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

bkRm;tk þ "t

ht ¼ a þ b"2t

1 þ cht1

(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 bk 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 bk) is significantly negative for all size groups and for both (3 and 5) lag

specifications. In the regression with 3 lags,Pk

k¼1 bk 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

b1 0.0173 0.0571 0.0763 0.0171 0.0562 0.0754

b2 0.0261 0.0282 0.0403 0.0263 0.0282 0.0396

b3 0.0059 0.0103 0.0046 0.0058 0.0097 0.0043

b4 0.0076 0.0093 0.0197

b5 0.0059 0.0189 0.0029

Pk

k¼1 bk 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

bkRm;tk þ "t

ht ¼ a þ b"2t

1 þ cht1

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 bk 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 t1 divided by market equity for

December of t1. 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

bkRm;tk þ gst þ "t

ht ¼ a þ b"2t

1 þ cht1

(2)

and

Rg;t ¼ a þ b0Rm;t þX

k

k¼1

bkRm;tk þ gst þ "t

ht ¼ a þ b"2t

1 þ cht1

(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 bk 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

b1 0.1800 0.2109 0.0010 0.0541 0.0436 0.0376

b2 0.0477 0.0311 0.0109 0.0134 0.0242 0.0103

b3 0.0333 0.0352 0.0249 0.0092 0.0008 0.0041

b4 0.0394 0.0425 0.0006 0.0119 0.0168 0.0068

b5 0.0324 0.0199 0.0167 0.0012 0.0079 0.0014

P

k

k¼1

bk 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 likelihood3022.09 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

bkRm;tk þ gst þ "t

and ht ¼ a þ b"2t

1 þ cht1

ð2Þ

Glamour Rg;t ¼ a þ b0Rm;t þ P

k

k¼1

bkRm;tk þ gst þ "t

ht ¼ a þ b"2t

1 þ cht1

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 bk 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 t1 divided by market equity for December of t1. 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

bkRm;tk þ gst þ "t

ht ¼ a þ b"2t

1 þ cht1

ð2Þ

while the OLS Dimson market model for value stocks is specified as follows:

Rv;t ¼ a þ b0Rm;t þX

k

k¼1

bkRm;tk 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 bk 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

b1 0.0439 0.0446 0.0432 0.0436

b2 0.0254 0.0253 0.0253 0.0242

b3 0.0069 0.0008 0.0069 0.0008

b4 0.0101 0.0168

b5 0.0047 0.0079

P

k

k¼1

bk 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

bkRm;tk þ "t ð4Þ

Rv;t ¼ a þ b0Rm;t þ P

k

k¼1

bkRm;tk þ gst þ "t

ht ¼ a þ b"2t

1 þ cht1

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 bk 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 t1 divided by market

equity for December of t1. 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%, t¼3.91). For the same post-earnings period, glamour stocks have a negative

alpha, but statistically insignificant (0.2789%, t¼1.16). 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 cCARi;q BMi;q þ dCARi;q IDIOi;q

þ eCARi;q VOLUMEi;q þ "i;q (6a)

QEAi;q ¼ a þ bCARi;q þ cCARi;q BMi;q þ dCARi;q IDIOi;q

þ eCARi;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 cCARi;q BMi;q þ dCARi;q IDIOi;q þ eCARi;q VOLUMEi;q þ "i;q ð6aÞ

QEAi;q ¼ a þ bCARi;q þ cCARi;q BMi;q þ dCARi;q IDIOi;q þ eCARi;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 days255 to2 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 bBMi;q þ cIDIOi;q þ dVOLUMEi;q þ "i;q (7a)

QEAi;q ¼ a þ bBMi;q þ cIDIOi;q þ dSIZEi;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 bBMi;q þ cIDIOi;q þ dVOLUMEi;q þ "i;q ð7aÞ

QEAi;q ¼ a þ bBMi;q þ cIDIOi;q þ dSIZEi;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 times1.0 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 t1 divided by the market equity for December of t1. 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. (VG) 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. (VG) 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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