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3. Annexure Default Prediction Model

Empirical Estimation

Based on the warning signals discussed above, we construct a vector of regressors which we incorporate within a logit regression model of the type: -

Equation 1

Ln(yi) = a0 + b1 MRK/BK + b2CASHFLOW + b3 s(DBT)/BK + b4(INVESTM) + ei

where yi is the odds ratio pi/(1-pi), pi is the probability of default and pi = 1 if the firm's bond has fallen to a D grade and is 0 otherwise. Note that the logistic regression model requires fewer assumptions than the common linear probability model: p = Xb + e.

In addition, the linear model has a major shortcoming: predictions based on the linear version sometimes have no interpretation. For example, using the estimated vector ß and multiplying it by a forecast design matrix, the model can predict default probabilities pit that can be either negative or greater than one. However, this shortcoming can be easily overcome when the model assumes a logit function which generates predicted posterior probabilities between 0 and 1. This is the essence of the approach adopted in this paper.

The model is estimated by the method of maximum likelihood. Under certain assumptions (See Amemiya 1989), the estimated coefficients of the model are asymptotically normally distributed. This last property is used to compute chi-square statistics to determine the level of significance of the variable coefficients included in the model.

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* Contributed by -
Saurabh Joshi & R. T. Sivasubramaniyan,
PGDM - II Finance,
SCMHRD, Pune.