Credit Risk Management of a Portfolio of Loans to Listed Firms

Student Name: R. Shanthanakrishnan

First and second moments of loss from a portfolio of loans were derived using marginal and joint probabilities of default. Default was assumed to occur if the Asset of a company fell below its payable Liability at a given point of time. Since Asset of a firm was not directly observable, its mean level and volatility were derived using Black-Scholes formula by viewing the value of the Asset as the price of the underlying spot, outstanding Liability as the strike price, and Market Capitalization as the price or premium of a call option. Since the Liabilities and Market Capitalizations were observable from the books or stock exchanges (and hence the clause ``listed firms'') marginal default probabilities could be estimated assuming a Normal distribution for the Asset distribution. Joint default probabilities could be estimated under the assumption of Bivariate Normality of Asset distributions of firms in the portfolio, if one had an estimate of the Asset correlation, as the means and variance had already been obtained in the last step. In the literature, the Asset correlation is typically assumed to be same as the Equity correlation, which could be estimated by appealing to the Capital Asset Pricing Model (CAPM) together with the assumption of conditional independence of Equities given the market index. However along with this conventional approach, Asset correlations were also estimated in a straight-forward manner using the Asset value series, which were derived in the first step under the option theoretic framework. The results were then empirically compared on a sample portfolio of loans to five listed firms. Since no significant difference was found in the final moments of loss in the portfolio of loans in the two approaches, the second new approach was recommended because of its computational simplicity, which did not require estimation and additional assumptions of CAPM.