Credit Portfolio Risk and Probability of Default Confidence Sets Through the Business Cycle

Abstract

Transition matrices are an important determinant in risk management and VAR calculations for credit portfolios. It is well known that rating migration behavior is not constant through time in that it shows cyclicality and significant change over the years. We investigate the effect of changes in migration matrices on credit portfolio risk in terms of expected loss and value-at-risk figures for illustrative loan portfolios. The estimates are based on historical transition matrices for different time horizons and a continuous-time simulation procedure. We further determine confidence sets for the probability of default (PD) in different rating classes by a bootstrapping methodology. Our findings are that there are substantial changes in VAR as well as in the width of estimated PD confidence intervals.

Keywords: transition matrices, VAR, credit portfolios, migration matrices, value-at-risk, loan portfolios, PD, probability default, bootstrapping