Correlated Default Risk SANJIV

Copyright © 2006 R ecently, an unusually high number of firms in the economy defaulted, with the default rate for Moody’s-rated speculativegrade issuers reaching as high as 10.2% in 2001. In their annual review, Moody’s summarized these credit events as follows, “Record defaults —unmatched in number and dollar volume since the Great Depression—have culminated in the bankruptcies of well-known firms whose rapid collapse caught investors by surprise.”1 What factors cause the economy-wide default rate to change over time, and why does it vary as much as it does? In this article, we investigate the likelihood of joint default across firms in the economy by examining the covariation of individual firms’ default probabilities.2 This, in turn, provides insight into how, and why, the economy-wide default rate varies over time. We provide a comprehensive empirical investigation of how default probabilities covary using a database of issuer-level default probabilities for the period 1987–2000. This database provides a unique opportunity to understand how default risk behaves both in the cross-section of firms and in the time-series for almost all U.S. public non-financial firms. More importantly from the standpoint of using the results, the dataset lends quantitative expression to this behavior. For instance, our analysis allows us to understand the extent to which the record defaults of 2001 were, indeed, a surprise. Defaults of firms in the economy will cluster if there are common factors that affect individual firms’ default risk. The structural model of Merton [1974]3 identifies two of these factors as the firm’s debt ratio and volatility. Co-variation of individual firms’ debt ratios or volatilities will result in their default probabilities being correlated. The economy-wide default rate will vary widely if, first, debt ratios or volatilities across firms are correlated, and second, if there is wide variation in debt ratios, volatilities, or their correlations over time. By relating the co-variation in default probabilities to variation in debt, volatility, and their correlations, we also provide an economic understanding of why the economy-wide default rate varies over time. In short, we examine the contribution of the correlation between default probabilities, i.e., the first part of the standard reduced-form structure of doubly stochastic processes, to joint default risk. Recent evidence in Das, Duffie, Kapadia and Saita [2005] shows that after conditioning on default intensities, the residual correlation that may be ascribed to conditional default is of the order of 1 to 5% only. That is, the majority of joint default risk emanates from covariation in default probabilities, the focal point of the investigation in this article. Specifically, we observe that although both debt levels and firm volatilities change over time, firm volatilities—and their correlations—vary much more than debt levels. In Correlated Default Risk