries, I first group firms into three size portfolios (top 30 percent, middle 40 percent, and bottom 30 percent) according to their market value of equity, then I estimate the following system of 19 I skip a week in order to fully purge the impact of firm size. Preliminary work finds that the lead-lag relation between the high E/P portfolio and the low E/P portfolio is insignificant in week t-1, but becomes significant in week t-2 and persists onto longer lags. This suggests that firm size, which is negatively correlated with earnings-to-price ratio, might be confounding the inferences. 20

21 equations using returns on the portfolio of large firms (P3) and returns on the portfolio of small firms (P1). 20 1, t 1, t 3, t 3, t = a = b 0 0 = d = e k = 1 4 k = 1 4 k = 1 4 k = 1 a b k d e k k k 1, t k 1, t k 3, t k 1, t k + v + + 1, t, 4 k = 1 + v 4 3, t k= 1 c f k, k 3, t k 3, t k + u + u 1, t, 3, t. (5) (6) (7) (8) The strength of the lead-lag effect within each industry is then estimated using the following variable: Leadlag = 2 from model (6) 2 from model (5) - 2 from model (8) 2 from model (7). (9) This 2 -based measure captures the difference between the ability of lagged returns on the portfolio of big firms (P3) to predict current returns on the portfolio of small firms (P1), and the ability of lagged returns on the small firm portfolio (P1) to predict current returns on the big firm portfolio (P3). Alternatively, I measure the strength of the intra-industry lead-lag effect with the average return of a self-financing strategy that is designed to take advantage of the information in the lead-lag relation between the two size portfolios (P1 and P3) within each industry. For each week t between 1964 and 1997, returns on P1 and P3 from week t-52 to week t- 1 are used to estimate equation (6) and (8). I then use the estimated equations to predict the returns on P1 and P3 in week t. In order to focus on the information contained in cross-autocorrelations, I zero out the autoregressive coefficients ( b k s and f k s, k=1 to 4) when making the forecast. A self-financing strategy is then formed to buy the portfolio with higher predicted return and short the portfolio with lower predicted return at the 20 This is done 48 times once for each industry. 21

22 beginning of week t. The strategy is rebalanced after a week. Finally, the returns on this strategy are averaged over the whole sample period to measure the strength of the leadlag relation within an industry. I name it Profit. In Table V, Leadlag and Profit are regressed on industry concentration 21, industry median size, and industry median book-to-market ratio. I find the three industry characteristics explaining a significant portion of the cross-industry variation in the lead-lag effect, as the -squared for both regressions are more than 40 percent. The regression coefficients on industry concentration are highly significantly positive with t-statistics more than 5, indicating that the lead-lag effect in highly concentrated (less competitive) industries is stronger than that in less concentrated (more competitive) industries. So it appears that news spreads rather quickly in a competitive industry (where industry output is divided among many firms) than in a concentrated industry (where industry output is divided among only a few firms). There also exists a positive and statistically significant relation between the measures of lead-lag intensity and industry median book-to-market ratio, which suggests that value industries tend to have stronger intra-industry lead-lag effect than growth industries do. The coefficient on industry median firm size is negative and significant, indicating a weaker lead-lag effect in big industries. 6. Lead-Lag Effect and Industry Momentum Effect A number of papers have documented the existence of momentum in stock returns. For example, Jegadeesh and Titman (1993) report that past winners outperform past losers over an intermediate horizon of six to twelve months. ecent findings on this momentum anomaly suggest that investigating the intra-industry lead-lag effect could provide additional insights. Moskowitz and Grinblatt (1999) report that the individual stock momentum is largely driven by the momentum in industry portfolio returns. Since they find little evidence of intra-industry individual stock momentum, they conclude that the 22

23 industry momentum must be due to a lead-lag effect between firms within the same industry. 22 In this section, I test their prediction by interacting the industry momentum with the intra-industry lead-lag effect in a Fama-MacBeth (1973) cross-sectional regression framework. Every week, I estimate a cross-sectional regression on the smallest 70 percent stocks from every industry. Individual stock returns are regressed on various industry momentum variables (industry returns over past one month, six months and twelve months) and intra-industry lead-lag variables (lagged returns from week t-1 to week t-4 on the portfolio of the largest 30 percent firms in the industry to which each stock belongs). 23 I also include size and book-to-market ratio on the right hand side of the regressions as controls. The coefficients from the weekly regressions are averaged over time and reported in Table VI, along with their time-series t-statistics. Each industry momentum variable, taken alone, is highly significant in the crosssectional regressions. But when they are included simultaneously as independent variables, we see the significance of the six-month and twelve-month industry momentum variables weakened by the one-month industry momentum variable. This is consistent with the result in Moskowitz and Grinblatt (1999) that the industry momentum strategy is strongest at the one-month horizon. When I add in lagged returns on portfolios of large firms to study the interaction between the intra-industry lead-lag effect and the industry momentum effect, I find all three industry momentum variables lose their significance, whereas the lead-lag variables remain highly significant. This confirms the Moskowitz and Grinblatt conjecture that the intra-industry lead-lag effect drives the industry momentum. 21 Industry concentration is measured by the Herfindhal index, which is the sum of the squared industry sales share of all firms in an industry. Hou and obinson (1999) find highly concentrated (less competitive) industries earn lower returns on average than less concentrated (more competitive) industries do. 22 Grundy and Martin (1999) make a similar point. 23 In my sample, the industry momentum strategies that are based on past one-month, six-month and twelve-month industry returns generate average weekly profits of 25 basis points (t-statistic=7.24), 18 basis points (t-statistic=5.10) and 22 basis points (t-statistic=5.85), respectively. 23