Conditioned likelihood estimation of nonnormal distributions: risk estimation of credit portfolios in stressed markets

ABSTRACT Tail loss estimation accounts for risk in a portfolio conditioned on a set of worstcase outcomes, ie, estimates of a returns distribution below a predetermined threshold from which default probability measures can be obtained. However, during periods of market stress or contagion, the returns distribution of financial instruments will tend to exhibit nonnormal return characteristics. This paper presents an empirical model to assess the risk in credit portfolios in distressed markets, based on an information measure obtained by applying the Box-Cox transform to the probability density function. We apply the technique to generate a loss function which is used to assess aggregate risk exposure in actively traded CDO tranches. Based on an analysis of contracts in the CDX NA IG indexes, we examine various likelihood estimators and parameterizations over the period 2007-12. We show that the empirical model provides for a more consistent measure of risk beyond that of standard approaches, particularly during periods of extreme market distress.