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

• DOI: http://doi.org/10.1111/j.1468-036X.2013.12029.x
• Published date: 01 June 2015
• Date: 01 June 2015

The Empirical Determinants of Credit

Default Swap Spreads: a Quantile

Regression Approach

Pedro Pires

Nova School of Business and Economics, Portugal

E-mail: pedro.pires@novasbe.pt

João Pedro Pereira and Luís Filipe Martins

ISCTE –University Institute of Lisbon, Av. Forcas Armadas, 1649‐026 Lisboa, Portugal

E-mail: joao.pereira@iscte.pt; luis.martins@iscte.pt

Abstract

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, profitability, and ratings, the results

indicate that CDS premiums are strongly determined by CDS illiquidity costs,

measured by absolute bid‐ask spreads. The quantile regression approach reveals

that high‐risk firms are more sensitive to changes in the explanatory variables that

low‐risk firms. Furthermore, the goodness‐of‐fit 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

firms 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 Santa‐Clara, 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/EGE‐GES/119274/2010 is gratefully acknowledged.

European Financial Management, Vol. 21, No. 3, 2015, 556–589

doi: 10.1111/j.1468-036X.2013.12029.x

© 2013 John Wiley & Sons Ltd

recover.

1

However, both of these variables are unobservable and hard to estimate. This

has created the need for empirical research on good, easy‐to‐measure 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 option‐implied

volatility, put skew, historical stock return, firm size, accounting‐based measures of

leverage and profitability, credit ratings, and macroeconomic factors. Additionally, we

introduce CDS liquidity, measured by the CDS bid‐ask 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 finance to

describe relations where the conditional distribution of the dependent variable changes

significantly with the regressors.

2

In our particular application to CDS spreads, the QR

allows the impact of a change in a given regressor to be different between firms 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.

3

Using a panel data of monthly CDS spreads across 260 firms from the European and US

markets, from Aug/2002 to Feb/2007, we find the following main results.

First, we find that CDS premiums are strongly correlated with the equity implied

volatility, put skew, equity historical returns, leverage, profitability, and absolute CDS

bid‐ask spreads. While the first variables have been used in other papers, the results on

bid‐ask spreads are an important contribution of this paper. More precisely, we find that

CDS premiums significantly increase with absolute bid‐ask spreads across all conditional

quantiles of the CDS distribution. Since the scarce theoretical literature on CDS liquidity

1

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 reduced‐form approach

of Jarrow and Turnbull (1995), Duffie and Singleton (1999), and others. For recent attempts to

reconcile the two approaches see, e.g., Duffie and Lando (2001).

2

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.

3

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 bid‐ask spreads is of first‐order importance. While CDS premiums

increase with CDS absolute bid‐ask spreads, they decrease with relative bid‐ask spreads.

This may help to reconcile the apparently conflicting results of Tang and Yan (2007) and

Acharya and Johnson (2007), who describe a negative relation between CDS premiums

and relative bid‐ask spreads, and the contemporaneous work of Bongaerts et al. (2010),

who find a positive relation with absolute bid‐ask spreads (like we do).

Second, we find that the sensitivity of CDS spreads to most explanatory

variables is much stronger for firms with high CDS spreads (i.e., firms in high

conditional quantiles) than for firms 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 firm already has a high CDS premium relative to other firms with

the same implied volatility, i.e., when the firm is in a high conditional quantile.

Furthermore, the goodness of fit is also an increasing function of the conditional quantile

of the CDS distribution, going from a rather poor fit for low‐risk firms to a very strong fit

for high‐risk firms.

Interestingly, we find that the results from a standard linear regression are similar to the

results in the higher quantiles (where the goodness‐of‐fit 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 ‘center’of 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 high‐risk firms. 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 fit 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 low‐risk names, while not under-

estimating so severely the spreads for high‐risk names (see, e.g., Huang and Huang

(2003)). Our results confirm that the variables motivated by structural models have a

strong explanatory power for high‐risk firms, but that other variables may be necessary to

fully explain the spreads of low‐risk firms. In particular, our finding that CDS liquidity is

significant 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 firms. 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 firms with conditionally high CDS spreads.

The empirical work on CDS determinants is recent and scarce. Collin‐Dufresne et al.

(2001) were the first to study directly bond credit spreads, instead of yields. However, they

find that market volatility and jump probability have a rather limited explanatory power.

More encouragingly, Campbell and Taksler (2003) find that firms’equity idiosyncratic

volatility can explain as much cross‐sectional variation in corporate yield spreads as credit

© 2013 John Wiley & Sons Ltd

558 Pedro Pires, João Pedro Pereira and Luís Filipe Martins