Price Shocks, News Disclosures, and Asymmetric Drifts Hai Lu, Kevin Q. Wang, and Xiaolu Wang ∗ March 12, 2012 ∗ Hai Lu, an associate professor of accounting, and Kevin Q. Wang, an associate professor of finance, are at University of Toronto. Xiaolu Wang is an assistant professor of finance at Iowa State University. Emails: [email protected] (Hai Lu); [email protected](Kevin Wang); [email protected] (Xiaolu Wang). We are grateful to Qiang Cheng, Siu Kai Choy, Esther Eiling, Raymond Kan, Ryan LaFond, Dongmei Li, Jeffrey Ng, Lars Norden, Lukasz Pomorski, Gord Richardson, Hollis Skaife, Lakshmanan Shivakumar, Kevin Veenstra, Rodrigo Verdi, Ross Watts, Jason Wei, Franco Wong, Liyan Yang, Bin Zhao, and seminar participants at BlackRock Asset Management, McGill University, MIT, University of Toronto, University of Wisconsin-Madison, China International Conference in Finance, and the Northern Finance Association conference for helpful comments and suggestions. We thank Social Sciences and Humanities Research Council of Canada for financial support.
Transcript
Price Shocks, News Disclosures, and Asymmetric Drifts
Hai Lu, Kevin Q. Wang, and Xiaolu Wang∗
March 12, 2012
∗Hai Lu, an associate professor of accounting, and Kevin Q. Wang, an associate professorof finance, are at University of Toronto. Xiaolu Wang is an assistant professor of finance at
Bamber, Barron, and Stober [1997], Hong and Stein [2007]), suggesting that earnings an-
nouncements increase disagreement in the short term. On the other hand, a few studies
conclude in the opposite direction. For example, Brown and Han [1992] show that analyst
forecast dispersion declines after the announcements. Berkman et al. [2009] find that stocks
with high opinion divergence earn significantly lower returns around earnings announce-
ments. They conclude that earnings announcements reduce opinion divergence because
managers make conscious efforts to communicate information to the market. Rogers, Skin-
ner, and Van Buskirk [2009] show that management earnings forecasts increase short-term
volatility. The effect arises mainly from forecasts that convey bad news, especially when
firms release forecasts sporadically. They show that in the longer run, the uncertainty
declines after the earnings announcements. Patell and Wolfson [1981] and Jennings and
Starks [1985] also discuss and test potential resolution of uncertainty from earnings an-
nouncements and the speed of adjustment of stock prices. In general, the argument that
corporate public disclosures reduce information uncertainty/asymmetry in the long run is
consistent with the intended purpose of accounting disclosures.
Corporate news disclosures play a critical role in explaining the evolution of stock returns
(e.g., Shin [2006]). Over past decades, numerous studies in accounting examine properties
of corporate disclosures and effects of these disclosures such as implications for the cost
of capital and liquidity (see Verrecchia [2001] and Healy and Palepu [2001] for reviews).
However, little attention is paid to separating disclosure effects from price shock effects. For
example, Kandel and Pearson [1995] focus on earnings announcements and naturally they
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do not touch the issue of different interpretations about no-news price shocks. Garfinkel
and Sokobin [2006] find that unexpected trading volume at the earnings announcement
positively correlates with future returns. Like other studies on earnings announcements,
the benchmark for comparison in the testing is not set out to control for effects of price
shocks on stock returns.
Cutler, Poterba, and Summers [1989] show that nearly half of the return variance of the
aggregate stock market cannot be explained by public news on fundamentals. The study,
together with Roll [1988] which raised the same point, indicates that more studies are
needed to understand price shocks. These papers are helpful for motivating our study, since
they demonstrate that no-news price shocks are quite common. Our study differs from these
papers in two important ways. First, we provide an investigation of cross-sectional effects
instead of the aggregated time-series variation considered in the above papers. Second, we
demonstrate that no-news price shocks are important and offer a novel angle to examine
disclosure effects. A tantalizing question generated from these studies is whether large price
shocks without accompanying disclosures about fundamentals are important for investors.
In other words, do such shocks have implications for future returns? The question is also in
the spirit of the argument in Richardson, Sloan, and You (2011) which demonstrates that
investor recognition is a distinct and significant determinant of stock price movements.5
Intuitively, stock returns after large price shocks may be related to activities of retail
investors. The role of retail trading has received considerable attention in recent years
(e.g., Barber and Odean [2008], Kumar [2009]). In a related study, Bali, Cakici, and
Whitelaw [2011] argue that retail investors prefer lottery-like stocks, which are stocks that
are experiencing large positive shocks. They find that stocks with extreme positive price
changes in the ranking month have significantly negative returns in the subsequent month.
The lottery explanation is that retail investors prefer such lottery-like stocks and their
post-shock purchases inflate the prices of the stocks, generating the negative returns over
5Our effect can not simply be due to increase of investor recognition. Since news increases recognition,
the asymmetric drifts should be stronger for shocks with news, which is opposite to the empirical evidence
that we document.
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the subsequent month. Their motivation and focus clearly differ from ours, as we pursue a
disagreement explanation of price shocks and study effects of news disclosures. In addition,
we extend their study. While we do find the negative returns following positive shocks,
we find there is no strong buying activities of retail investors after these shocks, which is
inconsistent with the explanation based on the retail investor’s preference of lottery-like
stocks.
2.2 Empirical Predictions
We focus on large short-term stock price changes, which are referred to as price shocks
throughout the paper. Based on investor disagreement theories while assuming both the
existence of heterogeneous priors and the presence of short-sales constraints, our first pre-
diction is that a jump in opinion divergence following large price shocks (especially no-news
price shocks) gives rise to negative abnormal returns over a subsequent period. When price
shocks lead to an increase of opinion divergence among investors and the disagreement de-
creases slowly, we should expect asymmetric abnormal return drifts, i.e., a negative shock
is followed by a negative drift but a positive shock is also followed by a negative drift. The
asymmetric drifts are illustrated in Diagrams A and B of Figure 1.
Our second prediction is based on the informational role of disclosure events. We predict
that the negative drifts following price shocks that are not associated with news events are
stronger than those associated with news disclosures. This prediction, depicted in Diagrams
C and D of Figure 1, follows from the hypothesis that corporate disclosures help reduce
information uncertainty/asymmetry, and thus reduce investor opinion divergence. For both
predictions, the key driver behind the novelty of our targets is no-news price shocks, which
is based on an empirical division of stocks with price shocks into two groups. Stocks in
the news group have firm-specific news in the window from three days before to three days
after the price shocks while stocks in the no-news group do not. Corporate news events
used in our study are analyst earnings forecasts, conference calls, earnings announcements,
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seasoned equity offerings, mergers and acquisitions, management earnings forecasts, analyst
recommendations, and dividend declarations.6
2.3 Empirical Approach
Price shocks are defined by maximum and minimum three-day abnormal returns in the
ranking month (month ).7 The three-day market adjusted abnormal return for a stock is
the difference between the stock return and the market return over three consecutive trading
days, where the market return is the return of the value-weighted portfolio of all NYSE,
AMEX and NASDAQ stocks. The three-day window of either maximum or minimum
abnormal return could be at any time in the ranking month. We sort all stocks into
deciles based on the maximum three-day abnormal return (positive shock) or the minimum
three-day abnormal return (negative shock). When sorting stocks using the maximum or
minimum three-day abnormal return, we focus on the extreme deciles that contain the
largest positive and negative shocks respectively (i.e., decile 10 ranked on positive shocks
and decile 1 on negative shocks).
Our first step is to examine links between price shocks and disagreement proxies. Using
return volatility, turnover, unexpected volume and analyst earnings forecast dispersion as
proxies for disagreement, we verify whether price shocks generate opinion divergence that
will decrease gradually. We also examine variation in the sidedness measure of Sarkar and
Schwartz [2009], which is available only for a short time period, to seek further evidence
on the link between price shocks and disagreement.
After confirming that price shocks increase investor opinion divergence, we test whether
we can observe asymmetric drifts following negative and positive price shocks. Specifically,
we examine the pattern of stock returns over the twelve months following these shocks. The
overlapping portfolio approach of Jegadeesh and Titman [1993] is applied. Stocks are sorted
6The informativeness of these news events is documented in many studies (see Ecker, Francis, Olsson,
and Schipper [2006]).7Alternative definitions of one-day or five-day abnormal returns are considered. The results are similar.
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into decile portfolios, using either maximum or minimum three-day abnormal returns in
the ranking month. The 12-month holding period returns, the alphas with respect to the
Fama-French three factor model (Fama and French [1993]) and the alphas with respect to
the Carhart four factor model (Carhart [1997]), are obtained. We also construct a difference
portfolio by holding a long position on decile 10 and a short position on decile 1.
The decile 1 ranked by negative shocks (containing largest negative shocks) and decile
10 ranked by positive shocks (containing largest positive shocks) are further divided into
news and no-news subgroups, depending on whether at least one news event occurs for the
stock within three days before and three days after the price shock. These sorts and the
regressions tests discussed later on provide a novel way to test disclosures-related effects.
Differing from studies in the extant literature, our tests use the no-news price shocks as
the benchmark to investigate effects of news disclosures that generate large price changes.
A basic presumption for our predictions is that short-sales constraints exist. We check
whether short-sales constraints affect the degree of overpricing such that the post-shock
drifts are stronger for stocks with strong short-sales constraints. Furthermore, we exam-
ine whether our empirical findings are robust to various alternative explanations including
post-earnings announcement drifts (Ball and Brown [1968]), risk change and uncertain in-
formation hypothesis (Brown, Harlow, and Tinic [1988, 1993]), idiosyncratic volatility and
its change (Ang et al. [2006, 2009], Bali, Scherbina, and Tang [2010]), and speculative
preferences of retail traders (Han and Kumar [2009], Kumar [2009], and Bali, Cakici, and
Whitelaw [2011]). Finally, we design a test to show the economic significance of our find-
ings. Putting the price-shock effects in a momentum framework, we demonstrate that the
profitability of the momentum strategy could be significantly improved.
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3. Data and Portfolio Characteristics
3.1 Data
We use stock returns, trade sizes, institutional holdings, and various firm-specific news
events in our analyses. The stock data are from CRSP. Our analyses include all stocks
traded on NYSE, AMEX, and NASDAQ. To guard against microstructure effects associ-
ated with the small-cap and low-priced stocks, we exclude stocks in the smallest market
capitalization decile and those with prices lower than $5 at the end of the ranking month.
We collect event dates of a number of firm-specific news events: analyst earnings fore-
casts, conference calls, earnings announcements, seasoned equity offerings, mergers and
acquisitions, management earnings forecasts, analyst recommendations, and dividend dec-
larations. The sample periods for these events vary with the availability of the databases.
These events are collected from the following data sources: Standard and Poor’s Com-
pustat (earnings announcements, 1972 to 2006), CRSP (dividends, 1963 to 2006), IBES
(analyst recommendations, 1993 to 2006), First Call (analyst revisions on annual earnings
and management forecasts, 1989 to 2006), BestCalls.com (conference calls, 1999 to 2006),
and SDC (M&A and SEO, 1978 to 2006). In addition, we use trade sizes to separate retail
trades from non-retail trades. The trade sizes come from NYSE TAQ and ISSM intraday
trading file from 1983 to 2000. We use Thomson-Reuters Mutual Fund Holdings and Insti-
tutional Holdings (13F) databases to compute the breadth of mutual fund and institutional
ownership.
3.2 Portfolio Characteristics
Table 1 presents characteristics of the decile portfolios constructed from sorting on either
negative or positive shocks. The listed variables include firm size, book-to-market ratio, the
ranking month return, and the 12-month return before the ranking month. These variables,
used as control variables in the cross-sectional regressions in Section 5, correspond to the
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four known effects of the cross-section of stock returns: the size effect, the value effect,
the short-run return reversal, and the Jegadeesh-Titman momentum effect. Idiosyncratic
volatility (ivol) and retail trading proportion (RTP) are variables that we will use in Section
5 for checking alternative explanations. The magnitude of the minimum/maximum three-
day shocks (−/+) is presented in each panel. For each of these variables, we first
obtain the cross-sectional mean in a given month, and then report the time-series average
of the mean. The average number of stocks in each decile portfolio is shown at the bottom
of each panel.
Panels A1 and A2 in Table 1 are for the decile portfolios from sorting on the minimum
three-day abnormal return (negative shocks). Panel A1 is for negative shocks without
accompanying news events, while Panel A2 is for stocks with news events. Most of the
characteristics display significant variation across the deciles, and the patterns are similar
for both stocks with and without news events. Firm size, for instance, increases monoton-
ically from decile 1 to decile 10. For stocks with negative shocks and without news events,
decile 1 has an average size of $169 million in contrast to $1,511 million for the stocks in
decile 10. For stocks with negative shocks and news events, decile 1 (10) has the average
size of $486 (3,849) million. The ranking month returns are lower for the bottom deciles
than those for the top deciles. However, the pre-ranking 12-month returns are higher for
the bottom deciles than those for the top deciles. There is no significant difference in the
book-to-market ratio. Furthermore, both ivol and RTP decrease monotonically from decile
1 to decile 10. The mean of the minimum three-day abnormal return for decile 1 of the
no-news group (−15.21%) is close to the mean for decile 1 of the news group (−16.12%).
Panels B1 and B2 present cases in which the ranking is based on the maximum three-day
abnormal returns (positive shocks). Panel B1 (B2) is for the case of positive shocks without
(with) corporate news events. Both panels show that there are significant variations in most
portfolio characteristics across the deciles. Stocks in the top deciles (i.e., deciles with large
positive shocks) are smaller in size and stocks with news events are larger in size than stocks
without news events. There is no significant difference in the book-to-market ratio. Both
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the ranking month returns and the pre-ranking 12-month returns are higher for the top
deciles than those for the bottom deciles. Decile 10, the portfolio with the largest positive
price shocks, has the largest values of ivol and RTP. The means of the maximum three-day
abnormal returns for decile 10 for the no-news group and the news group are very close,
21.19% and 20.84% respectively.
4. Empirical Tests
4.1 Price Shocks and Investor Disagreement
The hypothesis that price shocks increase opinion divergence is intuitive. It would be
difficult for many investors to immediately assess the precise impact on the future cash
flows when they observe a large sudden change in stock price, especially when there is
no corporate disclosure associated with the price change. To examine whether opinion
divergence responds to price shocks, we investigate variations of several proxies for opinion
divergence around price shocks. We check whether they increase around the time of price
shocks and then decline gradually after the price shocks. We investigate four measures
of opinion divergence: idiosyncratic volatility, stock turnover, unexpected trading volume,
and analyst earnings forecast dispersion. Though each of the measures is subject to certain
limitations (e.g., Garfinkel [2009]), examining all of them may give us a useful view of the
dynamics of opinion divergence around price shocks.
Panels A and B of Table 2 report the change of disagreement proxies in raw value and
percentage, respectively. We focus on stocks with extreme price shocks; that is, stocks
in decile 1 of negative shocks and decile 10 of positive shocks. We do not separately
report negative and positive shocks as they yield similar results. The first number in the
third column of Panel A, under the term − −1, shows that the median idiosyncratic
volatility (ivol) increases from month − 1 to by 0.773, which is significantly different
from 0. The number in Panel B suggests that ivol increases by 30.2% from month − 1 tomonth . Compared to the three-month average before the price shock (−3−1), ivol for
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month () is also significantly higher. The difference is with a value of 0.704 (column
4 of Panel A), equivalent to an increase of 26.2% (column 4 of Panel B). For the post-
shock quarters, however, Panel A shows that the signs of all the three-month changes for
idiosyncratic volatility are negative, consistent with the hypothesis that disagreement drops
after the initial jump in ranking month . Panel B indicates that after a 21.4% drop in
the first quarter following the ranking month, ivol continues to drop by about 3.5% in the
second quarter. The incremental drops in ivol in the next two quarters are 2.1% and 1.5%
approximately, which are all statistically significant.
For turnover and unexpected volume, the results are qualitatively similar to those for
idiosyncratic volatility. For example, the median turnover for month increases by 0.089 in
comparison to the value for month − 1, while for unexpected volume, the value increasesby 0.046 from month − 1 to . The post-shock changes for turnover and unexpected
volume are all negative. For unexpected volume, for instance, the largest change is over
the first three-month post-shock period, over which the unexpected volume drops by 0.043.
The three-month changes of unexpected volume over quarters between +3 and +12 are
all negative and statistically significant.
Overall, the results from idiosyncratic volatility, turnover, and unexpected volume are
consistent with the hypothesis that disagreement increases around price shocks and it
decreases over a long post-shock period.
For analyst dispersion, however, all the numbers are insignificant except for the changes
frommonth to the first quarter after the shocks.8 The results are likely due to the fact that
it is problematic to use analyst dispersion in a dynamic setting even though the measure
is viewed by many as an empirical proxy for opinion divergence cross-sectionally. Because
earnings are announced every quarter, the dispersion on annual earnings at month + 3
and at month + 9 for instance may not share the same target. While the former is the
dispersion on earnings for year , the latter may be the dispersion on earnings for year
+ 1. Therefore, the two dispersion estimates may not be directly comparable, and one
8The percentage change in dispersion over the first post-shock quarter is 2.7%, which is quite modest.
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may not observe any decline of the dispersion measure even if disagreement actually drops.
This issue is much less serious for studies that focus on cross-sectional variation (rather
than time-variation) of dispersion (e.g., Diether, Malloy, and Scherbina [2002]). Another
issue is that analysts may not adjust their forecasts immediately after price shocks. Given
the large uncertainty about implications from price shocks, analysts may play safe such
that they may be reluctant to adjust the forecasts that are disclosed to the public. Thus
analyst dispersion may not rise even if their opinions diverge.
The sidedness measure of Sarkar and Schwartz [2009] is a new proxy for disagreement.
The measure is constructed using the NYSE TAQ intraday data from 1993 to 2006. We
treat the checks using the sidedness measure as supplementary because the measure is based
on a short estimation period and limited to NYSE firms. The sidedness is estimated as the
correlation between the numbers of buyer- and seller-initiated trades. The correlation is
computed daily, using trades sampled at 5-minute intervals.9 Sarkar and Schwartz argue
that belief heterogeneity is reflected in sidedness. A relatively high value of the sidedness
measure implies that trades are more likely to be driven by disagreement. We average daily
sidedness into monthly sidedness and inspect its variation around large price shocks. The
results are presented in Figure 2.
Panels A and B of Figure 2 correspond to negative and positive shocks respectively,
including both news and no-news cases. Variation in the sidedness measure is shown from
two months before the shock to twelve months after the shock (from − 2 to + 12).
The measure is typically negative, reflecting that large buyer- and seller-initiated trades
tend to occur in different time intervals over the day. The post-shock pattern for no-news
shocks are supportive to the hypothesis that shocks generate or increase disagreement, and
then the different opinions converge gradually after shocks. The post-shock pattern for
shocks with news is somewhat surprising. The sidedness measure goes down over the first
two months after the shocks and then stays fairly flat for a while. It is puzzling that the
9Choy and Wei [2010] construct the measure using all transactions from 9:30am to 4:00pm for each day
and each stock. We thank Siu Kai Choy and Jason Wei for providing us with access to their sidedness
dataset.
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measure is relatively high at the end of the holding period. A potential explanation is that
news events tend to be of periodic nature (e.g., quarterly earnings announcements) and one
year is a common cycle that they share. It should be noted that trading-based proxies such
as turnover and sidedness may not capture investors who have negative opinions about a
stock but do not trade it. For example, for mutual funds that have negative views about
a stock but do not own any shares, the funds do not participate in the trading at all. The
existence of such pessimistic investors can create the case in which negative information is
gradually impounded into prices.
In summary, the results of Table 2 and Figure 2 suggest that although there are various
limitations of the disagreement proxies, the variations in the proxies are generally consistent
with our hypothesis that opinion divergence increases around price shocks and decreases
gradually afterward.
4.2 Asymmetric Post-Shock Drifts
In this section, we present findings about how price shocks and news events affect future
stock returns. In Table 3, Panel A presents the results from portfolio sorts using the cross-
section of stocks. Reported in the table are the average monthly returns, the Fama-French
three factor alphas, and the Carhart four factor alphas for decile 1, decile 10, and the
difference portfolio (decile 10 minus decile 1). The difference portfolio is constructed by
taking both a long position on decile 10 and a short position on decile 1. The holding
period consists of 12 months after the ranking month . Columns 3 and 2 show that
the three factor alpha is positive (0.16%) for decile 10 and negative (−0.69%) for decile1 of negative price shocks. The alphas imply annualized abnormal returns of 1.92% and
−8.28% respectively. The evidence suggests that when there is a large price drop, a long
term downward drift indeed occurs following the drop (decile 1). The annualized alpha for
the difference portfolio (column 4) is 10.20%, which is significant with a robust -value of
6.78. In contrast, column 6 shows that stocks in decile 10 of positive shocks (large price
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hikes), have a monthly three-factor alpha of −0.40% (i.e., −4.80% annually) with a robust-value of −5.16. Thus, both extreme negative and positive price shocks are followed bynegative abnormal returns over the next twelve-month period.
In addition, untabulated results suggest that negative abnormal returns are not limited
to the extreme deciles. For negative shock deciles, the three factor alphas for deciles 2 and
3 are in annual term equal to −3.96% and −2.04%, with robust -values of −4.95 and −2.83respectively. For positive shocks, both deciles 8 and 9 have significantly negative alphas.
These results further support the robustness of our findings. Finally, the last row of Panel
A shows that the above results are robust to the Carhart [1997] four factor model.
Panel B of Table 3 reports the impact of news events on the price-shock effects. We
focus on large positive shocks (decile 10) and large negative shocks (decile 1) as stocks in
these deciles have the most extreme price shocks. For positive shocks, the news subset of
stocks in decile 10 has significantly higher abnormal return than the no-news subset. The
difference between the monthly three factor alphas (news minus no-news) is 0.48%. The
difference is 0.52% when the alphas are calculated with the four factor model. News stocks
in decile 1 of negative shocks also have significantly higher abnormal returns than no-news
stocks. The difference in the monthly three factor alphas between the two subgroups is
0.12% with robust -value 2.05.
These results are consistent with the argument that news events mitigate the negative
drift associated with the increase of disagreement caused by price shocks. In contrast,
untabulated analysis shows that decile 10 of negative shocks and decile 1 of positive shocks,
which contain stocks having small price shocks (in terms of the magnitude of the shock),
display no significant difference in alphas between the news and no-news groups. Again,
the last row of Panel B shows that all results on the news effect are robust to the Carhart
[1997] four factor model.
The post-shock abnormal returns are persistent. Table 4 reports the average monthly
returns, the Fama-French three factor alphas, and the Carhart four factor alphas for the
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difference portfolio (decile 10 minus decile 1) for four three-month intervals (quarters) after
the ranking month . Panel A illustrates the case where the ranking variable is the minimum
three-day abnormal return in month .10 Several conclusions can be drawn from Panel A.
First, regardless of whether there is a news event accompanying the shocks, the difference
portfolio always has significant long-lasting abnormal returns. Over the holding period
from month +1 to month +12, the three-factor and four-factor alphas for the difference
portfolio (either with or without a news event) are positive and statistically significant for
every three-month interval. Second, the alpha for the news group is always lower than the
alpha for the no-news group. The difference in the alphas between the two groups (news
minus no-news) is always negative.
Panel B presents the case where stocks are ranked by the maximum three-day abnormal
return. This panel shows that for the no-news group the three-factor and four-factor alphas
of the difference portfolio are negative and statistically significant for the first three quarters
after positive shocks. But most of the alphas for the news group are insignificant. In the last
quarter (months 9 to 12), the four factor alpha for the news group even becomes significantly
positive. The difference between the alphas from the no-news and news groups is significant
for all three-month intervals. These findings indicate that stocks with large positive shocks
tend to suffer a relatively large, persistent reversal for the 12-month holding period after
the ranking month. This reversal, however, is mitigated by the existence of news events.
In sum, the results from Tables 3 and 4 support our predictions that are laid out in
Figure 1. Diagrams A and B show that there are long-lasting negative abnormal returns
following both negative and positive price shocks. Diagrams C and D show that for both
negative and positive shocks, the effects are stronger for no-news shocks.
4.3 Impact of Short-Sales Constraints
Existence of short-sales constraints is an important assumption of disagreement models.
10Note that for the difference portfolio in Panel A, decile 1 contains largest negative price shocks.
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In this subsection, we test whether the post-shock drift pattern varies with the degree of
short-sales constraints. If the drifts are indeed related to opinion divergence, we expect
that they are more significant among stocks with stronger short-sales constraints.
Following Chen, Hong and Stein [2002], we use mutual fund holding breadth as a proxy
for short-sales constraints. The measure is motivated by the fact that many mutual funds
are not allowed to short-sell even if they hold pessimistic views about any of the stocks.
The breadth is defined as the ratio of the number of mutual funds that hold a long position
in the stock to the total number of mutual funds for that quarter reported in Thomson
Financial Mutual Fund Holdings database. We define the smallest (largest) third as "Low
(High) Breadth" sample. In other words, the "Low Breadth" sample consists of stocks in
the lowest third when sorting by the value of their breadth. Based on disagreement models,
we expect that the post-shock abnormal return drifts are more salient among stocks with
low breadth which are associated with stronger short-sales constraints.
In Table 5, Panel A presents the results. In the case where the sorting variable is the
negative shock, the Fama-French three factor alpha for the difference portfolio (decile 10
minus decile 1) for low breadth stocks is 1.13% with -statistic of 6.55. The alpha for high
breadth stocks is 0.61% with -statistic of 3.35. When using the Carhart four factor alphas,
the contrast is more impressive. The four factor alpha for the difference portfolio for low
breadth stock is 0.86% with -statistic of 3.99, while that for high breadth stocks is only
0.05% with -statistic of 0.37. In the case where the sorting variable is the positive shock,
the three factor and four factor alphas for the difference portfolio for low breadth stocks
are −0.49% and −0.47% respectively, with -statistics of −2.73 and −2.55. In contrast,the alphas for high breadth stocks are −0.30% and −0.08% respectively, with -statistics of−1.67 and −0.49. These findings confirm that post-shock drifts are stronger for stocks withstronger short-sales constraints, providing further evidence that the persistent post-shock
abnormal returns are a disagreement-based effect. Panel B of Table 5 presents the news
effect. For negative shocks, the news effect is insignificant in both low and high breadth
groups. For positive shocks, although the news effect is significant in both low and high
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breadth groups, the effect is much stronger in the low breadth group.
Motivated by findings of Asquith, Pathak, and Ritter [2005] and Nagel [2005], we also
use institutional ownership as an alternative proxy for short-sales constraints. Stocks with
low institutional ownership are more expensive to borrow. Institutional ownership is the
percentage of shares outstanding owned by institutions as reported in Thomson Finan-
cial Institutional Holdings (13F) database. Stocks are first divided into thirds based on
institutional ownership. The lowest (highest) third is classified as “Low (high) institu-
tional ownership” group. Similar to those in Table 5, untabulated results show that the
price-shock effects are much stronger among stocks with low institutional ownership. For
example, in the case of sorting on negative shocks, the Fama-French three factor alpha for
the difference portfolio (decile 10 minus decile 1) for low institutional ownership stocks is
1.24% with -statistic of 6.44. The alpha for high institutional ownership stocks is 0.61%
with -statistic of 3.94. The results in the case of sorting on positive shocks show that
the alpha for the difference portfolio is significantly negative only for the stocks with low
institutional ownership.
5. Economic Significance of Price Shock Effects
We present a set of conditional tests to demonstrate the economic significance of our
findings in this section. The goal is to show the significance of price shocks conditional
on the well-documented momentum effect (Jegadeesh and Titman [1993]). The test helps
reflect the significance of losses that optimistic investors would incur due to information
uncertainty and how disclosures mitigate such wealth transfer. Our specific predictions
are depicted in Figure 3. We first create momentum portfolios by ranking stocks into
portfolios based on returns from month − 12 to month − 1 to generate the winner andloser portfolios. Table 6 reports the Fama-French three factor alphas and the robust -
statistics. For winner stocks, the alpha is 0.21% per month. For loser stocks the alpha is
−0.70% per month. As expected for the momentum effect, both alphas are statistically
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significant. The difference portfolio’s alpha is 0.90% per month, which is also consistent
with findings in the momentum literature.
The winner and loser portfolios are each divided into two groups: one with price shocks
and the other without shocks. The alpha for the losers with price shocks (−1.15%) is sig-nificantly lower than that for the losers without price shocks (−0.60%).11 This is consistentwith our expectation as illustrated in Diagram C of Figure 3. In contrast, the alpha for the
winners with price shocks (−0.02%) is significantly lower than the alpha for the winnerswithout price shocks (0.24%), again supporting the conjecture highlighted in Diagram B
of Figure 3. The evidence from both winners and losers suggests that price shocks add a
significantly negative drift to the return continuation of either winners or losers over the
twelve months following the ranking month.
Table 6 also reports the results from testing the effect of news disclosures. If public news
events reduce opinion divergence, we would expect a significant difference in the alphas
between news and no news sub-groups in both winners and losers with price shocks. The
results support our conjectures illustrated in Diagrams D and E of Figure 3. For loser stocks
with shocks that are not accompanied by any news events, the alpha is −1.29%. However,for those loser stocks with shocks accompanied by news events, the alpha is significantly
higher at −0.90%. For winner stocks, the effect of news events is directionally the same.The alpha for the group with shocks without accompanying news events is −0.16%, whileit is 0.44% for those with the shocks accompanied by news event. The -statistic for the
difference between the two winner portfolio’s alphas is 4.78.
In summary, the evidence in this section is consistent with the argument that price
shocks increase opinion divergence and the convergence of the disagreement may take a
long time. As a result, a negative price drift due to such divergence is added to the
existing momentum effect. News disclosures mitigate the shock-induced increase of opinion
divergence. The economic significance of these effects can be demonstrated by the improved
11All the alphas in Table 6 are from the three factor model. Since the portfolio sorts are conditional on
momentum, we present only the results from the three factor model.
22
profitability of a revised momentum strategy. Using this revised strategy, one buys winner
stocks having price shocks associated with explicit corporate news disclosures and short-
sells loser stocks that have no-news price shocks. The revised hedge portfolio provides a
three factor alpha of 1.73% (= 044%− (−129%)), equivalent to an annualized abnormalreturn of 21%. With respect to the three factor alpha of the regular momentum strategy
(which equals to 0.90%), the revised strategy improves the profitability by 92%.
6. Other Potential Explanations
In this section, we consider other potential explanations. We first distinguish the asym-
metric drifts documented in our study from the well-known post-earnings announcement
drifts. We then try to reconcile the asymmetric drifts with the findings in Brown. Har-
low and Tinic (1988). Furthermore, we explore whether our findings can be captured by
idiosyncratic volatility or retail trading. Finally we discuss results from the robustness
tests when controlling for multiple effects including changes in risk, microstructure effects,
liquidity, delay, and skewness.
6.1 Post-Earnings Announcement Drifts
Post-earnings-announcement drift (PEAD) is a well known phenomenon documented
in the accounting literature (e.g., Ball and Brown [1968], Bernard and Thomas [1990]). It
refers to the tendency of a stock’s post-announcement cumulative abnormal return to move
in the direction of an earnings surprise. As positive (negative) earnings surprises are more
likely to be associated with positive (negative) price shocks, we expect a symmetric post-
shock drift pattern due to PEAD. Does this symmetric drift pattern exist in our sample? Is
the asymmetric drift pattern following price shocks mainly due to stocks without earnings
announcements around the portfolio formation time? We report the results in Table 7.
In Panel A, we focus on stocks with earnings announcement in the window from three
days before to three days after the price shock. These stocks are ranked into deciles by
23
the negative and positive shocks. Equal-weighted decile portfolios are formed and held for
12 months, following the overlapping portfolio approach of Jagadeesh and Titman [1993].
Reported in the panel are the Fama-French three factor alphas and the Carhart four factor
alphas for decile 1, decile 10, and the difference portfolio (10 - 1). The difference portfolio
is constructed by taking both a long position on decile 10 and a short position on decile 1.
For this sample, we predict that the PEAD effect dominates the asymmetric drift pattern,
and expect to observe positive (negative) drifts following positive (negative) shocks.
Consistent with our expectation, Panel A shows that price shocks associated with earn-
ings announcement are followed by symmetric instead of asymmetric drifts in the following
year. For example, the monthly Carhart four factor alpha is −0.31% (with a robust -
statistic of −2.21) for earnings announcement associated with largest negative price shock(decile 1 of negative shocks). Earnings announcements associated with large positive price
shocks, on the other hand, have a monthly Carhart four factor alpha of 0.26% (with a
robust -statistic of 2.26). Significantly positive drifts following positive price shocks with
earnings announcement are in contrast to the negative drifts following no-news positive
shocks. These findings present evidence that PEAD exists in our sample, and that the
asymmetric drift pattern identified in Section 4.2 is mainly due to shocks unrelated to
earnings announcements.
In Panel B, we present the drift pattern for stocks with large price shocks (i.e., decile 1
sorted on negative shocks and decile 10 sorted on positive shocks) but without an earnings
announcement from three days before to three days after the shocks. Panel B confirms that
the asymmetric drift pattern following price shocks and the news effect on the post-shock
drift is not due to PEAD. With shocks associated with earnings announcements excluded,
the news group of negative price shocks shows a weaker downward drift (with a three
factor alpha of −0.49% and a four factor alpha of −0.12%), and therefore a stronger newseffect, than that reported in Panel B of Table 3. This result is consistent with the fact
that negative earnings announcements are followed by negative drifts. For the news group
of positive price shocks, we do not find any significant change in post-shock drift after
24
excluding stocks with earnings announcements, suggesting that PEAD is not the driver for
the significant news effect identified among stocks with large positive price shocks. These
findings are robust to alternative event windows. Specifically, we check two alternative
event windows: seven days before to seven days after the price shock, and 15 days before
to 15 days after the price shock. The results are very similar.
6.2 Risk Change and Uncertain Information Hypothesis
Risk adjustment is a common concern in event studies (e.g., Ball [1978]). It is possible
that extreme price shocks lead to a change in the risk level of the stocks, and investors
rationally revise their expectations to reflect this change. Brown, Harlow, and Tinic [1988,
1993] develop and test an uncertain information hypothesis (UIH), which predicts that risk
averse investors respond to unanticipated price changes by adjusting their risk estimates
and expected returns. Under UIH, we should observe positive drifts following both positive
and negative price shocks. In this subsection, we first examine variation in total risk and
systematic risk around the price shocks. We then replicate the study of Brown, Harlow,
Tinic (1988) and compare the UIH test results with our findings. The tests suggest that
it is unlikely that the asymmetric post-shock drifts that we document are associated with
changes in the risk measures. Although we document some weak positive drift among a
subset of large firms like Brown, Harlow, and Tinic (1988), we find that the asymmetric
drifts following large price shocks (in our extreme deciles) subsume the UIH effect.
Our findings are based on the alphas from the Fama-French three factor (or the four
factor) model, and thus presumably risk change in the post-shock period has already been
accounted for. To provide further insights, we examine patterns of changes in the standard
deviation of stock returns, the loadings of the market, size, and book-to-market factors.
Panel A of Table 8 documents the results. We only present the results from the pooled
sample as the patterns are similar for both positive and negative shocks. The first two
rows in Panel A show that these risk measures (except for the book-to-market factor) for
25
the stocks with large shocks are higher in the ranking month with respect to the average
values of the previous one or three months. The increase in risk level is consistent with
the findings in various accounting studies (e.g., Bernard and Thomas [1989]) that examine
specific corporate events. However, these changes in risk measures are temporary. The
last row of Panel A compares risk estimates in the twelve months before and after the
ranking month. The results indicate that the difference between the before- and after-
ranking-month magnitudes of the risk measures is insignificant, suggesting that there is no
permanent change in the risk level. Further examination reveals that the increase in the
risk level around price shocks identified in the first two rows is largely offset by a decrease
that occurs in the first quarter after the shocks. Thus, it is unlikely that changes in the
common risk proxies can explain our finding that the asymmetric post-shock drifts persist
over the twelve-month holding period.
In the uncertain information hypothesis (UIH), Brown, Harlow, and Tinic [1988, 1993]
propose that risk averse investors would respond to unanticipated price changes by adjusting
their risk estimates and expected returns. Specifically, UIH predicts positive average returns
following both positive and negative price changes. They test the hypothesis with the
largest 200 stocks in the S&P 500 index, and they find consistent evidence in the first 60
trading days after significant price changes (higher than 2.5% or lower than -2.5%). We
replicate their analysis and report the results in Panel B of Table 8. To be consistent with
BHT, we use the 200 largest S&P 500 firms and also examine returns within the three
months after the price shocks. The first two rows of Panel B show evidence consistent with
the uncertain information hypothesis. The three-month abnormal returns are significantly
positive following both positive and negative price changes (2.5% cutoff). We further
examine the overlap between the BHT sample and our extreme deciles.12 We find that
the asymmetric drifts subsume the UIH effect in this subsample. Reported in the third
and fourth rows, the results show that the three month abnormal returns are negative
following both positive and negative shocks (-0.64% and -2.60%, respectively). The results
12Recall the mean returns in our extreme negative and positive deciles are about -16% and 21%, respec-
tively.
26
suggest that the effect uncovered in our study is also present among large-cap firms. The
findings from BHT and ours do not seem hard to reconcile, given the possibility that the
disagreement effect may be more relevant in the presence of large price shocks.
We notice that certain indirect evidence is also not in favor of the risk explanation.13
If the post-shock drifts arise from investors’ rational reaction to changes in risk, one would
expect that this effect should be stronger among stocks with higher institutional ownership
since institutional investors tend to be more sophisticated. The results that we have briefly
discussed in Section 4.3, however, are contradictory to this prediction. The analysis shows
that the price shock effects are weaker for the high institutional ownership group, which
provides further support that the price shock effects are not driven by a rational risk story.
6.3 Idiosyncratic Volatility and Its Change
Stocks with large price shocks in the ranking month tend to have large idiosyncratic
volatility (ivol) in the same month. Ang et al. [2006, 2009] document a high idiosyncratic
volatility low return puzzle. They sort stocks on the basis of their idiosyncratic volatility
measure, computed using the Fama-French three factor model. They find that stocks with
high idiosyncratic volatility earn low future returns. Thus, a natural hypothesis is that
the persistent return patterns following price shocks may be just a manifestation of the
idiosyncratic volatility puzzle.
We test this hypothesis using Fama-MacBeth cross-sectional regressions, checking whether
the post-shock return patterns are robust after controlling for the idiosyncratic volatility
effect. The dependent variable is the 12-month holding period stock return. We include
in the regression both negative shocks (−) and positive shocks (+), news event
dummies, and the interaction term of −/ + with the news event to capture the
price shock effects and the disclosure effects. Idiosyncratic volatility (ivol) is included
as a competing variable, along with the four control variables size, book-to-market ratio,
13Such evidence may be interesting, as it does not require measurement of time-varying risk.
27
stock return in month , and the stock returns in the preceding 12 months. If + and
− remain significant in the predicted direction after ivol is included, we can infer that
asymmetric drifts following price shocks are not a manifestation of the high idiosyncratic
volatility low return puzzle. In such a case, the results would suggest that ivol does not
fully capture opinion divergence triggered by price shocks if both ivol and price shocks are
proxies for disagreement. We also expect that the two interaction terms be significant if
news events have any effect on mitigating disagreement.
We report test results in Table 9. Panel A presents the Fama-MacBeth regressions
with various specifications. Model 1 only consists of ivol and four control variables: size,
book-to-market ratio, ranking month returns, and the returns in preceding 12 months.
The regression replicates high idiosyncratic volatility low return puzzle. The coefficient
on ivol is −1.94 with a robust -statistic of −3.82. Models 2 and 3 separately examinethe negative drifts following either negative or positive shocks after controlling for ivol.
The results show that price shock effect is robust to the control of ivol effect, which is
also significant. The coefficients on − and + are significantly positive (0.36) and
negative (−0.37), respectively, suggesting that both negative and positive price shocks yieldsignificantly negative returns in the holding period. The news effect is significant in the
predicted direction for the positive shocks only.14
Model 4 is a full model, including all the controls, the shocks, and the interaction terms.
The coefficients on all the variables of interest are significant in the predicted directions.
The coefficients on − is 0.30 (=4.66). The coefficients on + and its interaction
term with news event are −0.34 (= −7.24) and 0.32 (=8.10). These results stronglysuggest that negative return drifts follow large price shocks and news events mitigate the
impact of these price shocks. The mitigating role of news events on negative shocks is rela-
tively weaker than that on positive shocks, consistent with the argument in literature that
managers have less incentives to bring investors up to date quickly regarding bad news (e.g.,
14In the portfolio sorting analysis in Panel B of Table 3, we show that the difference portfolio for negative
shocks is also significant although it is not as strong as this for positive shocks. The regression analysis
suggests that the control variables take away the news effect for negative shocks.
28
Hong, Lim, and Stein [2000], Kothari, Shu, andWysocki [2009]). Importantly, we find that,
when both − and + are controlled for, the coefficient on ivol becomes insignifi-
cant, i.e., the high idiosyncratic volatility low return puzzle disappears. In summary, the
above results indicate that idiosyncratic volatility does not explain the asymmetric drifts
related to positive and negative price shocks.
Bali, Scherbina, and Tang [2010] find that stocks with large changes in the idiosyncratic
volatility (ivol shocks) over the ranking month have negative returns for the subsequent
month + 1. They use ivol shocks to proxy unusual news events and suggest that investor
disagreement created by the unusual news generates negative future returns. In Panel B,
we examine whether the price shock effects are robust when the ivol shocks are included in
the Fama-MacBeth regressions. Model 1 confirms the strong negative effect of ivol shock
on future stock returns. The coefficient on ivol shock is −0.44 with robust -statistic of−10.84. Models 2 and 3 show that both negative and positive post-shock drifts are robustin the presence of ivol shocks. The coefficients on − and + are 0.43 (-stat=1.87)
and −0.39 (-stat=−2.05) respectively. The news effect is significant for the positive priceshocks with a coefficient of 0.31 (-stat=7.90). After introducing either negative or positive
price shocks into the regression, ivol shock, however, becomes only marginally significant
with -values of −1.87 and −1.66, respectively. The full model (Model 4) results indicatethat our findings remain robust after controlling for ivol shocks. When both negative
and positive shocks are introduced into the regression, the ivol shock variable is no longer
significant (with a -stat of −0.84). Therefore, the above results suggest that ivol shocksdo not explain the asymmetric drifts following positive and negative price shocks.
6.4 Retail Trading
Are the price shock effects mainly due to irrational trading of a subset of investors who
prefer volatility and skewness? Kumar [2009] shows that stocks with high volatility and
high skewness are attractive to retail investors who exhibit a greater propensity to gamble.
29
Han and Kumar [2009] find that stocks with a high proportion of retail trading tend to
earn lower future returns. Bali, Cakici, and Whitelaw [2011] argue that retail investors’
preference for lottery-like stocks leads to negative returns following positive price shocks.
We will explicitly control for skewness later on in the multivariate regressions. Here we
conduct a battery of tests to examine whether the drifts subsequent to stock price shocks
are explained by speculative preferences or heuristic trading of retail investors.
Many empirical studies separate retail trades from institutional trades using the dol-
lar value or the number of shares traded in each transaction. The underlying intuition is
that individuals (institutions) are more likely to trade using small-size (large-size) trades.
The cutoffs vary across different studies. For example, Battalio and Mendenhall [2005]
consider any trades less than 500 shares as small trades, while Malmendier and Shan-
thikumar [2007] classify trades below $20,000 as small trades. Typically, robustness with
different classifications is tested (e.g., Malmendier and Shanthikumar [2007], De Franco,
Lu, and Vasvari [2007], and Mithail, Walther, and Willis [2007]). We have examined
three different classifications yet only report one in Tables 10 and 11. Reported results
are based on $7,000/$30,000 classification, i.e., trades of less than $7,000 as retail trades
and trades of greater than $30,000 as institutional trades (Mikhail, Walther, and Willis
[2007]). The other two classifications we examined are 1,000/10,000 shares (Lee [1992]),
and $5,000/$5,000 (Han and Kumar [2009]). The results on the other two classifications
are similar and not reported for brevity.
To calculate retail trading proportion (RTP), we first sum up the shares of each transac-
tion to get the daily trading volume for retail and institutional traders, respectively, using
the intraday data from TAQ and ISSM databases. The daily RTP is computed as the
total retail trading volume divided by the sum of trading volume of retail and institutional
trades in a given day. We exclude trades between the two cutoffs (e.g., $7,000/$30,000 for
the reported results) since it is much more difficult to attribute trades in the middle to
retail investors or institutions. The monthly RTP is the average of the daily RTP over
the ranking month. In recent years, institutional investors have used algorithmic trading
30
platforms to execute their orders. When large orders are broken into small orders, the
classification contains significant errors. To mitigate this concern, for RTP based tests, our
sample period stops at year 2000.
In Table 10, we examine whether RTP can explain the price shock effects using cross-
section regressions with the 12-month post-shock return as the dependent variable. The
results show that including RTP and the interaction terms between RTP and price shocks
(− and +) into regression does not take away the significance of price shocks,
suggesting that RTP cannot capture the cross-sectional return effects of price shocks. The
coefficient of RTP is not significant in any of the models. The marginally significant coef-
ficient of the interaction term between RTP and − in the full model (model 3) shows
some evidence that the negative drift following negative price shocks is stronger among
stocks with high RTP.
In Table 11, we use retail order imbalance after price shocks to shed light on retail
investors’ post shock trading activities. The Lee and Ready [1991] algorithm is used to
classify buyer- or seller-initiated trades. The first (last) four columns report the retail
order imbalance following negative (positive) price shocks. During the nine days after
price shocks, the numbers are all significantly positive for negative shocks and negative for
positive shocks, suggesting that retail investors are buying after negative shocks and selling
after positive shocks. If the post-shock negative drift is due to retail investors’ preference
for volatility, skewness, or lottery-like stocks, we should expect that retail investors to buy
after price shocks, especially following positive price shocks. The results in Table 11 are
not consistent with this prediction as suggested by Bali, Cakici, and Whitelaw [2011].
The pattern of retail order imbalance following positive and negative shocks makes it
more difficult to link retail trading with the negative drifts following both types of shocks.
Furthermore, Table 11 shows that the pattern of retail order imbalance is not long-lasting.
The positive retail order imbalance after negative shocks dies out around 20 days after
the shocks. The negative retail order imbalance after positive shocks becomes insignificant
around 60 days after the shocks. Therefore, it is unlikely that the retail trading can explain
31
the long-lasting post-shock negative drift identified in this study.
In untabulated tests, we include the retail order imbalance in cross-sectional regressions
and find that retail order imbalance cannot take away the significance of the price shocks.
In summary, the results presented in Tables 10 and 11 suggest that retail trading cannot
explain the asymmetric post-shock drifts.
6.5 Other Robustness Checks
In this subsection, we point out some other robustness checks which are not tabulated
for brevity. First, we examine the price shock effects conditioning on abnormal trading
volume. Although there have been numerous studies on trading volume following Beaver
[1968], their findings do not yield a clear view. For example, Verrecchia [1981] and Kim and
Verrecchia [1991] discuss the difficulties associated with interpreting volume reactions to
public announcements and conclude that no unambiguous inferences can be drawn about
investors’ beliefs when a volume reaction is observed. Bamber and Cheon [1995], Kandel
and Pearson [1995], and Kim and Verrecchia [1997] also emphasize that abnormal trading
volume occurs even in the absence of price changes. Including abnormal trading volume in
the multivariate regressions, we find that abnormal trading volume does not capture the
price shock effects.
Second, we perform a cross-sectional regression test to jointly control for multiple effects.
We control for microstructure effects, liquidity, delay, and skewness, together with proxies
for idiosyncratic volatility and retail trading. The empirical proxies are selected following
previous studies: spread (Demsetz[1968]), turnover and volume (Chordia, Subrahmanyam
and Anshuman [2001]), illiquidity (Amihud [2002]), delay (Hou and Moskowitz [2005]), and
skewness (Barbaris and Huang [2008]). The table is omitted for brevity (but available upon
request). The test results show that the post-shock drifts remain robust after controlling
for various effects. None of the effects can account for the asymmetric persistent patterns in
returns after positive and negative shocks. Furthermore, news events in general reduce the
32
impact of price shocks, although the mitigating effect appears stronger for positive price
shocks.
Finally, we explore the possibility that the price shock effects arise because investors
interpret no disclosure as management withholding negative information. In such a case,
the stock price reflects the expectations of potential bad news (e.g., Dye [1985], Diamond
and Verrecchia [1987], Lev and Penman [1990]). We examine abnormal returns around
the subsequent earnings announcements in the twelve-month holding period for stocks that
are experiencing large positive and negative price shocks. First, we estimate the three day
abnormal return around each of the earnings announcements. Next, we calculate the total
abnormal return over all the announcements in the holding period. The total abnormal
returns are only −0.01% and −0.44% for the portfolios with large negative and positive
shocks. This evidence is inconsistent with the argument that negative information related
to future cash flows has been withheld for those stocks at the time of large shocks.
7. Conclusions
Stock price shocks are visible and often attention-grabbing. The occurrence of stock
price shocks in the absence of public announcement of firm specific news is particularly
puzzling. Private information, liquidity shocks, and manipulations can all generate the
shocks. The existence of noise traders and different interpretations of price signals can
effectively prevent investors from reaching consensus quickly after price shocks. We take
advantage of this natural and yet novel setting to test investor disagreement theory.
The main finding of our study is that no-news price shocks are important such that
they are followed by significant and long-lasting abnormal returns. The drifts that our
tests uncover are asymmetric - return continuation following negative price shocks and re-
turn reversal following positive shocks. This finding is in sharp contrast to what we had
learned in the event study literature. Moreover, we find that price shocks with informa-
tion disclosures, compared to those without public announcements, are followed by weaker
33
downward drifts. The evidence suggests that reduction of information asymmetry, as a
result of public information disclosures, weakens disagreement-induced overpricing. We
carry out a number of robustness tests. The results are consistent with predictions of dis-
agreement models while inconsistent with other explanations. In particular, the price-shock
effects are not a reflection of either the idiosyncratic volatility puzzle or the overpricing due
to speculative preferences in retail trading.
The importance of price shocks per se suggests the need to separate disclosure effects
from price shock effects. The findings from our conditional tests give rise to an interesting
perspective about the role of regulations on corporate disclosures as the empirical results
suggest that public disclosures actually improve market efficiency through the reduction of
investor disagreement. As for the empirical implementation, we recognize that our news
events are not exhaustive. The disclosures identified in the data are only a subset of all the
disclosures that actually occurred. Moreover, not all of the identified events are informative.
Therefore, the results related to news should be cautiously interpreted. Nevertheless, when
missing any significant news events, some price shocks associated with news would as a
result be misclassified into the no-news group. This omission would work against us as the
misallocation would likely weaken our results.
Our findings also have useful implications for portfolio management. The revised mo-
mentum strategy, an approach to buying winner stocks with price shocks associated with
explicit corporate news disclosure and short-selling loser stocks having no-news price shocks,
would improve the profitability of the simple buying-winner-selling-loser momentum strat-
egy by 92%. The revised hedge portfolio has a three-factor alpha of 1.73%, equivalent to an
annualized abnormal return of 21%. In general, our empirical results suggest that if indi-
viduals chase stocks that recently have had large price shocks, they would suffer substantial
losses. In that sense, corporate disclosures effectively mitigate the wealth transfer.
While we argue that the evidence is consistent with the predictions of disagreement
models, there are caveats that should be noted. First, as emphasized by Fama [1998], it is
important to have a unified theory to explain why the same investors underreact in some
34
cases but overreact in others. We do not assume an ad hoc combination of underreaction
and overreaction as an alternative explanation for the asymmetric drifts. We pursue a the-
ory that can simultaneously explain the abnormal return patterns following both negative
and positive shocks. Nevertheless, it is difficult, if possible at all, to rule out that the
asymmetric drifts can be explained by a combination of two different theories - a theory
for underreaction and another for overreaction. Second, we conjecture that price shocks
generate opinion divergence and we verify that following price shocks there is a long term
decay process of opinion divergence measures, such as unexpected volume, turnover, and
volatility. However, trading-based disagreement proxies and return volatility may not cap-
ture the existence of investors who have pessimistic views about a stock and currently do
not participate in the trading of the stock. The existence of such investors, however, may
be sufficient to generate the post-shock abnormal returns.
35
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40
TABLE 1
Portfolio Characteristics
deciles: 1 2 3 4 5 6 7 8 9 10
(low) (high)
Panel A1. Ranked by Negative Price Shocks, without News
This table reports summary statistics for decile portfolios sorted on either positive (+) or negative
(−) price shocks. Each decile portfolio is further divided into ‘news’ and ‘no news’ groups, based on
whether a corporate news event occurs in the window from three days before to three days after the shock.
Size is the market capitalization of the firm measured in millions of dollars. B/M is the book-to-market
ratio of the firm. Ranking month stock return and cumulative stock return in the 12-month period prior to
the ranking month are denoted by return t and return 12. Ivol is the idiosyncratic volatility, computed as
the standard deviation of the residual from the Fama-French three-factor regression using daily returns in
the ranking month. RTP is the average daily retail trading proportion, i.e., retail trades/(retail trades +
institutional trades), in the ranking month. Trades smaller than $7,000 (larger then $30,000) are classified
as retail (institutional) trades. The reported values of all variables are first averaged across stocks in a given
month, and then averaged over time. In addition, the average number of stocks in each group is also reported
in the table. The sample period for RTP is 1983.1—2000.12. The sample period for all remaining variables
is 1963.7—2006.12.
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TABLE 2
Variation in Disagreement Proxies
Panel A. Change in Disagreement Proxies
− −1 − −3−1 ∆1 ∆2 ∆3 ∆4
ivol Est. 0.773 0.704 -0.765 -0.104 -0.064 -0.047
-stat 28.22 25.64 -26.61 -6.67 -4.31 -3.14
turnover Est. 0.089 0.066 -0.082 -0.025 -0.015 -0.011
-stat 12.21 10.65 -11.16 -6.14 -4.10 -3.14
unexpected volume Est. 0.046 0.034 -0.043 -0.016 -0.011 -0.009
-stat 12.24 10.63 -11.31 -7.43 -6.00 -5.56
analyst dispersion Est. 0.012 0.032 0.219 0.020 -0.038 -0.036
-stat 2.03 1.16 4.43 0.44 -0.98 -0.85
Panel B. Percentage Change in Disagreement Proxies
−−1|−1|
−−33−1|−3−1| %1 %2 %3 %4
ivol Est. 0.302 0.262 -0.214 -0.035 -0.021 -0.015
-stat 36.63 33.68 -42.39 -6.44 -3.82 -2.52
turnover Est. 0.277 0.190 -0.148 -0.048 -0.019 -0.010
-stat 36.31 18.00 -19.37 -4.61 -1.82 -0.88
unexpected volume Est. 0.300 0.252 -0.198 -0.071 -0.046 -0.035
-stat 19.44 13.64 -18.85 -9.05 -6.98 -5.65
analyst dispersion Est. 0.000 -0.002 0.027 -0.002 -0.014 -0.011
-stat 0.33 -0.41 3.83 -0.29 -1.89 -1.48
This table presents the variation in investor disagreement around extreme price shocks. Panels A and B
report the change in disagreement proxies in raw values and percentages, respectively. Columns 2 and 3 in
both panels examine whether price shocks increase investor disagreement in the ranking month relative to
month −1 or the average of months −3 to −1. Column 4 presents the change in disagreement in the firstquarter after month relative to month . The remaining three columns report the change in disagreement
in the second, third, and fourth quarter after month relative to the previous quarter. The sample covers
stocks with extreme price shocks, i.e., positive (negative) shocks in the highest (lowest) decile. We use
four proxies for investor disagreement, (1) ivol, the idiosyncratic volatility measure defined in Table 1; (2)
turnover, computed as the ranking month volume divided by the shares outstanding at the end of the month;
(3) unexpected volume; and (4) analyst dispersion, measured as the standard deviation of annual earnings
estimates by analysts in the ranking month, standardized by absolute mean annual earnings estimates. The
43
unexpected volume in a given day is measured as turnover in excess of market turnover of the day minus
the average daily excess turnover in a benchmark period, which we choose to be the three months before the
ranking month. The monthly unexpected volume is the average daily measure in that month. The analyst
dispersion measures are included for stocks with at least three analysts. We first compute the cross-section
median of disagreement change. Time series averages of the median are reported in the table. Newey-West
-statistics based on time series are reported in the row below the estimate.
This table examines price shock effects in a momentum setting. At the end of the ranking month ,
stocks are ranked into deciles based on the cumulative return from month − 12 to month − 1. Stocksin the highest (lowest) decile are classified as winners (losers). Equal-weighted portfolios are formed for
winners and losers, and held for 12 months, following the overlapping construction of Jegadeesh and Titman
[1993]. Column 3 reports Fama-French three factor alphas for the winner portfolio, the loser portfolio, and
the winner minus loser (“W - L”) difference portfolio. The winner and loser groups are further divided into
two groups: stocks with price shocks and those without. Stocks in decile 1 (decile 10) ranked on negative
(positive) price shocks are classified as stocks with price shocks. Fama-French alphas are reported for the
price shock portfolio, the no price shock portfolio, and the “shock - no shock” difference portfolio in Column
4, 8 and 9. The two price shock groups are classified into news and no news subgroups, based on whether a
corporate news event occurs in the window from three days before to three days after the price shock. Three
factor alphas are reported for the news portfolio, the no news portfolio, and the news minus no news (“diff”)
difference portfolio in Column 5—7. Newey-West -statistics are presented for all alphas in the table.
48
TABLE 7
Earnings Announcements
Panel A. Price Shocks Associated with Earnings Announcements
Fama-MacBeth cross-section regressions are conducted to test whether idiosyncratic volatility (Panel
A) and idiosyncratic volatility shock (Panel B) can capture the price shock effects. The average regression
coefficients and the corresponding Newey-West -statistics are reported. The dependent variable is the 12-
month holding period return. The independent variables are variables computed at the end of the ranking
month : − and + are the minimum and the maximum three-day market-adjusted returns (i.e.,
51
negative and positive price shocks) in month ; news− (news+) is a dummy variable indicating whethera corporate news event is associated with the negative (positive) price shock; log(size) is the log market
capitalization in millions of dollars; B/M is the book-to-market ratio; return is the ranking month return;
return 12 is the cumulative return from month − 12 to − 1; ivol is the idiosyncratic volatility; and ivolshock is the idiosyncratic volatility shock (Bali, Scherbina, and Tang [2010]), which is defined as the residual
from the cross-sectional regression of ivol in month on the average ivol from month − 27 to − 4 and tenindustry dummies. The sample period is 1963.7 — 2006.12.
52
TABLE 10
Retail Trading
model 1 model 2 model 3
Est. -stat Est. -stat Est. -stat
Intercept 0.15 3.08 0.15 3.04 0.17 3.32
news− 0.00 -0.64 0.00 -0.55
− 0.79 3.64 0.44 3.67
−×news− -0.15 -2.22 -0.06 -1.20
news+ -0.01 -2.2 -0.01 -1.99
+ -0.75 -4.06 -0.53 -4.01
+×news+ 0.34 9.12 0.32 8.78
log(size) 0.00 0.27 0.00 0.15 0.00 -0.09
B/M 0.02 1.40 0.02 1.43 0.02 1.39
return 0.04 0.82 0.29 7.72 0.18 7.53
return 12 0.04 2.92 0.04 2.92 0.05 3.01
RTP 0.02 0.83 -0.01 -0.36 0.00 0.09
RTP×− 0.25 1.58 0.24 1.86
RTP×+ 0.18 1.02 0.23 1.42
This table examines the effect of retail trading proportion on the price shock effect. The table is similar
to Table 9, but we replace ivol with RTP to investigate the effect of retail trading on the 12- month holding
period return in the cross-sectional regressions. The interaction terms between RTP and the two price shocks
(− and +) are also included in the regression. The sample period is 1983.1—2000.12.
