Portfolio Probability of Default: An Alternative to Simple Average

Abstract

In this paper we propose a statistically derived measure as an alternative to the simple average PD to provide more accurate risk assessment at portfolio level. The theoretical analysis is followed by a numerical example in sections 3 and 4. We then assess the accuracy and representativeness between the simple average and the proposed measure using maximum likelihood analysis. The statistical properties of the proposed approach is discussed in section 5 together with graphical illustration of the inferences based on the joint probability distribution on portfolio level. The proposed alternative works well with current industry risk management frameworks and procedures. Our proposal address several flaws that comes with the ordinary simple average approach and reconfirms the common understanding that the credit default are of Bernoulli nature with non-identical distributions.