Transition Matrices Conditional on Macroeconomic Cycles: A Portfolio Stress-Test Application

Abstract

Transition matrices show the probabilities of credit rating migrations for a pool of ratings within a particular industry, geographical area, time-horizon, etc. Regulation, in the form of Basel accords, has opted for standards in banking that among other techniques use transition matrices, and thus the probability of default, for internally-based risk-assessment, as well as incorporating the external credit rating in the capital requirement calculation. We address credit-risk through the lens of the recent regulation, IFRS 9, which regulates the immediate recognition of losses on credit for loans entire lifetime if there has been a significant increase in credit-risk from future uncertainty in the macroeconomic environment. Our chosen approach is to simulate Markov chains, for credit ratings, conditional on background information (cycles in the economy). To quantify the effect on losses for a bank, we apply the transition matrices to a portfolio of bonds under the CreditMetricsTMframework for portfolio stress-tests, and use the pricing formula for defaultable bonds given by Jarrow, Lando, and Turnbull (1997) to value the portfolio. We use data on rating changes from Standard & Poor’s for 934 U.S. companies during 1986 – 2018 to estimate the generator matrix, the Weibull-distribution of upgrade and downgrades, and the transition matrix. We compare simulations with a constant rate to the empirical results, to analyze how well the Markov property holds for each rating transition. The rates are then calibrated for macroeconomic cycles in each company’s simulated Markov chain. We allow for two cycles in the economy (”expansion” and ”contraction”) and three magnitudes of the cycles (”low”, ”medium” and ”huge”). The transition matrices are applied to stress-tests in discrete-time for 10-years forward, under time-homogeneous models that analyzes consecutive years of economic expansion and contraction, as well as in a Mixture of Markov chains-model, by Fei et al. (2012), which mixes a Markov chain for business cycles with the Markov chain for ratings. We find that in scenarios of consecutive years of economic contraction and expansion respectively, the future loss distribution is apparent to be affected by the magnitude of the cycles, for those cycles assumed to be low and huge.