The Correlation in Credit Risk in the market - Free Essay Example

Correlation in credit risk is a well-known phenomenon. Understanding the causes of correlated credit losses is crucial for many purposes, such as managing a portfolio, setting capital requirements for banks, and pricing structured credit products that are heavily exposed to correlations in credit risk; for example, collateralized debt obligations (CDO). This issue has become particularly important because of the rapid growth of structured credit products in the financial markets in recent years. But despite much research on the subject, we do not understand many aspects of correlation in credit risk; this paper attempts to move the literature forward. First, we explore the economic importance of contagion in credit risk correlation. This is an open empirical question. Many credit models are based on the doubly stochastic assumption that, conditional on observable risk factors, defaults are independent of each other. This assumption is widely accepted and implemented in banking to determine capital requirements.Evidence exists that contagion has a notable impact on the correlation in credit risk of firms subject to significant credit events. On the basis of these findings, some researchers have tried to include contagion in credit models. However, the economic importance of contagion in a firms credit risk correlation is not clear from the literature. If the role of contagion is statistically significant but not economically significant, modeling contagion may not be of first-order importance. But even though some researchers and practitioners reject the doubly stochastic assumption, they find that the proportion of correlation in credit risk that cannot be explained by observable risk factors is small (1 to 5 percent), which suggests that unobservable risk factors may be of minor importance in credit risk models. In this paper, we attempt to clarify this issue. We also explore the credit risk correlation pattern over time and across firms with varying credit quality. The academic literature cannot agree on these patterns either. These questions are important because credit risk has been and still is the biggest risk facing banks. And with securitization and the new products that have been developed in the financial market, credit risk has been spread out beyond the banking sector to various market segments. Ambiguity regarding these issues poses serious challenges for investors, practitioners, and regulators. In this paper, we approach cred it risk in two ways. First, unlike earlier studies, we use data from the credit default swap (CDS) market. Most researchers examine the correlation in a firms credit risk using either estimated default intensity based on actual default observations or implied default probability derived from the Merton (1974) model. The former approach may not be reliable, because some default events are strategic decisions and, therefore, may not correspond to economic default.1 Also, some financially distressed companies may be able to negotiate debt restructuring to avoid default or may be acquired with bankruptcy looming on the horizon, and these informal resolutions of financial distress are difficult to identify.2, 3 The problem of reliable numbers is a serious challenge-default is a low-frequency event, and any misclassification may have a major impact on the precision of parameter estimates. Thus, the estimated default intensity might be contaminated, and this weakness could be behind some r ather surprising findings in the literature. On the other hand, default probability estimated from the Merton model could be confounded by the oversimplified assumptions behind the model. In contrast, the CDS market enables the direct measurement of credit risk by many market participants. CDS is insurance against a default by a particular company or sovereign entity (known as the reference entity). The buyer of the CDS contract makes periodic payments to the seller for the right to sell a bond issued by the reference entity for its face value if the issuer defaults. So the price of CDS contracts (or the CDS spread) is a direct measure of the credit risk of the reference entity. Because CDS spreads can be based on a wide array of credit risk models, it is also a comprehensive measure of credit risk. The second way we approach credit risk in this paper is by investigating the observable factors and their contributions to the correlation in risk. Although previous studies have i ncorporated some macroeconomic factors into modeling credit risk, the impact of these variables is not consistent across studies, and some results are counterintuitive. We study the impact on credit risk of various macroeconomic variables as well as firm- and market-level variables, and we model the industry effect on the credit risk of individual firms. Although many researchers have suggested that the industry effect partially accounts for the correlation in credit risk, the literature has yet to provide conclusive evidence. On the basis of monthly changes in CDS spreads from January 2001 through December 2006, we find that changes in CDS spreads are positively correlated, with an average correlation of 21 percent. Observable variables at the firm level can reduce the correlation by 8 percent, resulting in a correlation of 13 percent among the regression residuals. Market-level and macroeconomic variables are significantly associated with changes in CDS spreads, with the expect ed signs of the regression coefficients. These variables, together with firm-level variables, can reduce the correlation by two-thirds to 7 percent. We also confirm the existence of the industry effect and find that firms in less cyclical industries have lower correlations in credit risk. Although industry variables are significantly related to CDS spread changes in the right directions, the industry effect can be responsible for less than 1 percent of the correlation in CDS spread changes after we control for firm-level, market-level, and macroeconomic variables. When all observable variables are combined, they can account for about 14 percent of the correlations, leaving 7 percent unaccounted for. The main observable variables that contribute to the correlations are firm-level variables and credit spreads, which can be affected by both contagion and systematic risks. Excluding these variables, the mean correlation among the residuals is 12 percent. These findings suggest that c ontagion could contribute from 33 percent to 57 percent of the correlation in credit risks. We also investigate the potential nonlinearity in the relationship between credit risk and observable variables, and find that accounting for nonlinearity does not qualitatively change our findings. Thus, the evidence suggests that contagion does play an economically important role in the credit risk correlation. In addition, we find that the correlation in credit risk is countercyclical; that is, it is higher during economic downturns and lower during booms. Also, it is higher among firms with low credit ratings than among those with high credit ratings. These findings are consistent with some theoretical predictions but not with the findings based on measures from the Merton model. We believe that the results derived from CDS spreads are more reliable because of the oversimplified assumptions behind Mertons model and the evidence in the literature that the Merton default probability m easure does not forecast default probability well. Since the study period was short, it included one full business cycle; thus, the results have general implications. The study period did not include the recent market turmoil; however, if contagion is a major phenomenon during severe economic downturns, failing to include the recent period of turmoil is biased only against the finding that contagion plays an important role. The evidence, therefore, suggests that modeling the unobservable risk factors should be of first-order importance for future research in credit modeling. This paper is organized as follows. In section II, there is a review of the current literature. In section III, description of the sample is given. Discussion of observable risk factors and their contributions to the correlation in credit risk is given in section IV. Section V presents results on the correlation in credit risk over time and by rating groups. In the last section, a brief conclusion is given . II. Literature Review Modelling Correlation in Credit Risk The two branches of credit risk measurement are (1) the structural approach and (2) the reduced-form approach. Structural models originate from the Merton (1974) model and assume that a company will default if the value of its assets is below a certain level; for example, the amount of its outstanding debt. The key to structural modelling is to capture the stochastic asset diffusion process, and default correlation between two companies is introduced by assuming that the stochastic processes followed by the assets of the two companies are correlated. Correlation in the stochastic asset diffusion processes of two firms can be caused by both observable risk factors and unobservable risk factors, such as contagion. The advantage of structural models is the flexibility in modeling correlation in credit risk; the disadvantage is the difficulty in implementing them empirically. The general theoretical predictions from this school are that credit ri sk correlation is higher for firms with a low credit rating than for those with a high credit rating, and that the correlation increases during economic downturns The reduced-form models assume that a firms default time is driven by a default intensity that varies according to changes in macroeconomic conditions In other words, when the default intensity for company A is high, the default intensity for company B tends to be high as well, which induces a default correlation between the two companies. The reduced-form models usually assume that observable risk factors are the main drivers of firm credit risk and that, after controlling for observable factors and default intensity, defaults should be independent. This is the doubly stochastic assumption. Because of its mathematical tractability, most researchers and practitioners gravitate toward this approach; thus, the doubly stochastic assumption is behind many commonly used reduced-form models to predict default, such as the dur ation models and the survival time copula models. The doubly stochastic assumption is also the key assumption behind the proprietary models. For instance, Moodys KMV Risk Advisor considers systematic factors using a three-level approach: (1) a composite market risk factor, (2) an industry and country risk factor, and (3) regional factors and sector indicators. The factor loading for an individual firm for each of the factors is estimated using asset variances obtained from the option theoretical model, and the factor loadings are then used to calculate co-variances for each pair of firms. In Credit Metrics, the credit transition matrix is conditioned on a credit cycle index, which shifts down when economic conditions deteriorate. The credit cycle index is obtained by regressing default rates for speculative grade bonds on the credit spread, 10-year Treasury yield, inflation rate, and growth in gross domestic product (GDP). In contrast, Credit Risk Plus incorporates cyclical facto rs by allowing the mean default rate to vary over the business cycle. Credit Risk Plus models find that correlation in credit risk is higher among firms with low credit ratings. In summary, the doubly stochastic assumption plays a critical role in the vast majority of credit models used in research and practice. The findings say that variations in the observable factors cannot fully explain the correlation in credit risk and that the doubly stochastic assumption is violated; however, the proportion of the correlation that cannot be explained by observable factors is rather small. The conclusion may be contaminated in two ways. First, the evidence could result from the misspecification associated with the model to predict default intensity. A different model could lead to two possibilities: (1) observable factors may be sufficient to account for the correlated default risk, or (2) the proportion not explained by observable factors could be much larger. It is not clear from the literature how the correlation in credit risk varies over business cycles and across firms with different credit quality, as studies on these subjects have yielded conflicting results. This lack of clarity poses a major challenge for investors, portfolio managers, bankers, and bank regulators. Macroeconomic Impact in Credit Risk Modelling Some studies incorporate macroeconomic conditions into credit risk models; however, researchers have used different macroeconomic variables, and some variables that are important in one paper are found to be unimportant in another. Also, some empirical results are quite counterintuitive. Some researchers find intuitive relations between credit risk and macroeconomic variables. For example, Collin-Dufresne, Goldstein, and Martin (2001) examine determinants of changes in credit spreads using changes in 10-year Treasury rates, changes in the slope of the yield curve, changes in market volatility, and monthly SP 500 returns. They find that all these variables are significantly related to changes in credit spreads, with the direction implied by structural models. Carling and colleagues (2007) investigate how macroeconomic conditions affect business defaults using a corporate portfolio from a leading Swiss retail bank. They find that the output gap, the yield curve, and consumers expectations of future economic development can help explain a firms default risk. In summary, the impact of macroeconomic variables is not consistently documented in the literature, and some results are counterintuitive. These findings add to the puzzle of whether observable risk factors can explain the correlation in credit risk. We believe that the inconsistent and sometimes counterintuitive findings may be contaminated by the noise in the default data, as default events are rare and can contain misclassifications that lead to estimation errors. CDS data are more suitable for this purpose. III. Data Description and Sample Statistics The Sample The primary data in this study are the monthly CDS data from January 2001 through December 2006. We use the five-year CDS, as this instrument is the most liquid in the CDS market. We use monthly data to match the monthly macroeconomic variables because price movements in monthly data are less contaminated than daily or weekly data by temporary imbalances between supply and demand. The CDS spread measures total credit risk, which includes both default probability (DP) and losses given default (LGD). It is widely documented that DP and LGD are positively correlated thus, the CDS spread is a comprehensive measure of total credit risk. The sample includes 523 firms (25,113 firm-month observations)-376 investment-grade firms and 147 speculative-grade firms, based on the average rating for each firm during the sample period. Our sample period (2001-2006) includes one full business cycle consisting of varying economic conditions: an economic downturn in the early period, a recovery in 2003, and a normal period afterward. Variables at the Firm, Industry, and Market Levels We use three firm-level variables to explain the changes in CDS spreads: monthly stock returns, monthly stock volatility change, and firm leverage change.According to the structural model, a firms default risk is higher when either volatility or leverage is high. Also, stock returns indicate the markets assessment of a firms future performance. Lower returns imply a dimmer outlook, which should correlate with a higher credit risk, so stock returns should be negatively associated with changes in CDS spreads. We use the following market-level variables: changes in implied market volatility (VIX), changes in market leverage, and changes in market returns (measured by NYSE-AMEX-NASDAQ value-weighted returns). An increase in either market volatility or market leverage, or a decrease in market returns, suggests a worsening economic outlook, which should be associated with an incr ease in credit risk. We define industry variables similarly-changes in industry volatility, changes in industry leverage, and changes in industry aggregate returns-and the same logic should hold at the industry level if there is an industry effect. Macroeconomic Variables We use real GDP growth rate and changes in capacity utilization rate to describe the business cycle. If credit risks are higher during an economic recession, we would see changes in CDS spreads negatively related to both real GDP growth rate and changes in capacity utilization rate. We also include inflation among our list of macroeconomic variables. Since previous studies have shown a negative relationship between real activity and inflation, we expected a positive relationship between inflation and credit risk. We use the following interest rate variables: changes in three-month T-bill rates, changes in term spreads (difference between the yields of 10-year T-bonds and three-month T-bills), and changes i n credit spreads between BBB and AAA bonds and between AAA bonds and 10-year T-bonds. The relationship between the three-month T-bill rate and credit risk should be negative for two reasons. First, the Feds monetary policy is pro-cyclical. Second, a higher interest rate can increase the risk-neutral drift of the process of firm value, thus reducing credit risks Collin-Dufresne and colleagues (2001) and Duffee (1998) both documented a negative relationship between interest rate and credit risk. Credit risk should also be negatively related to the term spread (Estrella and Hardouvelis 1991, Estrella and Mishkin 1996, and Fama and French 1989) and positively related to both measures of credit spread (Chen 1991, Fama and French 1989, Friedman and Kuttner 1992, and Stock and Watson 1989). Data Description Table 1 provides summary statistics of the sample. For all firms, the mean CDS spread is 126.27 basis points (bps). The median and standard deviation suggest that the distribution of CDS spreads is quite skewed and volatile. The mean change in CDS spreads is small (-0.07 percent), but the range is wide (-17.78 to 23.43 percent). Both the high and low in CDS spread changes are found among the speculative-grade firms; these firms also have higher mean changes in CDS spreads. As expected, all three measures (CDS spreads, equity volatility, and firm leverage) are lower among investment-grade firms and higher among speculative-grade firms. Panel B of table 1 shows that the average CDS spread was highest in 2002; it declined sharply in 2003 and 2004, then leveled off.11 The average monthly return on the NYSE-AMEX-NASDAQ index was 0.47 percent during the sample period, and the average annualized volatility was 19.08 percent. Over the entire sample period, the mean market leverage was 0.23. The average return across the industry portfolios was 0.57 percent, and the mean annualized industry volatility was 25.27 percent. Table 1. Descriptive Statistics Table 1 shows the summary statistics of the variables used in the study. Panel A presents the descriptive statistics for the firm-level variables: five-year CDS spreads (in basis points), CDS spread percentage changes, equity returns, equity volatility, and leverage. The monthly equity volatility is computed as the annualized standard deviation based on daily returns. The firm leverage is computed as the ratio of book debt value to the sum of market capitalization and book debt value. The data are from January 2001 through December 2006. Investment-grade refers to firms with ratings at BAA or above; speculative-grade refers to firms with ratings below BAA. Panel B presents the descriptive statistics of CDS spreads by year. Panel C presents the summary statistics of the market and industry variables. VIX is the implied volatility of the SP 500 index options obtained from the Chicago Board Options Exchange. The market return is the NYSE-AMEX-NASDAQ value-weighted index returns. Other market (industry) variables are the value-weighted average from all firms in the market (industry). We use the Fama-French 12-industry classification. Panel A. Firm Characteristics Variables Mean Median Minimum Maximum All firms CDS (bps) 126.27 63.10 8.65 1,632.36 CDS change (%) -0.07 -0.46 -17.78 23.43 Equity return (%) 1.23 1.13 -4.26 4.86 Equity volatility 0.31 0.28 0.13 0.78 Leverage 0.32 0.29 0.00 0.94 Investment-grade CDS (bps) 60.22 47.10 8.65 444.89 CDS change (%) -0.42 -0.60 -5.06 7.93 Equity return (%) 1.18 1.13 -0.80 4.39 Equity volatility 0.27 0.25 0.16 0.64 Leverage 0.28 0.24 0.00 0.94 Speculative-grade CDS (bps) 295.23 223.24 53.81 1,632.36 CDS change (%) 8.26 5.78 -17.78 23.43 Equity return (%) 1.34 1.34 -4.26 4.86 Equity volatility 0.41 0.39 0.13 0.78 Leverage 0.44 0.43 0.06 0.92 Table 1. Descriptive Statistics (contd.) Panel B. Summary Statistics of CDS Spreads (bps) Year Mean Median Minimum Maximum 2001 151.67 83.33 17.83 3,249.57 2002 212.29 99.70 15.22 3,232.04 2003 150.72 69.62 9.84 2,508.39 2004 109.33 49.27 8.72 1,843.10 2005 107.17 44.90 5.21 2,181.16 2006 94.39 41.40 3.98 2,396.08 Panel C. Market- and Industry-Level Variables Variables Mean Median Minimum Maximum Market aggregate return (%) 0.47 1.11 -10.01 8.41 VIX (%) 19.08 16.69 10.91 39.69 Market leverage 0.23 0.23 0.19 0.27 Industry return (%) 0.57 1.57 -12.64 10.23 Industry volatility (%) 25.27 20.21 11.91 80.57 Industry leverage 0.23 0.17 0.07 0.48 IV. Observable Risk Factors and Correlation in Credit Risk Because most of our analyses involve panel data, our estimates are based on robust standard errors. We estimated these errors by assuming independence across firms, but we accounted for possible autocorrelation within the same firm. We use the contemporaneous variables on the right-hand-side variables . Market and Macroeconomic Effect Table 2 shows the effect of firm-level variables on changes in CDS spreads. We calculate the pairwise correlations (of the raw CDS spread changes or residuals from the regressions) and report the means in the last row of the table. The first column of table 2 shows that, without controlling for any observable covariates, the average correlation in changes in CDS spreads in the entire sample is 21 percent. The correlation ranges from a minimum of -30 percent to a maximum of 72 percent, and the interquartile spans a range of 30 percent. Table 2. Effect of Firm Characteristics on the Correlation in Changes in CDS Spreads Independent Variables Model 1 Model 2 Model 3 Model 4 Model 5 Equity returns -0.567*** -0.473*** [0.023] [0.025] Change in firm leverage 1.662*** 0.318*** [0.114] [0.084] Chance in equity volatility 0.199*** 0.148*** [0.015] [0.012] Constant 0.003*** -0.002*** -0.003*** 0.003*** [0.001] [0.001] [0.001] [0.001] Observations 25,113 25,113 25,113 25,113 25,113 R2 9% 5% 3% 11% Correlation/residual correlation 0.21 0.17 0.14 0.16 0.13 Industry Effect Table 5 shows the average pairwise correlation in CDS spread changes among firms in each of the 11 Fama-French industries.12 The table shows much variation in correlation in credit risk among firms in the same industry. Over the study period, the energy sector has the highest correlation among all industries, whereas the health care sector has the lowest correlation. Only four of the 11 industries h ave a higher average correlation than the overall average of 21 percent. The ranking of correlation by industry changed over the six-year study period. The financial industry had the highest correlation in 2001 and 2002, suggesting that an economic downturn affects financial firms more than others. The energy industry had the highest correlation from 2004 to 2006, likely driven by volatile price movements in oil. The health care, medical equipment, and drug industries had the lowest correlations in three of the six years, and consumer nondurable goods had the lowest correlation in two years. These findings suggest that less cyclical industries have lower correlations in credit risk. Table 5. Correlation in CDS Spread Changes Across Industries Year Ind1 Ind2 Ind3 Ind4 Ind5 Ind6 Ind7 Ind8 Ind9 Ind10 Ind11 2001 0.12 0.44 0.44 0.63 0.24 0.36 0.51 0.28 0.41 0.65 2002 0.13 0.43 0.26 0.26 0.14 0.41 0.43 0.38 0.24 0.17 0.45 2003 0.20 0.33 0.15 0.24 0.05 0.13 0.25 0.36 0.17 0.03 0.29 2004 0.24 0.26 0.21 0.35 0.17 0.21 0.26 0.32 0.23 0.14 0.30 2005 0.22 0.28 0.23 0.55 0.18 0.22 0.22 0.35 0.20 0.23 0.31 2006 0.06 0.07 0.09 0.33 0.17 0.11 0.12 0.26 0.22 0.06 0.13 2001-2006 0.16 0.28 0.18 0.35 0.18 0.17 0.16 0.29 0.19 0.11 0.22 V. Conclusions In this paper, we examine the correlation in credit risk using CDS data. We find that observable variables at the firm, industry, and market levels, as well as macroeconomic variables, cannot fully explain the correlation in credit risk, leaving at least one-third of the correlation in credit risk unaccounted for during the study period (2001-2006). These findings suggest that contagion may be a common phenomenon in an economy and that the doubly stochastic assumption may not hold in general. Because of the large proportion of correlation that cannot be explained by observable risk factors, future research in credit modeling should focus on incorporating unobservable risk factors into models. We also find that credit risk correlation is higher during economic downturns and higher among firms with low credit ratings than among those with high credit ratings. These findings are consistent with the theoretical predictions but inconsistent with some empirical findings based on the M erton default probability measure. We contend that our results are more reliable because of the oversimplified assumptions behind Mertons model and the evidence in the literature that the Merton default probability measure cannot accurately forecast default probabilities.