What is the drawback of the default correlation measure and what alternative measure is used in measuring portfolio credit risk?

Question

What will be an ideal response?

Answer 1

The drawback of the default correlation measure found in structural models relates to asymmetrical dependence among firms in regards to defaulting. Alternative models developed to measure portfolio risk treat default as an exogenous variable so that one does not have to depend on default being determined by other variables. These alternative models are reduced-form models. More details on the drawback of the default correlation measure are given below (details on reduced-form models were discussed in previous questions).

Although correlation quantifies the dependence between two variables, it should be noted that correlation is often incorrectly used to mean any notion of dependence between two variables. However, correlation is only one of several measures in statistics used to quantify a dependence structure, and there are reasons this measure is not a suitable one in the case of credit risk modeling. One reason is that the independence of two random variables implies a correlation that is equal to zero. However, conversely, a correlation of zero does not imply independence.

To see the relevance for credit risk management, suppose that there are numerous potential suppliers of a particular part to the automotive industry. Assume that ABC Company is one such supplying firm. From the perspective of the ABC Company, defaults of firms in the automotive industry are likely to have severe adverse economic consequence, potentially leading to its bankruptcy. Hence, from the perspective of an investor in ABC Company's bond, there is high default risk between ABC Company and the automotive industry. However, from the holder of the corporate bonds of companies in the automotive industry, the default of ABC Company is highly unlikely to have any impact on these companies. Thus, from the perspective of the automotive industry, the impact on default risk is likely to be zero.

Because of this asymmetrical dependence and other drawbacks of correlation as a measure of risk, many developers of credit risk models use different measures of dependence to understand the multivariate relationship between all of the bonds in a portfolio. The combination of individual default probabilities (or default distributions) and their dependence are known mathematically as a "copula." What is important to understand is that by using copulas rather than simple correlations to gauge the nature of the dependency between two variables, a modeler can better handle the modeling of extreme events.