Effect of Stochastic and Correlated Defaults and Recoveries on CDO Tranche Returns

Abstract

This article summarizes an analysis designed to determine the effects of stochastic recovery rates (generated by Monte Carlo simulations) and their negative correlation with defaults on different tranches of a given set of CDOs. Following earlier studies that have revealed a negative correlation between default and recovery rates on corporate bonds, with a resulting negative impact on risk-adjusted return projections, the authors cite more recent studies finding a similar negative relationship between overall levels of defaults and recovery rates for CDOs. In periods of high default rates, recovery values in default tend to be low, whereas recovery rates tend to be high when default rates are low. Such a negative relationship has important implications for asset pricing and valuation of credit portfolios; ignoring it may lead to underestimating losses, volatility in the distribution of those losses, and value at risk (VaR) for different tranches of a CDO— particularly in worst-case default scenarios—with the effect on each tranche dependent on its attachment point and its size in the capital structure.