Download Is Default Risk Priced in Equity Returns?

Is Default Risk Priced in Equity Returns?
Is Default Risk Priced in Equity Returns?
Caren Yinxia G. Nielsen
The Knut Wicksell Centre for Financial Studies
Caren Yinxia G. Nielsen | The Knut Wicksell Centre for Financial Studies
Size and book-to-market equity (BM) strongly explain stock returns’ cross section; the risk they capture is the
relative distress of small and value stocks. This study examines the default risk’s pricing power, measured by
U.S. firms’ market-revealed credit-default-swap premiums (2004–2010), in average returns across stocks. It
also explores whether the size and BM effects stem from proxying the default-risk effect. In the tests, size
dominates the size–default-risk effect, while BM and default risk work together. Therefore, size and BM
partially proxy the default-risk effect. As expected, size is priced with a negative risk premium and BM is
positive. However, higher default risk only engenders higher expected stock returns when BM is below a
threshold and unpriced. Additionally, size indeed proxies sensitivity to the default-risk factor. Furthermore,
the Fama–French factors SMB (small-minus-big) and HML (high-minus-low) share some common information with the default-risk factor in asset-pricing tests.
Knut Wicksell Working Paper 2013:2
Keywords: Asset Pricing; Equity Returns; Size Effect; Book-to-Market Effect; Default-Risk Effect; CreditDefault-Swap Premium
JEL classification: G12
Working papers
The Knut Wicksell Centre for Financial Studies
The Knut Wicksell Centre for Financial Studies conducts cutting-edge research in financial economics and
related academic disciplines. Established in 2011, the Centre is a collaboration between Lund University
School of Economics and Management and the Research Institute of Industrial Economics (IFN) in Stockholm.
The Centre supports research projects, arranges seminars, and organizes conferences. A key goal of the
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topics related to financial markets.
Lund University
School of Economics and Management
Working paper 2013:2
The Knut Wicksell Centre for Financial Studies
Printed by Media-Tryck, Lund, Sweden 2013
Editor: F. Lundtofte
The Knut Wicksell Centre for Financial Studies
Lund University
School of Economics and Management
Is Default Risk Priced in Equity Returns?
1
Is Default Risk Priced in Equity Returns?
Caren Yinxia G. Nielsen*
Abstract
Size and book-to-market equity (BM) strongly explain stock returns’ cross section; the risk
they capture is the relative distress of small and value stocks. This study examines the default
risk’s pricing power, measured by U.S. firms’ market-revealed credit-default-swap premiums
(2004–2010), in average returns across stocks. It also explores whether the size and BM
effects stem from proxying the default-risk effect. In the tests, size dominates the size–
default-risk effect, while BM and default risk work together. Therefore, size and BM partially
proxy the default-risk effect. As expected, size is priced with a negative risk premium and
BM is positive. However, higher default risk only engenders higher expected stock returns
when BM is below a threshold and unpriced. Additionally, size indeed proxies sensitivity to
the default-risk factor. Furthermore, the Fama–French factors SMB (small-minus-big) and
HML (high-minus-low) share some common information with the default-risk factor in assetpricing tests.
Keywords: Asset Pricing; Equity Returns; Size Effect; Book-to-Market Effect; Default-Risk
Effect; Credit-Default-Swap Premium
JEL classification: G12
*
Department of Economics, Knut Wicksell Centre of Financial Studies, Lund University, P. O. Box 7082,
S-220 07 Lund, Sweden. Tel.: +46 46 222 4290; E-mail: [email protected]. I started
this paper when I was a visiting student at Århus University in Denmark.
Is Default Risk Priced in Equity Returns?
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The capital asset pricing model (CAPM) developed by Sharpe (1964) and Lintner (1965) has
paved the way how people think about asset returns and market risk. However, in empirical
research, there exist portfolios not included in the CAPM, the “anomalies,” that successfully
explain average stock returns. One typical example is the success of the zero-investment
SMB and HML1 portfolios from Fama and French (FF; 1992, 1993, 1995 and 1996).
Fama and French state that size or market equity (ME, stock price times number of
shares) and book-to-market equity (BM, ratio of a common stock’s book value to its market
value) strongly explain the cross section of stock returns. Stocks with smaller ME and higher
BM earn higher expected returns. As FF (1993) suggest, the reasons for these ME and BM
effects lie in ME’s and BM’s association with financial distress. Therefore, small and value
stocks (with high BM) should be compensated due to their high sensitivities to state variables,
such as specific business-cycle factors. More aggressively, the three-factor model (the factors
are the excess market return over the risk-free rate, SMB and HML) is an equilibrium pricing
model, a three-factor version of Merton’s (1973) intertemporal capital asset pricing model or
Ross’s (1976) arbitrage pricing theory (FF; 1993, 1995 and 1996). In this view, SMB and
HML mimic combinations of two underlying risk factors or state variables of special hedging
concern to investors. However, they could not identify these two state variables.
The explanation of the ME and BM effects remain a puzzle. While some researchers,
such as Lakonishok et al. (1994), Daniel and Titman (1997) et cetera, explore behavioral
stories, others investigate whether the equity market prices a firm’s financial distress with a
positive premium in the framework of the rational pricing theory.
However, the conclusions of the studies in the rational pricing field do not agree.
Some find a positive value premium, a possible explanation of the ME and BM effects, with
1
SMB (HML) is small minus big (high minus low), referring to the difference in returns on portfolios of small
(high book-to-market) stocks and large (low book-to-market) stocks.
Is Default Risk Priced in Equity Returns?
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default risk as the proxy for the financial distress. Chan et al. (1985) measure default risk by
the credit spread between low-grade bonds and long-term government bonds, explaining a
large portion of the ME effect. Vassalou and Xing (2004) employ the default probabilities,
computed by Merton’s (1974) option pricing model, as the proxies for individual firms’
default risks, concluding that both the ME and BM effects can be viewed as default effects
and that SMB and HML appear to contain additional information that is not related to default
risk. Chan-Lau (2006) uses a systematic default-risk measure extracted from collateralized
debt obligations, referring to standardized North America investment-grade credit-derivative
indices. He finds that the systematic default risk is an important determinant of equity returns
beside the Fama–French three factors. Chava and Purnanandam (2010) use ex ante estimates
of expected returns based on the implied cost of capital and apply hazard-rate estimation and
expected default frequency to measure default risk. They find a positive relationship between
expected stock returns and default risk when including ME and BM as control variables.
However, others reveal a negative distress premium or mispricing argument of the
BM effect. Dichev (1998) shows that bankruptcy risk, through Altman’s (1968) Z-score and
Ohlson’s (1980) O-score, is not rewarded by higher returns. Campbell et al. (2008) estimate
bankruptcy risk with a dynamic logit model: Financially distressed stocks have delivered
anomalously low returns. Avramov et al. (2009) use credit ratings, finding higher returns for
low-credit-risk than high-credit-risk firms. Griffin and Lemmon (2002) apply Ohlson’s Oscore as a proxy for distress risk, demonstrating BM effect reveals among firms with the
highest distress risk; this BM premium is due to the mispricing of high distress risk rather
than the risk-based explanation.
The disagreement of previous research appears to result from using different proxies
for financial distress. We consider default risk as the most intuitive proxy. However, how
much of the default-risk information is of special hedging concern to investors varies with the
Is Default Risk Priced in Equity Returns?
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state of the economy and government policies. Therefore, this study employs the default risk
under the risk-neutral measure revealed from the credit-default-swap (CDS) market.
This choice of the proxy for financial distress is also consistent with Ozdagli’s (2010)
theoretical argument that the positive value premium and the negative distress premium result
from using the risk-neutral and real default probability, respectively. His model also predicts
that firms with higher risk-neutral default probabilities, such as those revealed from credit
default swap premiums (CDSP), should have higher stock returns.
Additionally, the advantages of choosing the CDS market also lie in the properties of
the CDS and its importance in financial markets.
First, a CDS is a contract of protection against default. The protection buyer pays
periodic premiums to the protection seller in exchange for compensation in the event of
default by the reference entity. CDS isolates default risk from other risks faced by a firm.
Therefore, it could be argued to be a clean measure of default risk.
Second, the CDSP is market based, not accounting data as O-score and Z-score that
suffer from being backward looking. The market-quoted CDSP directly reflect the market
perceptions of the referred firms’ default risk. In this study, the default risk is the uncertainty
surrounding a firm’s ability to service its debts and obligations, rather than the risk of facing
bankruptcy (Chapter 11) or liquidation. Even though these two concepts are correlated, in the
view of the pricing power in equity returns, the risk of not paying debts is normally an earlier
negative shock and more powerful in driving investors’ expectations compared to the risk of
bankruptcy or liquidation. Furthermore, CDS is the most liquid default derivative and takes
the biggest proportion of the market trading.
Finally, many studies have demonstrated that the CDS market is more important in
revealing the information of credit risk compared to the bond market (Longstaff et al., 2003;
Blanco et al., 2005; Norden and Weber, 2009; Forte and Peña, 2009). Elton et al. (2001)
Is Default Risk Priced in Equity Returns?
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display that much of the information in the default spread in bonds is unrelated to default risk.
Equity traders have turned their attention first to the CDS market before trading has been
reported, especially during the recent financial crisis (Gaffen, 2008).
From the perspective of asset pricing, default risk could affect investors’ expectations
of future wealth, consumption and investment opportunities, which are linked to state
variables. During financial turmoil, the marginal utility of buying protection against default
risk, such as a CDS contract, is much higher simply because the situation of other assets is
very bad. This intertemporal shift of marginal utility could reveal changes in the state
variables. Therefore, default risk could be systematically priced and even help price other
assets. Furthermore, Ferguson and Shockley (2003) demonstrate that the true CAPM should
include both equity and debt claims in the market portfolio. This theoretical model explains
why the debt-related variables, such as ME and BM, have strong explanatory power for the
cross section of average returns. Hence, default risk, proxied by the CDSP, has a relation to
the ME and BM effects from the perspective of asset pricing.
The purpose of this study is to investigate the pricing power of default risk, measured
by the CDSP, in average stock returns and to determine whether the ME and BM effects are
due to their proxying for the default risk. The overall analysis considers three aspects. First, it
examines whether a default-risk effect exists for portfolios and individual stocks to
demonstrate whether default risk is priced in equity returns. Second, it explores the
relationship between the default-risk effect and the ME and BM effects for portfolios and
individual stocks. Third, it tests whether ME and BM are related to the loadings on the
default-risk factor, assumed to be one of the underlying common risks in stock returns.
My contribution to the research is to use only the default risk of concern to the
investors in the market, the default risk under the risk-neutral measure revealed from the
CDS market, to investigate the pricing of firms’ financial distress. Additionally, this study
Is Default Risk Priced in Equity Returns?
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specifically focuses on the explanation of the ME and BM effects. Furthermore, the CDSP
data are for individual U.S. firms (2004–2010), rarely used in studying equity returns, and
hand picked to match existing data from accounting and the stock market.
In brief, I find that there exists a joint effect of ME or BM with default risk on
portfolio returns. Furthermore, the ME effect dominates its joint effect with default risk,
while both BM and default risk co-work for their joint effect. Fama and MacBeth’s (FM;
1973) regressions on individual firms prove that ME and BM have explanatory power for the
variation of returns across stocks, but the BM effect is only significant when the default-risk
term and an interaction term of BM and default risk are also in the regressions. ME is priced
with a negative risk premium; BM is priced with a positive risk premium. Only when BM is
below a certain level, and is not priced, is higher default risk priced with higher stock returns.
Additionally, the factor loadings of portfolios show that ME does proxy sensitivity to the
default-risk factor. Therefore, default risk could be the underlying risk factor of the ME effect.
Although tests on the asset pricing models cannot provide strong evidence that DHML (high
minus low for the default-risk factor) should be considered a significant factor in asset
pricing, DHML does share common information with other factors and cannot be ignored.
I process the analysis as follows. Section 1 describes the data. Section 2 investigates
the relationship of the default-risk effect and the ME and BM effects by intuitive portfolio
groupings. To analyze these relationships more formally, Section 3 applies FM regressions to
individual stocks to examine the explanatory power of ME, BM and default risk in stock
returns and their relationships. Section 4 examines the factor loadings and investigates
whether ME and BM proxy for the sensitivities to the default-risk factor, which has been
declared as one explanation for the ME and BM effects. Section 5 conducts the asset-pricing
tests on the factors using discount-factor pricing models. Section 6 concludes.
Is Default Risk Priced in Equity Returns?
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1. Data
This study applies the analysis to all individual nonfinancial firms in the U.S. market with
matched data from the equity market, accounting and credit-derivative market. The data set is
the intersection of daily common stock files on major stock exchanges (NYSE, AMEX,
NASDAQ) from the Center for Research in Security Prices (CRSP), balance-sheet data in
COMPUSTAT’s fundamentals quarterly file and CDS data from Credit Market Analysis
(CMA)2. Each firm’s annual reports are checked to ensure the firms from the different data
sets match. The data set consists of 467 firms with matched data. The market returns, T-bill
rates and SMB and HML data are from Kenneth R. French’s home page3.
Stock and accounting data are from January 2003 through September 2010 and CDS
data are from January 2004 to September 2010 because more recent CDS data are more
efficient due to the newness of the market, and we need one year preceding 2004 for stocks to
estimate market βs used in the FM regressions. The study uses weekly data to minimize the
microstructure effects of high-frequent data and also to maintain the tests statistical power.
Firms’ weekly returns are holding-period returns adjusted for all distributions (such as
dividends and splits) from the first to last trading date of a week (with Friday as the end of a
week). The value-weighted returns of all stocks on the main exchanges (NYSE, AMEX and
NASDAQ) proxy for market returns.
The book equities (BE, book value of common equity plus balance-sheet deferred
taxes) of stocks are quarterly data from COMPUSTAT because quarterly data reflect the
performance of a firm more effectively and quarterly earnings lead trading activities. When
calculating the BM ratio in each week, I use the ME on the last trading date before the BE
recording date for comparison to ensure a stock’s market information is publicly known
2
CMA data are collected through Thomson Datastream Navigator.
3
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/
Is Default Risk Priced in Equity Returns?
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before the accounting data are recorded. This ratio is influential only when ME and BE are
comparable; therefore, it is updated when BE is updated. Normally, firms are required to file
form 10-Q quarterly reports within 40 or 45 days and form 10-K annual reports within 75 or
90 days with the Securities and Exchange Commission. Therefore, assuming a two-month lag
on quarterly data (fiscal quarters 1, 2 and 3) and a three-month lag on annual data (fiscal
quarter 4)4 is reasonable. I measure a firm’s ME by its weekly ME, which is a stock’s price
multiplied by the number of share outstanding on the last trading date of a week.
The CDS data are the mid-premiums of 5-year senior CDSs from CMA. The prices of
the same security from different data sources, such as CMA, GFI, Fenics, Reuters EOD,
Markit and JP Morgan, differ to some degree. Compared to the other sources, CMA uses a
buy-side aggregation model and employs data from a variety of contributors, including major
global investment banks, hedge funds and asset managers. Furthermore, Mayordomo et al.
(2010) use the most liquid single-name 5-year CDS of the components of iTraxx and CDX to
compare the above six major data sources and find that the CMA database quotes lead the
price discovery process compared to the other data sources. I use Veracity Code provided by
CMA to control the quality of the data, eliminating all quotes with scoring higher than three,
because three or lower Veracity Score verify that the quote is associated with an actual trade
or that the quote is an indication provided by a market participant, not derived from a model.
2. ME, BM and Default Risk—Portfolio Approach
This section uses portfolio groupings to investigate the relationship between the ME or BM
effect and the default risk effect—as proxied by the CDSP. There are two hypotheses to test
in this sample. One is whether each of these three effects exists. This is equivalent to whether
ME, BM or CDSP explains the differences in average returns across stocks and whether
4
Standard & Poor’s analysis also uses these lags (http://www.standardandpoors.com).
Is Default Risk Priced in Equity Returns?
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stocks with smaller ME, higher BM or higher CDSP are rewarded with higher expected
returns. The other hypothesis concerns whether the ME or BM effect can be interpreted as the
default-risk effect; whether a default-risk effect exists after controlling for ME or BM or a
ME or BM effect exists after controlling for default risk. This test aims to explore the
interaction between the ME or BM effect and the default-risk effect, the joint effect and the
exclusive effect.
2.1. Correlations between ME, BM and CDSP
Table 1 displays the time-series averages of the cross-sectional correlation coefficients
between ME, BM and CDSP for all individual stocks and the corresponding p-values (for the
null hypothesis that the correlation is zero). The data are weekly data for the period from
January 2004 to September 2010.
The average cross-sectional correlation between ME and BM is significantly negative
at the 6% level. On average, CDSP is significantly negatively correlated with ME across
stocks. These results are consistent with the story that smaller stocks tend to have higher BM,
which results from their poor prospects, and smaller firms carry higher financial distress,
which induces a higher CDSP. Thus, the ME effect may interact with the BM effect and
proxy for a default-risk effect. The cross-sectional correlation between BM and CDSP does
not provide any information because on average, the correlation is essentially zero.
Table 1: Time-Series Average Correlation between ME, BM and CDSP
BM
CDSP
ME
Correlation
–0.1340*
–0.2195**
p-value
0.0572
0.0050
BM
Correlation p-value
1.0000
–0.0503
0.3308
ME is size; BM is book-to-market equity; CDSP is credit-default-swap premium. This table shows the timeseries averages of the cross-sectional correlation coefficients. “*”and “**” denote significances of the statistics
at 10% and 5% levels, respectively.
Is Default Risk Priced in Equity Returns? 10
2.2. Outline of the Analysis
To help readers understand the concepts more easily, this section provides an overview of the
analysis in the rest of Section 2 and brings up a summary of the results. Briefly, Section 2
examines the joint effect of ME and default risk, of BM and default risk, and the exclusive
effect of ME or BM after controlling for default risk and of default risk after controlling for
ME or BM. Joint effect here means the intersection of two effects, while exclusive effect
indicates the relative complement of one effect in the other effect. These analyses are used to
picture the interactions of the ME or BM effect with the default-risk effect.
Section 2.3 analyzes the relationship between the ME effect and the default-risk effect.
The results show that the ME effect dominates the joint effect of ME and default risk, there is
a strong ME effect after controlling for default risk, but the default-risk effect after
controlling for ME is very weak. The left picture in Graph 1 displays the overall relationship,
where the intersection of the two ellipses stands for the joint effect of ME and default risk
and the relative complement of one ellipse in the other stands for the exclusive effect
represented by the other ellipse. The ellipses’ relative sizes represent the effects’ relative
strengths.
Section 2.4 explores the relationship between the BM and default-risk effects. The
evidence suggests that both BM and default risk work for the joint effect, there is a BM effect
after controlling for default risk, but there is no default-risk effect after controlling for BM.
Additionally, compared to the case for ME, the exclusive effect of BM is weaker. The right
picture in Graph 1 gives an overview.
Is Default Risk Priced in Equity Returns? 11
Graph 1: Interrelation of ME or BM Effect and Default-Risk Effect
BM Effect,
Size Effect
Size
Effect
Default
Risk
Effect
BM Effect
Default Risk
Effect
The black ellipse represents the ME or BM effect and the grey one the default-risk effect. The intersection of the
two ellipses stands for the joint effect of ME or BM and default risk. The relative complement of one ellipse in
the other stands for the exclusive effect represented by the other ellipse. Furthermore, the relative sizes of the
ellipses show the relative strengths of the effects.
These findings provide evidence that part of the ME or BM effect could be interpreted
as default risk, especially for the BM effect. This is consistent with FF’s reasoning that small
stocks and value stocks earn higher expected returns because they are under relatively higher
financial distress. However, ME and BM contain more information than the financial distress
regarding the explanatory power for cross-sectional stock returns. Furthermore, the default
risk proxied by CDSP provides additional information about stock returns that cannot be
explained by ME.
2.3. The ME Effect and the Default-Risk Effect
2.3.1. Portfolios Formed on ME and CDSP Independently
To focus on the relation between ME effect and default-risk effect, we perform an
independent two-pass portfolio sort based on ME and CDSP. This sort is useful in exploring
the joint ME and default-risk effect on expected equity returns and their interaction in the
joint effect.
Is Default Risk Priced in Equity Returns? 12
Portfolios are formed quarterly5 . In the first week of each calendar quarter from
January 2004 to September 2010, all stocks are allocated into three size portfolios according
to the ME breakpoints determined using the market capitalizations of NYSE stocks6 . Then
each ME tertile is subdivided into three CDSP portfolios based on CDSP breakpoints
determined from all firms. Thereafter, we calculate the equal-weighted weekly returns,
market capitalizations, BM and CDSP for the resulting nine portfolios for the rest of the
quarter and the first week of the next quarter. Here, the values of ME and CDSP for each
stock are the same across each calendar quarter. Table 2 shows the time-series average of the
equal-weighted returns, ME, BM and CDSP, and the post-ranking market
for each of the
nine portfolios, as well as for each of the portfolios sorted on just ME or CDSP (All). The
market
is an estimator of the time-series slope of the portfolio’s excess returns over risk-
free rates on the excess market returns. Additionally, Panel B displays the average returns on
some specific zero-investment portfolios to further explore the joint effect of ME and default
risk.
Panel A shows that for the whole sample (All), average stock return does increase
monotonically as ME decreases or as default risk increases. Though the return differences are
statistically insignificant, these effects are still considerable. The return difference between
small- and big-stock portfolios (Small–Big) is 0.126% weekly (6.552% annually) and that for
high- and low-default-risk portfolios (High–Low) is 0.058% weekly (3.016% annually).
Additionally, the insignificance might result from the small cross-sectional sample used in
this study.
5
Although forming portfolios more frequently might produce more significant results, this study applies quarterly formation
because accounting data are updated quarterly.
6
Breakpoints are based on the NYSE because capitalization is closed relative to the stock exchange and NASDAQ stocks
are mainly small. Robustness tests using all stocks to determine size breakpoints produced qualitatively similar results.
Is Default Risk Priced in Equity Returns? 13
Table 2: Portfolios Formed on ME and CDSP Independently
All
Panel A: Average Return
All
ME-Small
0.249
ME-Medium
0.210
ME-Big
0.124
Small–Big
0.126(0.78)
CDSP-Low
0.165
0.237
0.227
0.130
0.107(1.09)
CDSP-Medium
0.189
0.252
0.196
0.134
0.118(1.57)
CDSP-High
0.223
0.234
0.217
–0.052
0.286(1.25)
Panel B: Average Return of Zero-Investment Portfolio
SH-ML
0.007(0.03)
SH-BL
SH-BL
0.104(0.44)
SH-BM
MH-BL
0.087(0.66)
SM-BL
SL-MH
0.020(0.17)
BH-SL
SL-BH
0.288(2.06)
BH-SM
ML-BH
0.279(2.06)
BM-SL
0.104(0.44)
0.100(0.52)
0.122(1.28)
–0.288(–2.06)
–0.304(–2.18)
–0.102(–1.23)
Panel C: Average ME
All
ME-Small
2.48
ME-Medium
9.16
ME-Big
49.78
42.90
3.54
9.94
60.40
13.56
3.09
9.28
31.13
5.44
2.13
8.20
23.81
Panel D: Average CDSP
All
ME-Small
392.8
ME-Medium
134.2
ME-Big
60.4
35.2
43.6
37.8
33.5
82.2
85.2
84.1
76.6
0.058(0.28)
–0.003(–0.01)
–0.010(–0.08)
–0.182(–1.30)
471.0
553.0
312.5
270.5
Panel E: Average BM ratio
All
ME-Small
0.669
ME-Medium
0.473
ME-Big
0.389
0.373
0.591
0.417
0.335
0.548
0.633
0.525
0.498
0.611
0.692
0.453
0.459
Panel F: Market
All
ME-Small
ME-Medium
ME-Big
0.840
1.141
0.848
0.814
1.067
1.134
1.061
1.013
1.692
1.817
1.472
1.235
1.596
1.107
0.896
High–Low
Portfolios are independently formed quarterly on size (ME) and credit-default-swap premium (CDSP) each with
6 to 66 stocks on average. This table shows the time-series average of the equal-weighted returns (in percent),
ME (in billions of dollars), book-to-market equities (BM) and CDSP (in basis points), and the post-ranking
market for each of the portfolios, as well as for each of the portfolios only sorted on ME or CDSP (All).
Small–Big and High–Low indicate the return differences between small and big stocks and between high- and
low-default-risk stocks, respectively. Corresponding t-statistics calculated from Newey-West standard errors are
in parentheses.
The rest of the analysis focuses on the nine portfolios displayed in the centers of
Panels A, C to F and the specific portfolios in Panel B. Panel A provides evidence of an
interaction between the ME and default-risk effects. First, an overview picture shows that
there are ME and default-risk effects on stock returns. Among the nine portfolios, the average
returns on small-stock portfolios (higher than 0.23% per week) are higher than those on big-
Is Default Risk Priced in Equity Returns? 14
stock portfolios (lower than 0.14% per week). There is also a sign of the correspondence
between high default risk and high average return. The average returns on the high-defaultrisk portfolios, with small and medium ME, are higher than 0.21%, while the average return
on the low-default-risk portfolio, with big ME, is 0.13% weekly. Second, there is a joint ME–
default-risk effect. Small- and high-default-risk stocks deliver quite high average return
(0.23% per week) and big- and low-default-risk stocks deliver quite low average return
(0.13% per week). Third, for the joint ME–default-risk effect, the ME effect dominates the
default-risk effect. This is the case because the average return on the portfolio of big stocks
but with high default risk is negative (–0.05% per week), and stocks with small or medium
ME but low default risk earn average returns higher than 0.22% per week.
To explore this joint effect, Panel B exhibits the average returns on some specific
zero-investment portfolios. The first label of each portfolio is for ME (S, M and B for small,
medium and big) and the second is for CDSP (H, M and L for high, medium and low). The
upper part of Panel B explores the joint effect of ME and default risk. The upper-left part
displays the return differences of high- and low-default-risk stocks with variant differences in
ME (long positions in smaller stocks and short positions in bigger stocks). These three zeroinvestment portfolios show the joint effect of ME and default risk with a focus on the defaultrisk effect. The average returns are all positive although statistically insignificant. Similarly,
the upper-right part presents the joint effect with a focus on the ME effect. The average
returns of these portfolios are slightly higher, especially for the portfolio SM-BL on which
the return has a high t-statistic. The positive average returns on these six zero-investment
portfolios provide evidence that there is a joint ME–default-risk effect.
Which effect plays a more important role in this joint effect? What is the interaction
of ME and default risk in this joint effect? The lower part of Panel B answers these questions
where we perform a different investment strategy by emphasizing one effect and reversing
Is Default Risk Priced in Equity Returns? 15
the other one completely. The lower-left part presents the portfolios with long positions in
smaller stocks but with low default risk and short positions in bigger stocks but with high
default risk (emphasizing the ME effect and reversing the default-risk effect); the lower-right
part shows the portfolios with long positions in higher default-risk stocks of big ME and
short positions in lower default-risk stocks of small ME (emphasizing the default-risk effect
and reversing the ME effect). The outcomes are used to distinguish the possible different
strengths of the two effects in the joint effect.
That the ME effect dominates the default-risk effect is obvious. Compared to the
corresponding portfolios in the upper part, the portfolios with reversed positions implied by
the default-risk effect (the lower-left part) exhibit stronger ME effect, but the portfolios with
reversed positions implied by the ME effect (the lower-right part) show no sign of any
default-risk effect.
The rest of Table 2 presents the ME, CDSP, BM ratios and market s of the nine
portfolios. There is only a large variation in ME or CDSP among the portfolios. This
confirms that the variation of the average returns is due to the variations of ME and default
risk. Furthermore, the ME and CDSP verify the results from Panel B that there is a joint
effect of ME and default risk, but the ME effect dominates the default-risk effect. The
portfolio with the smallest ME ($2.13 billion) and highest CDSP (553 basis points) has a high
average return (0.234% per week); the portfolio with the largest ME ($60.4 billion) and
lowest CDSP (33.5 basis points) has a relatively low average return (0.13% per week).
However, the portfolio with the highest average return (0.252% per week) is the one with a
small ME ($3.09 billion) but medium CDSP (85.2 basis points); the portfolio with the lowest
average return (–0.052% per week) is characterized with a big ME ($23.81 billion) but high
CDSP (270.5 basis points).
Is Default Risk Priced in Equity Returns? 16
For the nine portfolios, the BM ratio tends to increase as ME decreases or default risk
increases, but the relation is not monotonic and the variation of BM is not great. Notice that
there is a strong relation between market
medium-CDSP portfolio, market
and CDSP or ME. Except for the small-ME–
increases monotonically as ME decreases or CDSP
increases within each ME or CDSP tertile. However, when we rank all nine portfolios
together, this trend breaks down dramatically for ME, but remains strong for CDSP. Notably,
the portfolios with high market s (higher than 1.2) are characterized with high default risk.
This provides evidence that default risk is linked to market risk and should be priced in
equity returns.
2.3.2. Portfolios Formed on ME and CDSP Sequentially
In this section, stocks are sorted sequentially on ME and CDSP to examine the existence of
one effect after controlling for the other, the exclusive effect. The sequential sorts are
performed here because independent sorts applied in Section 2.3.1 cannot separate the two
effects completely; the ME and CDSP breakpoints derived from the whole sample are
possibly correlated. For example, within each ME tertile, the default-risk effect might be
related to ME because of the significant negative correlation between CDSP and ME for the
whole sample. Another advantage of sequential sorts is that the number of stocks in each
portfolio is even greater, which results in more reliable t-statistics.
First, we perform a two-pass sort on CDSP and then ME to investigate the ME effect
after controlling for default risk. Portfolios are formed quarterly. In the first week of each
calendar quarter, all stocks are allocated to three CDSP portfolios according to the CDSP
breakpoints for all firms. Then each CDSP tertile is subdivided into three ME portfolios by
the ME breakpoints only for the stocks in the tertile. Table 3 shows the time-series average of
the equal-weighted returns, ME, BM and CDSP, and the market
for each of the nine
resulting portfolios, as well as for each of the portfolios only sorted on CDSP or ME (All).
Is Default Risk Priced in Equity Returns? 17
Table 3: Portfolios Formed on CDSP and then ME
All
ME-Small
Panel A: Average Return
All
CDSP-Low
0.165
CDSP-Medium
0.189
CDSP-High
0.223
0.249
0.226
0.234
0.343
Panel B: Average Size
All
CDSP-low
42.90
CDSP-Medium
13.56
CDSP-High
5.44
2.48
8.68
3.24
1.21
Panel C: Average CDSP
All
CDSP-low
35.2
CDSP-Medium
82.2
CDSP-High
471.0
392.8
38.6
86.1
696.4
ME-Medium
0.210
0.197
0.181
0.137
9.16
22.65
8.74
3.32
134.2
36.4
83.2
401.8
ME-Big
Small–Big
0.124
0.079
0.161
0.193
0.126(0.78)
0.147(2.51)
0.073(1.01)
0.150(0.75)
49.78
92.97
27.67
12.03
60.4
30.9
77.9
301.7
Panel D: Average BM Ratio
All
CDSP-low
0.373
CDSP-Medium
0.548
CDSP-High
0.611
0.669
0.450
0.631
0.809
0.473
0.378
0.525
0.556
0.389
0.299
0.493
0.458
Panel E: Market
All
CDSP-low
CDSP-Medium
CDSP-High
1.596
0.889
1.149
2.078
1.107
0.887
1.055
1.543
0.896
0.751
1.008
1.430
0.840
1.067
1.692
Portfolios are formed quarterly on credit-default-swap premium (CDSP) and then size (ME) sequentially. On
average, there are 32 to 35 stocks in each of the resulting nine portfolios. This table shows the time-series
average of the equal-weighted returns (in percent), ME (in billions of dollars), book-to-market equities (BM)
and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the
portfolios only sorted on ME or CDSP (All). Small–Big indicates the return difference between small and big
stocks. In the parentheses are the corresponding t-statistics calculated from Newey-West standard errors.
Is there any ME effect after controlling for default risk? Panel A shows that within the
CDSP-low and CDSP-medium tertiles, average return is negatively monotonically related to
ME, and the return difference is positive within each CDSP tertile. Especially within the
CDSP-low tertile, the average return difference between the small and big stocks is 0.147%
weekly (7.644% annually) and statistically significant. Therefore, after controlling for default
risk, ME does capture some common risk factors in stock returns.
The rest of the table confirms that the effect we found is due to the variation of ME
not to variations in other variables. There is indeed a large variation in the market
capitalizations of stocks within each CDSP tertile, especially within the CDSP-low tertile.
Is Default Risk Priced in Equity Returns? 18
Second, we examine the existence of any default-risk effect after controlling for ME.
A two-pass sequential sort is performed on ME and then CDSP in the same way as in the
previous part. Table 4 presents the properties of the resulting nine portfolios.
Only within the ME-medium tertile is there a monotonic positive relationship
between CDSP and average return. The rest of the table verifies that this variation of the
average returns for stocks with medium ME is due to default risk. However, the return
difference within the ME-medium tertile is very small with a low t-statistic. Therefore, this
default-risk effect after controlling for ME is very weak.
Table 4: Portfolios Formed on ME and then CDSP
All
Panel A: Average Return
All
ME-Small
0.249
ME-Medium
0.210
ME-Big
0.124
CDSP-Low
0.165
0.259
0.204
0.096
Panel B: Average CDSP
All
ME-Small
392.8
ME-Medium
134.2
ME-Big
60.4
35.2
78.9
39.7
26.2
Panel C: Average Size
All
ME-Small
2.48
ME-Medium
9.16
ME-Big
49.78
42.90
3.15
9.87
76.07
CDSP-Medium
0.189
0.207
0.210
0.158
82.2
231.3
81.7
42.2
13.56
2.55
9.35
42.77
CDSP-High
0.223
0.283
0.216
0.120
0.058(0.28)
0.024(0.10)
0.011(0.10)
0.024(0.30)
471.0
874.2
281.4
113.2
5.44
1.73
8.27
30.14
Panel D: Average BM Ratio
All
ME-Small
0.669
ME-Medium
0.473
ME-Big
0.389
0.373
0.628
0.431
0.272
0.548
0.837
0.515
0.407
0.611
0.541
0.474
0.491
Panel E: Market
All
ME-Small
ME-Medium
ME-Big
0.840
1.145
0.850
0.718
1.067
1.608
1.061
0.920
1.692
2.039
1.411
1.052
1.596
1.107
0.896
High–Low
Portfolios are formed quarterly on size (ME) and then credit-default-swap premium (CDSP) sequentially. On
average, there are 32 to 34 stocks in each of the resulting nine portfolios. This table shows the time-series
average of the equal-weighted returns (in percent), ME (in billions of dollars), book-to-market equities (BM)
and CDSP (in basis points), and the post-ranking market for each of the portfolios, as well as for each of the
portfolios only sorted on ME or CDSP (All). High–Low indicates the return difference between high- and lowdefault-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in parentheses.
Is Default Risk Priced in Equity Returns? 19
2.4. BM Effect and Default-Risk Effect
This section focuses on the relationship of the BM effect and default-risk effect and evaluates
whether the BM effect captures the relative-distress effect, which results from the fact that
the market judges the prospects of firms with high BM (value stocks) to be poor relative to
firms with low BM (growth stocks). The methodology is the same as in Section 2.3.
2.4.1. Portfolios Formed on BM and CDSP Independently
Analogously to Section 2.3.1, this section uses the intersection of independent sorts of stocks
on BM and CDSP to investigate the joint BM–default-risk effect on expected equity returns.
Portfolios are formed quarterly as in Section 2.3.1. The BM breakpoints are
determined by the BMs for all stocks. The stocks with negative BM are separated and
denoted BM-neg. Table 5 displays the results.
For the whole sample (All) in Panel A, average stock return does increase
monotonically as BM or default risk increases. The return difference of high- and lowdefault-risk stocks is 0.058% weekly (3.016% annually); the return difference of value and
growth stocks is 0.086% weekly (4.472% annually). Therefore, the BM and default-risk
effects are still considerable even though the return differences are not significant.
The rest of the analysis focuses on the nine portfolios displayed in the center of
Panels A, C to F and some specific portfolios in Panel B, and BM-Neg. An overview of Panel
A verifies the existence of a BM–default-risk joint effect. Value stocks with high default risk
deliver a relatively high average return (0.176% per week), and growth stocks with low
default risk have the lowest average return (0.082% per week). However, Panel A does not
show a clear picture of the dominance of BM or default risk in the joint effect. The portfolios
with returns above 0.2% per week hold low-default-risk value stocks and high-default-risk
stocks with medium BM.
Is Default Risk Priced in Equity Returns? 20
Table 5: Portfolios Formed on BM and CDSP Independently
All
Panel A: Average Return
All
BM-Neg.
0.211
BM-Low
0.136
BM-Medium
0.211
BM-High
0.223
High–Low
0.086(0.71)
CDSP-Low
0.165
0.082
0.137
0.231
0.148(2.31)
Panel B: Average Return of Zero-Investment Portfolio
HH-ML
0.039(0.18)
HH-LL
0.094(0.40)
MH-LL
0.124(0.79)
HL-MH
0.024(0.16)
HL-LH
0.094(0.56)
ML-LH
0.000(0.00)
Panel C: Average BM Ratio
All
BM-Neg.
–0.824
BM-low
0.230
BM-Medium
0.466
BM-High
0.997
Panel D: Average CDSP
All
BM-Neg.
932.8
BM-Low
113.5
BM-Medium
133.0
BM-High
252.5
Panel E: Average ME
All
BM-Neg.
4.73
BM-Low
36.06
BM-Medium
18.27
BM-High
9.55
Panel F: Market
All
BM-Neg.
BM-Low
BM-Medium
BM-High
1.631
0.999
1.140
1.412
CDSP-Medium
0.189
0.115
0.151
0.110
–0.005(–0.07)
HH-LL
HH-LM
HM-LL
LH-HL
LH-HM
LM-HL
CDSP-High
High–Low
0.223
0.058(0.28)
0.137
0.206
0.176
0.039(0.29)
0.055(0.33)
0.069(0.52)
–0.054(–0.23)
0.094(0.40)
0.061(0.31)
0.028(0.37)
–0.094(–0.56)
0.027(0.20)
–0.116(–1.26)
0.373
0.548
0.611
0.220
0.442
0.827
0.249
0.469
0.847
0.230
0.491
1.129
35.2
82.2
471.0
32.4
36.6
39.7
74.9
79.9
81.9
408.8
326.4
411.7
42.90
13.56
5.44
55.49
33.99
21.77
16.20
14.00
12.33
8.08
6.65
4.28
0.840
1.067
1.692
0.797
0.934
0.837
1.081
1.083
1.026
1.513
1.507
1.744
Portfolios are independently formed quarterly on book-to-market equity (BM) and credit-default-swap premium
(CDSP) with 14 to 52 stocks on average in each of the nine resulting portfolios. This table shows the time-series
average of the equal-weighted returns (in percent), sizes (ME, in billions of dollars), BM and CDSP (in basis
points), and the post-ranking market for each of the portfolios, as well as for each of the portfolios only sorted
on BM or CDSP (All). High–Low indicates the return difference between value and growth stocks or between
high- and low-default-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in
parentheses.
As in Section 2.3.1, the average returns on some specific zero-investment portfolios
in Panel B of Table 5 explore the interaction of BM and default risk in the joint effect. The
first label of each portfolio is for BM (H, M and L for high, medium and low) and the second
Is Default Risk Priced in Equity Returns? 21
is for CDSP (H, M and L for high, medium and low). The upper-left part displays return
differences of high- and low-default-risk stocks but with variant differences in BM ratios
(long positions in higher BM stocks and short positions in lower BM stocks). These three
zero-investment portfolios exhibit the joint effect of BM and default risk with a focus on the
default-risk effect. The average returns are all positive, though not statistically significant.
Similarly, the upper-right part demonstrates the interaction of the two effects with a focus on
the BM effect. The average returns of these zero-investment portfolios are positive but
generally slightly lower. Overall, there is a joint BM–default-risk effect.
The zero-investment portfolios in the lower part of Panel B assess the relative
strength of each effect in the intersection of the two effects. The strategy is to emphasize one
effect but reverse the other one completely. First, we buy higher BM stocks with low default
risk and sell lower BM stocks with high default risk (the lower-left part) to detect the power
of the BM effect with opposite positions for the default-risk effect. Second, we buy higher
default-risk stocks with low BM and sell lower default-risk stocks with high BM (the lowerright part) to test the power of the default-risk effect with opposite positions for the BM
effect. Compared to the portfolios in the upper part, the BM effect is weaker without the
default-risk effect (the lower-left part), and the default-risk effect disappears or turns weaker
without the BM effect (the lower-right part). These results suggest that both BM and default
risk work for the join effect.
The rest of Table 5 confirms that the variation of the average returns is due to the
variations of BM and default risk. It is noteworthy that the average default risk of stocks with
negative BM ratio is extremely high and the average return of these stocks is quite high.
Panel E provides additional information that there is some variation of ME, which is
negatively related to CDSP or BM, especially the former. This may result from the joint ME–
Is Default Risk Priced in Equity Returns? 22
default-risk effect analyzed in Section 2.3. Notice that as in Section 2.3.1, market
is
strongly negatively related to ME and positively related to default risk.
2.4.2. Portfolios Formed on BM and CDSP Sequentially
Analogously to Section 2.3.2, this section applies sequential sorts to examine the disjoint of
the BM and default-risk effects, specifically one effect after controlling for the other. First,
portfolios are formed quarterly on CDSP and then BM sequentially to reveal any BM effect
after controlling for default risk. Table 6 displays the time-series average of the equalTable 6: Portfolios Formed on CDSP and then BM
All
Panel A: Average Return
All
CDSP-Low
0.165
CDSP-Medium
0.189
CDSP-High
0.223
Panel B: Average BM Ratio
All
CDSP-Low
0.373
CDSP-Medium
0.548
CDSP-High
0.611
Panel C: Average CDSP
All
CDSP-Low
35.2
CDSP-Medium
82.2
CDSP-High
471.0
Panel D: Average ME
All
CDSP-Low
42.90
CDSP-Medium
13.56
CDSP-High
5.44
Panel E: Market
All
CDSP-Low
CDSP-Medium
CDSP-High
BM-Neg.
BM-Medium
BM-High
High–Low
0.086(0.71)
0.140(2.25)
–0.022(–0.33)
0.050(0.35)
0.211
0.136
0.102
0.168
0.196
0.211
0.156
0.208
0.245
0.223
0.242
0.146
0.246
–0.824
0.230
0.172
0.278
0.313
0.466
0.325
0.499
0.641
0.997
0.630
0.853
1.371
932.8
4.73
1.631
0.840
1.067
1.692
BM-low
113.5
31.3
76.0
377.1
36.06
53.68
15.26
7.67
0.999
0.752
1.092
1.526
133.0
34.2
80.2
327.6
18.27
50.59
14.66
6.01
1.140
0.869
1.082
1.576
252.5
38.9
81.2
455.9
9.55
27.23
12.35
3.56
1.412
0.912
1.016
1.835
Portfolios are formed quarterly on credit-default-swap premium (CDSP) and then book-to-market equity (BM)
sequentially with 32 to 33 stocks on average in each of the nine portfolios. Stocks with negative BM are shown
separately. This table shows the time-series average of the equal-weighted returns (in percent), sizes (ME, in
billions of dollars), BM and CDSP (in basis points) and the post-ranking market for each of the nine
portfolios, as well as for each of the portfolios only sorted on BM or CDSP (All). High–Low indicates the return
difference between value and growth stocks. Corresponding t-statistics calculated from Newey-West standard
errors are in parentheses.
Is Default Risk Priced in Equity Returns? 23
weighted returns, ME, BM and CDSP, and the market
for each of the resulting nine
portfolios, as well as for each of the portfolios only sorted on CDSP or BM (All).
Panel A shows that within the CDSP-low and CDSP-high tertiles, average returns
tend to increase with BM. Further, within the CDSP-low tertile, the return difference between
value and growth stocks is positive and statistically significant, about twice the whole-sample
return difference. However, there is no sign of a BM effect in the CDSP-medium tertile.
Does this variation of average return found result from the BM variation? Indeed,
there is a substantial BM variation within each CDSP tertile, but the BM ratio cannot capture
the returns’ variation for stocks with medium default risk. The rest of the table confirms that
the effect on the average returns across stocks is due to the BM ratio, not other variables.
Second, portfolios are formed on BM and then CDSP sequentially to reveal any
default-risk effect after controlling for BM. Table 7 demonstrates the properties of the
resulting nine portfolios.
Within each BM tertile, the relationship between average returns and CDSP is not
linear. Although, as expected according to a default-risk effect, high-default-risk stocks
deliver higher average returns than low-default-risk stocks. The large variation of CDSP
within each BM tertile cannot capture the variation of the portfolios’ average returns.
Therefore, we declare here that there is no default-risk effect detected after controlling for
BM. Notice that there is some variation of ME within each BM tertile, but this variation
cannot explain the average stock returns either.
Is Default Risk Priced in Equity Returns? 24
Table 7: Portfolios Formed on BM and then CDSP
All
Panel A: Average Return
All
BM-Neg.
0.211
BM-Low
0.136
BM-Medium
0.211
BM-High
0.223
Panel B: Average CDSP
All
BM-Neg.
932.8
BM-Low
113.5
BM-Medium
133.0
BM-High
252.5
Panel C: Average ME
All
BM-Neg.
4.73
BM-Low
36.06
BM-Medium
18.27
BM-High
9.55
Panel D: Average BM Ratio
All
BM-Neg.
–0.824
BM-low
0.230
BM-Medium
0.466
BM-High
0.997
Panel E: Market
All
BM-Neg.
BM-Low
BM-Medium
BM-High
1.631
0.999
1.140
1.412
CDSP-Low
CDSP-Medium
CDSP-High
High–Low
0.165
0.189
0.223
0.058(0.28)
0.064
0.136
0.218
0.104
0.135
0.096
0.103
0.223
0.212
0.039(0.30)
0.087(0.78)
–0.006(–0.03)
35.2
82.2
471.0
26.4
37.6
58.5
47.8
76.9
142.8
268.5
286.2
559.5
42.90
13.56
5.44
68.99
33.43
16.43
28.04
14.05
8.82
10.43
7.19
3.37
0.373
0.548
0.611
0.209
0.443
0.845
0.243
0.468
0.907
0.238
0.489
1.240
0.840
1.067
1.692
0.714
0.936
0.939
0.932
1.049
1.349
1.356
1.436
1.950
Portfolios are formed quarterly on book-to-market equity (BM) and then credit-default-swap premium (CDSP)
sequentially with 32 to 33 stocks on average in each of the nine portfolios. Stocks with negative BM are shown
separately. This table shows the time-series average of the equal-weighted returns (in percent), sizes (ME, in
billions of dollars), BM and CDSP (in basis points), and the post-ranking market for each portfolio, as well as
for each of the portfolios only sorted on BM or CDSP (All). High–Low indicates the return difference between
high- and low-default-risk stocks. Corresponding t-statistics calculated from Newey-West standard errors are in
parentheses.
With respect to the whole analysis in Section 2, it is important to notice that the first
decile breakpoint for ME in our sample is about the 55th and 40th percentile breakpoint in
2004 and 2010, respectively for ME in the FF sample. This is the case because there are not
that many CDS contracts written referring to very small firms. This property of our sample
could be one of the reasons the default-risk effect interacts more with the BM effect than with
Is Default Risk Priced in Equity Returns? 25
the ME effect. Additionally, Lacking of very small firms in our sample also emphasizes the
ME effect we found. This consideration also applies to the rest of this paper.
3. ME, BM and Default Risk—Regression Analysis
Section 2 investigated the ME, BM and default-risk effects and their interaction by portfolio
groupings. However, the small sample size might lead to insignificant results, so this section
conducts the analysis on the individual stocks to avoid the loss of information caused by the
portfolio grouping. We apply FM’s (1973) cross-sectional regression approach to more
efficiently investigate the issue, which is the explanatory power of ME, BM and default risk
on average stock returns and the interaction between ME or BM and default risk.
Each week, the cross-sectional stock returns are regressed on variables hypothesized
to explain expected returns. Then the time-series average of the cross-sectional regression
slopes for each explanatory variable tests whether the variable is on average priced.
The explanatory variables here are market , size (measured by the log value of
market capitalization
(ME)), BM and default risk (measured by the log value of CDSP
(CDSP)). We choose these measures to guarantee that they are all nonnegative so that we
can easily interpret the results. Each explanatory variable is valued on an individual basis
including the market , an estimator of the slope from the time-series regression of the
stock’s excess returns over risk-free rates on the previous 52 weeks’ excess market
returns7 .ME, BM and CDSP are valued in the previous week. To analyze the interaction
between default risk and other variables, we convert market ,
(ME) and BM orthogonal to
default risk.
7
In the cross-sectional regressions, we correct the error-in-variable problem caused by the fact that the market
is
estimated; therefore the choice of 52 weeks used in the estimation does not control our inference. Also, due to the short
period in our sample and the high-frequent data, we consider 52 weeks enough to maintain a small variation in the market .
Is Default Risk Priced in Equity Returns? 26
We correct the error-in-variable problem caused by the estimated market
in the
cross-sectional regressions using Litzenberger and Ramaswamy’s (1979) approach, applying
the generalized least square to adjust for heteroskedasticity. The average risk premium of
each explanatory variable is then estimated by a simple average of the time-series slopes
from the cross-sectional regressions. To adjust for the assumption that the time series is not
correlated over time, we use a long-run variance matrix from Newey and West (1987) to
estimate the variance of each risk premium. Table 8 displays the results.
Table 8: FM Regressions of Stock Returns on Market , Size, BM and Default Risk
a
0.223
(1.21)
ln(ME)
–0.087**
(–2.31)
BM
–0.090
(–1.41)
ln(CDSP)
ln(ME)* ln(CDSP)
BM* ln(CDSP)
0.094
(0.96)
0.032
(0.10)
0.055
(0.17)
0.095
(0.29)
0.086
(0.88)
0.075
(0.81)
0.077
(0.85)
–0.086**
(–2.32)
0.094
(0.55)
0.122
(0.70)
–0.089
(–1.42)
–0.088
(–1.42)
0.623*
(1.84)
0.026
(0.29)
0.021
(0.23)
0.012
(0.14)
–0.036
(–0.87)
–0.044
(–1.02)
–0.151**
(–2.02)
0.222
(1.21)
0.082
(0.87)
–0.084**
(–2.25)
0.455
(1.31)
0.083
(0.26)
0.079
(0.84)
–0.090**
(–2.34)
0.573*
(1.76)
–0.112*
(–1.68)
0.015
(0.16)
–0.141**
(–2.08)
Stock returns are weekly returns of individual stocks with matched data from CRSP, COMPUSTAT and the
CDS market from January 2004 to September 2010. Stocks with negative book-to-market equity (BM) are not
included in the tests. Size, BM and default risk are measured by the log value of market capitalization (ME, in
millions of dollars), by BM and by the log value of CDSP (in basis points) in the previous week, respectively.
This table shows the average intercepts (a) and slopes from the week-by-week FM cross-sectional regressions of
individual stock returns on market , size, BM and default risk in the previous week. In parentheses under each
estimate is its t-statistic calculated from the Newey-West standard error. “**”and”*” denote significance of
estimates at the 5% and 10% level, respectively.
The result shows that size has significant explanatory power for the cross section of
stock returns and is priced with a negative risk premium, but when we include the product of
(ME) and
(CDSP) in the regression, the ME effect is insignificant. This phenomenon
indicates that size and default risk share some common information, but size is dominant in
explaining stock returns. It is difficult to interpret the product term due to the negative
Is Default Risk Priced in Equity Returns? 27
correlation between ME and CDSP. In addition, this result is consistent with the findings in
Section 2 that the ME effect dominates the joint effect of ME and CDSP.
With respect to BM ratio, it is only significant in explaining the cross section of stock
returns when the default-risk term and an interaction term of BM and default risk are also in
the regressions. This close relationship between BM and CDSP is consistent with the result
from Section 2 that both variables contribute the joint effect on stock returns’ cross section.
As expected, BM is priced with a positive risk premium significant at 10%. However,
the product of BM and ln(CDSP) is priced with a negative risk premium. To investigate this
term further, we check the values of this product. They range from small negative numbers
for stocks with very high CDSP and low BM to large positive numbers for stocks with high
CDSP and very high BM. Furthermore, as the value of this product increases, BM increases
but CDSP decreases first and then increases. Then the negative risk premium for this product
term demonstrates that higher default risk is priced with higher stock return, especially for
growth stocks with high default risk, only when BM is below a certain level (the product
term is negative and BM is negatively correlated with CDSP) and BM is not priced. Again,
this strong BM–default-risk interaction is consistent with the results from Section 2.
Even though ln(CDSP) alone (the default-risk information not contained by other
variables) has no significant power in explaining stock returns, it is positively related to stock
returns. Furthermore, the BM effect is significant only if we include ln(CDSP) and the BM–
default-risk interaction terms. Therefore, default risk is of concern to investors.
4. Factor Loadings
This section assesses the factor loadings of different portfolios on the risk factors that explain
stock returns. This study is important because the reason ME and BM explain the differences
in average returns across stocks is argued to be that they proxy for the sensitivities to the
Is Default Risk Priced in Equity Returns? 28
underlying common risk factors in stock returns. Could default risk be one of these common
risk factors? If so, the ME and BM effects can be explained as a default-risk effect.
To test this hypothesis, we construct a default-risk factor and examine the test assets’
loadings on this factor. If default risk were one of the common risk factors, we would observe
some relationship between ME or BM and the factor loadings on the default-risk factor. More
specifically, this section conducts time-series return regressions of test assets on mimicking
risk factors to investigate the relationship between ME or BM and the factor loadings.
FF’s two mimicking portfolios, SMB and HML, are adopted here. These are two
zero-investment portfolios as proxies for the risk factors in returns related to ME and BM.
SMB is the difference between the returns on small- and big-stock portfolios with about the
same weighted-average BM. HML is the difference between returns on high- and low-BM
portfolios with about the same weighted-average ME. To incorporate a risk factor mimicking
default risk, we construct DHML in the same manner.
First, we perform a three-pass independent sort on all stocks with matched data from
CRSP, COMPUSTAT and the CDS market excluding stocks with negative BM. In the first
week of each calendar quarter, stocks are sorted into two CDS portfolios (high-H and low-L);
each CDS portfolio is then subdivided into two BM portfolios (high-H and low-L); in the end,
stocks within each CDS-BM portfolio are allocated into two ME portfolios (small-S and bigB). Then we calculate the value-weighted weekly excess returns over risk-free rates on the
resulting eight portfolios,8 which are the test assets in the time-series regressions for the betapricing models. We sort stocks only into two groups on each variable because the study’s
cross-sectional sample is small.
8
We use value-weighted portfolios here to guarantee that the default-risk factor is consistent with FF factors. We also test
robustness using equal-weighted portfolios for test assets, and the result is qualitatively the same.
Is Default Risk Priced in Equity Returns? 29
Table 9 presents the time-series average of excess returns, ME, BM and CDSP for
each of the eight portfolios. In the first column of each section in the table, the first letter of
the label denotes the BM class and the second the ME class. For example, HS represents the
portfolio with high BM and small ME. In the first row of each section, the labels denote the
CDSP, such as H for high. The overview shows stocks with higher default risk, higher BM or
smaller ME tend to deliver higher excess returns.
Table 9: Summary Statistics on the Eight Portfolios Formed on CDSP, BM and ME
Average Excess Return
H
L
HS
0.388
0.271
LS
0.311
0.304
HB
0.143
0.218
LB
0.266
0.110
HS
LS
HB
LB
Average BM
H
0.955
0.301
0.714
0.315
L
0.787
0.319
0.675
0.268
HS
LS
HB
LB
HS
LS
HB
LB
Average ME
H
L
3.47
4.97
4.12
6.22
18.84
31.17
20.52
51.28
Average CDSP
H
L
355.8
61.1
321.4
55.6
167.8
50.7
137.8
40.0
Portfolios are formed quarterly on credit-default-swap premium (CDSP), book-to-market equity (BM) and size
(ME) independently. On average, there are 17 to 76 stocks in each of the resulting eight portfolios. The stocks
with negative BM are not included in the tests. This table presents the time-series averages of excess returns (in
percent), ME (in billions of dollars), BM and CDSP (in basis points) of the portfolios. The labels in the first
column of each section denote the BM and ME classes; the labels in the header rows denote the CDSP classes.
Finally, we construct a default-risk factor DHML as the difference, each week,
between the simple average of the returns on the four high-CDSP portfolios and that of the
returns on the four low-CDSP portfolios.
Then the four mimicking risk factors as the explanatory variables in the time-series
regressions are market excess returns over risk-free rates (MK), SMB, HML and DHML.
Table 10 displays the statistics of these risk factors and the correlations between them. Panel
A shows that each risk factor carries a positive, but insignificant, risk premium.
Is Default Risk Priced in Equity Returns? 30
Table 10: Statistics of the Risk Factors and Correlations between Them
Panel A: Statistics of the Risk Factors
Averages
Standard Deviations
MK
0.042
2.834
SMB
0.032
1.181
HML
0.056
1.441
DHML
0.051
1.437
Panel B: Correlations between the Risk Factors
MK
SMB
SMB
0.258
1
HML
0.535
0.022
DHML
0.724
0.242
t-Statistic
0.28
0.50
0.71
0.66
HML
1
0.585
The mimicking risk factors are MK (market excess returns over risk-free rates), SMB (small minus big), HML
(high minus low) and DHML (high minus low for default risk). This table displays each risk factor’s average (in
percent), standard deviation (percent) and t-statistic (zero-risk-premium null hypothesis) and their correlations.
To focus on testing whether ME and BM proxy sensitivity to the default-risk factor,
DHML, we conduct time-series regressions with DHML as the only factor and with DHML
as an additional factor in the FF model (the augmented FF model). Table 11 presents the
results.
Panel A clearly shows that the factor loadings on DHML tend to increase as ME
decreases when BM ratios and CDSP remain. For example, portfolio HSH (high BM, small
ME and high CDSP) loads (2.31) more on DHML than portfolio HBH (high BM, big ME and
high CDSP; 1.82). Analogously, except for the small-ME and high-CDSP portfolios, a
higher-BM portfolio loads more on DHML than a lower-BM portfolio when ME and default
risk are at the same level. Therefore, ME and BM could proxy sensitivity to the default-risk
factor and default risk might be the source of the ME or BM effect. However, all portfolios
load positively on the default-risk factor, which may result from the high correlations
between DHML and other factors and the fact that we are only concerned with this one factor
here.
Is Default Risk Priced in Equity Returns? 31
Table 11: Time-Series Regressions of the Portfolios’ Excess Returns on Risk Factors
Panel A:
α
H
L
0.27
0.21
(2.19)*
(1.69)
0.18
0.24*
(1.63)
(2.02)
0.05
0.17
(0.48)
(1.60)
0.18
0.07
(1.69)
(0.77)
HS
LS
HB
LB
R2
DHML
H
2.31*
(17.43)
2.52*
(18.27)
1.82*
(13.24)
1.73*
(10.41)
L
1.29*
(9.30)
1.25*
(9.19)
1.01*
(7.04)
0.84*
(5.75)
H
0.64
L
0.37
0.71
0.37
0.60
0.31
0.58
0.29
L
0.92*
(22.99)
0.91*
(35.16)
0.88*
(35.96)
0.85*
(46.43)
H
0.39*
(6.01)
0.24*
(3.77)
–0.20*
(–3.04)
–0.11*
(–2.46)
Panel B:
α
HS
LS
HB
LB
H
0.29*
(4.63)
0.23*
(4.07)
0.09
(1.82)
0.23*
(3.85)
MK
L
0.22*
(3.35)
0.26*
(4.30)
0.19*
(3.95)
0.10*
(3.28)
H
1.18*
(26.94)
1.31*
(43.61)
1.06*
(33.63)
1.11*
(28.33)
SMB
R2
DHML
HS
LS
HB
LB
H
0.56*
(7.31)
0.33*
(3.92)
0.28*
(4.61)
–0.17*
(–2.69)
L
0.18
(1.63)
0.03
(0.61)
–0.02
(–0.42)
–0.35*
(–9.39)
H
0.52*
(5.14)
1.00*
(7.01)
0.43*
(6.06)
0.65*
(6.57)
L
0.05
(0.86)
0.25*
(3.76)
–0.22*
(–5.04)
–0.24*
(–6.32)
L
–0.32*
(–2.10)
–0.30*
(–2.95)
–0.46*
(–8.54)
–0.31*
(–8.23)
H
0.93
L
0.82
0.94
0.86
0.92
0.89
0.88
0.95
Column labels denote the BM (high-H and low-L) and size (small-S and big-B) classes and those in the header
row represent the default-risk (high-H and low-L) classes. MK is the excess return on the value-weighted stock
market portfolio over the T-bill rate. α is the pricing error, is the sensitivity and
is the adjusted R squared.
The statistics in the parentheses under the coefficients are Newey-West t-statistics. “*” denotes 5% significance.
Therefore, we convert DHML to be orthogonal to other factors and incorporate other
factors in explaining stock returns. Panel B displays the result for the augmented FF model. It
is clear that
is monotonically related to ME, and
is monotonically related to the
BM ratio, which is not surprising based on the construction of the factors. Notice that
is
systematically related to not only BM, but also ME.
grows from negative for low-default-risk stocks to positive for high-defaultrisk stocks.
is monotonically correlated with not only the level of default risk, but also
ME . For the portfolios with the same classes of default risk and BM,
monotonically
Is Default Risk Priced in Equity Returns? 32
increases as ME decreases. This provides some evidence that default risk is one of the
underlying risk factors for the ME effect and ME proxies sensitivity to a firm’s distress. But
the results show no sign of that BM proxies sensitivity to DHML because value stocks load
lower on the default-risk factor than growth stocks with the same ME and CDSP classes.
5. Asset Pricing Test
The previous analysis reveals the strong relationships between ME or BM and default risk in
explaining returns across stocks. In addition, default risk contains more information about the
variation of stock returns than that included in ME and BM. Is this default-risk effect
systematically significant? Should it be included in the asset-pricing model?
This section applies the stochastic discount factor model to examine whether default
risk is systematically priced in equity returns and whether it helps price test assets. The
default-risk factor is the one constructed in Section 4. In order to reach a large dispersion of
average returns on test assets, we form 18 value-weighted portfolios sequentially on CDSP
(three groups), BM (three groups) and then ME (two groups)9 in the same way as in Section 2.
The average excess return ranges from 0.036% to 0.633% per week.
5.1. Models and Methodology
The tests are based on two benchmark models, the CAPM and the FF three-factor
model10 ,and the same models augmented with the default-risk factor, DHML, as an
additional factor.
The augmented CAPM:
The augmented FF model:
9
This choice of portfolio formation is arbitrary. We test the robustness using other portfolios with enough dispersion of
average returns and standard deviations and receive qualitatively similar results.
10
Momentum is not considered as a risk factor here because it is outside the scope of this paper.
Is Default Risk Priced in Equity Returns? 33
where
is the discount factor, also called the pricing kernel.
Recall that the test on
of factor is to examine whether factor helps price test
assets given the other factors; the test on the risk premium in the corresponding beta-pricing
model is to examine whether factor is priced or whether its factor-mimicking portfolio
carries a positive risk premium. If the default-risk factor helps price test assets, we would
expect
to be significantly different from zero. If the default risk is priced, the risk premium
of the default-risk factor implied by this model should be significantly positive.
Another important aspect of the tests is to detect in which model an
is constructed
to better price the set of assets under examination. We apply different tests on the overall
performance of the models, especially the augmented compared to the benchmark models.
To achieve efficiency in our tests, we employ Hansen’s (1982) generalized method of
moments with the statistically optimal weighting matrix, S. Notably, iterating this method’s
consistent estimates avoid spurious estimates due to incorrect choice of the weighting matrix.
5.2. Results
Table 12 presents the results of the estimation and tests. Panel A displays the classical CAPM.
The estimated coefficient, b, of MK in the pricing kernel is significantly different from zero.
The risk premium is positive and significant. As expected, these are equivalent tests because
there is only a single factor in the model. The p-value for the J-test is large, which implies
that the model fits well for the test assets. The large p-values (for the hypothesis that the
pricing errors are zero) for Chi-H and Chi-L (statistics for the
difference tests) tell us that
the model prices well both high- (DH) and low-default-risk (DL) portfolios.
Is Default Risk Priced in Equity Returns? 34
Table 12: Optimal GMM Estimation of Models
Panel A: The CAPM Model
MK
b
4.212**
t-value
(2.08)
Risk premium
0.337**
t-value
(2.08)
Chi-H
3.44
(0.75)
Chi-L
3.08
(0.80)
Chi-H
2.94
(0.82)
DHML
–4.548
(–0.78)
0.064
(0.74)
Chi-L
1.48
(0.96)
HML
–0.318
(–0.05)
0.075
(0.68)
Chi-H
4.18
(0.65)
Chi-L
9.16
(0.16)
Panel D: The Augmented Fama–French Model
MK
SMB
HML
b
4.387*
19.362**
2.554
t-value
(1.73)
(2.06)
(0.35)
Risk premium
0.377**
0.280**
0.075
t-value
(2.56)
(2.18)
(0.65)
Wald
J-test
Chi-H
Statistic
9.60**
15.03
2.56
p-value
(0.05)
(0.38)
(0.86)
DHML
–6.706
(–0.95)
0.101
(1.22)
Chi-L
7.31
(0.29)
Statistic
p-value
J-test
19.55
(0.30)
Panel B: The Augmented CAPM
MK
b
5.347*
t-value
(1.92)
Risk premium
0.295*
t-value
(1.83)
Wald
J-test
Statistic
4.29
19.22
p-value
(0.12)
(0.26)
Panel C: Fama–French Model
MK
b
3.457
t-value
(1.63)
Risk premium
0.426**
t-value
(2.86)
Wald
Statistic
10.30**
p-value
(0.02)
SMB
18.070*
(1.95)
0.281**
(2.20)
J-test
15.58
(0.41)
D-test
19.87
(0.42)
HJ-distance
0.058**
(0.01)
HJ-distance
0.059**
(0.00)
D-test
16.06
(0.31)
HJ-distance
0.049**
(0.00)
HJ-distance
0.046**
(0.00)
This table shows the results of generalized method of moments (GMM) estimation for the CAPM, augmented
CAPM, FF model and the augmented FF model. The risk factors are market excess returns (MK), SMB, HML
and DHML, as in Section 4. The J-test is Hansen’s (1982) test on overidentifying model restrictions. Chi-H and
Chi-L are statistics for difference tests on the pricing errors of the portfolios formed with high- and lowdefault-risk stocks, respectively. The D-test is a difference test on the restriction implied by the model with
the corresponding augmented model as the unrestricted model. HJ-distance is the distance between the pricing
kernel of a given model and the set of all discount factors that price the test assets correctly. It is from Hansen
and Jagannathan (1997) and estimated here according to Jagannathan and Wang (1996). Risk premiums are in
percent. “**” and “*” denote significance at the 5% and 10% level, respectively.
Panel B presents the results for the augmented CAPM. MK is only significant at 10%,
and the new factor, DHML, does not help price test assets. The D-test (Panel A) with the
augmented CAPM as the unrestricted model suggests the difference between the original and
Is Default Risk Priced in Equity Returns? 35
augmented CAPM is insignificant. Furthermore, the HJ-distance of the augmented CAPM is
larger. Thus, the augmented CAPM cannot compete with the CAPM. Nevertheless, the J-test
cannot reject the misspecification of the augmented CAPM.
Panel C reports the estimation and test results for the FF model. MK and SMB are
both priced significantly with positive risk premiums. The Wald test shows that the joint
effect of the three factors is significant and the model passes the J-test, even though MK and
HML are not significantly helping price test assets.
Panel D shows the results when we consider the default-risk as an additional factor in
the FF model. As in the FF model, MK and SMB are both systematically priced with
significant positive risk premiums. Compared to the FF model, in the presence of DHML, the
coefficients of other factors are all changed and t-statistics are greater. MK and SMB are
more significant in pricing test assets; the sign of the HML coefficient flips; and the t-statistic
for HML’s pricing power is much greater. This proves that the other three factors share some
common information with DHML.
This is also consistent with the previous analysis that there is some interaction
between the default-risk effect and the ME or BM effect, but SMB and HML contain much
more information about stock returns than the default-risk factor. Furthermore, with default
risk included, the pricing kernel better prices DH and DL portfolios. Although the D-test
shows that there is no significant difference between the two models, the augmented FF
model reveals a smaller HJ-distance to the true pricing kernel compared to the FF model. The
risk premium of DHML is not that significant, but it is sufficiently larger than the risk
premium of HML that we cannot ignore it.
The tests in our sample cannot provide strong evidence that DHML should be
considered as a significant factor in asset pricing. Ironically, it is the same case for HML.
However, the augmented models containing DHML do demonstrate some advantages, and
Is Default Risk Priced in Equity Returns? 36
the strong interaction between DHML and other variables still shows that default risk should
be of hedging concern to investors. As to the model tests, more thorough tests should be
performed on a larger sample available in future.
6. Conclusion
The strong explanatory power of ME and BM on the cross section of stock returns has been
interpreted as them proxying for firms’ relative distress. Small stocks and value stocks tend
to have poor prospects and higher expected returns. To test this hypothesis, we proxy a firm’s
financial distress by the default risk under risk-neutral measure indicated by the marketquoted CDSP. This paper examines whether default risk is priced in equity returns and
whether the ME and BM effects proxy for the default-risk effect.
First, portfolio groupings show that there exists a joint effect of ME or BM and
default risk. Furthermore, the ME effect dominates the joint ME–default-risk effect, while
both BM and default risk co-work for the joint BM–default-risk effect. These findings
provide evidence that part of the ME or BM effect can be interpreted as a default-risk effect,
especially for the BM effect. As for the exclusive effect, there is a strong ME effect after
controlling for default risk, but the default-risk effect after controlling for ME is very weak;
there is a BM effect after controlling for default risk, but there is no default-risk effect after
controlling for BM. Therefore, ME and BM contain more information about the crosssectional stock returns than default risk.
Second, the formal tests of FM regressions prove that both ME and BM have strong
explanatory power for the variation of returns across stocks, but the BM effect is only
significant when there is also the default-risk term and a BM–default-risk product term in the
regressions. ME is priced with a negative risk premium, and BM is priced with a positive risk
premium. Furthermore, higher default risk is priced with higher expected stock returns,
especially for growth stocks with high default risk only when BM is below a certain level and
Is Default Risk Priced in Equity Returns? 37
is not priced. Notice that default risk cannot replace ME and BM when explaining the cross
section of stock returns.
Third, factor loadings exhibit a link between ME and loadings on the default-risk
factor. It is argued that ME and BM explain the differences in average returns across stocks
because they proxy sensitivity to the underlying common risk factors in stock returns. We
conduct tests on this hypothesis using the risk factors SMB and HML from FF (1993), which
mimic the risk factors in returns related to ME and BM, respectively, and DHML, which is
constructed to mimic the default-risk factor. The factor loadings of test portfolios on these
factors prove that ME indeed proxies sensitivity to DHML. Therefore, default risk could be
one of the underlying risk factors of the ME effect.
Finally, the asset-pricing tests on the discount-factor models could not provide strong
evidence that the default-risk factor DHML should be included, but they do demonstrate
some advantages when default risk is of hedge concern to investors. MK and SMB are
systematically priced with significantly positive premiums and play important roles in pricing
test assets. Even though DHML is not significant in pricing test assets or being priced with a
positive premium, the tests show strong evidence that DHML shares some common
information with other factors and it cannot be ignored. However, more thorough tests should
be performed on a much larger sample available in future.
Acknowledgement
I am grateful for support and valuable comments from Björn Hansson, Hans Byström,
Hossein Asgharian, Bent Jesper Christensen, and Peter Nyberg. All errors are my
responsibility. The grant from Bankforskningsinstitutet is gratefully acknowledged for
funding this research.
Is Default Risk Priced in Equity Returns? 38
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Is Default Risk Priced in Equity Returns? 40
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Is Default Risk Priced in Equity Returns?
Is Default Risk Priced in Equity Returns?
Caren Yinxia G. Nielsen
The Knut Wicksell Centre for Financial Studies
Caren Yinxia G. Nielsen | The Knut Wicksell Centre for Financial Studies
Size and book-to-market equity (BM) strongly explain stock returns’ cross section; the risk they capture is the
relative distress of small and value stocks. This study examines the default risk’s pricing power, measured by
U.S. firms’ market-revealed credit-default-swap premiums (2004–2010), in average returns across stocks. It
also explores whether the size and BM effects stem from proxying the default-risk effect. In the tests, size
dominates the size–default-risk effect, while BM and default risk work together. Therefore, size and BM
partially proxy the default-risk effect. As expected, size is priced with a negative risk premium and BM is
positive. However, higher default risk only engenders higher expected stock returns when BM is below a
threshold and unpriced. Additionally, size indeed proxies sensitivity to the default-risk factor. Furthermore,
the Fama–French factors SMB (small-minus-big) and HML (high-minus-low) share some common information with the default-risk factor in asset-pricing tests.
Knut Wicksell Working Paper 2013:2
Keywords: Asset Pricing; Equity Returns; Size Effect; Book-to-Market Effect; Default-Risk Effect; CreditDefault-Swap Premium
JEL classification: G12
Working papers
The Knut Wicksell Centre for Financial Studies
The Knut Wicksell Centre for Financial Studies conducts cutting-edge research in financial economics and
related academic disciplines. Established in 2011, the Centre is a collaboration between Lund University
School of Economics and Management and the Research Institute of Industrial Economics (IFN) in Stockholm.
The Centre supports research projects, arranges seminars, and organizes conferences. A key goal of the
Centre is to foster interaction between academics, practitioners and students to better understand current
topics related to financial markets.
Lund University
School of Economics and Management
Working paper 2013:2
The Knut Wicksell Centre for Financial Studies
Printed by Media-Tryck, Lund, Sweden 2013
Editor: F. Lundtofte
The Knut Wicksell Centre for Financial Studies
Lund University
School of Economics and Management