The Empirical Determinants of Credit Default Swap Spreads: a Quantile Regression Approach

AuthorLuís Filipe Martins,Pedro Pires,João Pedro Pereira
Published date01 June 2015
Date01 June 2015
The Empirical Determinants of Credit
Default Swap Spreads: a Quantile
Regression Approach
Pedro Pires
Nova School of Business and Economics, Portugal
João Pedro Pereira and Luís Filipe Martins
ISCTE University Institute of Lisbon, Av. Forcas Armadas, 1649026 Lisboa, Portugal
We study the empirical determinants of Credit Default Swap (CDS) spreads through
quantile regressions. In addition to traditional variables, such as implied volatility,
put skew, historical stock return, leverage, protability, and ratings, the results
indicate that CDS premiums are strongly determined by CDS illiquidity costs,
measured by absolute bidask spreads. The quantile regression approach reveals
that highrisk rms are more sensitive to changes in the explanatory variables that
lowrisk rms. Furthermore, the goodnessoft of the model increases with CDS
premiums, which is consistent with the credit spread puzzle.
Keywords: credit default swap, credit risk, liquidity, quantile regression
JEL classification: G12, G13, C21
1. Introduction
The existing theoretical models show that credit spreads depend on the probability of
rms defaulting and on the fraction of the promised payments that bondholders are able to
We are grateful for the helpful comments and suggestions of Rodrigo Alfaro, Aaron Brown,
Miguel Ferreira, Lidija Lovreta, Lars Norden, Eduardo Ortas, Pedro SantaClara, Oliver
Woll, two anonymous referees, and seminar participants at the 2008 International
Conference on Price, Liquidity, and Credit Risks at the University of Konstanz (Germany),
2011 FMA European Conference, and European Financial Management 2011 Conference.
We thank Til Schuermann and Peter Tufano for featuring an extended abstract of this paper
in the GARP Risk Review, 43 (2008). Financial support from FCT Fundação para a Ciência
e Tecnologia under project PTDC/EGEGES/119274/2010 is gratefully acknowledged.
European Financial Management, Vol. 21, No. 3, 2015, 556589
doi: 10.1111/j.1468-036X.2013.12029.x
© 2013 John Wiley & Sons Ltd
However, both of these variables are unobservable and hard to estimate. This
has created the need for empirical research on good, easytomeasure proxies for those
fundamental variables.
This paper examines the empirical determinants of Credit Default Swap (CDS) spreads.
Following the existing literature, we study the explanatory power of optionimplied
volatility, put skew, historical stock return, rm size, accountingbased measures of
leverage and protability, credit ratings, and macroeconomic factors. Additionally, we
introduce CDS liquidity, measured by the CDS bidask spread, as an explanatory variable
of CDS premiums. However, we show that the appropriate measure to compare
transaction costs across different CDS names is the absolute, rather than the relative, bid
ask spread. While this is an intuitive result from the way CDS prices are quoted in the
market, it is contrary to the correct use of relative spreads in the stock and bond markets.
We study the determinants of CDS spreads using quantile regressions (QR). While the
classical linear regression only describes the conditional mean, the quantile regression
describes the entire conditional distribution of the dependent variable. The QR has thus
the potential to uncover differences in the response of the dependent variable across its
different quantiles. The QR has been useful in several areas of economics and nance to
describe relations where the conditional distribution of the dependent variable changes
signicantly with the regressors.
In our particular application to CDS spreads, the QR
allows the impact of a change in a given regressor to be different between rms with
conditionally high or low credit risk. Hence, our approach is able to produce a robust and
complete picture of the determinants of CDS spreads.
Using a panel data of monthly CDS spreads across 260 rms from the European and US
markets, from Aug/2002 to Feb/2007, we nd the following main results.
First, we nd that CDS premiums are strongly correlated with the equity implied
volatility, put skew, equity historical returns, leverage, protability, and absolute CDS
bidask spreads. While the rst variables have been used in other papers, the results on
bidask spreads are an important contribution of this paper. More precisely, we nd that
CDS premiums signicantly increase with absolute bidask spreads across all conditional
quantiles of the CDS distribution. Since the scarce theoretical literature on CDS liquidity
There are two main approaches to credit risk modelling: the structural approach of Merton
(1974), Black and Cox (1976), and many subsequent papers; and the reducedform approach
of Jarrow and Turnbull (1995), Dufe and Singleton (1999), and others. For recent attempts to
reconcile the two approaches see, e.g., Dufe and Lando (2001).
For example, Bassett and Chen (2001) use quantile regressions to characterise mutual fund
investment styles; Barnes and Hughes (2002) apply quantile regressions to study the cross
section of stock market returns. In labor economics, quantile regression is now regarded as a
standard analysis tool for wage and income studies. Other applications of quantile regression
can be found in hydrology and ecology. Buchinsky (1998) and Koenker and Hallock (2001)
survey the literature.
At the risk of simplifying too much, the advantage of using quantile regressions instead of the
classical linear regression is akin in a univariate setting to describing a random variable with
more than just the mean. Knowing that a random variable has a mean of zero may be enough if
the variable has a narrow distribution, like 2, 1, 0, 1, 2. If instead the distribution is wide, like
22, 1, 0, 11, 12, it may be important to independently characterise the lower quantiles for,
say, risk management purposes.
© 2013 John Wiley & Sons Ltd
The Empirical Determinants of Credit Default Swap Spreads 557
is ambiguous as to whether liquidity should have a positive or negative effect on CDS
spreads, our robust empirical evidence favors models where the liquidity premium is
earned by the protection seller. Furthermore, our results show that the choice between
relative and absolute bidask spreads is of rstorder importance. While CDS premiums
increase with CDS absolute bidask spreads, they decrease with relative bidask spreads.
This may help to reconcile the apparently conicting results of Tang and Yan (2007) and
Acharya and Johnson (2007), who describe a negative relation between CDS premiums
and relative bidask spreads, and the contemporaneous work of Bongaerts et al. (2010),
who nd a positive relation with absolute bidask spreads (like we do).
Second, we nd that the sensitivity of CDS spreads to most explanatory
variables is much stronger for rms with high CDS spreads (i.e., rms in high
conditional quantiles) than for rms with low CDS spreads (i.e., low conditional
quantiles). For example, a given increase in implied volatility has a stronger effect in the
CDS premium when the rm already has a high CDS premium relative to other rms with
the same implied volatility, i.e., when the rm is in a high conditional quantile.
Furthermore, the goodness of t is also an increasing function of the conditional quantile
of the CDS distribution, going from a rather poor t for lowrisk rms to a very strong t
for highrisk rms.
Interestingly, we nd that the results from a standard linear regression are similar to the
results in the higher quantiles (where the goodnessoft and estimated slopes are higher),
but quite different from the results for the median CDS. Quantile regressions thus provide
important information to complete the picture obtained from standard linear regressions
(as used in several previous empirical studies). While one typically assumes that a
standard conditional mean regression describes the centerof the distribution, our
analysis shows that the OLS results are dominated by extreme outlier values, thus
describing the right tail, rather than the center, of the CDS distribution. The empirical
determinants of CDS spreads found through classical regressions are therefore only
successful for the subset of conditionally highrisk rms. In other words, the standard
approach fails to account for the heterogeneity of the CDS data and the quantileregression
is required to get a more robust description of the data.
The result that the t of the model increases with the conditional quantile of CDS
spreads is consistent with the credit spread puzzle, that is, with the fact that structural
models strongly underestimate credit spreads for lowrisk names, while not under-
estimating so severely the spreads for highrisk names (see, e.g., Huang and Huang
(2003)). Our results conrm that the variables motivated by structural models have a
strong explanatory power for highrisk rms, but that other variables may be necessary to
fully explain the spreads of lowrisk rms. In particular, our nding that CDS liquidity is
signicant across all quantiles is consistent with the standard notion that the puzzle is
partly explained by liquidity, that is, with the idea that illiquidity drives most of the spread
of low risk rms. From an applied trading perspective, a stronger link between equity
options and credit spreads for riskier entities implies that typical hedging or arbitrage
strategies, such as capital structure arbitrage, are expected to be more effective when
applied to rms with conditionally high CDS spreads.
The empirical work on CDS determinants is recent and scarce. CollinDufresne et al.
(2001) were the rst to study directly bond credit spreads, instead of yields. However, they
nd that market volatility and jump probability have a rather limited explanatory power.
More encouragingly, Campbell and Taksler (2003) nd that rmsequity idiosyncratic
volatility can explain as much crosssectional variation in corporate yield spreads as credit
© 2013 John Wiley & Sons Ltd
558 Pedro Pires, João Pedro Pereira and Luís Filipe Martins

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