Risk-neutral versus objective loss distribution and CDO tranche valuation

Abstract

This paper considers the risk-neutral loss distribution as implied by index collateralised debt obligation (CDO) tranche quotes through a ‘scenario default rate’ model as opposed to the objective measure loss distribution based on historical analysis. The risk-neutral loss distribution turns out to assign greater probability to large realisations of the loss with respect to the objective distribution, thus implying the well-known presence of a risk premium. In the spirit of Elton et al. (2001), the paper measures this premium, regressing the tranche excess returns against the three Fama-French factors, augmented by the credit index excess returns. However, on the basis of the limited available sample data, it finds no evidence of a significant risk premium. Following Tarashev and Zhu (2007), the paper quantifies the correlation premium, pricing CDO tranches and indices under two distributions: risk-neutral and objective. Instead of building a time nonhomogeneous default dependency as per Tarashev and Zhu, the paper assumes a time-homogeneous default correlation, as can be found in the S&P CDO Evaluator. En passant, the paper analyses the implied risk-neutral default-rate distributions calibrated from April 2004 through April 2006, noting the persistence through time of the distinctive ‘bump’ in the distribution tail.