Use of Discriminant analysis in Credit Risk Models

Discriminant analysis is a technique used for classifying a set of observation into groups or classes. It is widely used in finance particularly in loan or credit appraisal.

Credit scoring model assigns a numerical value to a firm which indicates whether a firm is likely to default or not. It is used to assess the creditworthiness of a firm for giving approval of loan in a short span of time.

Some of the models that use Discriminant analysis are

1. Fisher Linear discriminant Analysis
2. Parametric discrimination
3. K-nearest neighbor

Fisher Linear Discriminant Analysis segregates a larger group into homogeneous subgroups. The larger group could be potential borrowers and subgroups could be good and bad borrowers. Altman’s Z score is a famous example of discriminant analysis.

In Altman Z Score the equation use to calculate score is as follows

Z = 0.012T1 + 0.014T2 + 0.033T3 + 0.006T4 + 0.999T5.
Where
T1 measures liquidity, T2 measure profitability, T3 measures operating efficiency, T4 measure market fluctuation of equity and liability and T5 measures sales turnover.

Based on the score (Z score) calculated from the above equation, new borrowers are classified into default or non default subgroups. This model is highly successful in manufacturing sector and is extensively used by banks and other institutions before the sanctioning of loans. Variant of this model is also developed for other sectors. The greatest advantage of this model is its simplicity; it uses only few balance sheet items and requires a minimal time and resources to compute. The basic concept behind this model is Linear Discriminant Analysis.

In Parametric discriminant approach, a score function is used to determine the members of the subgroup. It uses regression, Logit or other statistical techniques for analysis. Whether the value of the score falls above or below a certain threshold determines which subgroup the observation is placed.

In K-nearest neighbor approach, properties of firms that have already fallen into the categories of interest and categorizes a new entrant by how closely it resembles the members already in each of the groups. It is simplest of all machine learning algorithm in which an object is classified by a majority vote of its neighbors, with the object being assigned to the class most common amongst its K nearest neighbors. This method uses regression by simply assigning the property value for the object to be the average of the values of its k nearest neighbors. It can be useful to weight the contributions of the neighbors, so that the nearer neighbor contributes more to the average than the more distant ones.

The approach is depicted in the above figure. The green circle is taken as the sample and the elements in the inner circle are its nearest neighbor. Circles depict the clusters or groups segregated on the basis of the resemblance its test sample.

Various propriety and freely available software are available that provides facilities for discriminant analysis. Some of the softwares that provide discriminant analysis facilities (partial or complete) are SPSS, business objects, cognos and MS Excel.

Sources

1. Measuring Credit Risk and Managing Credit Risk by Arnaud de Servigny and Olivier Renault.
2. http://en.wikipedia.org/wiki/Altman_Z-score
3. http://en.wikipedia.org/wiki/Discriminant_analysis
4. http://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Submitted By:
Mrityunjay Kapoor
Roll Number: 12147
Finance Batch of 2009-11
SIBM Bangalore.