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.