## Wednesday, 31 August 2011

### Of faulty assumptions and more

Rationality and normal distribution of factors are the two assumptions that underlie most theories in finance. The most frequently quoted but unrealistic, may I add!!

So I came across this technique that uses discriminant analysis to predict the failure of a bank. And if the two assumptions mentioned above were actually true, we would have beaten the financial crisis hands down and saved the financial giants from going down in the dumps. Having said that though, this technique is at least worth discussing.

Firms are divided into failing and non-failing firms and each is given a ‘discriminant score’. The technique works as follows:
Discriminant analysis is used to derive a linear combination of two or more independent variables that best discriminate the two groups under consideration, failing and non-failing companies. The discriminant analysis derives a linear combination from the following equation

Z = w1x1+ w2x2+...+wnxn
Where

Z = discriminant score
wi (i=1, 2, ... ,n) = discriminant weights
xi (i=1, 2, ... ,n ) = independent variables, that are various financial ratios in this case

The discriminant score given to each firm is then compared to a cut-off score to determine which group the company in question belongs to (failing or non- failing firm).

Now, in the perfect world where everything followed the ‘norm’, discriminant analysis would have worked perfectly given that the variables in every group followed a normal distribution and the covariance matrices for every group were equal. However, past experiments have revealed that firms and more often than not, failing firms, often violate this condition. So an aberration from the assumption is more of a norm than just an exception.

However, being the ‘bean counters’ that we finance guys are accused of being, a favourable discriminant score should make for a good enough premise for us to declare a firm failing or non- failing. No room for faulty assumptions there!

Reference : Paper titled ‘Choosing Bankruptcy predictors,using Discriminant Analysis, Logit Analysis and Genetic Algorithms’ by the Turku Centre for Computer Science

Posted by
Jyoti Maheshwari
Finance