مدلسازی اثر عوامل اقتصاد کلان بر پیش فرض های شرکت ها و تحولات رتبه بندی اعتباری

We explore how general economic conditions impact defaults and major credit rating changes by fitting reduced-form Cox intensity models with a broad range of macroeconomic and firm-specific ratings-related variables. For all corporate issuers in the period 1981–2002 we find both types of factors strongly influenced the risk of a credit event. However, while the effects of ratings-related factors were consistent with expectations and very robust under different specifications, significance levels and even signs for the macro variable coefficients depended heavily on which other variables were included. This sheds light on the disparate results reported in earlier studies.

Models of corporate default fall into two broad categories, structural models and reduced form models. Structural models consider the evolution of the value of the firm, with default assumed to occur if firm value should fall below some insolvency threshold. They have the practical advantage of using the firm's current stock price, a sensitive barometer of its financial condition that is updated daily, unlike accounting statements that are only available quarterly.2 But structural models pose difficult problems, including the need to value all of the components of a real world firm's complex capital structure, to model their dynamics and estimate those models empirically, and to specify exactly where the default boundary lies. This is a challenging task in itself, as the literature shows, and it becomes extremely difficult to introduce very many additional variables related to conditions in the macroeconomy. Moreover, important non-default credit events, such as a ratings downgrade, do not fit conveniently into the structural framework. This paper focuses on the reduced form approach, which treats default as a random event that can strike any firm at any time. The paradigm might be thought of as formalization and extension of the familiar ratings transition matrices published by Moody's and other ratings agencies.3 In the basic reduced form model, a credit event corresponds to the first jump time of a Poisson process with a constant hazard rate. An “event” can be defined flexibly to be default, downgrade or upgrade from one bond rating category to another, or any other well-defined change of state. The reduced form approach has been widely used for credit risk analysis in both academic and real world research, e.g., Jarrow et al., 1995, Jarrow et al., 1997, Lando and Skødeberg, 2002 and Duffie et al., 2007, Koopman et al., 2008 and Koopman et al., 2009. The constant hazard rate formulation treats all issuers in a given credit class as homogeneous. But empirical evidence of non-Markovian behavior includes positive serial correlation in ratings changes, known as “ratings drift,” time variation in default probabilities, and cross-sectional differences in credit risk across issuers within a given rating. For example, Altman and Kao (1992) found ratings drift among firms that recently had a change in rating, and Hamilton and Cantor (2004) showed that the transition probability out of a rating class depends on whether the bond entered its current rating by an upgrade or a downgrade.4 Other kinds of non-Markovian behavior were described by Lando and Skødeberg (2002), who found that the probability of a rating change diminishes the longer the bond stays in the same rating; and by MacDonald and Van de Gucht (1999), whose results suggested a nonmonotonic aging effect. Results reported by Mann et al., 2003, Hamilton and Cantor, 2004 and Fledelius et al., 2004 indicate that within-class hazard rates for default and for ratings transitions vary considerably over time. These results support the belief that credit risk exposure is affected by conditions in the macroeconomy. In particular, Bangia et al., 2002 and Nickell et al., 2000 found that upgrade, downgrade and default intensities differ across different economic regimes. Xie, Shi, and Wu (2008) used the reduced form approach to extract (risk neutral) default intensities from investment grade corporate bond yields and found strong evidence of common factors, the strongest of which was the performance of the stock market. Numerous other studies showing that default probability is sensitive to macroeconomic factors include Kavvathas, 2001 and Carling et al., 2007, Couderc and Renault (2004) and Duffie et al. (2007). In this paper, we formulate and estimate extended reduced-form models for the occurrence of credit events, using the semi-parametric Cox regression model. This well-known approach adapted from survival analysis allows the hazard rate for a given issuer to be a function of both firm-specific factors and macroeconomic conditions.5 In place of a formal structural model, we assume that the important factors tied to a firm's capital structure are adequately reflected in its current bond rating and its credit rating history. Our concentration is on assessing the relative importance of a much broader selection of macro variables, both individually and in combination, than has been carried out previously with the Cox hazard model. Duffie et al. (2007) combined variables from both frameworks in developing a model for the term structure of credit risk as a function of a small number of structural and macro factors. But their focus on forecasting required building models for the time-series properties of their factors, which strictly limited the number of variables that could be considered.6 By contrast, we wish to establish “stylized facts” about which macro covariates are most important and the nature of their impact on credit risk, including allowance for lagged effects. We do not attempt to predict the future values or the dynamics of those factors. Default is the most important change in credit quality, but hardly the only one that matters to investors. Tables of historical transition frequencies among the ratings categories, and previous research on credit risk, have attempted to estimate the full transition matrix for ratings changes. We prefer to concentrate on the most important transitions rather than modeling the fine structure of the credit market.7 We therefore focus on three especially important credit events: transition from solvency into default, transition from investment grade (Moody's Baa and above) down to speculative grade (Ba or below), and the reverse transition (upgrade from speculative to investment grade).8 It seems intuitively obvious that macroeconomic conditions should affect credit risk. This is true both in absolute terms and also relative to the degree of credit risk implied by a bond rating. The latter expectation is due to the rating agencies' practice of “rating through the cycle,” i.e., assigning credit ratings based on each firm's creditworthiness relative to others in its cohort, and not adjusting the ratings as overall credit risk varies over the business cycle. But different researchers have obtained quite different results, depending on which macro variables were explored, how those variables entered the specifications (as contemporaneous values, with lags, or averaged over time), what other variables were included in the specification, and what time period was examined. Our comprehensive analysis sheds considerable light on these diverse results. A relevant macro factor should be one that has a broad impact on most firms' creditworthiness. An obvious candidate is the strength of the overall economy, but what is the best measure? Is it a high rate of GDP growth?; a low unemployment rate?; growth in industrial production?; strength in a composite variable such as the Chicago Federal Reserve's National Activity Index?; the NBER's indicator of recession and expansion? Rather than trying to choose among these possibilities a priori, we begin by grouping candidate variables into three broad classes: those related to general macroeconomic conditions (e.g., the unemployment rate, inflation, and the NBER recession indicator); those related to the direction in which the economy is moving (e.g., Real GDP growth and the change in consumer sentiment); and a remaining set loosely categorized as indicators of financial market conditions (e.g., interest rates and stock market returns). The last group includes the recent default rate among corporate borrowers in order to examine potential “contagion” in the credit market. The firm-specific factors we consider include the firm's current rating, its initial rating class, whether it entered its current rating by upgrade or by downgrade, and the length of time since the firm was first rated. To look at how the estimated influence of each macro variable is affected by other variables included in the model, we examine three specifications. First we include each one as the single macro variable in a specification with the full set of firm-specific ratings-related covariates. This indicates what the simplest specification with that macro variable would show, for example an initial exploratory analysis of the individual variables in a large set of candidates. We then run the full set of firm-specific and macro covariates together in a single comprehensive specification. In many cases, this produces a sharp change in the variable's significance level and even in the direction of its estimated effect. Finally, although most of the pairwise correlations among our macro variables are not that high, it seems clear that multicollinearity within the full set tends to hold down significance levels for individual coefficients. We therefore use stepwise regression to pare down the number of variables and obtain a third, parsimonious specification in which all of the estimated coefficients are statistically significant. This procedure is known as “backward selection” because it begins with the full set of covariates and eliminates the least significant ones, one at a time. We find that adding macroeconomic factors into a specification with ratings-related variables produces a highly significant increase in explanatory power, but it is not easy to identify a small number of specific variables that dominate the field of alternative measures, and some of the seemingly obvious candidates turn out to have insignificant or anomalous coefficients when combined with other macro variables in more comprehensive specifications. For example, while they are highly significant when examined one at a time, none of the variables related to general macroeconomic conditions have any power in explaining defaults when combined with the other macro factors. Strength in the stock market as measured by the return on the S&P 500 index is estimated to have an anomalous effect, increasing the risk of default and reducing the chance of upgrade. While failure to obtain a single dominant model specification for each transition may seem somewhat disappointing, we actually feel that this is one of our more important findings in helping to understand the complicated connection between credit risk and the macroeconomy. Our results show how earlier studies could arrive at quite different conclusions based on fitting similar but somewhat different models. They call into question any strong conclusions about the importance of any single macro variable among a set of related ones that might be drawn from such research. By contrast, the ratings-related variables perform consistently as expected, with higher ratings corresponding to significantly lower credit risk, and the aging and ratings drift effects strongly confirmed. Interestingly, while the coefficients on specific macro variables can change drastically depending on which other variables are included in the specification, the estimated effects of the ratings-related factors are largely unaffected by the addition of macroeconomic variables to the model. The question of contagion in defaults has been widely debated: holding other factors equal, does default by one firm increase the likelihood that other unrelated firms will also experience credit problems, independent of their objective creditworthiness? Or is the empirical observation that defaults appear to come in waves simply due to the fact that all firms are exposed to broad economic forces that affect credit risk for all of them at the same time?9 We do not offer a definitive answer to this question, but our results do shed some light on it. Along with a large set of variables measuring various aspects of the economic environment, we include the overall default rate in the corporate sector over the recent past. Consistent with the existence of contagion in the credit market, we find that even after allowing for the effects of the macro factors included in the specification, a high corporate default rate over the last year is still associated with a highly significant increase in the hazard rate for default and a decrease for rating upgrades. The estimated effect on downgrades from investment to speculative grade is also positive, but not significant. In the next section, we describe the Cox hazards model that will be used throughout the paper. 3, 4 and 5 describe, respectively, the ratings data from Moody's that is used to define the credit events we model, the ratings-based firm specific covariates, and the macroeconomic covariates used as explanatory variables. 6, 7 and 8 present estimation results for defaults, for downgrades from investment to speculative ratings classes, and for upgrades from speculative to investment grade, respectively. Section 9 summarizes our results and concludes.

This is the first study to examine such a broad range of rating history related and macroeconomic factors in a Cox model specification for credit risk. In this framework, we have been able to increase the number of observations in our sample by working with individual firm data, rather than aggregate default frequencies by ratings class as in earlier studies. We also have been able to access Moody's comprehensive database covering credit events in the full population of rated firms over a long time period. Finally, we limited the credit events under consideration to default and two major changes of ratings class, which allowed larger numbers of firms in the “at risk” population for each type of transition. This broad look at the problem suggests several conclusions. Overall, we confirmed that incorporating macroeconomic factors along with ratings-related variables in reduced form models of default intensity leads to a highly statistically significant increase in explanatory power. Our estimates of the effects of rating-specific factors confirm a variety of results from earlier studies. Specifically, we found that credit ratings reflected intensity differences correctly in every case. Higher rated firms had lower intensity of default than lower rated firms and had higher upgrade intensity. There is a “ratings drift” or “momentum” effect, by which a firm that has been downgraded (upgraded) in the recent past has a higher intensity of default or of being downgraded (upgraded) again than a firm in the same rating category that has not experienced a recent downgrade (upgrade). There is also evidence of an “aging” effect, such that the intensity of occurrence of a credit event depends on how long the firm has been rated. In particular, a recently rated firm has lower default intensity than a seasoned firm in the same ratings class. Similarly, a recently rated speculative grade firm in a B or Ba category has a lower intensity of being upgraded to the investment class. We found that the intensity of occurrence of credit events was different for firms that began as investment grade and were subsequently downgraded into a speculative ratings class (“fallen angels”), and for firms that started as speculative and have been upgraded (“rising stars”), than for firms that are still in the same broad investment or speculative grade category that they started in. One finding of considerable importance is that the coefficients on the ratings-based factors and their significance levels are only slightly affected by addition of macroeconomic factors to the specification. This implies that the information obtained from considering the macro variables is incremental to that contained in a firm's credit rating history alone. In the model of the transition into default with macro covariates, none of the four measures of General market conditions provided useful information about default hazards when firm-specific covariates and other macro variables, i.e., direction of economy and financial conditions variables, were included in the specification. Similarly, in the estimation of the hazard of the downgrade transition (from an investment grade to speculative grade), the model with the direction of economy and financial conditions variables statistically dominated the model with the GMC variables. This leads to the general conclusion that the direction of economy and financial conditions variables play a more important role in modeling downgrade transitions than the GMC variables. For both downward transitions, the Change in Consumer Sentiment was a highly significant variable, but it did not provide any explanatory power for upgrades from speculative to investment categories. Two GMC variables, unemployment and inflation, appear in the intensity model for the upgrade transition, in addition to Real GDP growth and three financial conditions variables. High unemployment and high inflation are both strongly associated with the reduction in the intensity of upgrade. Real GDP growth has a seemingly anomalous, but highly significant, negative effect on the intensity of upgrade. We suspect that this negative effect may indicate that it is easier for Moody's to distinguish a more creditworthy firm from other firms in its cohort when most firms are doing badly than when they all are doing well. In summary, our results represent a broad first cut at incorporating a wide range of measures of the macroeconomic environment and of firms' rating histories into reduced-form Cox models for the hazard rates of several important credit events. Further research along these lines is surely warranted and can be expected to refine our understanding of this important area.