Firm characteristics distress risk and average stock returns

Description
This paper aims to examine the empirical relationship between firm-level characteristics
and the variability of the average portfolio returns of distressed firms. The cross-sectional role of
momentum in the market mispricing of distressed firms is evaluated. Distress risk associated with size
and book-to-market ratio is also disentangled.

Accounting Research Journal
Firm characteristics, distress risk and average stock returns
Prodosh Simlai
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To cite this document:
Prodosh Simlai , (2014),"Firm characteristics, distress risk and average stock returns", Accounting Research
J ournal, Vol. 27 Iss 2 pp. 101 - 123
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Firm characteristics, distress
risk and average stock returns
Prodosh Simlai
Department of Economics, College of Business and Public Administration,
University of North Dakota, Grand Forks, North Dakota, USA
Abstract
Purpose – This paper aims to examine the empirical relationship between frm-level characteristics
and the variability of the average portfolio returns of distressed frms. The cross-sectional role of
momentumin the market mispricing of distressed frms is evaluated. Distress risk associated with size
and book-to-market ratio is also disentangled.
Design/methodology/approach – All of NYSE, AMEXand NASDAQstocks between January 1972
and December 2008 are used, and the individual and joint role of frm characteristics are studied in
detail. Using a measure of distressed stocks based on Campbell, Hilscher and Szilagyi (CHS, 2008), new
fndings on howstock return anomalies are related to the interactions between frmcharacteristics and
fnancial distress risk are provided.
Findings – The fndings showthat the size and value effects are not due to distress risk. Also, contrary
to the existing empirical evidence, momentum does not proxy for distress risk. Furthermore, in the
cross-sectional analysis, momentum subsumes the effect of size risk, and book-to-market acts as an
independent state variable.
Research limitations/implications – The exposition of the paper is limited in many directions. To
measure the extent of fnancial distress, only the model of CHS (2008) is used. As the level of distress is
the key input in the paper, it would be interesting to use some other measure of distress, such as Z-score
and O-score in the sample.
Practical implications – Collectively, the pricing results in this paper help to foster a better
understanding of the nature of distressed stocks, and the identifcation of distress risk premium. It will
help scholars and investment professionals to make robust portfolio management decisions.
Originality/value – Overall, this paper investigates an important research direction that can
potentially shed newlight on our understanding of the risk–return relationship of fnancially distressed
stocks. The individual effect of momentumon the variability of the distressed frm’s average returns is
highlighted. A formal cross-sectional test of the relationship between distress risk and frm
characteristics that include momentum is presented. None of them is quite known in the existing
literature.
Keywords Size effect, Momentum, Book-to-market ratio, Distress risk, Portfolio returns
Paper type Research paper
1. Introduction
This study provides newevidence that frm-level characteristics are associated with the
cross-sectional returns of distressed stocks. Since the seminal works of Chan and Chen
JEL classifcation – G12; G14; M41; M43
The author thanks the college of Business and Public Administration at the University of North
Dakota for fnancial support. The author is grateful to Steven Finney, various conference
participants and two anonymous referees for many insightful comments that have greatly
improved the paper. All remaining errors are those of the author.
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1030-9616.htm
Firm
characteristics
101
Accounting Research Journal
Vol. 27 No. 2, 2014
pp. 101-123
©Emerald Group Publishing Limited
1030-9616
DOI 10.1108/ARJ-06-2012-0046
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(1991) and Fama and French (1992), the concept of fnancial distress has been used
extensively to explain the anomalous nature of stock returns. Several papers have
subsequently examined the market mispricing of distressed frms and its relationship
with some anomalies, with conficting results[1]. As a consequence, the fnancial
performance of relatively distressed stocks and the associated distress risk premium
have faced intense scrutiny in academic research (Garza-Gomez, 1998; Ferguson and
Shockley, 2003; Chan and Lakonishok, 2004; Fama and French, 1996, 2008).
Despite the enormity of the existing literature, some simple questions remain
unanswered. It is not clear to what extent continuation of short-termmomentumaffects
the market mispricing of distressed frms. Is short-term momentum really a proxy for
distress risk? Can we rationalize distress risk associated with frm-level characteristics
such as market equity ( ME ) and book-to-market ratio (BE/ME )? In this paper some of
these issues are addressed[2]. The objective is to examine the interaction of distress risk
and momentum, in an effort to disentangle the anomalous behavior of stock returns with
respect to ME and BE/ME. Following Campbell, Hilscher, and Szilagyi (CHS, 2008), a
measure of distressed stocks is created and new fndings are provided on how stock
return anomalies are related to the interactions between ME, BE/MEand momentumon
the one hand, and fnancial distress risk on the other[3]. The individual and joint role of
momentum and distress risk in the cross-sectional return spread related to ME and
BE/ME are explored. The goal is to develop an empirical framework to simultaneously
account for major anomalous features of average stock returns, which are related to ME,
BE/ME and momentum, and the interaction of these features with fnancial distress. A
formal cross-sectional test of the relationship between distress risk, frmcharacteristics
and momentum is presented.
Two popular concepts that are associated with frm characteristics, such as ME and
BE/ME, are known as size effects and value effects, respectively[4]. In this paper, it is
found that the value effect in the sample is driven by a very small number of “winners”,
and that overall, the vast number of stocks with low relative valuations is properly
priced by the market, commensurate with their poor prospects. The author empirically
tests whether momentum is playing any role in the relationship between distress risk
and the spread in returns due to size and value. The results reinforce the viewthat, even
after controlling for momentum, the size and value effects are not due to distress risk. If
momentum is concentrated in highly distressed frms, it may be proxying for distress
risk, but the fndings suggest that this is not the case. The author joins existing studies
that examine the empirical association between frmcharacteristics and distress risk in
the cross-section and over time. Collectively, the pricing results in this paper help to
foster a better understandingof the risk–returnrelationshipof distressedstocks, andthe
nature of the distress risk premium.
The rest of the paper is organized as follows. In the next section, an overview of the
related literature is briefy presented. Section 3 explains the data and methodology used
throughout the paper. The main empirical results are presented in Section 4, and fnally,
Section 5 concludes.
2. Related literature and limitations of the study
The relationship between distressed frms’ returns and their characteristics has already
been investigated in numerous studies. First, almost all papers examining the abnormal
returns of distressed frms control for ME and BE/ME, and often for momentum, either
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directly in a regression setup using various factor models (Dichev, 1998; Lamont
et al., 2001), or by double sorting (Griffn and Lemmon, 2002), as performed in this study.
Second, several papers examine in more detail the interaction between distressed frms’
returns and other anomalies. For example, Avramov et al. (2007) show that momentum
exists only among highly distressed frms. Lewellen (2002) shows that size and BE/ME
portfolios exhibit momentum as strong as that in individual stocks.
Even though the existence of the distress risk premiumremains a controversial topic,
there is substantial empirical evidence on the role of fnancial distress in the
cross-sectional pattern of stock returns. In a series of recent works, Avramov et al. (2009,
2012) have documented negative stock returns following rating downgrades. In
contrast, Chava and Amiyatosh (2010) have used the implied cost of capital as an
alternative measure of the expected return and fnd evidence to support a positive
relationship between default risk and stock returns. Using Ohlson’s (1982) O-score as a
measure of distress risk, Griffn and Lemmon (2002) have argued that the value
premium is stronger in distressed frms. In contrast, Fama and French (1996) have
hypothesized that aggregate distress risk commands a premium and is responsible for
the size and value effects. Using the option-based distance-to-default model, also known
as the KMV measure, Vassalou and Xing (2004) have examined default risk in the
context of the Fama–French model[5]. They have presented evidence that the size and
value premia are stronger for high default probability frms. In an interesting study,
Campbell et al. (2008) have argued that earnings momentum might explain the low
average returns of the distressed stocks. They have found that stocks with high
predicted default probabilities earn lower returns, which contradicts the prediction of
Fama and French (1996). Campbell et al. (2008) do not however conduct any formal
cross-sectional tests of the relationship between distress risk and frm characteristics.
In other related works, Dichev (1998) has found that frms with a high probability of
bankruptcy underperformlow-risk frms. Ferguson and Shockley (2003) have provided
a theoretical rationale and argued that the observed size and value effects occur because
estimation errors in proxy betas are correlated with relative distress. Garlappi and Yan
(2011) have investigated whether the possibility of shareholder recovery on fnancial
distress affects the relationship between a frm’s expected returns and its likelihood of
default. Garlappi et al. (2008) fnd no signifcant difference in returns between distressed
and non-distressed frms. Overall, the existing empirical evidence suggests that some
anomalies originate during periods of fnancial distress and some others, such as size
and value, disappear or are mitigated by fnancial distress. Recently, work by
Hackbarth et al. (2012) has suggested that the Bankruptcy Reform Act of 1978 reduces
portfolio- and frm-level distress premia and changes the characteristics of distressed
stocks, such as market betas and return standard deviations.
With respect to the interaction of distress and momentum returns, some interesting
evidence has been found recently by Avramov et al. (2007). They focus solely on
Standard and Poor (S&P) credit-rated frms and found that momentum profts are
strong for low-rated frms and weak for high-rated frms. In contrast to Avramov et al.
(2007), the author uses a bigger universe of stocks and an extended sample period.
Another study that explores a potential link between distressed frms and short-term
momentumreturns is Agarwal and Taffer (2008). However, like Ferguson and Shockley
(2003), they use an accounting ratio-based z-score model as a proxy for default risk. The
measure of distress that is the primary focus of this paper is the probability of frm
103
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failure, as measured by a specifcation estimated in Campbell et al. (2008). This study is
essentially a replication of Agarwal and Taffer (2008) and Campbell et al. (2008).
However, this study differs fromAgarwal and Taffer (2008) in that it uses US data and
a different proxy for distress risk. It also differs from Campbell et al. (2008) in that the
author includes cross-sectional tests. In the empirical analysis, the author also uses the
KMV-Merton default probability (analogous to Crosbie and Bohn (2002), and Hillegeist
et al. (2004)) as an alternative measure of distress risk, and compares its predictions with
those of the failure indicator. Similar to Campbell et al. (2008), the author demonstrates
that the measure of distress risk has a higher predictive power over distance-to-default
measure.
The exposition of the paper is limited in many directions. It is important to note that
to measure the extent of fnancial distress, the author uses only the model of Campbell
et al. (2008). As the level of distress is the most important input in the paper, it would be
interesting to use some other well-known measure of distress, especially those used in
related studies, such as z-score (Altman, 1968), O-score (Ohlson, 1980) and credit rating.
Also, Campbell et al. (2008) have estimated fnancial distress/failure probabilities using
only past/historical data; i.e. the model is re-estimated using only historically available
data to eliminate look-ahead bias. This paper does not follow this estimation procedure
to eliminate look-ahead bias, a full-length discussion of which is beyond the author’s
scope. Furthermore, it will be interesting to investigate the potential survivorship bias in
the sample and see how this bias affects the identifcation of distress stocks. These
important procedures for estimating distress risk are not included in this approach.
Therefore, the contributions of this paper are limited by the robustness of the current
results.
3. Data and methodology
For empirical evaluation in this paper, the author utilizes the common shares of all
stocks from the NYSE, AMEX and NASDAQ universe between January 1972 and
December 2008. The stock return and market cap data are collected from the Center for
Research in Security Prices (CRSP) database, and all accounting-related data are
collected from the COMPUSTAT database. Similar to CHS (2008), the author combines
quarterly accounting data from COMPUSTAT with monthly and daily equity market
data from CRSP. Overall, the sample consists of 23,765 unique stocks in the 37-year
study period.
Following CHS (2008), the author calculates the following list of accounting
variables[6]:
• NIMTAAVG ?geometric average of net income over market-valued total assets;
• TLMTA ?total liability over market-valued total assets;
• EXRETAVG ?geometric average of log excess return over S&P 500 index;
• SIGMA ?past three months daily return volatility;
• RSIZE ?log ratio of markets cap with respect to S&P 500 total market cap;
• CASHMTA ? ratio of cash and short-term assets over the market-valued total
assets;
• MB ?market-to-book equity ratio; and
• PRICE ?log price per share of the frm.
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The author then constructs the distress measure following the third column in Table IV
of CHS (2008):
Distress
t
? ?9.164 ? 20.264 NIMTAAVG
t
? 1.416 TLMTA
t
? 7.129 EXRETAVG
t
? 1.411SIGMA
t
? 0.045 RSIZE
t
? 2.132 CASHMTA
t
? 0.075MB
t
? 0.058PRICE
t
(1)
The author forms four sets of portfolios, which are based on the above measure of
distress risk, and studies the relationship between average stock returns and frm
characteristics. The frst set of portfolios is based on the distress ranking. At the
beginning of each month t , the author ranks all NYSE, AMEXand NASDAQstocks into
ten portfolios sorted by the values of Distress
t?1
. By using NYSE, AMEXand NASDAQ
breakpoints, the author constructs value-weighted portfolio returns for the current
month. The second set of portfolios is based on the independent double-sort of size and
distress factor. For example, at the beginning of each month, the author frst sorts all
stocks into ME quintile breakpoints and then on fve distress risk quintiles. As a result,
the author forms 25 portfolios and constructs their value-weighted returns. Similarly,
the third set of portfolios is based on the fve-by-fve independent sort of BE/ME ratio
and distress risk. The author frst double-sorts on the BE/MEratio (using NYSEquintile
breakpoints) and on distress risk. The fourth set of portfolios is based on the fve-by-fve
independent sort of momentum and distress risk. For each month t, the author sorts
stocks into fve quintiles based on the values of Distress
t?1
. Within each distress quintile,
the author sorts stocks into fve momentumquintiles following Jegadeesh and Titman’s
(1993) convention. For each month t, the author assigns all NYSE, Amex and NASDAQ
stocks on their prior returns from month t ? 2 to t ? 7 (skipping month t ? 1), and
calculates the subsequent portfolio returns frommonth t to t ?5. As a result, the author
forms 25 portfolios from the intersections of the fve distress risk and fve momentum
groups[7].
While constructing the distress measure, the author uses the quarterly
COMPUSTAT data from four months ago and returns data from one month ago. The
cutoff points are based on all stocks. The author always rebalanced the portfolios
monthly. The author follows Campbell et al. (2008) to handle carefully the returns to
stocks that are delisted and thus disappear from the CRSP database. Note that, while
CHS examines the distress risk between 1963 and 2003, to avoid too few stocks in
various portfolios, the study focuses on the period between 1972 and 2008. Changing the
sampling period has no qualitative implication for the results.
To test the explanatory powers of various common risk factors, the author frst uses
the Fama–French three-factor (3F) model for each of the distress risk-based decile
portfolios:
R
it
? RF
t
? ?
it
? ?
it
?RM
t
? RF
t
? ? s
it
SMB
t
? h
it
HML
t
? ?
it
, i ? 1, …, N, t ? 1, …, T (2)
where RM
t
is the return of CRSP’s value-weighted index on all NYSE, Amex and
NASDAQ stocks; and RF
t
is the one-month T-bill rate obtained from Ibbotson and
Associates. So, the frst explanatory variable ( RM
t
?RF
t
) is the excess return of CRSP’s
value-weighted index on all NYSE, Amex and NASDAQ stocks. The second
explanatory variable, SMB (small minus big), is the difference each month between the
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simple average of the returns on the three small-stock portfolios and the simple average
of the three big-stock portfolios returns. The third regressor, HML (high minus low), is
the difference each month between the simple average of the returns on the two high-
BE/ME portfolios and the average of the returns on the two low- BE/ME portfolios.
Finally, ?
it
is the mean-zero stochastic error term. In addition to (2), the author also uses
Carhart’s (1997) four-factor (4F) model, which includes an additional factor momentum
(MOM
t
) in (2), and is given by:
R
it
? RF
t
? ?
it
? ?
it
?RM
t
? RF
t
? ? s
it
SMB
t
? h
it
HML
t
? p
it
MOM
t
? ?
it
, i ? 1, …, N, t ? 1, …, T
(3)
In model (3), the frst regression coeffcient ?
it
represents exposure to time-varying
market risk. Other regression coeffcients s
it
, h
it
and p
it
measure the exposure to size,
value and momentum, respectively. The returns on the momentum and Fama–French
risk factors are obtained fromKenneth French[8]. For empirical comparison, the author
implements the above two specifcations [i.e. (2) and (3)] for all of the double-sorted
portfolios; they are – size and distress, BE/MEand distress and momentumand distress.
The hope is that by looking at the alpha estimates, and the pattern of factor loadings
corresponding to various quintiles, the author should be able to judge more precisely the
relationship between frm characteristics and distress risk.
4. Empirical results and interpretations
4.1 Characteristics and factor loadings of distress-sorted portfolios
The author starts by evaluating the characteristics of the distress-sorted portfolios, and
their associated abnormal return estimate. The author frst clarifes the understanding
of the risk–return relationship for all decile portfolios (denoted by 01 through 10), which
are based on the distress measure (1). The author creates a zero-investment portfolio
(indicated by 0,110), which takes a long position in the lowest-distress portfolio and a
short position in the highest-distress portfolio. The author reports the information about
all the characteristics of decile portfolios and the long–short portfolio in Panel A of
Table I. The monthly average excess return and the standard deviation of the lowest
decile portfolio (i.e. the safest stocks) turn out to be 1.30 per cent and 3.53 per cent,
respectively. The highest-risk portfolio has a negative average excess return of ?0.40
per cent per month and a very high standard deviation of 9.29 per cent. Overall, the
average excess returns decreases and the standard deviation increases monotonically as
the author moves fromlower-risk portfolios to higher-risk portfolios, a fact also refected
through their Sharpe ratios. As expected, the long–short distress portfolio holds a
statistically signifcant average return of 1.70 per cent per month (with a t-statistics
value of 5.91), and a standard deviation of 6.05 per cent. Most of the distress risk
portfolios are highly skewed, and the returns of the high-distressed frms are more
leptokurtic than the low-distressed frms[9]. Not to the author’s surprise, most of these
observations are consistent with the preliminary results reported by CHS (2008)[10].
Next, the author investigates whether the expected returns of distress-sorted
portfolios can be explained by the market, size, value and momentum factors. Both
Fama–French 3F and Carhart 4F model are well-known in the literature as a benchmark
for any asset pricing tests. Panels Band C report the associated factor loadings of the 3F
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Table I.
Characteristics of
distressed stock portfolios
(January 1972-December
2008)
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107
Firm
characteristics
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P
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(
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and 4F model, respectively. The author compares the alphas of multifactor models and
the market model in Panel A. The author observes that the lower distress risk portfolios
have lower estimates of market beta and economically nugatory loadings on the size
factor. In contrast, higher distress risk portfolios have higher market betas and higher
size factor loadings, which are all statistically signifcant at the 1 per cent level of
signifcance. The result implies that the distressed portfolios consist mainly of small
frms, and their average excess returns are negatively correlated with the market betas.
The loadings of the value factor refect an interesting pattern as well. Both extremes
of failure risk distribution, which are represented by deciles 01 and 10, have small and
negative HML loadings. In contrast, portfolios closer to the median decile have high and
positive HML loadings. This suggests that the value factor is not essential for
disentangling the distress risk premium. The fndings that the distress risk premium
may not result fromfrms’ loading on the value factor are consistent with, but not limited
to, the lower past returns and lower past fundamental performance of value stocks. As
is shown in the existing literature, the return on distressed stocks may covary with the
return on human capital (Fama and French, 1996), and BE/ME may be a poor proxy for
distress (Shumway, 2001). Altogether, the results are consistent with the
characteristic-based explanations of Griffn and Lemmon (2002), who fnd that the
distress effect is strongest among growth stocks, where it is also most negatively related
to default probability. As it turns out, both lowest and highest distress risk portfolios,
despite their low loading on the value factor, earn the highest and lowest average
returns, respectively. It is entirely possible that some other risk measure might explain
the returns on the growth, high-distress stocks.
In the next step, the author corrects for risk using 4F model (3). The estimated result
in Panel C shows that the 4F specifcation hardly affects the market, SMB and HML
factors’ loading patterns. More importantly, when the author includes momentum, there
is no change in the loading patterns of the value factor. However, an interesting piece of
tangible evidence emerges from Panel C, and it is the visible trend of the momentum
factor’s slope estimate. The lower distress risk portfolios have positive loadings on the
momentum factor, which are statistically signifcant at the 5 per cent level. The
momentumloading decreases monotonically as the author moves to higher distress risk
portfolios.
The addition of the momentum factor affects the abnormal return estimates of all 10
decile portfolios. Compared to the capital asset pricing model (CAPM) and the 3F model,
the 4Fspecifcation produces smaller alphas for lower distress risk portfolios and bigger
alphas for higher distress risk portfolios. The value factors’ loading for the long–short
portfolio goes up slightly (from0.06 per cent with the 3F model to 0.24 per cent with the
4F model), even though both are statistically insignifcant[11]. The estimated alpha of
the long–short portfolios decreases marginally (from 2.02 per cent for the CAPM and
2.09 per cent for the 3F model to 1.37 per cent for the 4F model), which always remains
statistically and economically signifcant. The author observes that the low-distressed
stocks have positive loadings on the momentumfactor, and high-distressed stocks have
negative loadings on the momentum factor. Therefore, it is safe to say that the
high-distressed stocks have negative momentum, and the low-distressed stocks have
positive momentum. This unequivocally suggests that the momentum factor fails to
explain the low average excess returns of distressed stocks.
ARJ
27,2
108
D
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(
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To check the stability of alpha measure, the author also looks at the rolling alpha
estimate of the long–short distressed portfolio using all three models. Figure 1 display
the evolution of the time-varying alpha throughout the sample period. As the author can
see, the 4F model always produces an alpha that is close to the median estimate and has
the smallest variability. The market model generates a rolling alpha that is small before
1987 stock market crash. But after that particular event, the market model alpha
becomes highly volatile and relatively stronger in magnitude.
4.2 Size, BE/ME and distress risk in stock returns
The result from Table I implies that there is an abundance of small-size frms among
distressed stocks, and all the portfolios between the 40th and 70th percentiles have
economically signifcant value factor loadings. There is, however, no clear indication
whether the size or the value premium is solely responsible for the high average excess
returns of low-distressed stocks. Atraditional way to identify the individual roles of size
(and BE/ME ) in the evaluation of distressed stocks’ average returns is by creating
portfolios that are not only sorted by distress risk but also by size (and BE/ME ). In this
subsection, the author does so by frst double-sorting the portfolios using size and
distress risk. This is followed by the analysis of portfolios of stocks that are
double-sorted by BE/ME and distress risk. The corresponding results are reporteds in
Table II and III, respectively.
Panel A of Table II shows an overview of the average number of frms for each
quintile. Within each distress group, the average number of frms decreases
monotonically from 101 for the smallest-size quintile to 37 for the biggest-size quintile.
The panel shows that there are actually fewer small frms than large frms in the
high-distress group. Panel B presents the average excess returns of
25-size-and-distress-sorted portfolios. As seen earlier from Table I, now the average
excess return is highest among low-distressed frms and lowest among high-distressed
frms. Within various size quintiles, the smallest quintile commands the highest average
excess return.
Panels C and D show the alpha estimates from the time-series regressions of each
portfolio corresponding to multifactor models (2) and (3). The estimate of alpha refects
the size and distress effect in average returns. The author observes that, within each
distress quintile, the alphas of the smallest-size portfolios exceed the alphas of the
biggest-size portfolios. Also, within each size quintile, the alpha of the lowest-distressed
0
1
2
3
4
5
6
1
9
7
7
m
1
1
9
7
8
m
5
1
9
7
9
m
9
1
9
8
1
m
1
1
9
8
2
m
5
1
9
8
3
m
9
1
9
8
5
m
1
1
9
8
6
m
5
1
9
8
7
m
9
1
9
8
9
m
1
1
9
9
0
m
5
1
9
9
1
m
9
1
9
9
3
m
1
1
9
9
4
m
5
1
9
9
5
m
9
1
9
9
7
m
1
1
9
9
8
m
5
1
9
9
9
m
9
2
0
0
1
m
1
2
0
0
2
m
5
2
0
0
3
m
9
2
0
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5
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1
2
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6
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5
2
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7
m
9
A
l
p
h
a
e
s
?
m
a
t
e
s
CAPM alpha
3-Factor alpha
4-Factor alpha
Figure 1.
Rolling alphas of
long–short distressed
stock portfolios using
various models
109
Firm
characteristics
D
o
w
n
l
o
a
d
e
d

b
y

P
O
N
D
I
C
H
E
R
R
Y

U
N
I
V
E
R
S
I
T
Y

A
t

2
1
:
1
9

2
4

J
a
n
u
a
r
y

2
0
1
6

(
P
T
)
Table II.
Size and distress risk in
stock returns (January
1972-December 2008)
P
a
n
e
l
A
:
a
v
e
r
a
g
e
n
u
m
b
e
r
o
f
f
r
m
s
P
a
n
e
l
B
:
a
v
e
r
a
g
e
e
x
c
e
s
s
r
e
t
u
r
n
S
i
z
e
D
i
s
t
r
e
s
s
q
u
i
n
t
i
l
e
D
i
s
t
r
e
s
s
q
u
i
n
t
i
l
e
Q
u
i
n
t
i
l
e
L
o
w
2
3
4
H
i
g
h
L
o
w
2
3
4
H
i
g
h
L
S
S
m
a
l
l
1
4
9
.
2
0
(
7
.
4
2
)
9
4
.
4
2
(
3
.
8
0
)
8
7
.
9
4
(
5
.
0
1
)
6
8
.
0
1
(
2
.
3
9
)
1
0
7
.
1
5
(
0
.
4
3
)
1
.
9
3
*
*
(
7
.
1
5
)
1
.
4
1
*
*
1
.
3
9
*
*
0
.
9
3
*
*
0
.
1
8
1
.
7
5
*
*
2
6
9
.
8
3
(
6
.
5
6
)
5
8
.
6
2
(
5
.
3
1
)
5
0
.
2
1
(
4
.
7
1
)
4
5
.
0
6
(
2
.
8
9
)
4
1
.
9
3
(
0
.
4
0
)
1
.
6
9
*
*
(
5
.
0
3
)
1
.
4
7
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1
.
3
2
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*
0
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9
0
*
*
0
.
1
7
1
.
5
0
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*
3
7
7
.
7
5
(
5
.
7
2
)
6
1
.
4
3
(
5
.
0
5
)
7
8
.
4
(
4
.
3
5
)
5
5
.
3
9
(
2
.
8
5
)
4
2
.
6
0
(
1
.
7
9
)
1
.
4
3
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(
2
.
9
6
)
1
.
2
6
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1
.
1
3
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8
7
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4
8
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9
4
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4
6
2
.
5
8
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5
.
3
6
)
3
2
.
8
6
(
5
.
2
6
)
5
2
.
4
6
(
4
.
0
0
)
4
9
.
9
5
(
2
.
7
4
)
4
6
.
0
5
(
0
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0
2
)
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.
2
7
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3
.
6
1
)
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2
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1
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9
0
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1
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2
6
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i
g
4
5
.
0
9
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4
.
9
1
)
2
6
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9
0
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4
.
1
5
)
4
3
.
7
1
(
2
.
9
7
)
3
2
.
6
9
(
2
.
0
0
)
3
4
.
9
5
(
?
2
.
6
9
)
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0
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4
.
2
3
)
0
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9
2
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0
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7
7
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0
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6
6
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9
4
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2
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1
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L
S
0
.
8
6
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4
.
6
9
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4
9
(
1
.
6
4
)
0
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6
2
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(
3
.
2
4
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0
.
2
6
(
0
.
8
3
)
1
.
1
2
*
*
(
3
.
6
2
)
P
a
n
e
l
C
:
3
-
F
a
c
t
o
r
a
l
p
h
a
P
a
n
e
l
D
:
4
-
F
a
c
t
o
r
a
l
p
h
a
S
i
z
e
D
i
s
t
r
e
s
s
q
u
i
n
t
i
l
e
D
i
s
t
r
e
s
s
q
u
i
n
t
i
l
e
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u
i
n
t
i
l
e
L
o
w
2
3
4
H
i
g
h
L
S
L
o
w
2
3
4
H
i
g
h
L
S
S
m
a
l
l
1
.
1
2
*
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(
1
2
.
5
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3
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.
9
2
)
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5
2
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*
(
4
.
7
4
)
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0
.
0
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(
?
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2
9
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8
4
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4
.
7
4
)
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.
9
6
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(
9
.
5
5
)
1
.
0
7
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(
1
1
.
5
9
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5
3
(
1
.
8
3
)
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.
5
5
*
*
(
5
.
2
2
)
0
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1
0
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0
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3
1
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3
6
(
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1
.
7
5
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.
4
3
*
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(
6
.
7
6
)
2
0
.
9
9
*
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(
1
0
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9
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.
6
7
*
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(
6
.
9
9
)
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5
0
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(
6
.
6
2
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0
8
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0
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7
9
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8
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*
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(
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4
.
1
0
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8
2
*
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(
7
.
3
5
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0
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9
2
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(
9
.
1
8
)
0
.
6
5
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(
6
.
6
9
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5
6
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(
7
.
1
9
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0
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3
4
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3
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5
7
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2
9
(
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1
.
6
4
)
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2
1
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(
5
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1
1
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3
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7
6
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8
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0
4
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5
6
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6
.
2
9
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3
7
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(
4
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2
3
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1
3
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1
0
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4
3
(
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.
7
7
)
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2
0
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4
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0
5
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6
3
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1
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4
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5
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5
9
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4
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5
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0
7
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4
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3
.
9
9
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6
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7
2
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1
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7
0
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6
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7
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9
4
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3
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6
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7
4
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3
2
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3
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8
4
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1
2
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0
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8
1
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9
5
*
*
(
?
3
.
3
3
)
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6
3
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5
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1
9
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5
4
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5
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7
1
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5
8
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*
(
6
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2
3
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4
8
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(
6
.
1
1
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3
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5
2
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3
2
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2
4
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8
5
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(
3
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0
4
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B
i
g
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.
7
5
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(
9
.
7
2
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5
3
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(
7
.
3
7
)
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1
8
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2
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4
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0
6
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0
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6
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.
6
8
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.
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4
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4
3
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4
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4
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5
2
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*
(
7
.
9
0
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4
8
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(
6
.
8
4
)
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3
5
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4
.
0
2
)
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0
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3
.
0
1
)
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.
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1
*
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.
2
7
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.
9
3
*
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(
3
.
6
8
)
L
S
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.
3
6
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*
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3
.
4
4
)
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0
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?
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0
2
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3
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.
9
1
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6
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2
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4
.
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8
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1
7
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1
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9
3
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.
3
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(
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.
7
3
)
N
o
t
e
s
:
F
o
r
P
a
n
e
l
A
,
t
h
e
a
l
p
h
a
e
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ARJ
27,2
110
D
o
w
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a
d
e
d

b
y

P
O
N
D
I
C
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E
R
R
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U
N
I
V
E
R
S
I
T
Y

A
t

2
1
:
1
9

2
4

J
a
n
u
a
r
y

2
0
1
6

(
P
T
)
Table III.
Book-to-market and
distress risk in stock
returns (January 1972-
December 2008)
P
a
n
e
l
A
:
a
v
e
r
a
g
e
n
u
m
b
e
r
o
f
f
r
m
s
P
a
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l
B
:
a
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a
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e
x
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B
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D
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D
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2
3
4
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h
1
2
3
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2
7
9
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0
7
8
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3
3
.
3
8
1
0
9
.
0
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1
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0
1
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(
2
.
2
1
)
0
.
7
2
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2
.
0
8
)
1
.
0
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(
2
.
4
3
)
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.
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6
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3
4
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3
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3
0
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9
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2
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3
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7
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2
3
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6
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1
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8
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3
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w
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4
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3
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9
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0
6
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1
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2
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2
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7
5
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4
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(
2
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4
9
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3
5
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(
2
.
4
4
)
P
a
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l
C
:
3
-
f
a
c
t
o
r
a
l
p
h
a
P
a
n
e
l
D
:
4
-
F
a
c
t
o
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a
l
p
h
a
B
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/
M
E
D
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s
t
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2
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4
H
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9
3
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2
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1
7
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6
4
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1
.
9
9
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2
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1
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?
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.
5
5
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(
?
2
.
4
6
)
3
.
4
8
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(
3
.
2
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7
6
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2
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0
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1
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N
o
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s
:
F
o
r
P
a
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l
A
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111
Firm
characteristics
D
o
w
n
l
o
a
d
e
d

b
y

P
O
N
D
I
C
H
E
R
R
Y

U
N
I
V
E
R
S
I
T
Y

A
t

2
1
:
1
9

2
4

J
a
n
u
a
r
y

2
0
1
6

(
P
T
)
portfolios exceeds the alpha of the highest-distressed portfolios. The trend is clearly
visible irrespective of whether the author chooses the 3F or 4F model. Therefore, even
though the underperformance of distressed stocks is apparent for both small and big
frms, it is relatively strong for small-size frms. The alpha estimates for the long–short
distressed portfolios range from1.96 per cent per month (with a t-statistics value of 9.55)
for the smallest size to 3.43 per cent per month (with a t-statistics value of 4.04) for the
biggest size. The difference disappears slightly, as the author corrects for risk using the
4F model.
In Table III, the author shows the corresponding characteristics of the second set of
double-sorted portfolios, which are based on BE/ME and distress risk. In the sample, on
an average, there are more value frms than growth frms across all distress quintiles
(Panel A). The reverse argument, however, is not true. On average, there are 63 frms in
the highest-distress group and 80 frms in the lowest-distress group. The average excess
returns of all double-sorted portfolios from Panel B suggest a clear underperformance
of high-distressed stocks. Within various BE/ME quintiles, however, the
underperformance is worse for stocks with low- BE/ME ratios. The alpha estimates of
all the BE/ME-and-distress-sorted portfolios, which are reported in Panel C and D,
provide further evidence of the relative infuence of common risk factors in explaining
the average portfolio returns. The author fnds that the alpha estimates are related to
BE/ME, and the decrease in alpha fromlow- to high-distress portfolios for each BE/ME
quintile is rather monotonic.
The most surprising part of the results fromPanel Cand Dis the disappearance of the
contrasting performance of the value and growth stocks. As the author corrects for risk
(using either the 3F or 4F model), the alpha estimate for the low- BE/ME portfolios goes
up signifcantly in the lower-distress quintiles. Similar patterns are not visible for two of
the highest-distress quintiles. As a result, the average alpha estimate of the long–short
distressed portfolio is twice as high for the lowest BE/ME quintile as it is for the highest
BE/ME quintile. This absence of value effect for the safest stocks in the fndings is very
similar to the results previously reported by Griffn and Lemmon (2002) and CHS (2008).
4.3 Momentum and the predictable variation in distress risk premium
As an alternative specifcation check, next the author analyzes the third set of portfolios,
which are double-sorted using momentumand distress risk. The results of this third sort
are reported in various panels of Table IV. The spread in the average number of
high-momentumfrms (winners) and low-momentumfrms (losers) is uniformover two
extreme distress quintiles (Panel A). The number of losers that are in the high-distress
group is higher than the corresponding number for the winners. Similar to the earlier
fndings, this new double-sorting also generates high average excess returns for the
safest stocks and low average excess returns for the high-distressed stocks (Panel B).
The observation is true irrespective of any momentum quintiles the author considers.
Within each distress quintile however, the variability pattern of the average portfolio
returns is not uniform. The winners command the highest average excess returns for all
portfolios of stocks in the three lowest-distress quintiles. In contrast, the low-momentum
stocks display positive and statistically signifcant (at least at the 10 per cent level)
average excess returns only for the two lowest-distressed quintiles.
When the author corrects for risk using the 3F model, the anomalous poor
performance of the high-distressed stocks continues to hold (Panel C). Even though the
ARJ
27,2
112
D
o
w
n
l
o
a
d
e
d

b
y

P
O
N
D
I
C
H
E
R
R
Y

U
N
I
V
E
R
S
I
T
Y

A
t

2
1
:
1
9

2
4

J
a
n
u
a
r
y

2
0
1
6

(
P
T
)
Table IV.
Momentum and distress
risk in stock returns
(January 1972-December
2008)
P
a
n
e
l
A
:
a
v
e
r
a
g
e
n
u
m
b
e
r
o
f
f
r
m
s
P
a
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l
B
:
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r
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g
e
e
x
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.
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4
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9
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6
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9
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4
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7
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7
7
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5
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P
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C
:
3
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f
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p
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P
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:
4
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113
Firm
characteristics
D
o
w
n
l
o
a
d
e
d

b
y

P
O
N
D
I
C
H
E
R
R
Y

U
N
I
V
E
R
S
I
T
Y

A
t

2
1
:
1
9

2
4

J
a
n
u
a
r
y

2
0
1
6

(
P
T
)
magnitude changes slightly, two of the high-distressed portfolios display negative
abnormal returns. To the author’s surprise, the underperformance of the distressed
stocks is stronger for the winners than it is for the losers. The evidence also suggests
that the high-distressed stocks have negative momentum and the safest stocks have
positive momentum.
Correcting for risk using the 4Fmodel produces similar results. The result fromPanel
D indicates that the average alpha of the long–short distress portfolio is four-times
bigger for the winners than it is for the losers. The average alpha of the long–short
momentum (i.e. winner minus loser) portfolio is 0.42 per cent per month (with a
t-statistics value of 2.09) for the lowest-distress quintile, and ?1.11 per cent per month
(with a t-statistics value of ?2.38) for the highest-distress quintile. These implicitly
demonstrate that the high-distressed stocks underperform irrespective of whether they
contain losers or winners. The underperformance however is more pronounced for the
high-momentum stocks, which are strongly distressed. In contrast, the overall
performance of the safest portfolios is better for the winners, as they have positive
momentum, which are also economically and statistically meaningful.
4.4 Supplementary fndings and relative comparisons
To supplement the fndings so far, the author compares the observed average excess
returns to the returns predicted by the 4F model in Figure 2. Each curve uses the
third-order polynomial and represents portfolios of different distress risk within various
momentum quintiles. The vertical axis measures the average excess returns, and the
horizontal axis represents the predicted returns for all distress-and-momentum-sorted
portfolios. The author sees that, except for quintile 3, most of the points for other
quintiles lie closer to the 45
0
line, suggesting that the 4F model is indeed successful in
explaining the variability of the average returns. For quintile 3, the average return
shows very little dispersion; so it is not a surprise that some of the predictions are located
further away from the 45
0
line. Overall, the variation in momentum produces positive
non-linear association between the observed returns and the returns predicted by the 4F
model. It is likely that the high-distressed stocks that are recent past-winners are in more
severe fnancial distress (than the recent past-losers), and as a result, the author ends up
with a negative momentum for high-distressed stocks. The author can also conjecture
that the prevalence of positive momentum for the low-distressed (safest) stocks may
explain their high-abnormal returns[12].
Previous literature on the pricing of distressed frms has used some of the early
measures of bankruptcy prediction. It has largely been found that the distressed stocks
have low returns. To compare the performance of the distress-risk model with the
existing structural default model, the author replicates Table V of CHS (2008, p. 2,916).
The author essentially constructs a distance-to-default (DD) measure in the manner of
Hillegeist et al. (2004), and compares the predictive power of DD in the presence of the
failure indicator. The author includes four horizons of 0, 12, 24 and 36 months in the
regression analysis. In Table V, which reports the result, the author estimates two
linear regressions – a simple regression of the failure indicator on DD, and a multiple
regression of the failure indicator on DD and the reduced-form model variables. Panel
A reports the coeffcient estimates of DD, and Panel B reports the adjusted R
2
(R
–2
) and
root-mean-squared errors (RMSE) of the in-sample (1972-2001) and out-of-sample
(2002-2008) regressions. In the simple linear regression, DD commands a negative sign
ARJ
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for all four horizons of 0 to 36 months, and are always remains statistically signifcant
(at the 1 per cent level), which is what the author should expect. In the multiple
regression model however, the coeffcient on DDstays positive for up to 0 to 24 months’
horizon, and becomes negative at 36 months’ horizon. Note that, at the 24-month horizon,
the coeffcient of DD is not signifcant at the 1 per cent level. As it is known in the
literature (Bharath and Shumway, 2008), the inclusions of volatility and leverage with
free coeffcients must have affected the DD coeffcient.
Panel B indicates that two of the important measures of regression diagnostics – the
adjusted R
2
and RMSE, improve as the author uses the distress-risk model. The addition
of DD hardly has any infuence on both in-sample and out-of-sample performance over
all four horizons. In fact, as the author drops DD from the regression, the in-sample R
–2
increases from 0.16 to 0.18 for the two-year horizon, and from 0.09 to 0.11 for the
three-year horizon. The out-of-sample R
? 2
also shows signifcant improvement for the
distress risk model over the DD-only model. For example, the out-of-sample RMSE
decreases from2.92 for the DD-only model to 2.18 for the distress-risk model over the
12-month horizon (and decreases from 3.22 to 2.46 for the 24-month horizon).
Collectively, the in-sample and out-of-sample relative performance of the
distance-to-default and the distress-risk model over different horizons suggest that
the variation in the available data does not account for the fndings. DD adds little
forecasting power, particularly at short horizons. Also, in multiple regressions, DD
adds little to the CHS structural model. The in-sample R
? 2
for the distress risk model
and DD in the distress risk model is almost the same. At long horizons, DD catches
up and suggests that the distress model and DDare measuring similar things. As the
reduced form model accurately measures the risk of failure at different horizons, the
author obtains the premiumthat investors receive exclusively for holding distressed
stocks.
?1.5
-1
?0.5
0
0.5
1
1.5
?2 ?1.5 ?1 ?0.5 0 0.5 1 1.5
A
v
e
r
a
g
e
e
x
c
e
s
s
r
e
t
u
r
n
Predicted value
Quin?le 1
Quin?le 2
Quin?le 3
Quin?le 4
Quin?le 5
Figure 2.
Average excess return
versus prediction of the
Carhart 4F model
115
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Table V.
Distance to default and
our distress risk model
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4.5 Cross-sectional evidence
So far, the evidence from the previous subsections demonstrates that there is a link
between momentum and distress risk, and the multifactor models perform reasonably
well in uncovering the underperformance (or over-performance) of high-distressed
stocks (or safer stocks) at various quintiles of size and BE/ME ratio. It is however not
clear whether the performance of small-size and high- BE/ME stocks is tied to the fact
that they are relatively distressed. The author also observes that the role of size or value
factors is not much pronounced in the estimation, as their loading hardly explains the
overall variability of portfolio returns. Most importantly, it is not apparent to what
extent momentum infuences the size and value premium in an effort to uncover the
spread in returns of distressed frms. To disentangle this somewhat muddy relationship
between size, BE/ME and momentum, in this subsection, the author conducts a
comprehensive cross-sectional analysis by employing Fama and MacBeth’s (1973)
two-pass methodology.
To test whether various common risk factors can explain the cross-sectional
variability of average portfolio returns, which are related to distress risk, the author
proceeds as follows. For each month, frst the author ranks all stocks in the sample into
two groups – small and big, according to their market capitalization. Then the author
ranks each of theminto two groups – lowand high, according to their BE/MEratio. Each
of these resulting four groups is then ranked into two momentumgroups – winners and
losers, which are further subdivided into three distress groups based on their low-,
medium- or high-distress scores. This four-way ranking gives us 24 portfolios through
the intersections of size, BE/ME, momentum and distress risk. The dependent variable
is the excess returns of all the artifcial portfolios for each month. The set of the
explanatory variables, which can potentially explain the cross-sectional variation of
returns, consists of size, BE/ME, momentum, three dummy variables for three distress
groups and the interaction between momentum and distress dummies. In the second
step of the two-pass methodology, the author runs the following cross-sectional
multivariate regression for each month:
R
it
? RF
t
? ?
0,t
? ?
1t
?
i, t?1
? ?
2t
ln(Size
i,t?1
) ? ?
3t
ln(BM
i,t?1
) ? ?
4t
Mom
i,t?1
? ?
5t
D1
i,t?1
? ?
6t
D2
i,t?1
? ?
7t
D3
i,t?1
? ?
8t
(D1
i,t?1
*Mom
i,t?1
)
? ?
9t
(D2
i,t?1
*Mom
i,t?1
) ? ?
10t
(D3
i,t?1
*Mom
i,t?1
) ? ?
it
,
(4)
where R
it
?RF
t
is the excess return of portfolio i in month t; ?
i, t?1
is the beta of portfolio;
i estimated at period t ? 1; ln(Size
i,t?1
) and ln(BM
i,t?1
) are the natural logarithms of
average ME and BE/ME ratios, respectively, of stocks in portfolio i at period t ? 1;
Mom
i,t?1
average monthly momentum returns of all the stocks in portfolio i at period
t ? 1; D1
i,t?1
, D2
i,t?1
and D3
i,t?1
are three dummy variables indicating whether the
distress risk is low, medium or high, respectively. The author re-estimates the dummy
variables for each period with historically available data. The estimation results based
on various versions of (4) are reported in Table VI.
Several parts of the cross-sectional results are consistent with the previous fndings
from Tables II to IV. The estimation of the simplest model specifcation (i) suggests the
limited ability of the single-factor model to explain the cross-sectional differences in the
portfolio returns. Even though the price of market risk is quite high (?0.42 per cent per
117
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Table VI.
Fama–MacBeth
regressions of stock
returns on frm
characteristics and
distress risk dummy
variables
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month) and statistically signifcant (with an absolute value of t-statistics ?2.53), around
81 per cent of total variation in the average portfolio returns remain unexplained. When
the author includes all three dummy variables related to distress risk (model ii-iv), the
price of market risk decreases marginally, and the adjusted R
2
shows some
improvement. The coeffcient of the high-distress risk dummy is negative (?0.43 per
cent per month), which suggests raw underperformance of the high-distressed frms.
The coeffcient of the low-distress dummy is always positive and statistically
signifcant (at least at the 5 per cent level). When the author adds size and BE/ME ratio
in the cross-sectional regression (model v), the author fnds some interesting fndings.
There is modest negative size effect (the only time in all of the cross-sectional
experiments), as large frms underperform small frms by 19 basis points. There is also
a positive value effect. The high- BE/ME stocks outperform low- BE/ME stocks by 56
basis points.
Interestingly, when the author adds all three distress risk dummies, which is given
by model vi, the modest size effect disappears as the slope coeffcient of ln(Size) become
statistically insignifcant. This indicates that the distress risk may subsume the size
effect, or the size factor is not proxying for the distress risk, at least in the cross-section.
The addition of the distress risk dummies has a downward effect on ln(BE/ME), but its
slope remains statistically signifcant at the 1 per cent level (the corresponding
t-statistics takes a value of 2.61). When the author adds momentumin the model, which
is given by model vii, ln(Size) still remains insignifcant but the price of ln(BE/ME)
increases marginally. The addition of the momentumalso makes the price of market risk
statistically signifcant at the 5 per cent level (e.g. compare model vi and vii). When the
author adds all distress risk dummies in the presence of all three frmcharacteristics (i.e.
model viii), the coeffcient of momentum decreases to 0.39 per cent per month (with a
t-stat ? 2.34). The slope coeffcient of ln(Size) however shows no improvement.
Altogether, the cross-sectional results reveal that both size and momentum may proxy
for same type of systematic risk, whereas the BE/ME ratio proxies for some other
independent state variable[13].
Finally, the addition of the interaction variables between momentum and distress
risk dummies (i.e. model ix) suggests some interesting fndings. The slope coeffcients of
ln(BE/ME) and momentum still remain signifcant even though their magnitude
decreases slightly. The price of market risk and size becomes economically meaningless.
Only the low-distress risk dummy variable displays statistically signifcant slope
estimate. The addition of the interaction terms makes the other two dummy variables’
slope redundant. The interaction between momentumand low-distress dummy variable
displays a statistically signifcant (at the 5 per cent level) slope estimate of 18 per cent
per month. The addition of the distress factor dummies always increases the overall
explanatory power of the model, and the low-distress risk dummy is the only one that
acts as one of the important determinant of the cross-sectional variation in average
returns. Altogether, the cross-sectional results reinforce the viewthat the size and value
effects are not due to distress risk. Also, momentum is not concentrated in highly
distressed frms, and therefore is not proxying for distress risk.
5. Conclusions
The primary purpose of this paper is to investigate the relationship between frm-level
characteristics and the variability of the average portfolio returns of distressed frms.
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Using a recent measure of fnancial distress (Campbell et al., 2008), the author provides
empirical evidence on the existence of distress risk premium, and its interaction with
frmsize and book-to-market ratio ( BE/ME). The author highlights the individual effect
of momentum on the variability of the distressed frm’s average returns. The result
supports the view that distress generates a negative risk premium, and the size and
value effects are not due to distress risk.
The main surprising fnding of the paper is that, contrary to the existing empirical
evidence, momentumin the sample does not proxy for distress risk. The results indicate
that momentum may explain time-variation of average returns of low-distressed
portfolios, which consists of safer stocks. The author fnds that, in the cross-sectional
analysis, momentum subsumes the effect of size risk. Also, in the cross-section, the
BE/ME ratio acts as an unique proxy for some particular state variable, which is
independent of both momentum and size.
One can extend the research in many directions. While it is clear that a positive
distress risk premium is not associated with higher average returns of small-size and
high- BE/ME stocks, the analysis hardly throws any light on the characterization of
volatility persistence, and the limitations of common risk factors in the risk premium
estimation of distressed stocks. It is also not evident whether any shock to systematic
risk can play a role in explaining the negative distress risk premium. Finally, an
empirical study that includes both fnancial constraints and momentum in the analysis
of distress risk premium would be an interesting project.
Notes
1. The literature has also documented a number of asset pricing anomalies that persist following
their discovery. These include past returns (short-term momentum and long-run reversal),
earnings momentum, dispersion, accruals, credit risk (level and changes) and idiosyncratic
volatility effects.
2. Altogether, the argument that higher risk assets should generate higher returns is a puzzle in
the distress risk literature, which suggests that high distress risk is negatively associated
with future returns.
3. There is a subtle difference between the present approach and the method used by Campbell
et al. (2008). In contrast to Campbell et al. (2008), the author does not re-estimate the distress
probabilities using only historically available data. Furthermore, it is important to note that
the current results of this paper and Campbell et al. (2008) may not be reliably comparable.
Other studies such as Griffn and Lemmon (2002) also implemented rolling estimates of
distress scores using past data.
4. Numerous studies show that the abnormal returns gained by small frms have not persisted
after the period they were documented. Although momentum is still an anomaly, that is not
the case for size. Schwert (2003) provides a good summary of the disappearance of some of the
anomalies.
5. The idea of the KMVmeasure can be traced back to the Merton (1974) model, where corporate
debt is modeled as a risk-free bound less a put option on the value of the frm’s assets, with a
strike price equal to the face value of the debt.
6. For the details on the construction of these variables and related technical issues, please see
CHS (2008).
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7. Additional details about the construction and features of individual portfolios are available
from the author on request.
8.http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html#Research
9. In other results, which are related to portfolio characteristics, the author observes that the
average size of the lower decile stocks is larger than the higher decile counterpart (not
reported). Also, the book-to-market ratio of median stocks is lower than that of both high- and
low-distressed stocks.
10. Some descriptive statistics in this paper are however quite different to those in CHS (2008) and
deserve a comment. For example, CHS (2008) report annualized excess return of 0.97 per cent
for the second lowest-distress risk decile, while this paper reports monthly excess return of
0.98 per cent for the same decile. CHS (2008) report monthly excess return of 0.95 per cent for
the long–short portfolio, while this paper reports monthly excess return of 1.69 per cent for the
same portfolio. CHS (2008) report positive portfolio skewness for highest-distressed portfolio,
while in this case, the skewness is negative. The author conjectures that a different sample
period may attribute these differences. The results corresponding to CHS (2008) sample
corresponds closely to their paper.
11. In other words, the 3F model amplifes the poor performance of distressed stocks, and the 4F
model shows better performance (i.e. corrects for risk) than either the CAPM or the
three-factor model.
12. It is important to note that the fnding of distress-driven momentum strategy only for
low-distressed stocks is only partially consistent with Avramov et al.’s (2007) result. The
author supposes that it has something to do with fact that a broader set of stocks and an
extended period are used. In contrast to the sample, Avramov et al. (2007) use only the sample
of 3,578 stocks with valid credit rating from S&P. They also use a short sample period from
July 1985 to December 2003.
13. Note that, the author computes the distress score using control variables that includes size
proxy, BE/ME ratio and excess returns. As such, the distress score is potentially correlated
with frm size, BE/ME and momentum by construction. The author avoids the potential
multicollinearity problem by orthogonalization, and the cross-sectional test using the new
dummies also yields very similar results as in Table V.
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Financial Studies, Vol. 6 No. 3, pp. 659-681.
Chan, L., Jegadeesh, N. and Lakonishok, J. (1996), “Momentum strategies”, Journal of Finance,
Vol. 51 No. 5, pp. 1681-1713.
About the author
Prodosh Simlai is Associate Professor at the University of North Dakota, USA. His research
interest includes general fnancial markets, empirical asset pricing, portfolio management and
microstructure impacts of effciencies. He has authored numerous articles in economics and
fnance journals, as well as book chapters. He is an active member of the American Finance
Association, Eastern Finance Association, Midwest Finance Association, Southern Finance
Association and Southwestern Finance Association. He has worked in various consultancy
positions, and has given numerous seminars on risk modeling and the econometrics of fnancial
markets. He received his PhDin economics and MS in fnance both fromthe University of Illinois
at Urbana-Champaign, USA.
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123
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