Asymmetric Asset Price Reaction to News and Arbitrage Risk

Asymmetric Asset Price Reaction to News and Arbitrage Risk

JOHN A. DOUKAS1,2* and MENG LI3
1Graduate School of Business, Old Dominion University, Norfolk,Virginia, USA
2Judge Business School, Cambridge University, Cambridge, UK
3Walter E. Heller College of Business, Roosevelt University, Chicago, Illinois, USA

ABSTRACT
This study documents that high book-to-market (value) and low book-to-market (glamour)stock prices react asymmetrically to both common and firm-specific information. Specifically,we find that value stock prices exhibit a considerably slow adjustment to both common and firm-specific information relative to glamour stocks. The results show that this pattern of
differential price adjustment between value and glamour stocks is mainly driven by the high arbitrage risk borne by value stocks. The evidence is consistent with the arbitrage risk hypothesis, predicting that idiosyncratic risk, a major impediment to arbitrage activity, amplifies the informational loss of value stocks as a result of arbitrageurs’ (informed investors) reduced participation in value stocks because of their inability to fully hedge idiosyncratic risk.
Copyright # 2009 John Wiley & Sons, Ltd.

key words price speed of adjustment; high and low book-to-market stocks; limits to
arbitrage; idiosyncratic risk
jel classification G11; G12; G14; G32; G35


INTRODUCTION
Several past empirical studies show that the speed of price adjustment to information varies across stocks, suggesting that new information is not immediately reflected into stock prices.
In their influential study, Lo and MacKinlay (1990) document that the returns of large stocks lead those of smaller stocks. Brennan et al. (1993) find that firms with high analyst coverage tend to respond more rapidly to market returns than do firms with low analyst coverage.
Badrinath et al. (1995) show the returns of stocks with high institutional ownership lead the returns of stocks with the low institutional ownership. More recently, Chordia and Swaminathan (2000) report that trading volume is a significant determinant of the lead–lag
Review of Behavioral Finance, 1: 23–43 (2009)
Published online 22 July 2009 in Wiley InterScience
(www.interscience.wiley.com) DOI: 10.1002/rbf.2
* Correspondence to: J. A. Doukas, Department of Finance, School of Business and Public Administration, Old
Dominion University, Norfolk, VA 23529-0218, USA.
E-mail: jdoukas@odu.edu
Copyright # 2009 John Wiley & Sons, Ltd.
patterns observed in stock returns. Specifically, they find that returns on high volume
portfolios lead returns on low volume portfolios, controlling for firm size.
These empirical findings question the conventional view that asset prices are
informationally efficient and raise concerns about the ability of arbitrageurs to restore
informational efficiency in asset prices. While theoretical and empirical research has offered a
number of explanations for the stock price under-reaction to new information, such as
incomplete markets and limited stock market participation of neglected firms (Hirshleifer,
1988; Hou&Moskowitz, 2005; Merton, 1987; Shapiro, 2002), transaction costs (Stoll, 2000),
information constraints (Peng, 2005), investor judgment biases, as a result of investor
overconfidence (Daniel et al., 2001) and the disposition effect (Frazzini, 2006), how arbitrage
risk contributes, if any, to stocks’ under-reaction to new information remains an important
research issue.
Motivated by the arbitrage risk theory of Shleifer and Vishny (1997), which argues that
idiosyncratic risk, a major impediment to arbitrage activity, is the most likely cause for the
under-reaction (informational loss) of stock prices to new information, in this paper we
examine whether idiosyncratic risk contributes to stock prices’ slow speed of adjustment in
response to new information. The focus of this investigation centres on high book-to-market
(value) and low book-to-market (glamour) stocks. The choice of these two classes of stocks
was mainly dictated by (i) the ongoing controversy that surrounds the value–glamour
anomaly and that (ii) the differential speed of adjustment to information found in previous
studies might also be rooted in value and glamour stocks.1 Shleifer and Vishny (1997) argue
that idiosyncratic volatility deters arbitrageurs from completely and quickly eliminating
mispricing, and therefore it might prohibit stock prices to reflect new information in a timely
manner contributing to the differential speed of adjustment between value and glamour stocks
and the existence of book-to-market effect.2 Consequently, arbitrage risk has the potential to
explain the informational loss of value stock prices and why they trade at lower prices
realizing higher future returns than glamour stocks. This could happen because arbitrage risk
lowers the participation of informed investors in value stocks (i.e. increasing the amount of
risk borne by uninformed investors) causing uninformed investors to require lower prices as
compensation to bear the extra risk. Although Ali et al. (2003) show that the book-to-market
effect is more pronounced in stocks with higher idiosyncratic risk, they do not examine the
link between arbitrage risk and stock prices’ speed of adjustment to new information.
Shleifer and Vishny (1997) also claim that arbitrageurs are specialized in that they focus on
a single or limited number of investment strategies, implying that they are less likely to be
attracted by stocks with high idiosyncratic risk. Moreover, they highlight that most
arbitrageurs are professional fund managers that avoid idiosyncratic risk because it can cause
poor short-term performance, resulting in fund withdrawals by investors.3 Therefore,
1Proponents of the rational school of thought (e.g. Fama and French (1993)) argue that the higher returns of value
stocks are a direct compensation for bearing higher fundamental risk. Lakonishok et al. (1994) argue that value stocks
earn higher returns because investors make systematic errors in predicting future growth in earnings of value stocks.
This non-risk-based explanation is also known as the ‘extrapolation’ or ‘errors-in-expectations’ hypothesis (see La
Porta, 1996; La Porta et al., 1997).
2Prior empirical studies investigating the effect of costly arbitrage on asset prices focus mainly on the ‘cost’ or
transaction cost component of arbitrage activity (e.g. Barber et al., 2001; Garman & Ohlson, 1981; Knez & Ready,
1996; Stoll, 2000), not much on the ‘risk’ component of the arbitrage activity.
3Consistent with the prediction of the arbitrage risk hypothesis, Mendenhall (2004) finds that the PEAD rises with
idiosyncratic risk, suggesting that idiosyncratic risk hampers the immediate price adjustment to new information.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
24 J. A. Doukas and M. Li
arbitrageurs will be reluctant to take positions on high idiosyncratic risk stocks causing these
stocks to absorb and reflect new information with considerable delay. The implication of the
arbitrage risk hypothesis is that stocks that are less attractive to arbitrageurs, due to high
idiosyncratic risk, are likely to trade at prices away from their information-efficient values.
Hence, the lead–lag patterns in stock returns could be attributed to stocks’ underlying
idiosyncratic risk. Accordingly, the main hypothesis tested in this study is that if idiosyncratic
risk plays an important role in explaining the asymmetric price adjustment to new
information between value and glamour stocks, value stocks are expected to exhibit slower
speed of adjustment to new information than glamour stocks because they load heavily on
idiosyncratic risk.
Our empirical tests begin by investigating whether the prices of value and glamour stocks
exhibit asymmetric speed of adjustment to information. We then examine whether
idiosyncratic risk can explain the slow price adjustment to new information of the value
stocks. We find evidence that value stocks react to both common (i.e. market- and industrylevel
information) and firm-specific information with considerable lag relative to glamour
stocks.4 Consistent with the arbitrage risk hypothesis, our evidence demonstrates that
value stocks are associated with higher idiosyncratic risk, and the high idiosyncratic risk in
value stocks hampers their prompt price adjustment to new information. In addition, our
results show that value stocks not only have greater loading on idiosyncratic risk than glamour
stocks, but their returns are also more responsive to the idiosyncratic volatility than the
returns of glamour stocks. In fact, when idiosyncratic risk is introduced to the return
generating process, the abnormal returns of value stocks disappear, indicating that
idiosyncratic risk does play an important role on the existence of value–glamour anomaly,
and that this mispricing anomaly is largely caused by the limited arbitrage activities on the
part of value stocks.
The rest of the paper is organized as follows. The ‘Arbitrage Risk and Stock Price
Adjustment to Common Information’ section investigates whether idiosyncratic risk is
relevant in explaining the asymmetric price adjustment to common information between
value and glamour stocks. The ‘Arbitrage Risk and Stock Price Adjustment to Firm-specific
Information’ section examines whether the idiosyncratic risk can explain the asymmetric
price adjustment to firm-specific information between value and glamour stocks. The
‘Conclusion’ section concludes the paper.
ARBITRAGE RISK AND STOCK PRICE ADJUSTMENT TO
COMMON INFORMATION
This section describes the data and methodology employed to examine the asymmetric price
adjustment to common information across value and glamour stock, and test the hypothesis
that the high arbitrage risk borne by value stocks contributes to their slower reaction to
common information.
4King (1966) provides evidence that stock returns covary with market and industry returns. Roll (1988) finds that only
a small portion of stock return variation is attributable to the general market and industry movements, suggesting that
residual returns reflect the firm-specific information.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 25
Data and summary statistics
We obtain all daily returns of six size and B/M portfolios (two-by-three sorts on size and B/M)
from 1 July 1963 to 31 May 2005 from Professor Kenneth French’s website.5 Controlling firm
size is important because we already know from the evidence of Lo and MacKinlay (1990)
that returns of larger stocks always lead the returns of smaller stocks. Holding firm size
constant allows us to distinguish the value/glamour effect from a pure size effect on the lead–
lag structure across stock returns. To be consistent with earlier studies in the asymmetric
information assimilation literature (Conrad et al., 1991; Jegadeesh & Titman, 1995; Lo &
MacKinlay, 1990), empirical tests are conducted using weekly return data.6 One advantage of
using weekly rather than daily returns is that the positive cross-autocorrelation generated by
different non-trading probabilities for different portfolio groups is virtually eliminated. The
sample includes 2,188 weekly observations for each of the six size-B/M portfolios. The
weekly returns are calculated as average daily returns during the week. The summary
statistics of the weekly return for the six size-B/M portfolios is reported in Table A1.
Methodology
Following Brennan et al. (1993), we estimate the zero investment portfolio between the
lowest book-to-market (B/M) stocks (g) and the highest book-to-market (B/M) stocks (v) and
regress the return of this portfolio to current and lagged market returns, proxying for common
information, to assess the speed of adjustment differential between the low and high book-tomarket
stocks.7 A positive coefficient on the current market return and a negative sum of the
coefficients on lagged market returns would imply that g stocks react faster to common
information than v stocks. Essentially, this approach entails estimating current and lagged
market betas in Dimson (1979) regressions, which allow for information lags exceeding one
period. For each size group (i.e. small, big and all) we estimate the return on a zero net
investment portfolio between g and v stocks. However, recent studies provide evidence of
changing risk premium and returns variability over time (Campbell et al., 2001) and claim
that the unconditional CAPM, which specifies a constant risk premium, generates biased and
inconsistent beta and alpha estimates. To deal with this problem, we employ GARCH
specification in the Dimson regressions to capture the time-varying idiosyncratic volatility,
getting rid of heteroscedasticity, and therefore generate efficient beta estimates.We therefore,
estimate the following regressions for each size group:
Rg;t
Rv;t ¼ a þ b0Rm;t þX
k
k¼1
b
kRm;t
k þ "t
ht ¼ a þ b"2t

1 þ cht
1
(1)
where Rg,t and Rv,t are the contemporaneous excess returns of the lowest (glamour) and
highest B/M (value) portfolios. b0 is the current market beta andPk
k¼1 b
k refers to the sum
5Professor Kenneth French data URL is: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library
6We obtained similar results using the daily and monthly portfolio returns data.
7Brennan et al. (1993) testing the asymmetrical reaction of high and low analyst coverage firms to common
information used the zero net investment portfolio approach where the zero net investment portfolio return is
estimated as the difference between long investment position in high analyst coverage stocks and short position in low
analyst coverage stocks. Specifically, the zero net investment portfolio return is regressed on current and lagged
market returns proxying for common information. A positive coefficient on the current market return and a negative
sum of the coefficients on lagged market returns implies that high analyst coverage stocks react faster to common
information than low analyst coverage stocks.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
26 J. A. Doukas and M. Li
of lagged betas. Again, as in Brennan et al. (1993), regressions are fitted with 3 and 5 lags
(k¼3, 5).
Regression results
Table 1 reports Dimson regression results. Before, we focus on the main findings of this table,
it is interesting to note that all GARCH(1,1) terms (b, c) are significant at 1%, confirming the
existence of GARCH effects. Hence, these results provide statistical support for the use of the
GARCH specification. The coefficients of the current market return b0 are significantly
positive for all size groups and for both (3 and 5) lag specifications. In the regression
specification with 3 lags, b0 is 0.3025, 0.1925 and 0.2157 for small, big and all stocks,
respectively, indicating that glamour stocks are significantly more sensitive to contemporaneous
market information than value stocks. Furthermore, the sum of the lag coefficients
(Pk
k¼1 b
k) is significantly negative for all size groups and for both (3 and 5) lag
specifications. In the regression with 3 lags,Pk
k¼1 b
k is
0.0029,
0.0750 and
0.1212 for
small, big and all stocks, respectively. It is interesting to note that not only the sum of the lag
Table 1. Regressions of zero net investment on value-weighted market returns: July 1963–May 2005
(A) 3 Lags (B) 5 Lags
Small Big All Small Big All
a
0.1451
0.0601
0.0792
0.1447
0.0614
0.0769
b0 0.3025 0.1925 0.2157 0.3026 0.1927 0.2147
b
1 0.0173
0.0571
0.0763 0.0171
0.0562
0.0754
b
2
0.0261
0.0282
0.0403
0.0263
0.0282
0.0396
b
3 0.0059 0.0103
0.0046 0.0058 0.0097
0.0043
b
4 0.0076
0.0093
0.0197
b
5
0.0059 0.0189 0.0029
Pk
k¼1 b
k
0.0029
0.0750
0.1212
0.0017
0.0651
0.1361
a 0.0532 0.0335 0.0603 0.0542 0.0328 0.0586
b 0.1411 0.0681 0.0905 0.1432 0.0678 0.0889
c 0.8112 0.9109 0.8722 0.8081 0.9117 0.8749
log likelihood
2978.96
3494.77
3419.40
2976.09
3491.18
3416.06
R2 (%) 0.33 0.14 0.17 0.33 0.14 0.17
Note: This table reports the results from regressing the difference between the weekly returns on glamour and value
portfolios within each size group, on value-weighted market returns:
Rg;t
Rv;t¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ "t
ht ¼ a þ b"2t

1 þ cht
1
k ð1Þ
where Rg,t and Rv,t are the contemporaneous excess returns of the lowest (glamour) and highest B/M (value)
portfolios. b0 is the current beta andPk
k¼1 b
k refers to the sum of lagged betas. The regressions are fitted with 3 and 5
lags (k¼3, 5). The weekly returns are calculated as average daily returns during the week, and all the daily portfolio
return data from 1 July 1963 to 31 May 2005 are from Professor Kenneth French’s website. Portfolios are constructed
by a two-by-three sort on size and B/M.Within each of the two size quartiles, the stocks are further allocated to three
book-to-market portfolios. The size breakpoint for year t is the median NYSE market equity at the end of June of year
t. B/M for June of year t is the book equity for the last fiscal year ending in t
1 divided by market equity for
December of t
1. The B/M breakpoints are the 30th and 70th NYSE percentiles.
Significant at the 5% level.
Significant at the 1% level.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 27
coefficients is found to be negative, but also statistically significant at conventional levels.
The negative lag coefficients combined with positive current coefficients suggest that
glamour stocks react to common information faster than value stocks.
Arbitrage risk exposures of value and glamour stocks
To the extent that the slow speed of adjustment of value stocks is attributed to the lack of
arbitrage activity, value stocks should be associated with higher idiosyncratic risk. To address
this, we first compare the exposure of value and glamour stocks to arbitrage risk and second,
examine whether the returns of value stocks are more sensitive to the fluctuation of
idiosyncratic risk than glamour stock returns are.
Arbitrage risk is measured with idiosyncratic volatility, which is commonly estimated as
the residual variance from a regression of a stock return on the return of its proper substitutes.
The selection of proper substitutes varies from study to study based on the specific needs of
each study. Pontiff (1996) calculates idiosyncratic risk relative to the excess return of 10
mutual funds when he tests how the idiosyncratic risk relates to mispricing, measured by the
close-end fund discounts. Wurgler and Zhuravskaya (2002) estimated the idiosyncratic risk
relative to returns of the stocks of similar size, similar book-to-market ratio and of same
industry. Other studies constructed idiosyncratic risk relative to market index returns (Ali
et al., 2003; Mendenhall, 2004; Pontiff & Schill, 2004). As an empirical matter Mashruwala
et al. (2006) show that the construction of idiosyncratic volatility does not affect the results. In
this study, we estimate the idiosyncratic risk relative to the CRSP value-weighted index. To
minimize the possible size and value effects on the return residuals, we also estimate the
idiosyncratic volatilities using the Fama–French three-factor model.
The sample data for this test are obtained from two sources. Book-to-market data are from
COMPUSTAT and return data are from the Daily CRSP. Because B/M ratio data are only
available since 1986, the sample period spans from calendar year 1987 to 2005 for which
complete data are available, consisting of 66,568 total firm observations, including both
exchange-traded and NASDAQ stocks. The B/M ratio is defined as the ratio of book value of
common equity (item #60) to market value of the equity (item #199item #25) at prior
calendar year end.We exclude all ADRs, foreign firms and all financial companies.We form
three equal sized book-to-market portfolios at the beginning of each calendar year from 1987
to 2005 based on the B/M ratio computed at prior calendar year end.
Table B1 reports the detailed comparison of arbitrage costs across three equally sized B/M
ratio portfolios for each year over the 1987–2005 period. Consistent with our conjecture that
value stocks have higher idiosyncratic risk exposure, we find that idiosyncratic volatilities of
value stocks are significantly higher than those of glamour stocks in 13 out of 19 years. The All
yearmean idiosyncratic risk, as shown in the last column, estimated fromthe market model for
value stocks (4.7%) is 0.6% higher than that of glamour stocks (4.1%). Similarly, the All year
mean idiosyncratic risk estimated fromFama–French three-factormodel forvalue stocks (4.7%)
is 0.7% higher than that of glamour stocks (4.0%). The difference in idiosyncratic volatilities
betweenvalue and glamour stocks, regardless of asset pricingmodel, is statistically significant at
the 1%level. It is interesting to note that the idiosyncratic risk is not sensitive to the specification
of the asset pricing model, consistent with Mashruwala et al. (2006) who argue that the
estimation of idiosyncratic volatilities does not depend on the asset pricing specification.
Another interesting observation that emerges fromTable B1 is that while glamour stocks have a
lower loading on idiosyncratic risk than value stocks, they are not arbitrage risk free suggesting
that arbitrage risk is a widely spread phenomenon among stocks.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
28 J. A. Doukas and M. Li
Value and glamour stock return sensitivities to arbitrage risk
Since value stocks are associated with higher arbitrage risk than glamour stocks, value stock
returns should be more sensitive to arbitrage risk than glamour stocks returns. To address the
stock return sensitivities of value and glamour stocks to the fluctuation of idiosyncratic risk,
we use a GARCH-M Dimson market model. This estimation procedure entails that the
idiosyncratic volatility must be calculated with respect to the market model so that the effect
of idiosyncratic volatility on the mean return can be separated from the effect of the market
risk exposure on the mean return. The GARCH-M specification models the relationship
between conditional idiosyncratic volatility and mean returns allowing us to determine
explicitly whether the conditional idiosyncratic volatility has explanatory power beyond the
market risk premium. Finally, the use of the Dimson market model permits to account for
the effect of lagged market returns on portfolio returns. The regression specifications for the
return sensitivities of value and glamour stocks to idiosyncratic risk are as follows:
Rv;t ¼ a þ b0Rm;t þX
k
k¼1
b
kRm;t
k þ gst þ "t
ht ¼ a þ b"2t

1 þ cht
1
(2)
and
Rg;t ¼ a þ b0Rm;t þX
k
k¼1
b
kRm;t
k þ gst þ "t
ht ¼ a þ b"2t

1 þ cht
1
(3)
where Rg,t and Rv,t are the contemporaneous excess returns of the lowest (glamour) and
highest B/M (value) portfolios. b0 is the current beta and Pk
k¼1 b
k measures the sum of
lagged betas. These regressions are fitted with 5 lags (k¼5).8
Table 2 reports the GARCH-M Dimson regression results. As before, these regressions
show no signs of serious model misspecification. All GARCH(1,1) terms (b, c) are always
significant at 1%, confirming the existence of GARCH effect and providing statistical support
for the use of GARCH-M specification. The main findings that emerge from this table are that
the returns of value stocks are (i) more responsive to changes in idiosyncratic volatility and
(ii) less responsive to changes in market returns relative to glamour stocks. For the regressions
based on the full sample (All), the coefficient of current market return b0 for the value
portfolio (Equation (2)) is 0.8704, significantly smaller than the coefficient of current market
return for glamour portfolio (Equation (3)) of 1.0797. This result confirms that value stock
returns are less responsive to common (market-based) information than value stock returns.
The idiosyncratic volatilities of value stocks, measured by the GARCH-M terms (g), are
positive and statistically significant across all size groups. The coefficients of the
idiosyncratic volatilities for value stocks are 0.3889, 0.1854 and 0.1779 in small, big and
All stock regressions, respectively. In contrast, the coefficients of the idiosyncratic volatilities
for glamour stocks are all statistically insignificant in all regressions. These findings are
consistent with the view that value stock returns load more on idiosyncratic risk relative to
glamour stock returns. Moreover, our evidence suggests that the higher returns of value stocks
compensate for bearing higher arbitrage risk.
8Regressions fitted with 3 lags yield similar results.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 29
Value and glamour stock return sensitivities to arbitrage risk: An alternative test
Since the coefficient of the currentmarket return,b0,measures a stock return’s responsiveness or
the speed of adjustment to common information, we test the effect of arbitrage risk on value
stocks’ speed of adjustment to new information by comparing the b0 from the OLS Dimson
market model to the b0 from the GARCH-M Dimson market model where the idiosyncratic
volatility is explicitly modelled to account for its potential effects on stock returns. If arbitrage
risk hampers information diffusion (i.e. liable for value stocks low b0) it is expected that the
speed of price adjustment should be higher when the effect of arbitrage risk is explicitly
controlled for in the GARCH-M Dimson market model. That is, the b0 in the GARCH-M
Table 2. Regressions of B/M portfolio weekly returns on value-weighted market returns: July 1963—
May 2005
Small Big All
Equation (2) Equation (3) Equation (2) Equation (3) Equation (2) Equation (3)
a
0.1796 0.0399 0.0279
0.0270 0.0446
0.0386
b0 0.7860 1.1382 0.8861 1.0769 0.8704 1.0797
b
1 0.1800 0.2109
0.0010
0.0541 0.0436
0.0376
b
2 0.0477 0.0311 0.0109
0.0134 0.0242
0.0103
b
3 0.0333 0.0352
0.0249
0.0092
0.0008
0.0041
b
4 0.0394 0.0425
0.0006
0.0119 0.0168
0.0068
b
5 0.0324 0.0199
0.0167
0.0012 0.0079 0.0014
P
k
k¼1
b
k 0.3328 0.3396
0.0323
0.0898 0.0917
0.0573
g 0.3889
0.0046 0.1854 0.2362 0.1779 0.2651
a 0.052 0.0443 0.0144 0.0531 0.0295 0.0599
b 0.1171 0.0698 0.0736 0.1206 0.1143 0.1453
c 0.8382 0.9021 0.9091 0.7042 0.8601 0.6231
log likelihood
3022.09
3465.5
2725.6
1712.5
2699.7
1521.8
R2 (%) 73.36 78.61 75.58 94.43 77.58 95.28
Note: This table reports the results from regressing the weekly returns of glamour and value portfolios within each
size group, on value-weighted market returns:
Value Rv;t ¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ gst þ "t
and ht ¼ a þ b"2t

1 þ cht
1
ð2Þ
Glamour Rg;t ¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ gst þ "t
ht ¼ a þ b"2t

1 þ cht
1
ð3Þ
Rg,t and Rv,t are the contemporaneous excess returns of the lowest (glamour) and highest B/M (value) portfolios. s is
the standard deviation of the conditional variance of the error term. b0 is the current beta andPk
k¼1 b
k refers to the
sum of lagged betas. The regressions are fitted with 5 lags (k¼5). The weekly returns are calculated as average daily
returns during the week, and all the daily portfolio return data from 1 July 1963 to 31 May 2005 are from Professor
Kenneth French’s website. Portfolios are constructed in a two-by-three sort on size and B/M.Within each of the two
size quartiles, the stocks are further allocated to three book-to-market portfolios. The size breakpoint for year t is the
median NYSE market equity at the end of June of year t. B/M for June of year t is the book equity for the last fiscal
year ending in t
1 divided by market equity for December of t
1. The B/M breakpoints are the 30th and 70th
NYSE percentiles.
Significant at the 5% level.
Significant at the 1% level.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
30 J. A. Doukas and M. Li
Dimson market model should be larger than the b0 in the OLS Dimson market model. The
GARCH-M Dimson market model for value stocks takes the following specification:
Rv;t ¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ gst þ "t
ht ¼ a þ b"2t

1 þ cht
1
ð2Þ
while the OLS Dimson market model for value stocks is specified as follows:
Rv;t ¼ a þ b0Rm;t þX
k
k¼1
b
kRm;t
k þ "t (4)
As before, R(v, t) is the contemporaneous excess returns of the highest B/M (value)
portfolios. The b0 is the current beta and the Pk
k¼1 b
k refers to the sum of lagged betas.
Regressions are fitted with both 3 and 5 lags (k¼3, 5).
Table 3 reports the newregression results.Consistent with our expectation, the current betab0
is 0.05 higher for the GARCH-M model (b0¼0.8704) than for the OLS model (b0¼0.8200)
when 5 lags are included in themarketmodel.Whenwe use3 lags inthe marketmodel,we obtain
fairly similar results. The finding that value stocks become more sensitive to the current market
return when arbitrage risk is controlled for implies that arbitrage risk impedes the prompt price
adjustment of value stocks to market information. Hence, these regression results validate our
hypothesis that the higher arbitrage risk borne by value stocks partially contributes to their slow
reaction to common information. In addition,wefind that Jensen’s alphas (i.e. abnormal returns)
for value stocks become indistinguishable fromzero when we allow the idiosyncratic volatility
to enter explicitly into the return generating process in the GARCH-M model. This evidence
suggests that the superior return of value stocks is a premiumrequired by arbitrageurs for taking
positions in value stocks due to their high idiosyncratic (unhedgeable) risk. Alternatively,
uninformed investors knowing that arbitrage risk reduces the participation the informed
investors in value stocks (i.e. increasing the amount of risk borne by uninformed investors)
require lower prices as compensation to bear the extra risk. These findings provide additional
support for theviewthat thevalue anomaly (ormispricing) is caused by the failure of arbitrageurs
to hedge idiosyncratic risk embedded in value stocks.
ARBITRAGE RISK AND STOCK PRICE ADJUSTMENT TO FIRM-SPECIFIC
INFORMATION
So far we have shown that the slow speed of adjustment of value stocks to common
information is associated with arbitrage risk. In this section, we examine the asymmetric price
adjustment to firm-specific information across value and glamour stocks, and whether the
high arbitrage risk borne by value stocks contributes to their slower reaction to firm-specific
information as well. Bernard and Thomas (1989, 1990) argue that the post-earnings
announcement drift (PEAD) represents delayed response to firm-specific information. Hence,
earnings announcements provide an appropriate framework to test the asymmetric price
response of value and glamour stocks to firm-specific information in the context of arbitrage
risk. If value stocks, are indeed slow in reacting to firm-specific information, as a result of
having high exposure to arbitrage risk they should experience a more pronounced and longer
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 31
PEAD than glamour stocks. Therefore, this hypothesis predicts that value stocks should have
relatively higher (lower) abnormal returns following good (bad) earnings news.
To test this hypothesis we use quarterly earning announcements as firm-specific news
events (item RDQ in COMPUSTAT) from the 1st fiscal quarter of 1994 to the 3rd fiscal
quarter of 2005.9 Following Frazzini (2006), earnings surprises are measured using the
market model cumulative abnormal returns for the 3-day window (
1, 0 and 1) around the
quarterly earnings announcement date. As in Doukas et al. (2002), book-to-market is defined
Table 3. Regressions of value portfolio weekly returns on value-weighted market returns: July 1963–
May 2005
(A) 3 Lags (B) 5 Lags
OLS GARCH-M OLS GARCH-M
a 0.1980 0.0633 0.1978 0.0446
b0 0.8197 0.8694 0.8200 0.8704
b
1 0.0439 0.0446 0.0432 0.0436
b
2 0.0254 0.0253 0.0253 0.0242
b
3
0.0069 0.0008
0.0069
0.0008
b
4 0.0101 0.0168
b
5
0.0047 0.0079
P
k
k¼1
b
k 0.0624 0.0707 0.0670 0.0917
g 0.0869 0.1779
a 0.0310 0.0295
b 0.1156 0.1143
c 0.8571 0.8601
log likelihood
2703.74
2699.65
R2 (%) 77.78 77.58 77.80 77.58
Note: This table reports the results from regressing the weekly returns of value portfolios on value-weighted market
returns for both OLS Dimson model and GARCH-M Dimson model:
Rv;t ¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ "t ð4Þ
Rv;t ¼ a þ b0Rm;t þ P
k
k¼1
b
kRm;t
k þ gst þ "t
ht ¼ a þ b"2t

1 þ cht
1
ð2Þ
where Rv,t is the contemporaneous excess returns of the highest B/M(value) portfolios. s is the standard deviation of the
conditional variance of the error term. b0 is the current beta andPk
k¼1 b
k refers to the sumof lagged betas. Regressions
are fitted with both 3 and 5 lags (k¼3, 5). Theweekly returns are calculated as average daily returns during theweek, and
all the daily portfolio return data from 1 July 1963 to 31 May 2005 are from Professor Kenneth French’s website.
Portfolios are constructed in a two-by-three sort on size and B/M.Within each of the two size quartiles, the stocks are
further allocated to three book-to-market portfolios. The size breakpoint for year t is the median NYSEmarket equity at
the end of June of year t. B/Mfor June of year t is the book equity for the last fiscal year end in t
1 divided by market
equity for December of t
1. The B/M breakpoints are the 30th and 70th NYSE percentiles.
Significant at the 5% level.
Significant at the 1% level.
9The quarterly earning announcement dates (COMPUSTAT item RDQ) are only available for fiscal period of the first
quarter of 1994 to the third quarter of 2005.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
32 J. A. Doukas and M. Li
as the ratio of book value of common equity (item #60) to market value of the equity (item
#199item #25) at the end of the fiscal year preceding the quarterly earnings announcement.
We exclude all ADRs, foreign firms and all financial companies. To avoid any potential IPO
effects, we exclude the stocks with less than 255 days of return data prior to the earnings
announcement dates on CRSP. The final sample includes 154,864 total firm observations.
We assign stocks to portfolios based on the nature of earnings news and the B/M ratio.10
Starting with the first quarter of 1994, we classify quarterly earnings surprises into three equal
sized news groups based on the market model cumulative abnormal return for the 3-day
window (
1, 1), and we define the group with the lowest 33% CAR as the bad news group and
the group with the highest 33% CAR as the good news group. Within each group of stocks
with good and bad earnings surprises, stocks are further sorted into five equal sized B/M
quintiles based on the B/M ratio calculated at the end of the fiscal year preceding the quarterly
earnings announcement.
PEAD, monthly alphas by B/M ratio
To purge the drift factor from the size and value premium effects, we compute abnormal
returns from the Fama–French three-factor regression model. If the three-factor model
captures the cross-sectional variation in stock returns, the intercept from the regression [5]
should be statistically indistinguishable from zero.
Rit ¼ a þ bRmt þ dSMBt þ fHMLt þ "it (5)
where Rit is the monthly return of the highest (value) and the lowest B/M (glamour) portfolios
in excess of 1-month treasury bill rate (i¼value, glamour portfolio). Rmt is the valueweighted
market return in excess of 1-month treasury bill rate. SMB and HML are the size
and value premium factors, respectively. The alphas represent the abnormal returns. A
positive (negative) a, following good (bad) news, indicates the presence of post-event positive
(negative) drift. Under the hypothesis that value stocks produce stronger and longer drift than
glamour stocks, the alphas for value stocks expected not only to be larger, but remain more
pronounced subsequent to earnings announcements.
Table 4 reports monthly alphas of value and glamour portfolios for 1-, 2- and 3-month
periods subsequent to earnings announcements. As expected, following positive earnings
news, value stocks are associated with significantly positive alphas in all three post-earnings
announcement periods. The risk-adjusted returns for value stocks are 0.8527, 1.7069 and
2.8412% for the first, second and third months following positive earnings surprises,
respectively. The alphas of value stocks are systematically increasing after positive earnings
announcements. On the other hand, while the risk-adjusted returns for glamour stocks are
positive following similar earnings surprises they are considerably smaller than those of value
stocks and they do not exhibit the same rising pattern of the alphas found for value stocks.
Moreover, only one out of three post-earnings alphas is statistically significant. Specifically,
the risk-adjusted return 2 months after good earnings news is 0.5025% and statistically
significant (t¼2.40) at conventional levels. The corresponding risk-adjusted return for value
stocks (1.7069%, t¼8.87) is much higher. Hence, glamour stocks are not associated with the
positive (negative) price drift in response to good (bad) earning news, suggesting that they do
not under-react to earnings announcements.
10This is a standard approach in asset pricing, which reduces return variability.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 33
Table 4. Post-earnings announcement monthly alphas by B/M ratio: 1st quarter of 1994–3rd Quarter of 2005
Post-earnings announcement portfolio monthly alphas
Sorted by B/M ratio Month tþ1 Month tþ2 Month tþ3
Earnings news Earnings news Earnings news
Bad Good Bad Good Bad Good
Q1 (glamour)
0.2789 (
1.16) 0.1197 (0.48) 0.0231 (0.10) 0.5025 (2.40) 0.1329 (0.58) 0.3909 (1.66)
Q5 (value)
0.7945 (
3.91) 0.8527 (3.91) 1.4567 (6.93) 1.7069 (8.87) 1.6064 (6.63) 2.8412 (13.18)
Note: This table reports the monthly alphas of value and glamour portfolios for each of the 3 months following the earnings news. Starting from the first quarter of 1994, for each
quarterly earnings announcement we classify earnings surprises into three equal sized news groups based on the cumulative abnormal return in the 3-day window (
1, 0, 1), and we
define the group with the lowest 33% CAR as the Bad news group and the group with the highest 33% CAR as the Good news group.Within both the Good and Bad earnings groups,
stocks are further sorted into five equal sized B/M quintiles based on the B/M ratio calculated at the end of the fiscal year preceding the quarterly earnings announcement. D1 and D5
refer to the lowest (glamour) and the highest B/M (value) portfolios, respectively. Portfolio returns are equally weighted. Monthly alphas are computed relative to the following
Fama–French three-factor model:
Rit ¼ a þ b Rmt þ dSMBt þ fHMLt þ "it
where Rit is the monthly return of the highest (value) and the lowest B/M (glamour) portfolios in excess of 1-month treasury bill rate. Rmt is the value-weighted market return in
excess of 1-month treasury bill rate. The SMB and HML are size premium and value premium factors. Alphas represent the abnormal returns. The t-statistics are in parentheses and
above 5% statistical significance is indicated in bold.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
34 J. A. Doukas and M. Li
As expected, value stocks have larger alphas following bad earnings announcements. The
most pronounced negative reaction to negative earnings news is associated with the 1-month
post-earnings announcement period. This negative alpha is statistically significantly
(
0.7945%, t¼
3.91). For the same post-earnings period, glamour stocks have a negative
alpha, but statistically insignificant (
0.2789%, t¼
1.16). In sum, the monthly postearnings
announcement results show that value stocks exhibit stronger and longer PEAD than
glamour stocks following both good and bad earnings announcements. These results provide
supplemental support for the hypothesis that value stocks react slower to firm-specific
information as well.
Another interesting result that surfaces from Table 4 is that value stocks over-react to the
bad earnings announcements after the initial under-reaction. The risk-adjusted monthly
returns for value stocks are significantly positive in the second (1.4567%, t¼6.93) and third
months (1.6064%, t¼6.63) following bad earnings announcements. The fact that value
stocks exhibit under-reaction in the first month and over-reaction in the second and third
months subsequent to bad earnings announcements is consistent with the unified theory of
short-term under-reaction and long-term over-reaction to new information of Hong and Stein
(1999), which predicts that price reversals should be more pronounced in stocks for which
information diffuses more slowly. This return reversal pattern is also consistent with the view
that investors may follow a contrarian investment strategy, after value stocks have declined
1 month after the release of bad earnings news. In general, both under-reaction and overreaction
market biases are heavily associated with value stocks instead of glamour stocks
subsequent to earnings announcement surprises, suggesting that the high arbitrage costs
borne by value stocks force arbitrageurs to refrain from taking positions in eliminating
temporary mispricing in value stocks. Again these findings are consistent with the argument
that mispricing stems from the inability of arbitrageurs to fully hedge idiosyncratic risk.
Finally, another worth noting finding from Table 4 is that good earnings surprises produce
a more severe price drift than bad earnings announcements. Significant negative PEAD
occurs only in the first month following bad earnings announcements in value stocks, whereas
the significantly positive price drift following good earnings announcements is observed in
both value and glamour stocks, and lasts for 3 months for value stocks. These results imply
that stocks react to negative earnings surprises more promptly and strongly than they do in
response to positive earnings surprises. This is consistent with the documented asymmetric
price response to good and bad news. That is, bad news trigger a bigger shock to security
prices than good news do, and market reacts more strongly to bad news than to good news
(Bernard et al., 1997; Conrad et al., 2002; La Porta et al., 1997; Skinner & Sloan, 1998).
Arbitrage risk and the PEAD
The natural question that emerges from the previous results is whether arbitrage risk is liable
for the differential PEAD between value and glamour stocks. To examine whether
idiosyncratic risk, the conventional proxy for arbitrage risk, contributes to the asymmetric
PEAD between value and glamour stocks, we modify Mendenhall’s (2004) regression
specification by introducing the B/M ratio as an extra explanatory variable and expect to have
no explanatory power if idiosyncratic risk does matter for the PEAD. To the extent that
idiosyncratic risk, a deterrent to arbitrage activity, drives the differential price adjustment
process between value and glamour stocks in response to firm-specific news in the postearnings
announcement period, the B/M ratio should have no explanatory power.We estimate
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 35
the following set of regressions:
QEAi;q ¼ a þ bCARi;q þ c
CARi;q  BMi;q þ d
CARi;q  IDIOi;q
þ e
CARi;q  VOLUMEi;q þ "i;q (6a)
QEAi;q ¼ a þ bCARi;q þ c
CARi;q  BMi;q þ d
CARi;q  IDIOi;q
þ e
CARi;q  SIZEi;q þ "i;q (6b)
where QEAi,q is stock i’s compound abnormal return from the first month through the third
month following the quarter q’s earnings announcement.11 The compound abnormal return is
computed as the buy-and-hold compound return on each stock minus the buy-and-hold return
on the CRSP value weighted index. CARi,q is the earnings surprise measured as the market
model cumulative abnormal return for the 3-day window (
1, 1) around the earnings
announcement for stock i at quarter q. BMis book-to-market ratio calculated at the end of the
fiscal year preceding the announcement. IDIOi,q is the stock’s idiosyncratic risk, measured as
the mean residual error from the market model regression estimated over days
255 to
2
relative to the announcement for stock i at quarter q. VOLUMEi,q is the closing daily stock
price times daily shares traded averaged over trading days
255 to
2 relative to the
announcement for stock i at quarter q. SIZEi,q is the market value of the equity at the end of
the fiscal year preceding the earnings announcement for stock i at quarter q.
The motivation behind the use of the last two variables is to account for transaction costs.
Transaction costs have long been the focus of the market friction studies, and they have been
shown to play an important role in dissipating arbitrage profits and limiting rational arbitrage
positions (e.g. Barber et al., 2001; Garman & Ohlson, 1981; Knez & Ready, 1996).12 In this
study, we estimate the influence of transaction costs by running separate regressions to avoid
possible over-specification problems, since VOLUME and SIZE are highly correlated
(correlation of 0.73).
To account for the possible nonlinearities between dependent and explanatory variables,
we use rank scores for all explanatory variables (see e.g. Bartov et al., 2000; Bernard and
Thomas, 1990; Bhushan, 1994; Mendenhall, 2004). Specifically, we transform each
explanatory variable (CAR, BM, IDIO, VOLUME and SIZE) into coded scores based on their
rank within the pooled earnings announcement observations, and then scale the coded scores
from 0.0 to 1.0. Following Mendenhall (2004), we then subtract 0.5 from the coded scores.
Therefore, the final coded scores for each variable range between
0.5 and + 0.5. Coding an
independent variable from
0.5 to + 0.5 allows the intercept of a regression of abnormal
return on a dependent variable to represent the abnormal return for a hypothetical median
observation between the two middle deciles of the independent variable, which should be
11QEAi;q ¼ Qt¼1
3 ð1 þ RETi;q;tÞ
Qt¼1
3 ð1þRETmkt;q;tÞ.RETi;q;t is the raw return of the stock for month t relative to
the earnings announcement month for quarter q. RETmkt;q;t is the CRSP value weighted index return for month t
relative to the earnings announcement month for quarter q. Months, designated by t, run from 1 to 3 months relative to
the earnings announcement month.
12The transaction costs literature has been showing that both volume and size are negatively associated with
transaction costs: The higher the volume and the size, the lower the transaction costs. Stoll (2000) finds that recent
dollar trading volume is significantly related to the bid-ask spread. Bhushan (1994) argues that dollar trading volume
is negatively related to cost of trading like price pressure. Similarly, Stoll and Whaley (1983) argue that firm size is
negatively related to the bid-ask spread. Roll (1984) provides empirical evidence in support of the negative
correlation between size and bid-ask spread.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
36 J. A. Doukas and M. Li
close to zero. The slope coefficient can then be interpreted as the difference in abnormal
return between the highest and the lowest deciles of the independent variable.
Table 5 reports the results. The first regression shows that the B/M ratio plays a significant
role in determining PEAD. The coefficient of the interaction variable CARBM is 0.705
(t¼2.53), indicating that the spread between the post-earnings announcement abnormal
returns of the highest and lowest earnings surprise deciles is 0.705% larger for firms in the
highest B/M ratio decile than for firms in lowest B/M ratio decile. That is, the PEAD is more
pronounced for value than glamour stocks. However, in the following two regressions, when
we do control for idiosyncratic risk and transaction costs, the B/M ratio has no explanatory
power for the PEAD. The coefficients of the idiosyncratic risk and transaction cost variables
are statistically significant. A far more important result that surfaces from these regressions is
that idiosyncratic risk, major deterrent of arbitrage, plays a greater role in determining the
price drift than transaction costs, implying that the idiosyncratic risk of value stocks rives
their slower speed of adjustment to firm-specific information. The coefficients of the
idiosyncratic risk are larger than those of volume and size, proxies for transaction costs, in
terms of magnitude and significance.
For instance, when VOLUME is used to control for transaction costs, the coefficient of the
interaction between IDIO and CAR is 1.636 (t¼4.80), indicating that the spread between the
abnormal returns of the highest and lowest earnings surprise deciles is 1.636%larger for firms in
the highest idiosyncratic risk decile than for firms in lowest idiosyncratic risk decile. Whereas
Table 5. Determinants of asymmetric post-earnings announcement drift between value and glamour
stocks: 1st Quarter of 1994–3rd Quarter of 2005
Variables Post-earnings announcement 3 months compound abnormal return
Coefficients t-statistics Coefficients t-statistics Coefficients t-statistics
Intercept
0.564
23.25
0.556
22.92
0.555
22.87
CAR 1.871 22.28 1.698 18.97 1.695 18.97
CARBM 0.705 2.53 0.349 1.11 0.190 0.60
CARIDIO 1.636 4.80 1.196 3.04
CARVOLUME
0.660
1.89
CARSIZE
1.182
2.93
Adj-R2 (%) 0.29 0.31 0.31
Note: This table reports the estimation results of following regressions:
QEAi;q ¼ a þ bCARi;q þ c
CARi;q  BMi;q þ d
CARi;q  IDIOi;q þ e
CARi;q  VOLUMEi;q þ "i;q ð6aÞ
QEAi;q ¼ a þ bCARi;q þ c
CARi;q  BMi;q þ d
CARi;q  IDIOi;q þ e
CARi;q  SIZEi;q þ "i;q ð6bÞ
whereQEAi,q is stock i’s compound abnormal return from the first month through the third month following the quarter
q’s earnings announcement. The compound abnormal return is computed as the buy-and-hold return on each stock
minus the buy-and-hold return on the CRSP value weighted index. CARi,q is the market model cumulative abnormal
return for the 3-day window (
1, þ1) around the earnings announcements for stock i at quarter q. BMi,q is B/M ratio
calculated at the end of the fiscal year preceding the announcement for stock i at quarter q. IDIOi,q is the mean residual
error from market model regression estimated over trading days
255 to
2 relative to the announcement for stock i at
quarter q. VOLUMEi,q is the closing daily stock price times daily shares traded averaged over trading days
255 to

2 relative to the announcement for stock i at quarter q. SIZEi,q is the market value of the equity at the end of the fiscal
year preceding the earnings announcement for stock i at quarter q. ALL independent variables have been converted to
coded scores ranging from
0.5 to 0.5 based on their ranking within pooled earnings announcement observations. All
coefficients have been multiplied by 100. Above 10% statistical significance is indicated in bold.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 37
the coefficient of the interaction between VOLUME and a CAR is
0.60 (1.89) and about one
third of the magnitude of the coefficient of idiosyncratic risk interaction variable. These results
are consistent with Pontiff’s argument that idiosyncratic risk is the single most important
impediment to the market efficiency. Overall, this evidence provides additional support for our
hypothesis that higher arbitrage risk borne by the value stocks, not B/M ratio per se, contributes
to the slower price adjustment of value stocks to firm-specific information.
Arbitrage risk and the PEAD: Extreme earnings News
In order to test the relation between idiosyncratic risk and the price drift directly without
using interactive terms with earnings surprises, we replicated the previous analysis using a
subsample of observations consisting of extreme good or bad earnings surprises. The
rationale for this is that in extreme earnings news deciles, the relationship between earnings
surprises and the price drift is basically flat. Therefore, there is no need to control for the
earnings surprise in the extreme news subsample.13
We define earnings surprises the highest (lowest) 10% CAR decile as extreme good (bad)
news. Within these extreme earnings surprise deciles, we find low correlations of 0.01 and
0.03 between CAR and 3-month post-earnings announcement abnormal returns for good and
bad news deciles, respectively, demonstrating that the effect of CAR on the price drift is
negligible for the extreme news observations. Therefore, we pool observations in the extreme
good and bad news deciles together and estimate the following regressions:
QEAi;q ¼ a þ b
BMi;q þ c
IDIOi;q þ d
VOLUMEi;q þ "i;q (7a)
QEAi;q ¼ a þ b
BMi;q þ c
IDIOi;q þ d
SIZEi;q þ "i;q (7b)
where QEA is the dependent variable for extreme good earnings announcements and QEA
times
1.0 is the dependent variable for extreme bad earnings announcements. All
explanatory variables for this regression are coded decile scores ranging from
0.5 to 0.5
based on their ranking within extreme earnings announcements observations. Unlike
regressions (6a) and (6b), there are no interactive terms in regressions (7a) and (7b). Each
coefficient simply measures the effect of each explanatory variable on the post-earnings
announcement abnormal returns.
Consistent with the earlier results, Table 6 shows that idiosyncratic risk plays a dominant
role relative to the B/M ratio, indicating that it impedes arbitrage activity, which contributes
to the PEAD. The B/M ratio, as expected, enters both regressions with a statistically
insignificant coefficient. In addition, the idiosyncratic risk shows a reliable impact in
determining post-earnings announcement abnormal returns regardless of the model
specification. The coefficients of idiosyncratic risk are 0.752 (t¼2.91) and 0.468
(t¼1.63) when the effect of the volume and size is controlled for, respectively, suggesting
that for the extreme news observations, the highest idiosyncratic risk decile exhibits positive
(negative) post-announcement returns 0.752% higher (lower) than those in the lowest
idiosyncratic risk decile for good-news (bad-news) observations. Finally, while the coefficient
of the idiosyncratic risk becomes weaker when we use SIZE to control for transaction costs,
the M/B ratio remains statistically insignificant. SIZE seems to be a more important
transaction cost than VOLUME, especially in the subsample of extreme earnings news.
13See Mendenhall (2004) for a similar argument.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
38 J. A. Doukas and M. Li
CONCLUSION
This study examines the speed of adjustment process of high book-to-market (value) and low
book-to-market (glamour) stock prices to common and firm-specific information. We find
that value stock prices have considerably lower speed of adjustment to both common and
firm-specific information than glamour stocks.We also find that the slow adjustment of value
stock prices to new information is linked to high idiosyncratic risk borne by these stocks.
Consequently, our evidence suggests that arbitrage risk plays an important role in explaining
the slower price adjustment of value stocks to new information. These results are consistent
with the arbitrage risk theory of Shleifer and Vishny (1997), which predicts that idiosyncratic
risk, a major impediment to arbitrage activity, is the most likely cause for the low speed of
adjustment (under-reaction) of stock prices to new information due to the inability of
arbitrageurs to fully hedge the underlying stocks’ idiosyncratic risk. Finally, our results show
that arbitrage risk is priced into value returns, suggesting that the value–glamour anomaly
(mispricing) is linked to arbitrageurs’ inability to fully hedge value stocks’ idiosyncratic risk.
That is, the value premium, documented in previous studies, is a compensation for the
exposure of value stocks to arbitrage risk.
Table 6. Determinants of asymmetric post-earnings announcement drift between value and glamour
stocks: Extreme earnings news analysis
Variables Post-earnings announcement 3 months compound abnormal return
Coefficients t-statistics Coefficients t-statistics
Intercept 1.085 15.86 1.086 15.87
BM 0.005 0.02
0.159
0.59
IDIO 0.752 2.91 0.468 1.63
VOLUME
0.458
1.58
SIZE
0.878
2.74
Adj-R2 (%) 0.04 0.06
Note: This table reports the estimation results of following regressions for the extreme news observations:
QEAi;q ¼ a þ b
BMi;q þ c
IDIOi;q þ d
VOLUMEi;q þ "i;q ð7aÞ
QEAi;q ¼ a þ b
BMi;q þ c
IDIOi;q þ d
SIZEi;q þ "i;q ð7bÞ
Earnings surprises in the highest (lowest) 10% CAR decile is defined as extreme good (bad) news. CAR is the market
model cumulative abnormal return for the 3-day window (
1, þ1) around the earnings announcements. QEA is the
dependent variable for extreme good news announcements and QEA times
1.0 is the dependent variable for extreme
bad news announcements. QEAi,q is stock i’s compound abnormal return from the first month through the third month
following the quarter q’s earnings announcement. The compound abnormal return is computed as the buy-and-hold
return on each stock minus the buy-and-hold return on the CRSP value weighted index. BMi,q is B/M ratio calculated
at the end of the fiscal year preceding the announcement for stock i at quarter q. IDIOi,q is the mean residual error from
market model regression estimated over trading days
255 to 2 relative to the announcement for stock i at quarter q.
VOLUMEi,q is the closing daily stock price times daily shares traded averaged over trading days
255 to
2 relative
to the announcement for stock i at quarter q. SIZEi,q is the market value of the equity at the end of the fiscal year
preceding the earnings announcement for stock i at quarter q. ALL independent variables have been converted to
coded scores ranging from
0.5 to 0.5 based on their ranking within pooled earnings announcement observations. All
coefficients have been multiplied by 100. Above 10% statistical significance is indicated in bold.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 39
APPENDIX
Table A1. Summary statistics of size-B/M ratio portfolio weekly returns: July 1963–May 2005
SIZE B/M portfolio Mean Standard deviation Autocorrelations (AC)
Lag1 Lag2 Lag3 Lag4 Lag5
AC1 Q-Stat AC2 Q-Stat AC3 Q-Stat AC4 Q-Stat AC5 Q-Stat
Small LOW 0.1897 2.7284 0.197 85.308 0.087 101.970 0.087 118.500 0.033 120.950 0.019 121.730
MED 0.2920 2.0224 0.231 117.600 0.101 140.040 0.082 154.810 0.049 160.130 0.028 161.860
HIGH 0.3307 1.9883 0.242 129.300 0.133 168.100 0.097 188.630 0.045 193.060 0.028 194.830
Big LOW 0.2060 2.2907
0.010 0.207 0.012 0.511 0.038 3.756
0.043 7.862
0.010 8.083
MED 0.2258 1.9426 0.014 0.456 0.024 1.776 0.021 2.739
0.027 4.391
0.041 8.169
HIGH 0.2654 1.9648 0.052 5.931 0.056 12.897 0.018 13.631
0.024 14.906
0.044 19.096
All LOW 0.2010 2.2869 0.008 0.133 0.015 0.625 0.044 4.819
0.039 8.104
0.008 8.252
MED 0.2261 1.9283 0.032 2.270 0.028 4.026 0.021 5.017
0.022 6.088
0.029 7.902
HIGH 0.2889 1.9293 0.088 16.849 0.069 27.355 0.031 29.405
0.013 29.767
0.026 31.235
Note: Table 1 reports the summary statistics of size-B/M ratio portfolio weekly returns over the July 1963–May 2005 period. The sample includes 2,188 weekly observations for
each portfolio. The weekly returns are calculated as average daily returns during the week, and all the daily portfolio return data from 1 July 1963 to 31 May 2005 are from
Professor Kenneth French’s website. Portfolios are constructed in a two-by-three sort on size and B/M. Within each of the two size quartiles, the stocks are further allocated into
three book-to-market portfolios. The size breakpoint for year t is the median NYSE market equity at the end of June of year t. B/M for June of year t is the book equity for the last
fiscal year ending in t
1 divided by the market equity for December of t
1. The B/M breakpoints are the 30th and 70th NYSE percentiles. LOW, MED and HIGH refer to the low
30%, medium 40% and high 30% B/M portfolio in each size group.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
40 J. A. Doukas and M. Li
Table B1. Comparison of arbitrage risk of different B/M portfolios: 1987–2005
A. IDIO_MKT
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 All years
Value 0.038 0.038 0.038 0.050 0.054 0.055 0.050 0.045 0.044 0.043 0.042 0.053 0.055 0.057 0.064 0.053 0.046 0.031 0.028 0.047
Medium 0.033 0.030 0.027 0.033 0.033 0.035 0.034 0.034 0.035 0.035 0.035 0.040 0.042 0.048 0.045 0.039 0.030 0.026 0.025 0.035
Glamour 0.037 0.032 0.029 0.035 0.034 0.041 0.040 0.041 0.040 0.042 0.042 0.047 0.048 0.062 0.050 0.044 0.032 0.032 0.030 0.041
Diff. (V
G) 0.001 0.006 0.009 0.015 0.020 0.015 0.010 0.004 0.004 0.001 0.000 0.006 0.007
0.005 0.014 0.009 0.014
0.001
0.002 0.006
               
B. IDIO_FF
1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 All years
Value 0.037 0.038 0.038 0.050 0.054 0.055 0.050 0.045 0.044 0.043 0.042 0.052 0.055 0.056 0.063 0.053 0.046 0.031 0.028 0.047
Medium 0.032 0.030 0.027 0.032 0.033 0.035 0.034 0.034 0.035 0.035 0.035 0.039 0.042 0.048 0.044 0.039 0.030 0.025 0.025 0.035
Glamour 0.035 0.032 0.029 0.035 0.034 0.040 0.040 0.040 0.040 0.041 0.042 0.046 0.047 0.060 0.049 0.043 0.032 0.032 0.029 0.040
Diff. (V
G) 0.001 0.006 0.009 0.015 0.020 0.015 0.010 0.005 0.004 0.002 0.000 0.006 0.007
0.004 0.014 0.010 0.014
0.001
0.002 0.007
               
Note: Table 3 reports arbitrage costs statistics of three book-to-market portfolios. Value, medium and glamour portfolios are three equal sized book-to-market portfolios formed at
the beginning of each calendar year from 1987 to 2005. Value portfolio consists of highest 33% B/M ratio stocks, medium portfolio consists of medium 33% B/M ratio stocks and
glamour portfolio consists of lowest 33% B/M ratio stocks. All values are calendar year based data. B/M is the ratio of book value of common equity to market value of the equity at
prior calendar year end. IDIO_MKT is the residual standard error from a market model regression of the stocks’ daily excess returns on those of the CRSP value-weighted index
over a year. IDIO_FF is the residual standard error from a FF-three-factor model regression of the stocks’ daily returns over a year.
Significant at the 5% level.
Significant at the 1% level.
Copyright # 2009 John Wiley & Sons, Ltd. Review of Behavioral Finance, 1: 23–43 (2009)
DOI: 10.1002/rbf.2
Asymmetric Asset Price Reaction 41
AUTHOR BIOGRAPHIES
John A. Doukas earned his Ph.D. in Financial Economics at Stern School of Business, New York
University. He is a Professor of Finance,W. B. Spong, Jr., a Chair in Finance and Eminent Scholar at Old
Dominion University, Virginia, USA. He is also a Finance Research Associate (Honorary) at Judge
Business School of Cambridge University, UK. He is the recipient of the Graham & Dodd Award 2004
for his article ‘Divergent Opinions and the Performance of Value Stocks’ His research interests include
corporate finance, asset pricing, the role of information in capital markets, international financial
management, foreign investments and foreign exchange markets and he has published over 75 articles
on a wide range of finance and business-related issues in many academic journals including the Journal
of Finance, Journal of Financial and Quantitative Analysis, Journal of Corporate Finance, Journal of
Portfolio Management, Financial Analysts Journal, Journal of Banking and Finance, Journal of
International Money and Finance, Journal of International Business Studies, Journal of Investing,
Journal of Futures Markets, Journal of Applied Corporate Finance, Financial Management and
Financial Review.
Meng Li is a Finance Professor at the Walter E. Heller College of Business, Roosevelt University,
Chicago, IL 60605, USA.
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