Probability of Loss on Loan Portfolio

by Oldrich Vasicek of Moody's|KMV

February 12, 1987

Opening Paragraph: Consider a portfolio consisting of n loans in equal dollar amounts. Let the probability of default on any one loan be p, and assume that the values of the borrowing companies' assets are correlated with a coefficient ρ for any two companies. We wish to calculate the probability distribution of the percentage gross loss L on the portfolio, that is,

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