Modeling systematic consumer credit risk: Basel II and reality

RMA Journal, The, Dec, 2003 by Daniel Rosch, Harald Scheule

Asset correlations are a major driver of regulatory capital requirements in the new Capital Accord's IRB approach for retail loans. Daniel Rosch and Harald Scheule show that empirical values for the correlations might be much lower than assumed by the Accord, particularly when default risk is modeled on a point-in-time basis.

The Basel Committee on Banking Supervision in April 2003 issued its third proposal for a revision of the standards for banks' capital requirements. (1) A significant part is devoted to the evaluation of the credit risk of retail loan portfolios. Two important input parameters are default probabilities and correlations. For the Internal Ratings-Based Approach, the capital requirement is calculated as the product of exposure at default (EAD), loss given default (LGD), and conditional default probability (CPD). The conditional default probability can be interpreted as a "very bad case" default probability. It depends on the unconditional probability of default (PD) and the asset correlation (k).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [PHI](*) denotes the cumulative standard normal distribution function and [[PHI].sup.-1](*) its inverse.

The model assumes that a default event happens if the value of a borrower's assets falls short of the value of debt. (2) The asset returns are driven by a systematic and an unsystematic risk component. The weight of the systematic risk driver is given by [square root of ([kappa])]. It describes the impact of common risk sources on asset returns. Thus, the correlation of the asset values of two borrowers is an indicator for the degree of co-movements. Default correlations can be analytically derived from the asset correlations.

This capital requirement formula is based on a VaR (value at risk) approach. It is assumed that the value of the common risk factor is more or equally adverse than 99.9% of all possible outcomes. Thus, asset returns are jointly driven downward and default probabilities upward, leading to capital charges that seek to cover losses caused by this adverse environment.

While banks are permitted to provide their own estimates for default probabilities, the correlations are prescribed by the Basel Committee due to limited empirical evidence on their magnitude. Figure 1 shows that asset correlations specified by the Basel Committee depend on the default probability and exposure class:

* 15% for residential mortgage exposures.

* Depending on the PD, 2-11% for qualifying revolving exposures (e.g., credit card loans).

* Depending on the PD, 2-17% for other retail exposures.

[FIGURE 1 OMITTED]

If time series of default observations are available, asset correlations can also be empirically estimated. (3) Therefore, this article uses the annual delinquency rates filed by 400 representative U.S. banks from 1984 to 2002. We assume that the delinquency rate is a good approximation of the default rate for a given year. The delinquency rates are filed by the American Bankers Association (4) and are published separately for the categories shown in Figure 2.

In addition, we extend the data by U.S. macroeconomic risk factors obtained from the Organization for Economic Cooperation and Development.5 They serve as proxies for the business cycle and cover the following areas:

* Demand and output.

* Wages, costs, unemployment, and inflation.

* Supply-side data.

* Savings.

* Fiscal balances and public indebtedness.

* Interest and exchange rates.

* External trade and payments.

* Miscellaneous.

As is common in econometrics, changes of macroeconomic variables are taken as risk factors where appropriate and all risk factors are lagged by one year. The risk factors used in the analysis are:

* Current account balance in terms of GDP.

* Average real wage index.

* Change in consumer prices.

* Change in government consumption.

* Change in import prices.

* Change in unit labor costs.

* Lending interest rate.

* Change in exports of goods and services.

* Deposit interest rate.

* Gross national savings in terms of investments.

* Unemployment rate.

* Real effective exchange rate.

As a first step, we assume that the default probabilities are constant over time (through-the-cycle rating). In a second step, we assume that the default probabilities change during a business cycle and thus can be explained by observable macroeconomic risk drivers (point-in-time rating). As a matter of fact, the presented risk factors represent the respective point in time of the business cycle and are not necessarily responsible for the default probabilities themselves. Figure 3 shows the realized and estimated default rates of the exposure category "Automobile, direct" for the two rating approaches.

[FIGURE 3 OMITTED]

We tested the economic plausibility of all macroeconomic variables, e.g., that an increase of GDP leads to a lower default rate in the next year. Figure 4 shows the estimated average default rates and asset correlations for the two ratings systems.