A One-Parameter Representation of Credit Risk and Transition Matrices
by Lawrence R. Forest, Jr. of KPMG Peat Marwick,
Barry Belkin of Daniel H. Wagner Associates, and
Stephan J. Suchower of Daniel H. Wagner Associates
Third Quarter 1998
Overview: This paper presents a one-parameter representation of credit risk and transition matrices. We start with the CreditMetrics view that ratings transition matrices result from the "binning" of a standard normal random variable X that measures changes in creditworthiness. We further assume here that X splits into two parts: (1) an idiosyncratic component Y, unique to a borrower, and (2) a systematic component Z, shared by all borrowers. Broadly speaking, Z measures the "credit cycle", meaning the values of default rates and of end-of-period risk ratings not predicted (using historical average transition rates) by the initial mix of credit grades. In good years Z will be positive, implying for each initial credit rating, a lower than average default rate and a higher than average ratio of upgrades to downgrades. In bad years, the reverse will be true. We describe a way of estimating Z from the separate transition matrices tabulated each year by Standard & Poor (S&P) and Moody's. Conversely, we describe a method of calculating transition matrices conditional on an assumed value for Z.
The historical pattern of Z depicts past credit conditions. For example, Z remains negative for most of 1981-89. This mirrors the general decline in credit ratings over that period. In 1990-91, Z drops well below zero as the US suffers through one of its worst credit crises since the Great Depression. The relatively high proportion of lower grade credits inherited from the 1980's together with the 1990-91 slump (Z<0) accounts for a high number of defaults. Over 1992-97, Z has stayed positive and credit conditions have remained benign. The movements of Z over the past 10 years correlate closely with loan pricing.
Our focus here is on how Z affects credit rating migration probabilities. However, one can also model the effect of Z on the probability distribution of loss in the event of default (LIED), credit par spreads, and ultimately the value of a commercial loan, bond, or other instrument subject to credit risk. By parametrically varying Z, one can perform stress testing to assess the sensitivity of the value of an individual credit instrument or an entire credit portfolio to changing credit conditions. One can also quantify how volatility in Z translates into transaction and portfolio value volatility.
Published in: CreditMetrics Monitor, (Q3 1998), pp. 46-56.
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