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Dissertation and Job Market Paper
Information Diffusion and Asymmetric Cross-Autocorrelationsin Stock Returns
Kewei Hou1
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 lead-
lag 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. Returns
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 ([email protected],847-425-1945). I would like to thank Jonathan Arnold, Nicholas Barberis, Xia Chen, GeorgeConstantinides, Douglas Diamond, Eugene Fama, Kathleen Fitzgerald, Milton Harris, Owen Lamont,Richard Leftwich, Lubos Pastor, David Robinson, Andrew Wong, and especially Tobias Moskowitz, aswell as seminar participants at the University of Chicago for helpful comments and suggestions. All errorsremain my responsibility.
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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
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signaling the changes (usually market-wide or industry-wide) in the economic
environment. If the informed investors face substantial investment cost (information set-
up 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
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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. Returns 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 R&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
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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 cross-
autocorrelations 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 cross-
autocorrelation) 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.
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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 cross-
autocovariances between them, the positive cross-autocorrelation patterns described in
this paper can serve to reconcile the seemingly contradictory fact that portfolio returns
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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 VAR test of the Lead-Lag Effect
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 Research in
Security Prices (CRSP) for the period beginning in July 1963 and ending in June 1997. I
then match the CRSP 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 fiscalyearend and return series.4 I choose to measure the lead-lag effect at a weekly frequency to avoid the substantial bias introduced bynonsynchronous trading at daily level, but to have a large number of time series observations at the sametime. Forester and Keim (1998) estimate the likelihood for a typical stock going untraded for fiveconsecutive days to be 0.42 percent.5 Keim and Stambaugh (1984), Bessembinder and Hertzel (1993), Boudoukh et al. (1994), and Chordia andSwaminathan (2000) document seasonal patterns in weekly autocorrelations of stock returns.Autocorrelations calculated using Friday close to Friday close are too high and autocorrelations based onTuesday closes are too low, with autocorrelations of weekly returns ending on Wednesdays in the middle.
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before extraordinary items, and (2) income statement deferred tax, minus preferred
dividends. “Sales” is net sales, as reported by COMPUSTAT; “R&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
CRSP 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, 0.297 for P2 and 0.172
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. Returns 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) islikely to be dominated after 1973 by the small stocks from NASDAQ, which probably are most subject tonosynchronrous trading and other microstructure biases. Also, one might argue that institutional differencesbetween NYSE/AMEX and NASDAQ (specialist market vs. dealer market) could affect the wayinformation is diffused into stock prices. To address this issue, and more importantly to ensure that those
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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 VAR 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:
)2( .
)1( ,
1,3,3
1,10,3
1,1,3
1,10,1
∑∑
∑∑
=−
=−
=−
=−
+++=
+++=
K
ktktk
K
kktkt
K
ktktk
K
kktkt
uRdRccR
uRbRaaR
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. VAR 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 VAR 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
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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 VAR test, it predicts bk= ck=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
kk
K
kk cb
11
.7
The VAR estimation results are reported in Table I.C. For the 4-lag VAR, 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) (0.1843 vs. –0.0481), with the
Wald test statistic for the cross-equation restriction easily rejecting the null of
∑∑==
=K
kk
K
kk cb
11
at the 1 percent significance level. The bigger adjusted R-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 VAR result clearly shows a significant lead-
lag 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 VAR result is very similar to that of the 4-lag VAR.
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 asimple model of lagged price adjustment. They also show that the sum of the ck’s in equation (2) can benegative, if variance of the residual terms in (1) and (2) is sufficiently small.
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 VAR 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 0.2369 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.10
3. 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) isonly –0.0307 and remains statistically insignificant.10 As another way to account for the delayed reaction to market returns, I add lagged market returns fromweek t-4 to week t-1 to the 4-lag VAR. I obtain the same result.
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 VAR using dummy
variables for the direction of lagged price movements:
)4( ,
)3( ,
,31,321,31,311,121,11,110,3
,11,321,31,311,121,11,110,1
tttttttt
tttttttt
uRdDRdRcDRccR
uRbDRbRaDRaaR
+++++=
+++++=
−−−−−−
−−−−−−
where D1,t-1 (D3,t-1) take the value of 1 if R1,t-1 (R3,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 b1 and b2 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 b2 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 NBER). I find, for both cases, b2
in equation (3) is statistically significant while b1+b2 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 stockprices to bad news. See also Hong and Stein (1999).
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 Reinganum (1981), Basu
(1983), Cook and Rozeff (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. Forbrevity, 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) andweekly turnover (the number of shares traded in a week divided by the number of shares outstanding at theend 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 tradingvolume data is not available on the NASDAQ tape prior to 1983. I thus focus on the NYSE/AMEX marketto study the volume based lead-lag effect. Results form the NASDAQ market can be obtained from theauthor upon request. I find little, if any, evidence for the volume-based lead-lag effect on NASDAQ. Isuspect the institutional difference and data measurement error are partially responsible. Furtherinvestigation is warranted.
15
Results based on the above three size-volume portfolios are presented in Table II, and are
very similar to those in Table I. Returns 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 intra-
industry 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 size-
and volume-based lead-lag effects should come from firms within the same industry.
I assign all firms listed on NYSE/AMEX/NASDAQ16 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).
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 VAR 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 size-
based lead-lag effect – we know there is an effect, so it must come from either the inter-
industry 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 VAR 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 averagingacross industries.18 I also estimate the VAR for each industry separately, and find confirming evidence. Results can beobtained from the author per request.
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.
5.1. 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 intra-
industry lead-lag effect.
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 R&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 sales-
ranked 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 VAR 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 intra-
industry 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 size-
sales 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.
19
Panels D and E of Table IV present results of the lead-lag tests. The intra-industry sales-
based 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 intra-
industry lagged information diffusion. On the other hand, I find the intra-industry size-
based 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 lead-
lag effect that is related to trading volume remains significant after controlling for sales
(Table V, Panel G).
I also measure industry leadership using the R&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 R&D spending in the same industry.
This lead-lag effect remains significant after sales is controlled for (Table IV, Panel I).
5.2. “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 VAR results for intra-industry portfolios based
on earnings-to-price ratio while keeping size fixed, with one week skipped between
20
lagged returns on P1 and P3 and the returns they are explaining.19 Results from these two
VARs 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 VAR 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-to-
market 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.
5.3. 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 lead-
lag 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-lagrelation between the high E/P portfolio and the low E/P portfolio is insignificant in week t-1, but becomessignificant in week t-2 and persists onto longer lags. This suggests that firm size, which is negativelycorrelated with earnings-to-price ratio, might be confounding the inferences.
21
equations using returns on the portfolio of large firms (P3) and returns on the portfolio of
small firms (P1).20
)8( .
)7( ,
)6( ,
)5(
4
1,3,3
4
1,10,3
4
1,3,30,3
4
1,1,3
4
1,10,1
,,1
4
1,10,1
∑∑
∑
∑∑
∑
=−
=−
=−
=−
=−
=−
+++=
++=
+++=
++=
ktktk
kktkt
ktktkt
ktktk
kktkt
tk
ktkt
uRfReeR
vRddR
uRcRbbR
vRaaR
The strength of the lead-lag effect within each industry is then estimated using the
following variable:
(9) . (7) model from
(8) model from - (5) model from
(6) model from 2
2
2
2
RR
RRLeadlag =
This R2-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 ( kb ’s and kf ’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.
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 lead-
lag relation within an industry. I name it Profit.
In Table V, Leadlag and Profit are regressed on industry concentration21, 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 R-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. Recent 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
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 cross-
sectional 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 industrysales share of all firms in an industry. Hou and Robinson (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 andtwelve-month industry returns generate average weekly profits of 25 basis points (t-statistic=7.24), 18 basispoints (t-statistic=5.10) and 22 basis points (t-statistic=5.85), respectively.
24
Insofar as the lead-lag effect is due to lagged diffusion of negative information, the
results in this section are broadly consistent with the explanation of the momentum
anomaly that is based on slow diffusion of bad news (Hong and Stein (1999), and Hong
et al. (2000)). More importantly, they suggest that the lead-lag effect has implications for
longer horizon returns and anomalies.
7. Lead-Lag Effect and News in Earnings Announcements
In this section, I study the adjustment of small firm stock prices to earnings surprises on
big firms as another way to draw inferences on the information diffusion process between
firms. The information diffusion hypothesis would predict that the stock prices of small
firms react positively when big firms in the same industry announce unexpectedly strong
earnings, and negatively when they announce unexpectedly poor earnings.
The above prediction is tested using the Fama-MacBeth (1973) cross-sectional
regressions. Every week, I estimate a cross-sectional regression on the smallest 70
percent firms from every industry. Individual stock returns are regressed on size, BE/ME,
earning surprise on big firms (average earning surprise for the largest 30 percent firms in
the industry to which each stock belongs), and intra-industry lead-lag variables (lagged
returns from week t-1 to week t-4 on the portfolio of the largest 30 percent stocks in the
industry to which each stock belongs, included to study whether past earnings surprises
and past returns on big firms contain different pieces of information regarding the future
prospects of small firms). Earning surprise is measured by the standard unexpected
earnings (SUE), which is the change in earnings in the most recent past quarter from the
earnings four quarters ago, divided by the standard deviation of the unexpected earnings
over the past eight quarters.24 Estimation is conducted separately for the small firms
which did not make an earnings announcement in the most recent past quarter, and those
which did make an announcement. For the small firms which did announce earnings in
25
the previous quarter, I include their own standard unexpected earnings to test whether
earning surprises on big firms contain information about small firms that is not in the
small firms’ own earnings surprises. The time series averages of the regression
coefficients and their t-statistics are reported in Table VII.
For the non-announcing small firms (Table VII, Panel A), the average earnings surprise
on big firms enters the regression equation significantly with a t-statistic of 5.45,
consistent with my prior expectation that past earnings surprises on big firms predict
subsequent drifts in returns on small firms because the earnings announcements on big
firms contain information about the future profitability of small firms within the same
industry. 25 More interestingly, when I include lagged returns on large firms to account for
the lead-lag relation in stock returns, the earnings surprise variable becomes insignificant.
This indicates that as far as the information diffusion between small and big firms is
concerned, past price movements of big firms convey less noisy signals about the future
prospects of small firms than past earnings surprises on big firms do.
For the small firms which announced earnings in the most recent past quarter, the
measure of own earnings surprise is positively and significantly correlated with future
returns (Table VII, Panel B). This is consistent with the results in the literature of post-
earnings-announcement drift that, firms with positive earnings surprise outperform firms
with negative earnings surprises after the earnings announcements (see Latene and Jones
(1979), Bernard and Thomas (1989), and Chan et al.(1996), among others). The average
earnings surprise on big firms, taken alone, is significantly and positively correlated with
future returns on small firms. And it remains significant (though weaker) after including
small firms’ own earning surprise in the regression, suggesting that earning surprises on
big firms add information about the prospects of small firms not contained in small firms’
own earnings surprises. Then just like the case for the non-announcing small firms, the
24 The SUE variable is commonly used in the accounting and finance literature to measure earningssurprise. For example, see Foster et al. (1984) and Chan et al. (1996).25 In results not reported here, I also find that this drift on small firms remains significant over a period ofsix months to one year after the earnings announcements of the big firms.
26
inclusion of the lagged returns on big firms drives out the predictive power of the average
earnings surprise on big firms.
The exercise in this section proves to be useful as it provides additional evidence
reinforcing previous findings in this paper that lagged information diffusion induces the
lead-lag effect in stock returns.
8. Conclusion
In this paper, I investigate whether the lead-lag effect in short horizon stock returns is due
to slow diffusion of common information between firms. I present evidence consistent
with information cost and investment restrictions inducing lags in the price adjustment
process of small firms (and firms with low trading volumes) to information, especially
negative information, produced on large firms (and firms with high trading volumes). I
decompose the unconditional lead-lag effect into inter-industry and intra-industry
components, and find the intra-industry component contributes significantly to the
unconditional lead-lag effect. Returns on industry leaders lead returns on other firms
within the industry. In addition, returns on “distressed” firms lead returns on their “non-
distressed” industry peers. The strength of the intra-industry lead-lag effect varies with
the characteristics of the industry in question. It is stronger in industries that are
concentrated, “value” and small. I also find the intra-industry lead-lag effect drives the
industry momentum anomaly, as well as the drifts of small firms after the earnings
announcements of big firms.
It is very important to get a clear understanding on the process by which information is
diffused among firms and into stock prices, as it has profound implications for market
efficiency and asset pricing. This paper takes a first step towards that direction. There are
several venues worth pursuing in the future.
27
First, although the evidence in this paper is most consistent with the lagged information
diffusion explanation of the lead-lag effect, I have only checked two specific alternative
hypotheses (which are by no means exhaustive). Therefore, I cannot definitely rule out all
other variations of the risk-based and behavioral-based explanations. Identifying those
alternative theories and exploring the extent to which they can explain the additional
evidence on the lead-lag effect presented in this paper can help us determine the
relevancy of these potential alternatives and promote further understanding for the lagged
information diffusion process between firms.
Second, we can also benefit from more work on measuring the information frictions and
investment restrictions responsible for introducing the lags in the price adjustment
process, studying the extent to which they prevent the lead-lag effect from being
arbitraged away, as well as investigating how the strength of lead-lag effect changes
through time as information communication and market mechanisms evolve (for
example, the introduction of financial options may alleviate the distortionary effect of the
short sale constraint on the price adjustment process).
Third, I have shown in this paper that variables like firm size, E/P and BE/ME which
predict cross sectional variation in average returns also play important roles in
determining time series return cross-predictability. More work on linking time series
return predictability with cross sectional return predictability can hopefully provide
additional insights on some of the puzzling issues in asset price dynamics.
Fourth, I have presented some stylized facts linking the strength of the intra-industry
lead-lag effect to the characteristics of the industry in question. Further investigations
along this line on how the differences across industries in the product market and
financial market characteristics, legal environment, as well as growth opportunities
influence the way that information is transmitted within industries may also prove to be a
fruitful area of research.
28
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31
Table I: Lead-Lag Effect between Size PortfoliosTable I.A-I.G study the lead-lag effect using weekly returns on size-ranked portfolios of NYSE/AMEX/NASDAQ firms from July 1963 to June 1997 (1774weekly observations). Pi refers to the ith size-ranked portfolio, i=1 for the smallest size portfolio and i=3 for the largest size portfolio. ρ j, j=1 to 8, is the jth orderautocorrelation coefficient. Q8 is the 8th order Ljung-Box test statistic for autocorrelations. Ri,t-j, i=1 to 3 and j=0 to 4, is the equally-weighted return of sizeportfolio i in week t-j. Ri,t-1:t-k, i=1 and 3 and k=1 and 4, is the sum of the regression coefficients on the lagged returns of portfolio i. In Panel C and Panel D,
Wald Test refers to the Wald-statistic for the cross-equation restriction ∑∑==
=K
kk
K
kk cb
11
in equations (1) and (2) that, the ability of lagged returns on P3 to predict
current returns on P1 is equal to the ability of lagged returns on P1 to predict current returns on P3. In Panel E, Panel F and Panel G, Wald Test refers to theWald-statistic for the coefficient restriction b1+b2=0 in equation (3). R2 is the adjusted coefficient of determination. * is significant at 1 percent level. ** issignificant at 5 percent level. *** is significant at 10 percent level. Di,t-1, i=1 and 3, is a dummy variable which takes the value of one if Ri,t-1 > 0, and zerootherwise. DM,t-1 is equal to one if the return on the market portfolio in week t-1 is positive, and zero otherwise. DC,t-1 is equal to one if the economy in week t-1 isin expansion, and zero if in contraction, following the definition of the NBER. Asymptotic standard errors for the autocorrelation coefficients in Panel A and Bare equal to 0.0237 under the i.i.d. null.
Panel A: Summary StatisticsPortfolio Mean return Std. Dev. Of return ρ1 ρ2 ρ3 ρ4 ρ5 ρ6 ρ7 ρ8 Q8
P1 0.0043 0.0216 0.4290 0.2640 0.1950 0.1450 0.1030 0.0760 0.0130 -0.0120 584.96*P2 0.0027 0.0218 0.2970 0.1390 0.1040 0.0690 0.0370 0.0440 0.0110 -0.0500 229.45*P3 0.0026 0.0202 0.1720 0.0540 0.0560 0.0020 -0.0040 0.0260 0.0280 -0.0750 76.147*
Panel B: Autocorrelation MatricesR1,t R2,t R3,t R1,t-1 R2,t-1 R3,t-1 R1,t-2 R2,t-2 R3,t-2 R1,t-3 R2,t-3 R3,t-3 R1,t-4 R2,t-4 R3,t-4
R1,t 1.0000 0.9184 0.7720 0.4290 0.4201 0.3672 0.2640 0.2382 0.1904 0.1950 0.1869 0.1567 0.1450 0.1434 0.1209R2,t 0.9184 1.0000 0.9335 0.2670 0.2970 0.2904 0.1383 0.1390 0.1193 0.0882 0.1040 0.0998 0.0577 0.0690 0.0640R3,t 0.7720 0.9335 1.0000 0.1212 0.1537 0.1720 0.0525 0.0597 0.0540 0.0213 0.0469 0.0560 0.0034 0.0067 0.0020
32
Panel C: Vector-Auto Regressions for the Size Portfolios
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald Test(k=4)
R1,t 0.4373* 0.1843* 0.2084 7.3041*R3,t -0.0481 0.2827* 0.0361
(k=1)R1,t 0.3593* 0.0962* 0.1870 6.1480*R3,t -0.0275 0.1951* 0.0301
Panel D: Vector-Auto Regressions for the Size Portfolios, Market-Adjusted Returns
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald Test(k=4)
R1,t 0.4274* 0.2369** 0.1444 7.2042*R3,t -0.0307 0.1892* 0.0116
Panel E: Vector-Auto Regressions augmented by Dummy Variables for Lagged Price Movement
LHS R1,t-1D1,t-1 R1,t-1 R3,t-1D3,t-1 R3,t-1 R2 Wald Test
R1,t 0.2676* 0.1700* -0.2505* 0.2670* 0.1903 0.1741
R3,t -0.0179 -0.0150 0.0138 0.1853* 0.0279
Panel F: Vector-Auto Regressions augmented by Dummy Variables for Lagged Market Movement
LHS R1,t-1DM,t-1 R1,t-1 R3,t-1DM,t-1 R3,t-1 R2 Wald Test
R1,t 0.0357 0.3333* -0.1048*** 0.1548** 0.1859 0.8617
R3,t -0.0749 0.0151 0.0443 0.1694* 0.0286
Panel G: Vector-Auto Regressions augmented by Dummy Variables for Business Cycle
LHS R1,t-1DC,t-1 R1,t-1 R3,t-1DC,t-1 R3,t-1 R2 Wald Test
R1,t 0.2386* 0.1797* -0.2630* 0.2917* 0.1902 0.3665
R3,t 0.0513 -0.0661 -0.1119 0.2766* 0.0291
33
Table II: Lead-Lag Effect between Volume Portfolios, Controlling for SizeTable II.A-II.G study the lead-lag effect using weekly returns on volume-ranked portfolios, controlling for size, of NYSE/AMEX firms from July 1963 to June1997 (1774 weekly observations). Pi refers to the ith volume-ranked portfolio, i=1 for the lowest volume-ranked portfolio and i=3 for the highest volume-rankedportfolio. ρ j, j=1 to 8, is the jth order autocorrelation coefficient. Q8 is the 8th order Ljung-Box test statistic for autocorrelations. Ri,t-j, i=1 to 3 and j=0 to 4, is theequally-weighted return on volume portfolio i in week t-j. Ri,t-1:t-k, i=1 and 3 and k=1 and 4, is the sum of the regression coefficients on the lagged returns of
portfolio i. In Panel C and Panel D, Wald Test refers to the Wald-statistic for the cross-equation restriction ∑∑==
=K
kk
K
kk cb
11
in equations (1) and (2) that, the
ability of lagged returns on P3 to predict current returns on P1 is equal to the ability of lagged returns on P1 to predict current returns on P3. In Panel E, Panel Fand Panel G, Wald Test refers to the Wald-statistic for the coefficient restriction b1+b2=0 in equation (3). R2 is the adjusted coefficient of determination. * issignificant at 1 percent level. ** is significant at 5 percent level. *** is significant at 10 percent level. Di,t-1, i=1 and 3 is a dummy variable which takes the valueof one if Ri,t-1 > 0, and zero otherwise. DM,t-1 is equal to one if the return on the market portfolio in week t-1 is positive, and zero otherwise. DC,t-1 is equal to oneif the economy in week t-1 is in expansion, and zero if in contraction, following the definition of the NBER. Asymptotic standard errors for the autocorrelationcoefficients in Panel A and B are equal to 0.0237 under the i.i.d. null..
Panel A: Summary Statistics
Portfolio Mean return Std. Dev. of return ρ1 ρ2 ρ3 ρ4 ρ5 ρ6 ρ7 ρ8 Q8
P1 0.0038 0.0181 0.3410 0.1830 0.1460 0.0770 0.0200 0.0480 0.0170 -0.0550 315.32*P2 0.0032 0.0216 0.2570 0.1080 0.0920 0.0400 0.0140 0.0440 0.0100 -0.0670 163.20*P3 0.0025 0.0257 0.2000 0.0780 0.0550 0.0340 0.0110 0.0230 0.0100 -0.0550 93.065*
Panel B: Autocorrelation Matrices
R1,t R2,t R3,t R1,t-1 R2,t-1 R3,t-1 R1,t-2 R2,t-2 R3,t-2 R1,t-3 R2,t-3 R3,t-3 R1,t-4 R2,t-4 R3,t-4
R1,t 1.0000 0.9608 0.9161 0.3410 0.3514 0.3516 0.1830 0.1681 0.1586 0.1460 0.1381 0.1244 0.0770 0.0753 0.0729R2,t 0.9608 1.0000 0.9755 0.2395 0.2570 0.2676 0.1219 0.1080 0.1026 0.0942 0.0920 0.0789 0.0423 0.0400 0.0398R3,t 0.9161 0.9755 1.0000 0.1721 0.1894 0.2000 0.0963 0.0833 0.0780 0.0684 0.0684 0.0550 0.0325 0.0384 0.0340
34
Panel C: Vector-Auto Regressions for the Volume Portfolios
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald Test(k=4)
R1,t 0.2373** 0.1829** 0.1467 2.5450***R3,t 0.0520 0.2354** 0.0509
(k=1)R1,t 0.1162** 0.1724* 0.1258 8.3566*R3,t -0.0955 0.2612* 0.0406
Panel D: Vector-Auto Regressions for the Volume Portfolios, Market-Adjusted Returns
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald Test(k=4)
R1,t 0.1584** 0.2701* 0.1249 11.4932*R3,t -0.0359 0.3117* 0.0658
Panel E: Vector-Auto Regressions augmented by Dummy Variables for Lagged Price Movement
LHS R1,t-1D1,t-1 R1,t-1 R3,t-1D3,t-1 R3,t-1 R2 Wald Test
R1,t 0.4983* -0.2250** -0.3426* 0.3951* 0.1317 1.0265
R3,t 0.4145** -0.3794** -0.2844** 0.4461* 0.0411
Panel F: Vector-Auto Regressions augmented by Dummy Variables for Lagged Market Movement
LHS R1,t-1DM,t-1 R1,t-1 R3,t-1DM,t-1 R3,t-1 R2 Wald Test
R1,t 0.2359** -0.0305 -0.2034** 0.2898* 0.1266 1.7834
R3,t 0.1712 -0.2043 -0.1591 0.3537* 0.0392
Panel G: Vector-Auto Regressions augmented by Dummy Variables for Business Cycle
LHS R1,t-1DC,t-1 R1,t-1 R3,t-1DC,t-1 R3,t-1 R2 Wald Test
R1,t 0.1081 0.0427 -0.1762* 0.2433* 0.1248 1.3625
R3,t 0.1809 -0.2214 -0.1553 0.3667* 0.0393
35
Table III: Inter-Industry Lead-Lag EffectOne-lag vector-auto regressions are estimated using weekly returns on portfolios of industries based onmedian size or trading volume, from July 1963 to June 1997. Pi refers to the ith ranked portfolio, i=1 for thelowest ranked portfolio and i=3 for the highest ranked portfolio. Ri,t-j, i=1 and 3 and j=0 and 1, is the equal-weighted return on portfolio i in week t-j. Wald Test refers to the Wald-statistic for the cross-equationrestriction that, the ability of lagged returns on P3 to predict current returns on P1 is equal to the ability oflagged returns on P1 to predict current returns on P3. R2 is the adjusted coefficient of determination. * issignificant at 1 percent level. ** is significant at 5 percent level. *** is significant at 10 percent level.
LHS R1,t-1 R3,t-1 R2 Wald TestPanel A: Size Portfolios of Industries
R1,t 0.1954* -0.0478 0.0252 1.5007R3,t 0.0052 0.0158 0.0053
Panel B: Volume Portfolios of IndustriesR1,t 0.1975* -0.0333 0.0282 0.5761R3,t 0.0250 0.0485 0.0044
36
Table IV: Intra-Industry Lead-Lag EffectFour-lag (k=4) and one-lag (k=1) vector-auto regressions are estimated using weekly returns on intra-industry characteristic-ranked portfolios, from July 1963 to June 1997. Pi refers to the ith ranked portfolio,i=1 for the lowest ranked portfolio and i=3 for the highest ranked portfolio. Ri,t, i=1 and 3, is the equally-weighted return on portfolio i in week t. Ri,t-1:t-k,i=1 and 3 and k=1 and 4, is the sum of the regressioncoefficients on the lagged returns of portfolio i. Wald Test refers to the Wald-statistic for the cross-equationrestriction that, the ability of lagged returns on P3 to predict current returns on P1 is equal to the ability oflagged returns on P1 to predict current returns on P3. R2 is the adjusted coefficient of determination. * issignificant at 1 percent level. ** is significant at 5 percent level. *** is significant at 10 percent level.
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald TestPanel A: Intra-Industry Size Portfolios
(k=4)R1,t 0.3948* 0.1949* 0.1987 6.5744*R3,t -0.0439 0.2911* 0.0391
(k=1)R1,t 0.3286* 0.1061* 0.1785 6.3772*R3,t -0.0296 0.2031* 0.0328
Panel B: Intra-Industry Volume Portfolios(k=4)
R1,t 0.3315* 0.2086* 0.1748 5.2162**R3,t -0.0202 0.2162* 0.0259
(k=1)R1,t 0.2784* 0.1218* 0.1577 9.0662*R3,t -0.0451 0.1749* 0.0209
Panel C: Intra-Industry Sales Portfolios(k=4)
R1,t 0.3263* 0.2095* 0.1638 5.9275*R3,t -0.0702 0.3495* 0.0464
(k=1)R1,t 0.2721* 0.1172* 0.1467 4.7578**R3,t -0.0264 0.2229* 0.0404
Panel D: Intra-Industry Sales Portfolios, Controlling for Size(k=4)
R1,t 0.0212 0.4068* 0.1074 8.6258*R3,t -0.2646 0.6407* 0.0868
(k=1)R1,t 0.0941 0.2204** 0.0978 4.7043**R3,t -0.0641 0.3414* 0.0782
Panel E: Intra-Industry Sales Portfolios, Controlling for Trading Volume(k=4)
R1,t -0.0640 0.4441* 0.0864 7.5844*R3,t -0.2107 0.5358* 0.0647
(k=1)R1,t 0.1049 0.1978** 0.0725 2.6857***R3,t 0.0210 0.2182* 0.0586
37
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald TestPanel F: Intra-Industry Size Portfolios, Controlling for Sales
(k=4)R1,t 0.3915* 0.1133 0.1620 1.4031R3,t -0.0344 0.3138* 0.0492
(k=1)R1,t 0.3281 0.0560 0.1455 0.9269R3,t -0.0147 0.2173* 0.0419
Panel G: Intra-Industry Volume Portfolios, Controlling for Sales(k=4)
R1,t 0.4144* 0.0920** 0.1654 4.8685**R3,t -0.0081 0.2070** 0.0286
(k=1)R1,t 0.2885* 0.0960** 0.1455 5.4875**R3,t -0.0479 0.1871* 0.0419
Panel H: Intra-Industry R&D/Sales Portfolios(k=4)
R1,t 0.0216 0.3367* 0.0958 3.9406**R3,t -0.0147 0.3504* 0.0662
(k=1)R1,t 0.1296** 0.1539** 0.0885 2.7043***R3,t 0.1203 0.1413** 0.0549
Panel I: Intra-Industry R&D/Sales Portfolios, Controlling for Sales(k=4)
R1,t 0.2579* 0.1083** 0.0916 3.1217***R3,t -0.0961 0.3819* 0.0534
(k=1)R1,t 0.1902* 0.0797** 0.0834 3.6673**R3,t -0.0130 0.2078* 0.0470
Panel J: Intra-Industry E/P Portfolios, Controlling for Size (Skipping a Week)(k=4)
R1,t -0.0073 0.1679*** 0.0214 5.5763*R3,t -0.0906 0.2956* 0.0421
(k=1)R1,t -0.1090 0.2448** 0.0165 11.7446*R3,t -0.2236** 0.4005* 0.0326
Panel K: Intra-Industry E/P Portfolios, Controlling for Volume (Skipping a Week)(k=4)
R1,t 0.0036 0.0748** 0.0220 8.9846*R3,t -0.0107** 0.0501 0.0288
(k=1)R1,t -0.1322 0.2347* 0.0114 14.5781*R3,t -0.2344** 0.3715* 0.0240
38
LHS R1,t-1:t-k R3,t-1:t-k R2 Wald TestPanel L: Intra-Industry BE/ME Portfolios, Controlling for Size (Skipping a Week)
(k=4)R1,t -0.1264 0.3606*** 0.0233 3.6164**R3,t -0.3063 0.5618* 0.0367
(k=1)R1,t -0.0365 0.1924** 0.0187 8.4434*R3,t -0.1493** 0.3192* 0.0274
Panel M: Intra-Industry BE/ME Portfolios, Controlling for Volume (Skipping a Week)(k=4)
R1,t -0.1443 0.2972** 0.0127 3.9737*R3,t -0.2860 0.4611* 0.0222
(k=1)R1,t 0.0776 0.2204** 0.0121 9.5116**R3,t -0.1875** 0.3162* 0.0192
39
Table V: Cross-Industry Differences in Lead-Lag EffectTable V reports results of the cross-industry regression of Leadlag and Profit on industry concentration,industry median size, industry median BE/ME. Leadlag and Profit are defined in section 4 to measure thestrength of lead-lag effect within an industry. Industry concentration is the rank of an industry’s sales-basedHerfindhal index averaged over time. Industry median size, BE/ME are calculated in similar manner. R2 isthe adjusted coefficient of determination.
LHS IndustryConcentration
Industry MedianSize
Industry MedianBE/ME
R2
Leadlag 1.3377 -0.3858 0.6570 0.4350.22 0.19 0.29
Profit 0.0587 -0.0304 0.0409 0.4200.01 0.01 0.01
40
Table VI: Fama-MacBeth Cross-Sectional Regressions: Industry Momentum Effectand Lead-Lag EffectFama-MacBeth (1973) cross-sectional regressions are estimated each week from July 1977 to June 1997 onthe smallest 70 percent of stocks from each industry. Ln(Size) is the log of market capitalization of eachindividual firms. Ln(BE/ME) is the log of book-to-market ratio. Ind-1:-1, Ind-6:-1 and Ind-12:-1 are the returnson the value-weighted industry portfolio over past one month, six months and one year, respectively.Lagk(R3), k=1 to 4, is the return in week t-k on the equal-weighted portfolio of the largest 30 percentstocks from each industry. Reported are the time series averages of the coefficients from the weeklyregressions, as well as in Italics the t-statistics calculated using the standard error of the mean.
Ln(Size) Ln(BE/ME) Ind-1:-1 Ind-6:-1 Ind-12:-1 Lag1(R3) Lag2(R3) Lag3(R3) Lag4(R3)
-0.0008 0.0004 0.0481-7.43 3.70 19.40
-0.0008 0.0004 0.0112-7.55 3.72 12.04
-0.0008 0.0004 0.0063-7.51 4.00 10.59
-0.0008 0.0004 0.0387 0.0020 0.0029-7.57 4.01 14.55 1.52 3.60
-0.0008 0.0004 -0.0002 0.0014 0.0013 0.0955 0.0351 0.0333 0.0227-7.55 4.22 -0.06 1.05 0.84 16.15 6.08 5.74 4.04
41
Table VII: Fama-MacBeth Cross-Sectional Regressions: Past Earnings Surprisesand Lead-Lag EffectFama-MacBeth (1973) cross-sectional regressions are estimated each week from July 1977 to June 1997 onthe smallest 70 percent of stocks from each industry. Estimation is conducted separately for the small firmswhich did not make an earnings announcement in the most recent past quarter (Panel A), and the smallfirms which did make an announcement (Panel B). Ln(Size) is the log of market capitalization of eachindividual firms. Ln(BE/ME) is the log of book-to-market ratio. SUE is the standardized unexpectedearnings (the change in earnings in the most recent past quarter from the earnings four quarters ago, dividedby the standard deviation of the earning surprises over the past eight quarters) for each individual firm.SUE3 is the equal-weighted average of the standardized unexpected earnings for the largest 30 percentstocks from each industry. Lagk(R3), k=1 to 4, is the return in week t-k on the equal-weighted portfolio ofthe largest 30 percent stocks from each industry. Reported are the time series averages of the coefficientsfrom the weekly regressions, as well as in Italics the t-statistics calculated using the standard error of themean.
Panel A: Non-Announcing FirmsLn(Size) Ln(BE/ME) SUE SUE3 Lag1(R3) Lag2(R3) Lag3(R3) Lag4(R3)
-0.0011 0.0004 0.0007-8.59 3.31 5.45
-0.0011 0.0004 0.0014 0.0917 0.0806 0.0390 -0.0627-8.84 3.48 1.51 5.66 2.59 2.00 -0.70
Panel B: Announcing Firms
-0.0008 0.0003 0.0008-6.29 1.82 9.96
-0.0007 0.0003 0.0004-5.67 1.66 4.21
-0.0008 0.0003 0.0008 0.0002-6.26 1.97 9.77 2.69
-0.0008 0.0003 0.0008 0.0004 0.0928 0.0143 0.0607 0.0234-6.23 2.09 10.90 1.06 3.83 0.45 2.92 2.88
