Portfolio Credit Risk

Explained:

default mode

expected loss

mark-to-market mode

portfolio credit risk

portfolio credit risk model

unexpected loss

During the 1950s, Harry Markowitz championed the notion that market risk should be managed at the portfolio level. It took almost 50 years for researchers to develop effective models for doing the same thing with corporate credit risk. Certainly, retail credit risk—auto loans, mortgages, credit card debt—has been managed at a portfolio level for decades. This has been possible due to the relative homogeneity of retail obligors. Corporate obligations—loans, bonds, derivatives, etc.—are far less homogenous. Also, they represent greater concentrations of risk. We are more comfortable modeling 50,000 consumer loans of USD 10,000 each as homogenous than we are doing so with 10 corporate obligations of USD 50MM each!

Investors and counterparties have generally managed the portfolio-level implications of credit risk by diversifying their exposures and avoiding concentrations.

Several factors have contributed to the new interest in more systematically measuring and managing the sum credit risk of an entire portfolio of obligations—what is called portfolio credit risk. These include:

bank industry interest in having the Basel II accordpermit the use of internal models for calculating credit risk capital charges;

efforts to improve the application of risk limits and capital allocation for portfolio credit risk;

efforts to price credit derivatives linked to baskets of defaultable obligations;

the emergence of collateralized debt obligations, which represent customized interests in portfolios of defaultable bonds.

Portfolio credit risk models are financial models that assess portfolio credit risk. Output takes various forms. Many models can be run in either of two modes. In a mark-to-market mode fluctuations in a portfolio's market value resulting from defaults or changes in credit ratings are modeled. Output might be the standard deviation or some quantile of market value. This form of analysis differs from that of value-at-risk measures of market risk in that they consider changes in market value due only to obligor-specific credit events. It does not consider, for example, changes in credit spreads due to general market sentiment or changes in liquidity. In a default mode, portfolio losses due to actual defaults are modeled. Output generally includes what are known as:

expected loss: the expected value over some specified horizon of portfolio losses due to default;

unexpected loss: some metric related to the second moment of portfolio losses due to default over the same horizon. Metrics may be the standard deviation or some quantile of portfolio loss.

Both CreditMetrics and KMV offer mark-to-market and default modes.

Portfolio credit risk models are constructed by associating some sort of correlation model with a default model. The default model specifies unconditional probabilities of default for individual obligations. The correlation model assigns default correlations to pairs of obligations. A simple correlation model might assign all pairs of obligations the same correlation. This may be reasonable if obligations are fairly homogenous—perhaps all bank loans. More sophisticated are factor models (also called sector models). These split each obligation's default probability into two components. One is a function of some factor, such as the performance of the stock market. The other is obligor specific. For example, if the the factor is the stock market's performance and all obligors are publicly traded firms, the allocation might be made based upon the betas of the obligors' stocks. Having a common factor impact all of their default probabilities to a greater or lesser extent imposes a correlation on the obligations' defaults. Generalizations allow for multiple factors.

The literature on portfolio credit risk models is extensive. Crouhy et al. (2000) and Gordy (2000) survey the literature and compare standard models.