W E B E X T E N S I O N
22A
Multiple Discriminant
Analysis
A
s we have seen, bankruptcy
—
or even the possibility of bankruptcy
—
can cause
significant trauma for a firm
’
s managers, investors, suppliers, customers, and
community. Thus, it would be beneficial to be able to predict the likelihood of
bankruptcy so that steps could be taken to avoid it or at least to reduce its impact.
One approach to bankruptcy prediction is
multiple discriminant analysis (MDA)
,
a statistical technique similar to regression analysis. In this extension, we discuss
MDA in detail and illustrate its application to bankruptcy prediction.
1
Suppose a bank loan officer wants to segregate corporate loan applications into those
likely to default and those unlikely to default. Assume that data for some past period are
available on a group of firms that includes companies that went bankrupt as well as com-
panies that did not. For simplicity, we assume that only the current ratio and the debt/
assets ratio are analyzed. These ratios for our sample of firms are given in Columns 2
and 3 at the bottom of Figure 22A-1. The Xs in the graph represent firms that went
bankrupt; the dots represent firms that remained solvent. For example, Firm 2, which
had a current ratio of 3.0 and a debt ratio of 20%, did not go bankrupt. Therefore,
its current ratio and its debt/assets ratio are marked with a single dot in the two-
dimensional graph; this dot is labeled
“
A
”
and is shown in the upper left section of the
graph. Firm 19, which had a current ratio of 1.0 and a debt ratio of 60%, did go bank-
rupt, so an X is used to mark its current ratio and debt/assets ratio. This X is labeled
“
B
”
and is shown in the lower right section of Figure 22A-1.
The objective of discriminant analysis is to construct a boundary line through the
graph such that firms on one side of the line are unlikely to become insolvent
whereas those on the other side are likely to go bankrupt. This boundary line is
called the
discriminant function
, and in our example it takes this form:
Z
¼
a
þ
b
1
ð
Current ratio
Þ þ
b
2
ð
Debt ratio
Þ
Here Z is called the
Z score
, the term a is a constant, and b
1
and b
2
indicate the
effects of the current ratio and the debt ratio on the probability of a firm going
bankrupt.
Although a full discussion of discriminant analysis would go well beyond the scope of
this book, some useful insights may be gained by observing the following six points.
1
This section is based largely on the work of Edward I. Altman, especially these three papers: (1)
“
Finan-
cial Ratios, Discriminant Analysis, and the Prediction of Corporate Bankruptcy,
”
Journal of Finance
,
September
1968,
pp.
589
–
609;
(2)
with
Robert
G.
Haldeman
and
P. Narayanan,
“
Zeta
Analysis:
A New Model to Identify Bankruptcy Risk of Corporations,
”
Journal of Banking and Finance
, June 1977,
pp. 29
–
54; and (3) John Hartzell and Matthew Peck,
“
Emerging Market Corporate Bonds, A Scoring Sys-
tem,
”
Emerging Corporate Bond Research: Emerging Markets, Salomon Brothers
, May 15, 1995. The last arti-