Bankruptcy prediction

**Introduction**

Attempts to develop bankruptcy prediction models began seriously

sometime in the late 1960’s and continue through today. At least three

distinct types of models have been used to predict bankruptcy:• statistical models (primarily, multiple discriminate analyses-

MDA), and conditional logit regression analyses,

• gambler’s ruin-mathematical/statistical models,

• artificial neural network models.Most of the publicly available information regarding prediction

models is based on research published by university professors. Commercial

banks, public accounting firms and other institutional entities (bond

ratings agencies, for example) appear to be the primary beneficiaries of

this research, since they can use the information to minimize their

exposure to potential client failures.While continuing research has been ongoing for almost thirty years,

it is interesting to note that no unified well-specified theory of how and

why corporations fail has yet been developed. The available statistical

models derive merely from the statistical optimization of a set of ratios.

As stated by Wilcox, the „lack of conceptual framework results in the

limited amount of available data on bankrupt firms being statistically

‘used up’ by the search before a useful generalization emerges.“How useful are these models? Almost universally, the decision

criterion used to evaluate the usefulness of the models has been how well

they classify a company as bankrupt or non-bankrupt compared to the

company’s actual status known after-the-fact (that is ex post). Most of the

studies consider a type I error as the classification of a failed company

as healthy, and consider a type II error as the classification of a healthy

company as failed. In general type I errors are considered more costly to

most users than type II errors. The usefulness of fail/nonfail prediction

models is suggested by Ohlson (Ohlson, J.A., „Financial Ratios and the

Probabilistic Prediction of Bankruptcy,“ Journal of Accounting Research,

Spring 1980.):“…real world problems concern themselves with choices which have

a richer set of possible outcomes. No decision problem I can think of has a

payoff space which is partitioned naturally into the binary status

bankruptcy versus non-bankruptcy…I have also refrained from making

inferences regarding the relative usefulness of alternative models, ratios

and predictive systems… Most of the analysis should simply be viewed as

descriptive statistics – which may, to some extent, include estimated

prediction error-rates – and no „theories“ of bankruptcy or usefulness of

financial ratios are tested.”Subject to the qualifications expressed above, bankruptcy

prediction models continue to be used to predict failure.The early history of researchers’ attempts to classify and predict

business failure (and bankruptcy) is well documented in Edward Altman’s

seminal 1983 book, Corporate Financial Distress. There appears to be no

consensus on what constitutes business failure. However, most businesses

are considered to have failed once they have entered formal bankruptcy

proceedings.

**A Short Z-Score History**

In 1966 Altman selected a sample of 66 corporations, 33 of which

had filed for bankruptcy in the past 20 years, and 33 of which were

randomly selected from those that had not. The asset size of all

corporations ranged from $1 million to $26 million…approximately $5

million to $130 million in 2005 dollars.

Altman calculated 22 common financial ratios for all 66

corporations. (For the bankrupt firms, he used the financial statements

issued one year prior to bankruptcy.) His goal was to choose a small number

of those ratios that could best distinguish between a bankrupt firm and a

healthy one.

To make his selection Altman used the statistical technique of

multiple discriminant analysis. This approach shows which characteristics

in which proportions can best be used for determining to which of several

categories a subject belongs: bankrupt versus nonbankrupt, rich versus

poor, young versus old, and so on.

The advantage to MDA is that many characteristics can be combined

into a single score. A low score implies membership in one group, a high

score implies membership in the other group, and a middling score causes

uncertainty as to which group the subject belongs.

Finally, to test the model, Altman calculated the Z Scores for new

groups of bankrupt and nonbankrupt firms. For the nonbankrupt firms,

however, he chose corporations that had reported deficits during earlier

years. His goal was to discover how well the Z Score model could

distinguish between sick firms and the terminally ill.

Altman found that about 95% of the bankrupt firms were correctly

classified as bankrupt. And roughly 80% of the sick, nonbankrupt firms were

correctly classified as nonbankrupt. Of the misclassified nonbankrupt

firms, the scores of nearly three fourths of these fell into the gray area.

The Z Score IngredientsThe Z Score is calculated by multiplying each of several financial

ratios by an appropriate coefficient and then summing the results. The

ratios rely on these financial measures:

• Working Capital is equal to Current Assets minus Current Liabilities.

**• Total Assets is the total of the Assets section of the Balance Sheet.**

• Retained Earnings is found in the Equity section of the Balance Sheet.