Inferring Default Correlation from Equity Return Correlation

Published date01 March 2015
Date01 March 2015
DOIhttp://doi.org/10.1111/j.1468-036X.2013.12016.x
Inferring Default Correlation from
Equity Return Correlation
Sheen Liu
Washington State University, TriCities, Richland, WA, USA
E-mail: liusx@tricity.wsu.edu
Howard Qi
Michigan Tech University, Houghton, MI, USA
E-mail: howardqi@mtu.edu
Jian Shi
Fannie Mae, Washington DC, USA
E-mail: jian_shi@fanniemae.com
Yan Alice Xie
University of Michigan, Dearborn, Dearborn, MI, USA
E-mail: yanxie@umich.edu
Abstract
This paper presents a new approach for estimating default correlation by linking
default correlation to equity return correlation while preserving the fundamental
relation between default and asset correlations in the structural framework. Our
hybrid model thus overcomes a longstanding empirical difculty that default
correlation estimation relies on the unobservable asset process. The empirical
analysis shows that our hybrid model demonstrates a considerable improvement
over the existing structural model of Zhou (2001) for the sample periods of 1970
1993 and 19902010. We also illustrate the difference between the two models in
predicting default correlations over the period of the 2008 nancial crisis.
Keywords: Default correlation, equity (return) correlation, defaultable bonds,
structural model
JEL classification: G1, G2
We thank an anonymous referee, John Doukas (the editor), Chunchi Wu at the SUNY
Buffalo, and participants at the European Financial Management 2009 Symposium on Risk
Management in Financial Institutions and the Financial Management Association 2010
Meeting for valuable comments. We also thank the University of MichiganDearborn for
financial support. Sheen Liu would like to thank the support from the National Science
Foundation of China (No. 71071027). The authors are responsible for the contents of the
publication. Correspondence: Yan Alice Xie
European Financial Management, Vol. 21, No. 2, 2015, 333359
doi: 10.1111/j.1468-036X.2013.12016.x
© 2013 John Wiley & Sons Ltd
1. Introduction
Correctly estimating default corre lation is critical for credit risk managem ent because
portfolio losses depend on joint de fault events between obligors. Da s et al. (2001) nd
that default rates of debts in credit por tfolios are signicantly correlated and estimates of
credit losses are substantially biased if de fault correlation is ignored. The recent nancial
crisis is an acute example underscorin g the importance of understanding defau lt
correlation. As pointed out by Go rton (2009), the subprime panic th at triggered the
nancial crisis is caused by the lack of information about risks of defau lt loss on a number
of interlinked securities, spec ial purpose vehicles, and derivat ives, which are all related
to subprime mortgages. Jorion (200 9) states that the correlation struc ture used by rating
agencies underestimates defau lt correlation, which led to an und erstatement of the
default risk for tripleA tranch es of securities backed by subprime mortgages. As a result,
many banks that held these securities exper ienced large losses. Since the extant defau lt
correlation models are clearly inad equate, we propose a new method to infer def ault
correlation from equity return corr elation using a structural approach to improve mode l
prediction.
At present, the structural model is commonly used by nancial researchers and
practitioners to estimate default correlation. A major advantage of this type of model is its
ability to endogenously generate default probability as well as debt and equity values in a
unied framework. A common way to model default correlation using the structural
framework is to assume that rmsassets are correlated. Asset values are treated as a
function of common factors and rmspecic factors where common factors dictate asset
return correlation (asset correlation hereafter) between rms (e.g. Finger, 1999;
Zhou, 2001). While the structural approach provides a cohesive framework to relate
asset correlation to default correlation, implementation of this type of model faces the
problem that the asset value process is actually unobservable. To overcome this problem,
Zhou (2001) assumes that asset correlation is equal to equity return correlation (equity
correlation hereafter) and picks a constant asset correlation for differently rated bonds.
Similarly, the common practice in the nancial industry is to use equity correlation as a
proxy for asset correlation (see de Servigny and Renault, 2004). However, not only are
these solving methods theoretically inaccurate, but even as an approximation, they lack
empirical support as well. For example, the empirical study by Lopez (2004) suggests that
average asset correlation is a decreasing function of default probability and an increasing
function of asset size, which implies that the assumption of constant asset correlation is
not valid. de Servigny and Renault (2004) show that equitydriven default correlations are
weakly related to empirical default correlations, which suggests that it is questionable to
use equity correlation to proxy for asset correlation directly. Furthermore, the literature
has documented that the output of portfolio credit risk models is very sensitive to the input
of asset correlation (e.g. Gersbach and Lipponer, 2003; Jorion, 2009). Therefore, how to
obtain unobservable asset correlation accurately from observable data is a critical issue in
the structural approach to predict default correlation between rms.
The new method we propose in this paper tackles this critical issue. Our method rst
establishes the links between equity correlation and asset correlation and between asset
correlation and default correlation, respectively. The two links are then integrated to
eliminate the requirement for the information of asset correlation which is unobservable.
In this way, we are able to infer default correlation from observed equity correlation
reliably based on the structural framework.
© 2013 John Wiley & Sons Ltd
334 Sheen Liu et al.

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