Title Page
 Table of Contents
 List of Tables
 List of Figures
 The general analytic framework
 Multivariate discrimination...
 The empirical test of the hypothesis...
 Summary and conclusions
 Biographical sketch

Group Title: discriminant analysis of the bankruptcy of securities brokerage/dealer firms /
Title: A discriminant analysis of the bankruptcy of securities brokerage/dealer firms /
Full Citation
Permanent Link: http://ufdc.ufl.edu/UF00098136/00001
 Material Information
Title: A discriminant analysis of the bankruptcy of securities brokerage/dealer firms /
Alternate Title: Bankruptcy of securities brokerage/dealer firms
Physical Description: xviii, 308 leaves : ; 28cm.
Language: English
Creator: Afkham, Iraj, 1935-
Publication Date: 1975
Copyright Date: 1975
Subject: Brokers -- United States   ( lcsh )
Bankruptcy -- United States   ( lcsh )
Management thesis Ph. D   ( lcsh )
Dissertations, Academic -- Management -- UF   ( lcsh )
Genre: bibliography   ( marcgt )
non-fiction   ( marcgt )
Thesis: Thesis--University of Florida.
Bibliography: Bibliography: leaves 299-307.
Statement of Responsibility: by Iraj Afkham.
General Note: Typescript.
General Note: Vita.
 Record Information
Bibliographic ID: UF00098136
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved by the source institution and holding location.
Resource Identifier: alephbibnum - 000164402
oclc - 02787236
notis - AAT0765


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Table of Contents
    Title Page
        Page i
        Page ii
        Page iii
        Page iv
        Page v
    Table of Contents
        Page vi
        Page vii
        Page viii
        Page ix
        Page x
        Page xi
    List of Tables
        Page xii
    List of Figures
        Page xiii
        Page xiv
        Page xv
        Page xvi
        Page xvii
        Page xviii
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    The general analytic framework
        Page 32
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        Page 113
    Multivariate discrimination analysis
        Page 114
        Page 115
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        Page 117
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    The empirical test of the hypothesis and presentation of results
        Page 165
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    Summary and conclusions
        Page 247
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    Biographical sketch
        Page 308
        Page 309
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Full Text



Iraj Afkham






Iraj Afkham


To my family:

Maryam, my wife, and

Ladan and Mahnoosh, my daughters


The author wishes to express his grateful apprecia-

tion to his supervisory committee for their invaluable

thoughts, suggestions, and criticism throughout the course

of completing this dissertation.

A special word of appreciation is due to Dr. Robert

C. Radcliffe who took a far greater part in this endeavor

than could be expected from a person in his capacity. Even

the subject was proposed by him, but the author is the one

who is solely responsible for any defects in its contents.

Dr. Radcliffe generously and willingly spent numerous hours

in individual discussions and various meetings, and injected

invaluable insights into the study. His encouragement and

support at the time when they were most needed cannot be


The author is indebted to Dr. Henry R. Fogler and

Dr. Christopher B. Barry who generously gave their time,

thoughts, and enthusiasm during the previous abortive

research on some other dissertation topics.

This opportunity is taken as the most pleasant one

for extending the author's heartfelt gratitude to the

following persons who have, in one way or another, enriched

his education during his course of study at the University

of Florida: Drs. Fred D. Arditti, Sanford V. Pera, Clement H.

Donovan, Richard A. Elnicki, Jack M. Feldman, Frederick O.

Goddard, John H. James, Richard R. Jesse, Milton Z. Kafoglis,

Gary J. Koehler, Antal Majthay, John B. McFerrin, W.W. Menke,

Richard H. Pettway, James G. Richardson, Jack R. Vernon, Albert

R. Wildt, and William V. Wilmot.

Sincere appreciation is also extended to Dr. Donald

F. Chichester for his editorial assistance, Mr. Thomas A.

Readinger of SIPC for providing the author with some of the

data, Mr. William Ingram, III for assisting in computer

program trouble-shooting, and Mrs. Mary Watson McCoy for

her library assistance.

Finally, profound thanks should be extended to Ms. Kitty

Hinton for her dependable work and typing the manuscript under

most trying circumstances.


ACNKOWLEDGMENTS . . . . . . . . . .

LIST OF TABLES. . . . . . . . . .. xii

LIST OF FIGURES . . . . . . . . . xiii

LIST OF CHARTS . . . . . . . . ... xiv

ABSTRACT. . . . . . . . . ... . xv


I INTRODUCTION . . . . . . . . 1

The Backbone of the Capital Market . . 1
Literature Review . . . . . . 2

Review of SEC Records of the Demise
of Selected Broker/Dealers . . . 5
Study of Unsafe and Unsound Practices
of Brokers and Dealers . . . .. 6
Securities Industry Study by the
Subcommittee on Securities . . . 7
Securities Industry Study by the Sub-
committee on Commerce and Finance . 8
SIPC Study . . . . . . . . 9
The Early Warning Requirement of the
SIPC Act . . . . . . . . 10
The Existing Early Warning Systems . . 12

The Early Warning System of the SEC. . 13
The Early Warning System of the Self-
regulatory organizations . . .. 14

The NASD Failed Firms Project. . . ... 16
Differences Between the NASD Study and
the Present Work . . . . . .. 18

The A'alytic Framework .... . . 18
The Variable Sets. . . . . . ... 19
The Sources of Data . . . . . 19



Data Set . . . . . . . . 20
The Results. ...... . . ....... 20

Different Approaches . . ... . . 21

The Deterministic Approach . . . .. 21
The Probabilistic Approach . . . .. 23
The Blend Approach . . . . . .. 26

The Purpose of the Study . . ... . . 27
The Problem Encountered . . . . .. 27
The Organization of the Dissertation . 28
Notes . . . . . . . . . 30


Introduction . . ... . . . 32
The Hypothesis . . . . . . . 33
Net Cash-Flow Per Dollar of Assets . .. 39

Revenue . . . . . . 40

Internal Factors . . . . . . 40
External Factors . . . . . .. 44

Expenses . . . . . - . 48

Internal Factors . . . . . . 48
External Factors . . ... . . .. 49

Risk . . . .. . . . . . . 50

Definition ...... . . * 51
Common Measures of Risk . . . .. 52

Variance or Standard Variation of a
Single Variable . . . . .. 52
Semi-Variance . . . . . . 53
Third Moment . . ... . . 55
Rate of Growth . . ... . . . 56
Confidence Level . . . . . . 58
Covariance . . . ... . . 59
Correlation Coefficient. ....... 59
Variance of a Group of Variables . 60
The Probability of Disaster Level. ... 63



Risk Factors. . . . . . 65

Risk Associated with Cash-flow. ... . 65
Risk Associated with Revenue. . . ... 67
Risk Associated with Product Lines. . 70
Risk Associated with Places Occupied. 7
Risk Associated with Exchange Rate ... 80
Risk Associated with Age . . . 81
Risk Associated with Excenses . ... 83
Risk Associated with Labor. . . .. 86
Risk Associated with Liquid Assets. . 87
Risk Associated with Securities ... .90
Risk Associated with Credit Extending .. 94
Risk Associated with Inventories. . . 97
Risk Associated with Fixed Assets ... 99
Risk Associated with Patents. . . ... 100
Risk Associated with Debt . . ... 101
Risk Associated with Changes in Economic
and Market Factors . . . ... 103

Mismanagement . . . . . . . . 105
Summary and Conclusion . . . . . 107
Notes . . . . . . . . . 110


Introduction. . . . ... . . 114
General Assumptions . . . . . .. 117
Historical Development. . . . . . 119
Test of Equality of Dispersion Matrices . .121
Mathematical Formulations for Sample Use. . 126

The Two-Group Case. . . . . ... 127

Equal Dispersion Matrices . . . .. 127
Unequal Dispersion Matrices . . .. 131

The k-Group Case. . . . . . ... 134

Equal Dispersion Matrices . . . .. 134
Unequal Dispersion Matrices . . .. 138

Relation to Regression Analysis . . .. 141
The Reliability Tests . . . . . .. 143

The Original Sample Method. . . . .. 143
The Holdout Sample Method . . . . 143

vi ii


The Lachenbruch one-at-a-Time Holdoat
Method. . . . . . . . . 144
The Scrambled Yethod . . . . . .144

The Relative Importance of Variables. ... .146
Compute; Programs . . . . . . . 149

Cooley and Lohnes' Program. . . . ... 149
BMD04M. . . . . . . . . .. .149
BMD05M. . . . . . . . . .. 149
BMD07M. . . . . . . . . .. 150
SAS DISCRIM Procedure . . . . ... .150
SPSS DISCRIMINANT Program . . . ... .151
Eisenbeis and Avery's MULDIS Program. . 151

Application of MDA in Financial Area. . . 151
Notes . . . . . . . . . 158


Introduction. . . ... . . . . .165
Source of Data. . . . . . . .. .167
Selection of Samples. . . . . . .. .169

Failed Firms. . . . . . . .. .169
Nonfailed Firms . . . . . . .. .172

Data Set . . . . . . . . 172
Test I One Year in Advance of Bankruptcy. 175

Introduction. . . . . . . .. .175
Variable Set. . . . . . . .. .176
Discriminant Analysis . . . . .. 180

Methodology . . . . . . ... 180
The Selected Variables ....... . 184
H1 Test of Equality of Dispersion
Matrices. . . . . . . . . 188
The Discriminant Function and Its
Analysis .............. 189
The Differences Between the Group Means 199
The Overlap Between Groups. . . .. .200

Validity Tests. . . . . . . .. 201

Classification of the Original Sample . 204
Classification cf the Holdout Sample. . 208



Potential Biases. . . . . . .. 212

Potential Biases Due to the Sample. . 212
Potential Biases Due to Data. . . .. .216
Potential Biases Due to the Variation
in Reporting Daes. . . . . .. 219
Potential Biases Due to the Variable
Selection . . . . . . ... 222

Results . . . . . . . . . 222

Test II Two Years in Advance of Bankruptcy. 224

Introduction. . . . . . . .. .224
Variable Set. . .. .. ...... . 226
Discriminating Analysis . . . . .. .226

Methology ................ 226
The Selected Variables. . . . .. .227
HI Test of Equality of Dispersion
Matrices. . ...... ..... . 229
The Discriminant Function and Its
Analysis. . . . . . . .. .229
The Differences Between the Group Means 234
The Overlap Between Groups. . . .. .234

Validity Tests. . . . . . . ... 235

Classification of the Original Sample 235
Classification of the Holdout Sample. 235

Results . . . . . . . ... 239

Notes . . . . . . . . . . 243


Summsry . . . . . . . . . 247
Conclusion. . . . . . . . ... 254
Implications. . . . . . . . .. .255
Suggestions for Further Research . . . 257
Notes . . . . . . . . . . 258


A Failed Firms in the Original Sample . .. 259
B Nonfailed Firms in the Original Sample. .. .261



C Failed Firms in the Holdout Sample ... 263
D Nonfailed Firms in the Holdout Sample .. 265
E List of the Data Set Items . . . .. 267
F List of the Variables . . . . ... 270
G The Total Correlation Matrix of Test I. .. 274
H The Variable Structure of Total
Observations in One Year Prior to
Bankruptcy. . . . . . . .. 288
I A Profile of the Selected Variables for
the Reduced Sample. . . . . . 292
J The Linear and Quadratic Equations for
the Reduced Sample. . . . . .. 293
K Classification of the Reduced Sample Using
the Standard Method .......... 295
L Classification of the Reduced Sample Using
the Lachenbrucn Method. . . . .. 296
M Classification of the Original Sample
Using the "Normalized" Model. . . .. 297
N Classification of the Holdout Sample Using
the "Normalized" model. . . . .. 298

BIBLIOGRAPHY . . . ... . . . . . . 299

BIOGRAPHICAL SKETCH. . . . . . .... . . 308


Table Page

1. Some Selected Statistic Which Provide a
Brief Profile of the Securities Broker/Dealer
Firms for Years 1969-74.......................... 3

2. The Failed-Firm Population by Years in
Business........................................ 170

3. Results of the Forward and Backward Selections
in Runs V and VI of Test I........................ 183

4. A Profile of the Selected Variables of Test I... 192

5. The Overlap Between Groups in Test I............. 200

6. Classification of the Original Sample of Test I. 207

7. Classification of the Holdout Sample of Test I.. 211

8. A Profile of the Selected Variables in Test II.. 231

9. The Overlap Between Groups in Test II........... 234

10. Classification of the Original Sample of Test
II .............................................. 238

11. Classification of the Holdout Sample of Test
II .............................................. 240


Figure Page

1. A Pattern Classification System................. 115

2. Hotelling's T2; One Minus Significance Level
As a Function of Sample Size..................... 123

3. Hotelling's T2; One Minus Significance Level
As a Function of d for Several Values of r...... 123





1. Classification of the Original Sample
of Test I ....................................... 209

2. Classification of the Holdout Sample of
Test I... ....................................... 213

Abstract of Dissertation Presented to the Graduate
Council of the Univers ity of Florida in Partial
Fulfillment of the Requirements for the
Degree of Doctor of Philosophy



Iraj Afkham

December, 1975

Chairman: Henry R. Fogler
Co-Chairman: Robert C. Radcliffe
Major Department: Management

This dissertation is an attempt to meet the following

objectives: (1) to identify potential economic and non-

economic factors which might differentiate between finan-

cially distressed firms and those which appear to be

economically viable; (2) to statistically determine a set of

variables which has the highest discriminatory power; and

(3) to suggest both public and managerial action which might

be taken in light of the statistical results obtained in

point 2.

To begin the analysis, it was hypothesized that the

probability of financial distress of a firm at time t is a

function of the net cash-flow per dollar of assets at time

t, the extent of the risk exposure, and the mismanagement of

the firm.

Three poLtntial approaches for predicting failure

are discussed in the dissertation: deterministicc," prob-

abilistic, and blend approach. The deterministicc" approach

was meant to define the traditional method which uses the

financial ratios in conjunction with the MDA technique.

The probabilistic approach was stated to be the one which

does not treat the financial ratios and other related forces

as factors whose values can be determined with certainty at

any point of time in the near future. Rather, it attaches

some probability distribution to each factor, based upon its

historical performance. And, instead of using the MDA

technique, it relies upon the modern probability theories.

The probabilistic approach suggested in this study,

although intriguing, requires a great deal of research be-

fore it can be put to work. The blend approach, used in the

present study, was therefore proposed to act as a bridge

between the traditional and the probabilistic approaches.

It retains most of the favorable properties of the traditional

approach, specially with respect to the MDA technique, yet

incorporates some facets of the probabilistic approach.

After presenting an analytic framework for utilization

of the blend approach and providing a groundwork for the ap-

plication of the MDA technique in two successive chapters,

an effort was made to empirically test the hypothesis. Due

to the confidentiality of a part of financial data, however,

the hypothesis had to be modified by substituting the cash-

flow element with profitability.

Sixty SIPC failed and 60 nonfailed firms were selected

and the original and holdout samples were formed by halving

the entire observations and assigning each half randomly to

one sample. The main thrust of the empirical part rests

upon Test I whose predictive span is about one year. An

attempt was also made to extend the analysis to two years

prior to bankruptcy, in Test II.

Test I examines 83 variables and selects 12 of them

as an "optimal" subset by a multi-stage stepwise selection

procedure. The discriminant model developed in this test

successfully differentiates between failed and nonfailed

groups. The quadratic classification procedure correctly

classifies 98.33 percent of the original sample and mis-

classifies, on average, 13.33 percent of the holdout sample.

These results, along with the results of applying the

scrambled method, Lachenbruch classification procedure, and

"normalized" model, reveal the relatively high accuracy and

validity of the model.

The 12 selected variables measure profitability, risk,

and mismanagement of a firm. The relative discriminatory

powers of these variables in the model reveal that the risk

element is the most significant determinant of the firm's

survival. Profitability and mismanagement are in the second

and third places. This may help managements in making

decisions when considering risky ventures.


Contrary to Test I, the result of Test II was

expectedly less than successful. This was partly due to the

nature of the securities business and partly due to the

type of data available.



The Backbone of the Capital Market

During 1974, the market value of all security

transactions on the United States registered exchanges

amounted to $124.7 billion. The significance of the figure

may become more apparent if it is considered in conjunction

with the nation's Gross National Product in that year. The

GNP in 1974 amounted to $1,397.4 billion and the value of

the securities transactions was as large as an amount equal

to about 9 percent of the GNP. Although this is the lowest

percentage in the past few years (the highest is 23, in 1968),

it strikingly reveals the important role that the securities

broker/dealers play in flowing funds in the nation's capital


The huge volume of securities transactions in each

year is handled by several thousands of broker/dealer firms.

In 1973, for example, the number of registered broker/dealer

firms was 4,088. These firms had employed a total of about

349,000 employees to channel the savings of individuals to

corporate users and to transfer the ownership of outstanding

securities from one investor to another. The total assets

marshalled by the securities firms having gross securities

income of $20,000 and over amounted to $25.9 billion.

In order to present a brief profile of the securities

broker/dealer firms, similar statistics as those stated above

are tabulated in Table 1 for the period 1969-1974. This may

aid in understanding the general position of the securities

industry in the overall economy.

Literature Review

The maintenance of fair and orderly markets for

securities has long been one of the highly desired objectives

of the legislatures, administrators, courts, and various self-

regulatory organizations. The Securities Act of 1933 and

1934 along with the creation of the Securities and Exchange

Commission (SEC) to administer the acts, as well as the

pursuant amendment acts of 1939, 1940, 1964, 1970, 1974, and

1975 partially reflect the main concern of these authorities

in providing conditions designed to create securities mar-

kets capable of meeting the nation's need for investment

capital while operating in the public interest and serving

to protect the public investor.

For a long time, the going presumption was that the

efforts directed toward preventing fraudulent, deceptive

and manipulative acts in the securities.markets would pro-

tect the individual investors and the public interest. It

was not until 1970 that the hardship and sometimes disaster

which were faced by the individual investors whose broker/

dealers went bankrupt or underwent liquidation were widely


No. of Firms ( (9*
(2) (3) (5) (6) Operating Return on
Volume of GNP Firms with No. of (7)* Income Assets (Be-
(1) Securities (in Billions, (4) $20,000 or Employees Total (Before fore Taxes)
Year Transactions, $ Current $) Total More Income (in Thousands) Assets Taxes) (8)i(7)

1969 179,798 725.6 4,681 2,619 366 24,213 561 .023
1970 135,889 722.5 4,614 2,332 338 24,442 271 .011
1971 193,821 745.4 4,553 2,539 353 28,705 1,279 .044
1972 213,548 790.7 4,255 2,512 386 33,728 976 .029
1973 186,173 839.2 4,088 2,164 349 25,948 57 .002
1974 124,709 821.2 3,982 NA NA NA NA NA

*The figures in this column are related to the firms having gross securities income of $20,000 and over, as
reported in column (5).

IA indicates data not available.

Note: Figures in column 2 are for the U.S. registered exchanges only.

Source: For columns (2) and (3), 1974 Statistical Abstracts of the United States.1
For columns (4), (5), (6), (7), and (8), 1974 Securities and Exchange Commission Annual Reports.

realized. The substantial operational and financial

problems that the securities industry experienced during

the period from 1967 through 1970 had significantly dimin-

ished the investors' confidence in the markets; and the need

for urgent corrective action was felt everywhere.

In December 1970, Congress passed the Securities

Investor Protection Act to restore public confidence in the

safety of the securities markets. This legislation estab-

lished the Securities Investor Protection Corporation (SIPC).

And, the corporation provided a limited insurance for the

customer accounts of the securities industry.

During its four years of existence, SIPC has placed

a total of 109 failed firms in liquidation. It has received

a total of 97,230 customer claims. And, as of December 31,

1974, it has distributed securities and cash with an aggregate

value of $241 million to satisfy these claims. Of this

amount, approximately $202 million was derived from debtor

estates. The remaining $39 million, however, was provided

by SIPC through its advances to the trustees. SIPC's

assessments on member firms during the four-year period

totaled $106 million.3

To minimize the exposure of the SIPC fund, which is

backed by a billion dollars of taxpayers' monies, Congress

directed the SEC, at the time of passing the Securities

Investor Protection Act, to compile a list of unsafe and

unsound practices by broker/dealers and to report on the

corrective steps being taken. Before the SEC report is

reviewed, the results of another study which was published

prior to the completion of this report is presented.

Review of SEC Records of the Demise of
Selected Broker/Dealers

This is the title of a staff study undertaken for

the Special Subcommittee on Investigations of the Committee

on Interstate and Foreign Commerce of the House of Repre-

sentatives.4 The need for this study was stimulated by the

crisis of the securities industry over the period 1967-70

which had brought disaster to numerous broker/dealers and

financial hardship for the public investors. The study is

a review of the files of the commission's headquarters offi-

ces for 46 selected broker/dealers who went into some form

of liquidation during the 3-year period ending December 31,

1970. It also incorporates additional information obtained

from other sources; and includes case studies for all 46


The review concluded, among other things, that there

were many reasons for the failures of the subject firms and

the factors were both internal and external to the firms.

Internal factors included capital deficiency, operational

losses, mismanagement and inefficiency in operating the

firms' business, over-expansion of operations, inoperable

and overly expensive modernization programs, back-office

difficulties, irresponsible actions by principals, and

and fraud. External factors included a reduced volume of

trading and a large decline in prices of many stocks during

the period.

Study of Unsafe and Unsound Practices
of Brokers and Dealersa

This study was undertaken by the regular staff of

the SEC pursuant to Section 11(h) of the SIPC Act. Like the

previous study, this one is also on the financial and opera-

tional crisis of 1967-70, but on a larger scale and in a more

comprehensive way. It examines industry conditions and

practices which permitted the crisis to develop. To name

some, but not all, the report cites the following unsound


o Inadequacy and inpermanence of capital.

o Over-emphasis on sales and trading activities

at the expense of operational resources.

o Absence of control of securities traffic.

o Absence of an effective early warning system

in self-regulatory organizations and their

inability to respond to the crisis with

meaningful corrective measures.

o Lack of experience of principal members of

many, mainly small, firms.

The study reviews corrective measures already

instituted, and suggests further actions to be taken by the

broker/dealer firms, self-regulatory organizations, and the

SEC. The corrective measures detailed in the report include,

among other things, increasing capital requirements, revis-

ing or proposing rules to strengthen control over securities

and to provide greater protection for customers' free credit

balances and securities left with brokers, and taking measures

to provide the commission and self-regulatory authorities with

more effective early warning systems.

Securities Industry Study by the
Subcommittee on Securitiesb

During consideration of the SIPC legislation, the

Committee on Banking, Housing, and Urban Affairs of the

Senate concluded that a complete study of the securities in-

dustry and the securities markets should be undertaken by

its Subcommittee on Securities. And, after authorization by

the Senate in June 1971, the study was launched.

This study is the culmination of the analysis of

the information obtained from a variety of sources. Some

of the information was obtained directly from industry and

government sources including responses to a detailed ques-

tionnaire on institutional membership sent to 104 firms,

organizations and individuals. Other information was ob-

tained through holding 18 days of hearings and receiving

testimony from 78 witnesses. It includes also four detailed

case studies of the operation of the regulatory system in

the securities industry.

The contents of the study give the impression that

the sub-committee tends to rely more on the market mechanism

and its competitive nature than on regulations. It also

looks beyond the current problems to the long-range struc-

tural features of the industry, markets, and regulatory


The basic conclusions of the study include, but are

not limited to, the adaptation of greater flexibility in the

industry, the redefinition of the division of responsibility

between SEC and self-regulatory organizations, the provision

of fair, orderly, and open procedure in reaching important

decisions by these organizations, and giving more weight

to competition than to regulation. In the words of the sub-

committee report:

...Regulation, by government and by industry
groups, is an essential element in protection
of investors, but is not an effective substitute
for competition in assuring a flexible and
healthy industry.

The concept of industry self-regulation, sub-
ject to SEC oversight, is well-adapted to
dealing with problems of conduct and ethics,
but it is not well-adapted to dealing with
general economic questions involving competi-
tive interrelationships among firms within
the industry....7

Securities Industry Study by the Subcommittee
on Commerce and Financed

This study was undertaken in fulfillment of the

commitment made by the chairman of the committee on Inter-

state and Foreign Commerce with respect to the committee's

intention to make a complete study of the securities market

and exchanges.

The study is largely the outgrowth of an extensive

number of panel hearings, witness testimonies, views of

industry leaders, interviews in virtually every section of

the country, and reviews of previous and current studies on

the securities industry.

It includes chapters on what went wrong in the

securities business during the period 1967-70, criminal en-

forcement of securities laws, standards for entry into the

securities business, capital for broker/dealers, protection

of customers, accounting and auditing procedures, opera-

tional difficulties, cooperative regulations, central market

system, commission rates, membership qualification for

exchanges, antitrust aspects, and the SEC budget.

Space does not allow the enumeration of the large

number and variety of conclusions reached, but to provide a

feeling about the nature of this study, a sentence from the

related letter of transmittal signed by J.E. Moss, Chairman

of the subcommittee, is quoted here.

...This study is, to my knowledge, the only
comprehensive congressional examination
of the securities industry to have been
completed within the time span of one

SIPC Study

SIPC has also made inquiries of the trustees and

reviewed the reports of the staffs of the self-regulatory

organizations participating in the cases of the 94 broker/

dealer firms liquidated as of December 31, 1973, in an effort

to determine the cause of failure.

The study indicates that the matter of possible fraud

and manipulation which has surfaced in many of these liquida-

tions must be recognized as a major factor in these failures.

Large concentrations of speculative issues in the trading

activities contributed to other failures. Inadequate, in-

accurate, and sometimes nonexistent books and records were

another significant factor. In many cases, the operating

management did not have the qualifications or experience

needed to operate a general securities business. Lack of

adequate capital continues to be mentioned by the trustees

as a major factor in firm failures. According to the study,

this condition results from a number of factors including too

small a capital base, temporary illiquidity, over-commitment

in particular issues, inability to absorb an adverse market

movement, too rapid expansion, improper controls, and operat-

ing losses due to reduced volume. The study states that

there was over-reliance on subordinated capital in a number

of instances. In other cases, the subordination agreement

was allegedly improperly executed, fraudulently induced or

improperly withdrawn placing the firm in net capital viola-


The Early Warning Requirement of the SIPC Act10

Section 5(a)(1) of the SIPC Act requires that the

commission or the self-regulatory organizations notify SIPC

immediately upon discovery of facts which indicate that a

broker or dealer subject to their regulations is in or

approaching financial difficulty.

After recei"'in such notification, SIPC determines

whether to apply for a court decree to initiate liquidation

or to defer action until further information is obtained and

doubt is removed.

There are five conditions specified in Section 5(h)

of the Act. At least one of these conditions must be found

to exist by SIPC to apply for a court decree and by the court

to issue the decree in every case. The court shall issue a

decree if it finds that the member firm:

a. Is insolvent within the meaning of Section 1(19)

of the Bankruptcy Act, or is unable to meet its obligations

as they mature, or

b. Has committed an act of bankruptcy within the

meaning of Section 3 of the Bankruptcy Act, or

c. Is the subject of a proceeding pending in any

court or before any agency of the United States or any state

in which a receiver, trustee, or liquidator for such member

has been appointed, or

d. Is not in compliance with applicable requirements

under the 1934 Acts or rules or regulations of the commission

or any self-regulatory organizations with respect to financial

responsibility or hypothecation of customers' securities, or

e. Is unable to make such computations as may be

necessary to establish complaince with such financial respon-

sibility or hypothecation rules or regulations.

As was mentioned above, the SIPC Act requires that,

when it appears to the SEC or any self-regulatory organiza-

tion that a broker-dealer is in or approaching financial

difficulty, SIPC is to be notified immediately. The statute,

however, does not define "financial difficulty." Neither has

it seemed practicable for SIPC to attempt to define these

terms. In view of the number of self-regulatory organiza-

tions involved and the differences in their rules, procedures,

problems, and the manner in which the various reporting and

surveillance systems operate, SIPC has considered it approp-

riate, up to this point at least, to work with each organiza-

tion separately.

The regulators fulfill the Act's requirement through

regulatory procedures which integrate inspection and report-

ing programs with an early warning procedure for notifying

SIPC. The primary objective of these programs is the early

identification of those members which are in or approaching

financial or operational difficulty and the initiation of

action necessary to protect customers.

The Existing Early Warning Systems

All over the entire securities industry emphasis is now

on the early warning systems by which the financial difficulty

of the broker/dealers is to be detected in advance. The two

main purposes of such early warning systems are: (1) to

afford a self-regulatory organization an opportunity to

initiate procedures so that the broker/dealer in question

does not become a SPIC casualty, and (2) to provide a basis

for notification to SIPC. Inasmuch as these warning systems

are directly related to the subject matter of the present

study, further review of the related material seems approp-


The early warning system of the SEC. The SEC, in

discharging its duties, periodically reviews through on-site

inspections and in-house studies the early warning surveil-

lance tools of the self-regulatory organizations to ensure

that they constitute sound and effective programs.

The commission's early warning and surveillance tools

include Rule 17a-ll, Rule 17a-5(j), and Rule 17a-10. Rule

17a-ll was adopted to provide the commission and the self-

regulatory authority with an adequate and timely flow of

information on the financial and operational condition of

broker/dealers. Among other provisions, it requires a

broker/dealer to notify, by telegram, the commission and the

appropriate self-regulatory organization if it breaks

through certain specified financial or operational parameters.

Rule 17a-5(j) requires a broker/dealer to notify the commis-

sion if its exchange membership is terminated and becomes

subject to the commission's net capital rule. Rule 17a-10

requires a broker/dealer to file Form X-17A-10 annually with

the commission.

An additional financial responsibility rule, Rule

15c3-3, titled "Customer Protection--Reserves and Custody of

Securities," became effective on January 15, 1973. Failure

to comply with the requirements of this rule has, in a

number of instances, been the basis of the statutory condi-


In addition to these rules, the commission, working

together with the NASD and the self-regulatory authorities,

has developed a monthly, combined early warning list and a

Rule 17a-ll list for each regional office. Each month the

self-regulatory organizations submit, for the combined list,

data pertaining to the financial condition of troubled firms

within each commission region. The list is then speedily

transmitted to each regional office chief examiner for his

verification within 24 hours.

Finally, in many cases, the commission's application

for an injunction and the appointment of a receiver has

typically been based on violations of the net capital rules

or such inadequacy of books and records that the firm is un-

able to make such computations as may be necessary to

establish compliance with the rules concerning financial

responsibility or hypothecation of customers' securities.1

The early warning system of the self-regulatory

organizations. Over the years, the exchanges and the NASD

each has developed a complex system of surveillance both on

its own initiative and in compliance with Federal laws. As

a result, many different early warning systems have emerged.

Space does not allow a review of all of these systems indi-

vidually, here. It may, however, be relatively safe to

generalize that a self-regulatory organization places a mem-

ber firm under a special surveillance if its net capital is

deficient, the ratio of aggregate indebtedness to net capital

exceeds the related rules or guidelines, or if the firm's

operating losses in a given period exceed certain criteria.

As an example, the New York Stock Exchange has the following

early warning criteria for carrying organizations:13

1. Rule 325 Capital Ratio at, or in excess of

1,000 percent--as of the date of the Exchange's

Early Warning Report.

2. Cumulative losses during the most recent three-

month period equal to, or in excess of, 50 per-

cent of the organization's tentative net capital.

3. Any firm likely to begin liquidation within the

next six months because of losses, or scheduled

withdrawals of capital, which would jeopardize

their financial viability.

The final point to be noted relates to the case of

NASD. The organization has recently attempted to add a new

and significant feature to its operating early warning system.

Due to the similarity that exists between this feature and

the theme of the present study, it will be discussed in the

following section in more detail. At this point, however,

suffice it to say that, while all the previously-reviewed

studies and the warning procedures base their analysis on

the individual effects of a criterion in a selected set of

criteria, the NASD's additional feature and the present work

consider the collective effects of such factors. The two

approaches may bring about different solutions to the same

problem. But, the superiority of the second approach has

been well established.14

As an example, consideration of a violation of the

net capital rule on the basis of its individual effect may

lead to a different action from that which may be induced

when its effect is considered collectively, in combination

with some other factors) such as net income, for example.

As once noted by SIPC, although in a little different con-


...A violation of the net capital rule might
not portend as serious a situation from the
point of view of customer protection as
originally feared. This rule basically is a
test of liquidity as of a particular time.
It does not necessarily follow that a tem-
porary or possibly inadvertent failure to
comply with the net capital rule makes losses
to customers inevitable.15

The NASD Failed Firms Project16

When the present study was half-way through, it was

found cut that NASD has also undertaken a similar study, but

it has not been published yet.1 It was conducted by E.J.

Dervan and E.I. Altman. It applies the Multivariate Dis-

criminant Analysis (MDA) technique as a tool for predicting

the failure of firms.

The Failed Firms Project uses a sample of two group

firms: The Failed Group included 40 firms which were under

SIPC liquidation; the Active Group consisted of 113 firms.

None of the firms was a member of the New York Stock

Exchange or American Stock Exchange. The financial data

on these firms were obtained from the related Annual Finan-

cial Reports, Form X-17A-10.

The project had been launched to determine if the

reported financial experience of failed firms prior to

their failure could be utilized to establish an early warn-

ing system for identifying potential failures. For this

purpose, it was reported that a total of 82 financial ratios

and non-financial indicators such as age and type of organiza-

tion were examined. The following six variables were selected

as doing the best job, collectively, in discriminating be-

tween active and failed firms:

1. Net Income After Taxes/Total Assets.

2. (Total Liabilities + Subordinated Loans)/Owner's


3. Total Assets/Adjusted Net Capital.

4. (Ending Capital-Capital Additions)/Beginning Capital.

5. Scaled Age.

6. Composite (based on the ten separate variables

treated in a dichotomous way).

Among conclusions of the report were that a majority

of failures arise from a relatively small subset of NASD

member firms; the constructed model proved to be highly accu-

rate by classifying 90.1 percent of an original sample of

failed and active firms; the model is highly reliable, and

it appears to provide significant lead time in which to

initiate corrective action.

The discussion about the results of the NASD study

and their comparison with thosa of the present study is

partly relegated to the next section and partly to Chapter

IV, where the results of this study are presented in detail.

Differences Between the NASD Study
and the Present Work

Although the two studies are similar in a number of

ways, including the application of the MDA technique, they

differ from each other in analytic framework, source of

data, data set, and results. More specifically, the dif-

ferences lie in the following areas:

The Analytic Framework

The NASD study uses the traditional approach, which

may be dubbed deterministicc" to differentiate from the

"probabilistic" approach being presented in the following

section, in building up the prediction model. Whereas, the

approach taken in the present study is a blend of "determinis-

tic" and "probabilistic" approaches. This point will become

more clear when the following section on "Different Ap-

proaches" is reviewed.

The Variable Sets

Although the complete list of the mentioned 82

variables in the NASD study has not been reported, it is most

likely that the two variable sets used in building up the

models differ from one another. The difference is partially

due to the introduction of the "probabilistic" variables in the

present study, such as standard deviation of some financial

ratios and a version of Tchebycheff's inequality for estimat-

ing the probability that the value of some variables fall

below a disaster level, and partly due to the sources of

data which will be discussed below.

The Sources of Data

Form X-17A-10 was the source of data for the original

model of the NASD study. This form contains most of the

financial data which are ordinarily included in Income State-

ment and Balance Sheet. The present study, however, has used

information contained in Form X-17A-5. This form contains

only items which are ordinarily included in Balance Sheet and

lacks any income-statement item. The choice of the source

for the present study was inevitably due to the inavalibility

of Form X-17A-10 to the public.

Data Set

In the NASD study only an original sample has been

employed and it has consisted of 40 failed firms and 113

non-failed firms. In the present study, two independent

samples, i.e., the original sample and the holdout sample,

are used; each sample has 30 failed firms and 30 non-failed


The Results

It is very difficult, if not impossible, to compare

the results of the two studies. The first reason is the lack

of the very important financial elements, i.e., the income-

statement items, in the source of data of the present study.

The second reason is the absence of similar counterparts in

the two studies, especially with respect to the model which

predicts the bankruptcy two years in advance. The third, but

not the last, is the lack of the holdout sample in the NASD

study which might have been due to the nonexistence of suffi-

cient numbers of observations at the time of the study.

Given these limitations, a comparison will be made in Chapter

IV, wherever it is feasible.

Different Approaches

In predicting the financial position of a firm in a

near future, there are at least three potential approaches:

The first one, which has already been put to use, is finan-

cial ratio analysis, previously on the univariate basis and

recently on the multivariate scale. The approach may be

dubbed deterministic. The second one, which has not yet been

developed is a probabilistic approach. The reasons for con-

sidering such an approach, along with a brief illustration of

the concept, will be given in the following paragraphs. Then,

the difficulties associated with its implementation are dis-

cussed. As a consequence, the third potential approach,

which is a compromise between the first and second, emerges.

This last approach is the one which has been adopted in the

present study.

The Deterministic Approach

In the early years of the 1930's, Smith and Winakorl8

undertook a study of 133 financially troubled companies and

concluded that Working Capital/Total Assets, Net Worth/Total

Debt, and Net Work/Fixed Assets were effective indicators of

financial difficulties in firms. In 1931, in another study,

Fitzpatrickl9 employed 13 different ratios and concluded that

all the ratios predicted failure to an extent, and that the

best predictors were Net Worth/Total Debt and Net Profit/Net

Worth. Similar efforts were later made by Merwin,20 Tamari,21
and Beaver. But, none of these researchers came to the

same conclusion. What they had in common, however, was

their approach to the problem which was based on the uni-

variate analysis of the financial ratios.

Later, in 1967, Altman23 improved upon the above

approach by taking advantage of the properties of the multi-

variate discriminant analysis technique. This technique,

which drastically reduces the analyst's space dimensionality

and automatically assigns appropriate weights to appropriate

variables, removed some of the ambiguities, confusions, and

difficulties in the interpretation of the traditional ratio

analysis. Since then this approach has been utilized in

predicting the financial position of firms in various


Although the recent method is both theoretically and

operationally superior to the traditional ratio analysis, it

still shares some drawbacks with the latter: Both methods

treat the process in such a way as though the property of

cause and effect relation perfectly holds in a deterministic

manner. The implied assumption is that a specific stimulus

or a set of stimuli (i.e., changing the financial ratios)

produces a specific response from the firm (i.e., failure).

And, the required effort to predict the firm's state is

solely to identify such stimuli. Furthermore, it is

implicitly assumed that the firm is in isolation and no

external influence (such as changes in the market and eco-

nomic conditions) affects the future financial position of

the firm. In other words, the implied assumption is that

the state of the firm at some time in the future is determin-

istically ascertained by its current and past states.

In the face of widely prevalent uncertainty around

every aspect of the business world, it is obvious that

reliance on such far-out-of-reality assumptions is not

plausible. In fact, the firm is a system that can be re-

sembled to a "grey box," about which we have only a limited

knowledge. The numerous subsystems, including each indi-

vidual, with his own capricious and ever-changing charac-

teristics, constituting the firm, and numerous systems and

subsystems building up the socio-economic environment in

which the firm exists makes any certain inference or pre-

diction about the firm's behavior very difficult, if not

impossible. The complexity of actions and interactions

between these many systems and subsystems are such that we

may never be able to assert with certainty that a specific

input to the firm yields a specific output. Under such

conditions, the best way that we may expect is a vector of

possible outcomes (rather than a single.certain outcome)

with some probabilities attached to each of them.

The Probabilistic Approach

This approach, which has not been developed yet, is

based upon the same concept which drove the statistician to

replace the complexity by uncertainty. The statistician who

knew that in tossing a coin the prediction of the ultimate

position of the coin is conceivably possible by using the

laws of mechanics (given sufficient information about its

initial position, the way in which it is thrown, and the

specifications of the surface on which it falls) concluded

that it is far too difficult a problem for contemporary science

to be solved in this way. He therefore suggested a more op-

erational way of predicting the result of the tossing--the

0.5 probability of getting heads if the coin is a fair one.

Yet, the prediction of the firm's financial position

is not as simple as that of a fair coin. The firm's posi-

tion is a combinatorial phenomenon which is the result of yet-

unexplored special combinations of numerous internal and ex-

ternal (to the firm) factors, each of which has a special

probability distribution of outcome. The concept, neverthe-

less, is straightforward.

To illustrate, suppose that the probability of the

firm's financial distress is affected by only three proba-

bilistic factors A, B, and C, whose a priori probability

distributions may be estimated through past experiments. If

these three factors were mutually exclusive, the probability

of financial distress would equal to the probability of get-

ting any one of these three events. That is:

P(FD) = P(A or B or C) = P(A) + P(B) + P(C) (1)

If A, B, and C are not mutually exclusive, then equation (1)

would not hold. Depending upon the anticipated influence of

these factors on the probability of financial distress, there

are some other choices available. If we have reasons to

believe that each factor has effects individually, the more

relevant equation may be the following:

P(FD) = P(A or B or C) = P(A) + P(B) + P(C) P(A & B)

P(B & C) P(A & C) (2)

On the other hand, if the available evidence suggests that the

effect comes through the joint occurrence of all of the three

factors, then, equation (2) does not explain the case. If

A, B, and C are statistically independent, the proper equa-

tion may be the following:

P(FD) = P(A & B & C) = P(A)P(B)P(C) (3)

Otherwise, equation (4) may be more relevant:

P(FD) + P(A & B & C) = P(A)P(BIA)P(CIA & B) (4)

The crux of the problem lies in the fact that we know

neither all of the probabilistic factors affecting the

probability of financial distress, nor the relationships be-

tween such factors. While some of these factors, such as

long-term debt and short-term debt, may be mutually exclu-

sive, other factors such as revenues from different product

lines may not necessarily be so, and still other factors

such as cash-flow and expenses may be statistically dependent.

Furthermore, it is conceivable that the conditional

probabilities of two factors may not be equal, i.e. P(AIB) f

P(BIA). Such a case may arise when A represents, for ex-

ample, the revenue of the firm and B the general level of

economic activities. Thus, the relevant probability equa-

tion of the firm cannot be a simple equation such as any one

of those mentioned above. Conversely, it is likely that the

function is a combination of a great number of such equations,

embracing a wide range of relevant factors.

The Blend Approach

Although the probabilistic approach seems to be

intriguing, it requires a great deal of research before it

can be actually put to work. More specifically, the research

needed comprises: (1) identifying all the probabilistic

factors affecting the probability of the firm's financial

distress. (2) determining the inter-relationships between

these factors. (3) finding a suitable way to estimate the a

prior probabilities of such factors, and finally (4) for-

mulating the probabilistic model.

Faced with such a huge work, one may think about the

ways of reducing the load. One way to do this, is to bridge

between the deterministic and the probabilistic approach. And

this is the path taken in the present study.

While the blend approach retains all the favorable

properties of the deterministic approach, especially with

respect to the utilization of the MDA technique, it also

incorporates some facets of the probabilistic approach. Such

a midway selection may ultimately be helpful in the develop-

ment of the potentially more comprehensive probabilistic


The Purpose of the Study

The purpose of this study is three-fold:

1. To identify potential economic and non-economic

factors which might differentiate between finan-

cially distressed securities brokerage/dealer

firms and those which appear to be economically


2. To statistically determine a set of variables,

from among the factors in point 1, which has the

highest discriminatory power.

3. To suggest both public and managerial action

which might be taken in light of the statisti-

cal results obtained in point 2.

The Problem Encountered

When the work on the present study had been initiated,

it was hoped that no serious problem would be encountered with

respect to the data needed to test the suggested hypothesis.

Unfortunately, however, when the work on the theoretical part

of the dissertation was finished, and the time for collecting

the data came, the hope was replaced by regret.

The Public Reference Office of the SEC, although co-

operative in supplying the financial Forms X-17A-5 of the

selected companies, denied the accessibility of Forms X-17A-

10, on the ground that they were confidential.

Since Form X-17A-5 contains only items similar to

those of Balance Sheet and lacks about half of the highly

valuable financial information which is contained in Form

X-17A-10, especially with respect to the revenue and expense

items, a full test of the suggested hypothesis is not pos-

sible with the available data. It is hoped that in evalua-

tion of the results of the study, this limitation is kept in

mind. The results might hava been better if all the finan-

cial information could have been included in the analysis.

The Organization of the Dissertation

After the introductory chapter, the analytic frame-

work is set forth in Chapter II which discusses the suggested

hypothesis and determines the potential factors affecting

the probability of financial distress by expanding the

hypothesized function. Included in this chapter is a

section on risk which explores the possible measures of

risk and risk factors.

Chapter III provides a groundwork for the use of the

MDA technique in the analysis. It presents an overall pic-

ture of the MDA technique in application in a summary form.

Chapter IV integrates the materials included in

Chapters II and III into an empirical experiment consisting

of Test I and Test II. This chapter describes the sources

of data and data set, the procedure used in selecting samples,

and the research methodology employed to empirically test the

hypothesis. The greater part of this chapter is devoted to

Test I.

Finally, Chapter V comprises a summary of the

dissertation, the conclusion reached by the empirical ex-

periment, the implication of the results found, and the

suggestions for further research.


1. U.S. Department of Commerce, Statistical Abstracts of the
United States 1974, Washington, D.C.: U.S. Government
Printing Office, 1975.

2. Securities and Exchange Commission, Annual Report 1974,
Washington, D.C.: U.S. Government Printing Office, 1975.

3. Securities Investor Protection Corporation, Fourth
Annual Report, 1974, pp. 2 and 34.

4. U.S. House of Representatives, Review of SEC Records of
the Denise of Selected Broker-Dealers, Staff Study for
the Subcommittee on Investigations (Subcommittee Print),
Washington, D.C.: U.S. Government Printing Office, July

5. U.S. House of Representatives, Study of Unsafe and Un-
sound Practices of Brokers and Dealers, House Document
No. 92-231 of the 92nd Congress, 2nd Session, Washington,
D.C.: U.S. Government Printing Office, 1971.

6. U.S. Senate, Securities Industry Study, Report of the
Subcommittee on Securities, Committee on Banking,
Housing, and Urban Affairs (Committee Print), Washing-
ton, D.C.: U.S. Government Printing Office, February

7. Ibid., pp. 2-3.

8. U.S. House of Representatives, Securities Industry
Study, Report of the Subcommittee on Commerce and
Finance, (Subcommittee Print) Washington, D.C.: U.S.
Government Printing Office, August 23, 1972.

9. This section draws from SIPC, Third Annual Report 1973,
pp. 24-25, and SIPC, Second Annual Report 1972, pp. 25-

10. This section draws from SIPC, Third Annual Report 1973,
which contains an excellent review of the manner in
which SIPC's activities mesh with existing regulatory
and self-regulatory organizations and procedures (see
pp. 6-8 and 18-19 of the report).

11. This section draws from SEC Annual Report 1974, p. 59,
and SEC Annual Report 1973, p. 57.

12. SIPC Third Annual Report 1973, p. 7.

13. The New York Stock Exchange, Early Warning and Surveil-
lance Procedures, Unpublished, July 1974, p. 3.

14. See the Sub-section on the Deterministic Approach on
Page 21.

15. SIPC Third Annual Report 1973, p. 7.

16. E.J. Dervan, Jr. and E.I. Altman, The Failed Firms
Project, National Association of Securities Dealers,
Inc., Unpublished, August 31, 1973.

17. Thanks are due to J.L. Peterman of the SIPC who
brought to the author's attention the existence of such
a valuable study and provided a copy.

18. R.F. Smith and A.H. Winakor, Changes in the Financial
Structure of Unsuccessful Corporations, University of
Illinois: Bureau of Business Research, 1935.

19. P.J. Fitzpatrick, Symptoms of Industrial Failures,
Washington: Catholic University of American Press,

20. C. Merwin, Financing Small Corporations, New York:
Bureau of Economic Research, 1942.

21. M. Tamari, "Financial Ratios as a Means of Forecasting
Bankruptcy," Management International Review, Vol. IV
(1966), pp. 15-21.

22. W.H. Beaver, "Financial Ratios as Predictors of Failure,"
Empirical Research in Accounting, Selected Studies, 1966,
Institute of Professional Accounting (January 1967), pp.

23. E.I. Altman, "Financial Ratios, Discriminant Analysis
and Prediction of Corporate Bankruptcy," Journal of
Finance, Vol. XXIII (1968), pp. 589-609.

24. See, for example, R.O. Edmister, "An Empirical Test of
Financial Ratio Analysis for Small Business Failure
Prediction." Journal of Financial and Quantitative
Analysis (March 1972 pp. 1477-1493; R.R. Dince and
J.C. Fortscn, "Tne Use of Discriminant Analysis to
Predict the Capital Adequacy of Commercial Banks,"
Journal of Bank Research (Spring, 1972), pp. 54-62; and
J.S. Trieschmann and G.E. Pinches, A Multivariate
Model for Predicting Financially Distressed Property-
Liability Insurance Companies, unpublished.




This chapter presents an analytic framework for

identifying potential determinants of a firm's financial

distress. The analytic framework is presented here in a

general form, potentially applicable to all profit-

oriented private organizations. Its application to secu-

rities brokerage/dealer firms will be discussed in Chapter


The analysis begins with the hypothesis that the

probability of financial distress of a firm is a function

of net cash-flow per dollar of assets, risk exposure, and

mismanagement of the firm. By decomposing the cash-flow

equation, internal and external factors affecting revenue

and expenses are examined in some detail. Risk is then

defined, and after discussion of several measures of risk,

risk factors associated with different facets of a firm

are explained. Finally, a brief discussion is given of

factors comprising the "mismanagement" element in the

hypothesized function.

The analysis results in a widely expanded general

function that contains a large number of factors, each of

which possibly affects the probability of a firm's finan-

cial distress. What is needed, however, is a parsimonious

function which contains only a few important factors with

specific relations among them. Such a desired specific

function may be then derived from the expanded general

function by utilizing the multivariate discriminant analy-

sis described in Chapter III.

The Hypothesis

Every industry has its own problems and peculiari-

ties. So does each firm within each industry. Machine

tool companies suffer from significant swings in scales,

steel companies undergo labor strikes, and oil companies

are highly dependent on geological discoveries. Food

companies demonstrate sales stabilities, public utilities

are regulated by governments, and business machine com-

panies are characterized by growth.

In such diverse surroundings any specific analytic

framework for identifying potential determinants of a

firm's financial distress which fits a certain industry

will not be of much help to another industry. What is

needed, then, is a general analytic framework which may

be applicable to any profit-oriented private organization,

large or small, manufacturing or servicing.

The effort undertaken in this chapter hopefully

will meet such a need. It is necessary, however, to treat

most factors as being equally important. This is due to

the fact that a factor which is relatively less important

in one industry may be of greater importance in another

one. Such a treatment, however, may not be harmful, be-

cause, in applying the analytic framework to a specific

industry, appropriate weights will be assigned to the rela-

ted factors.

To start the analysis, it is hypothesized that the

probability of financial distress of a firm at time t,

P(FDt), is a function of the net cash-flow per dollar of

assets at time t (CASHFAt), the extent of the risk assumed

by and imposed upon the firm (RISK), and the mismanagement

of the firm (MISMGT).

P(FDt) = f (CASHFAt, RISK, MISMGT) (1)

The inclusion of these elements in equation (1) is

the consequence of the following line of reasoning;

With respect to the net cash-flow per dollar of

assets, it is both an index of the profitability of the

firm and that of the availability of funds to meet the

fixed obligations in time. This index, which has been

relieved from size effect of the firm, can in fact be

divided into two parts, the first part being the rate of

return on equity capital and the second part being a fund

ratio added to or deducted from this rate due to the changes

in assets (including decrease in the amount of fixed assets

and increase in cash due to the depreciation allowances or

assets sales) and liabilities.

The rate of return on equity capital should have a

direct effect on the probability of financial distress. If

the firm has a high rate of return (compared with either

its cost of capital or the market risk-free rate of inter-

est), it has a lower probability to become financially

distressed than otherwise, other things held constant. The

reason is that the high rate of return indicates that the

firm, in addition to wholly or partially satisfying the

expectations of the equity owners, depending on the height

of the rate and the level of the risk, has been able to

meet the requirements of the owners of debt and preferred

capital, thus alleviating situations which threaten the

existence of the firm. By contrast, a low rate of return,

and in extreme, a negative rate of return, signifies im-

pending inability of the firm to meet its obligations and/or

probable depletion of the equity capital in shock absorbing

the adverse situations. Such situations may develop very

rapidly in some industries such as the securities busi-

ness where the value of most assets is subject to the

changes in market and business activities and the ratio

of equity to debt capital is as high as 1 to 15. There-

fore, the lower is the rate of return on equity capital,

the higher is the probability of financial distress, other

things being equal.

Although the rate of return on equity capital

indicates the profitability of the firm, there have been

occasions that the profitable firm (as indicated by this

rate) has been unable to meet its fixed obligations in

time, due to unavailability of sufficient cash in its

account. On some other occasions the reverse has been

observed. That is, a temporarily unprofitable firm which

has had access to sufficient funds has escaped from finan-

cial distress.

Therefore, it is expected that cash-flow per dollar

of assets has a higher impact on the probability of finan-

cial distress than the corresponding rate of return on


Regarding the risk element in equation (1), it is

a complex factor which reflects the overall risk exposure

of the firm. It is a combination of the risk factors

assumed deliberately by the firm itself and those imposed

upon it by external forces. The factors range from those

associated with liquidity, borrowing and lending, to

business activities, and to changes in market and the

economy in general. This element will be discussed later

in more detail. But, at this point, it is necessary to

present the reason of its inclusion in equation (1).

By any relevant definition of risk in this context,

one would expect to observe some unfavorable, as well as

favorable, impact of risk factors on the performance of the

firm. Thus, it seems to be relevant to relate the prob-

ability of financial distress to risk. To illustrate the

point, consider two such risk factors, i.e., variance of

the rate of return and financial leverage.

Since the income of a firm is subject to the changes

in the level of general business activities (as well as to

many other factors), its rate of return is a random vari-

able. Therefore, the rate of return may vary from a low

point to a high point over time. If the range of this

variation is very wide, other things being equal, there is

a higher probability of facing financial distress, as a

result of several consecutive occurrences of low rates,

than otherwise.

Similar reasoning applies for the dependency of

the probability of financial distress upon the financial

leverage. The owners' equity capital acts as a shock

absorber in a car. If the equity capital constitutes a

larger part of the total capital of the firm, there is a

broader base to support the burden of adverse situations.

That is, when several consecutive losses occur, the fixed

charges of debt capital and other liabilities can be paid

through digging into the equity capital. But, if the

equity portion of the capital is not sufficiently large,

such obligations cannot be met adequately.

With respect to the mismanagement element (MISMGT)

in equation (1), the word may not suitably explain the

purpose. It was, however, intended to embrace and describe

all factors, such as fraud and poor books and records,

which do not fall within the domain of the other two ele-

ments in the equation but have some impact on the prob-

ability of the firm's financial distress.

In equation (1) the relationships between the

independent and dependent variables were considered only

in a general form. It is, however, desirable to obtain

at least the approximation of the true relations in a

specific form. Since each of the above independent vari-

ables is under the influence of numerous factors with some

possible complex interactions among them, error in com-

puting the approximation through their direct measurements

(which is only possible for CASHFA) may highly be magni-

fied. It seems, therefore, more appropriate to break down

the general relations, as far as possible, into several

simpler ones. This may be done by expanding equation (1)

in terms of all factors which seemingly underly the

independent variables. Then, measuring each of these

factors and statistically analyzing their joint effects

on the probability of financial distress may lead to a

better result.

Net Cash-Flow per Dollar of Assets

Starting the expansion of equation (1) by decom-

posing net cash-flow per dollar of assets at time t, it

is known that, by definition, CASHFAt is the ratio of the

available net cash-flow at time t, ACFt, to corresponding

assets, ASSETt. Thus:


Available cash-flow itself, however, is determined

by several other factors.2 To be more exact:


where NIAS = Net income available to shareholders,

DEP = Accounting depreciation and depletion

allowances put aside from operating

income to compensate the part of the

assets used up in generating the


GASSET=Growth in assets, and

GLIAB = Growth in liabilities.

From equation (3), it is seen that available cash-

flow is directly related to net income available for

shareholders as well as to depreciation allowances. An

increase in the assets, however, would have a negative

effect, whereas a decrease in the assets has a positive

effect on the available cash-flow. In contrast, an in-

crease in the liabilities would have a positive effect,

while a decrease in the liabilities has a negative effect

on the available cash-flow.

In order to be able to continue the analysis, first

equation (2) is restated in the following general form:


Subsequently observe that net income is a function of

revenue (REV) and expenses (EXP).

NIAS = h(REV, EXP) (5)


Revenue is the bloodstream of the firm. It is,

however, subject to numerous internal and external factors.

These factors may be grouped accordingly under INTREV and

EXTREV variables, respectively, as in equation (6).


Internal factors. The elements of this group

consist of factors which are more or less under control of

the firm. When managed appropriately, these factors have

positive effects on revenue, otherwise, their impacts are

negative. Such factors include the following:

Number of product lines (NPL) As number of

product or service lines increases, even though they may

not be complementary, they reach a broader market, thus

causing an increase in sales and presumably more revenue,

and vice versa.

Number of places it occupies (NOPLOC). An explana-

tion similar to that made for the number of product lines

applies to the number of places that a firm occupies.

Number of years in the business (NYR). The number

of years that a firm has been in the business should play

a role in its profitability. Nothing can replace the

experience obtained in practice. An established firm is

more likely to be a profitable one. Its mere lasting

existence is the evidence of its being profitable. The

relationship, however, may not be linear.

Research and development (R&D). In some industries,

research and development programs play a vital role in reve-

nue generation. More importantly, in many instances, the

mere existence of a firm in some industries depends on the

extent to which it focuses on R&D acitivites.

Number of patents (NOPAT). Yhe number of patents

and franchises that a firm has in its possession likely

affects revenue. These factors give a monopolistic power

to the firm having them, and leads to potential exploita-


Cash availability (CASHAV). Although availability

of cash is an absolute necessity to run most types of

businesses, and even in some instances taking advantage

of possible opportunities depends on this factor, excess

cash bears an opportunity cost. The income which could

be earned by putting the excess cash into a productive use,

is the associated opportunity cost. Leaving the excess

cash idle does not contribute to the profit; rather it de-

ducts from the potential revenue.

Securities marketability (SECMKT). Marketability

of some securities is a feature which provides the pos-

sibility of replacing a part of the required cash, which

brings no direct yield, with securities such as US

government bonds, which bring some additional yield at

practically no extra risk. If, however, the amount of this

item is in excess of what is necessary, in relation to cash

and other assets, the cost of unripe selling to obtain cash,

or the differential yield forgone by not putting the excess

amount of securities into a more productive investment, is

simply a deduction from actual or potential revenue,


Credit easiness (CREDIT). A mild credit extension

may improve sales, but over-easiness may bring about such

large bad-debt accounts and costs that it may actually

over-offset the increment revenue.

Inventory movement (INVENT). Similarly, a balanced

inventory may facilitate sales, whereas too much investment

in this item deducts from potential profit.

While the effects of CASH and SECMKT on REV are

negative after some point, the relations of CREDIT and

INVENT to REVare positive over a range.

Promotional efforts (PROMOT). Another factor which

is under control of the firm and has some effect on revenue

is promotional efforts. The relationship, however, is a

fuzzy one. The number of psychological and environmental

factors which act and react simultaneously is so many that it

makes clear-cut inferences too difficult, if not impossible.

Yet, the large promotional expense incurred every year in

all industries is an indication of its positive effect in


Accounts payable (ACCPAY). Accounts payable nor-

mally contribute to revenue. This is due to the poten-

tially better use of the funds relieved by such accounts.

Usage of accounts payable, however, is not without limi-

tations. It can reach a point beyond which its associated

costs over-offsets its potential benefits.

Debt capital (DBTCAP). In the world of existing

taxes, the tax treatment of interest expenses encourages

greater use of debt capital. If the firm is operating

profitably and the rate of interest on its debts remains

constant or rises slightly as the debt is increased, the

higher is the leverage, the higher becomes the profit.

Even under the above conditions, however, debt may not

always be profitable. Protective-covenant constraints

such as aminimumworking capital, a percentage limitation

of long-term debt to working capital, and capital expendi-

ture restrictions, which are imposed by debt owners, may

have a significant influence on the firm's profits. Sev-

eral theories have been advanced as to the optimal level

of debt.4 The controversy about them has not, however,

been solved yet.

Debt mix. The optimal mix of short-term (SHRTDT)

in relation to long-term (LONGDT) financing is also of

considerable importance. This is due to both interest

rate differential and other factors such as flexibility,

timing and etc.

There are of course some other internal factors,

but their effects on REV, individually and perhaps col-

lectively, is likely to be minor, relative to the

previously-mentioned factors. Therefore, the above dis-

cussion may be summarized in the following equation:




The relative importance of each of the above

factors in the profitability of a firm differs from one

industry to another and within subdivisions of each

industry. Therefore, the explanatory variables for

describing the impacts of such factors on the probability

of financial distress of the firm should fit to specific

industry and its subdivision to which the firm belongs.

External factors. The elements of this group

consist of factors over which the firm does not have any

control, yet they have some effects on the revenue of the

firm. Among these factors, general business activity has

a special place.

General business activity (GBA). General business

and economic activity is subject to recurrent but non-

periodic fluctuations, called business cycles, over a long

period of time. These fluctuations occur in aggregate

variables such as prices, GNP, investments, employment,

and income. The variables move at about the same time and

in the same direction, but their rates of change are dif-

ferent. Although the effect of these fluctuations on a

firm differs from one industry to another, no firm remains

immune from their impact. In general, over any period of

time, the revenue of a firm is a function of the level of

general business activity.

Interest rate (INTRR). The market prime rate of

interest has also some effects on the revenue of the firm.

This, of course, relates to the lending position of the

firm. For a firm which has a borrowing position the ef-

fect of interest rates on its performance comes through

expenses. If the firm is both lender and borrower at the

same time, the effect cones through both revenue and

expense sides. The net effect, then, may be either posi-

tive or negative, depending upon the net lending or

borrowing position of the firm.

Population (POPUL). Population is another impor-

tant external factor. Not only the number of inhabitants

in the related area matters; the population mix has also

bearing on the revenue. A firm which produces youth

products is more profitable in an area where the young

constitute a higher percentage of the population than in

other areas, other things being equal.

Per capital income (PCINC). Per capital income of

the inhabitants in the area where the firm runs its busi-

ness is another determinant of the firm's revenue. Per

capital income, which is an index of the purchasing power

of the people residing in an area, differs from one region

to another. The variation is due to difference in the mix

of industries and in the prevalence of large cities, where

wages are higher, than in small towns and rural areas.

Competition (COMP). Competition, if it exists,

diffuses the potential market power of the firm. Then,

the price which it puts on its products and, as a con-

sequence, its revenue, is governed by the market. In fact,

the effect of competition, which is the foundation of

capitalism, is to give rewards, in the form of profits,

to the firms which are able to survive, and penalties,

in the form of losses or bankruptcy, to those which are


Competition, in a broad sense, embraces all

factors of production--land (which includes all natural

resources), capital, labor, and cntrcpreneurshin. In

contrast to the firm's desire to have a monopoly position

in selling products and monopsony power in buying supplies

and services of labor, land, and capital, the actual situa-

tion which it faces may be exactly the opposite one. Ex-

istence of labor unions, monopoly in some raw materials,

branch banking systems in some states, and exclusively

governmental purchases are commonplace facts which are faced

by many firms. All these factors have bearings on the

firm's revenue. Indeed, wherever appropriate, COMP factor

should be broken down into the above four dimensions (cor-

responding to the factors of production) in evaluating the

firm's position with respect to competition.

Regulations (REGUL). Rules and regulations are

imposed by either governmental regulatory agencies or

self-regulatory organizations. They are intended to regu-

late various aspects of the activities of firms in dif-

ferent industries. These rules and regulations signifi-

cantly affect the firm's profit. Rules and regulations

governing the rates of public utility companies and rail-

roads can be mentioned as examples. The rules and regula-

tions sometimes go to extremes. In banking, for example,

the regulations require a relatively low marginal rate of

return on capital. Each industry has a set of regulations

relevant to itself. Therefore, in evaluating the position

of the firm in a certain industry with respect to the

prevalent rules and regulations in that industry, factor

REGUL should be broken down into an appropriate number of


The above discussion can be mathematically ex-



REGUL) (8)


The expense element (EXP) in equation (5) may also

be broken down into the part originated by internal fac-

tors (INTEXP), and that caused by external factors (EXTEXP).



Internal factors. Most of the internal factors

affecting the overall expenses of a firm can be categorized

into selling expenses (SELEXP), general expenses (GENEX),

and administrative expenses (ADMEXP). Although all firms

have these three types of expenses, the relative importance

of each type differs from one industry to another. Even in

the same industry the percentage of each type differs

among firms. This very difference may differentiate between

firms operating optimally or near optimally and those which

are run sub-optimally. In fact, there can always be found

one or more expense items which are conspicuous in a

specific industry. As an example, the communication

expenses of firms in the securities industry is prominent.

Evaluation of a firm's position with respect to such an

item may reveal some characteristics of the firm's per-

formance. To obtain such items, it is useful to break down

the above three types of expenses into more detailed com-

ponents peculiar to each industry. In any event, deprecia-

tion expenses, which may belong to one or more of the above

categories, should be singled out for calculating the net

cash-flow, as stated in equation (3). To summarize the

above discussion:


External factors. Although a little fuzzy, all

external factors which affect a firm's profit other than

through the revenue side fall in this category. One of

the most important elements in such factors is taxes.

Taxes (TAX). Aside from the economic purposes

of taxes, i.e., stabilization of economy, redistribution

of wealth, and reallocation of resources, businessmen

look at them as a compulsory payment to government. Indeed,

they reduce the firm's profit by a large percentage, called

tax rate. The legal tax rate varies over a period of time.

Whenever the rate is lower, the income remaining for share-

holders is larger, other things held constant, and vice


Interest rate (INTRR). The role of the interest

rate in the performance of the firm was discussed in the

revenue section. To avoid exclusion of such an important

factor from among the determinants of expenses, however,

it is reintroduced in this section as well. In fact,

since debt usually constitutes a main part of the capital

structure of most firms, the impact of the interest rate

coming through the expense side seems to be more important

for most firms. In any event, the higher is the interest

rate, the larger is the interest charge as part of the

firm's total expenses, and vice versa.

Environmental factors (ENVIRN). Other factors

such as anti-pollution expenses, benevolence expenses, and

the like may be grouped under environmental factors. Firms

manufacturing defense products may incur opportunity costs.

These costs, which are equal to the differential profit

forgone by not employing the resources in a more productive

way should rightly be considered as expenses. In summary:



It is now necessary to refer back to equation (1)

and make an effort to identify the components of the

overall risk of the firm which may play important roles

in determining the probability of financial distress.

Before going into details, however, a digression on de-

finition and measures of risk seems appropriate.


Risk has been defined differently in various

sources, both in view of context and in regard to content.

In Webster's Dictionary, it has been defined as the pos-

sibility of loss, injury, disadvantage, or destruction.6

Sloan and Zurcher defined risk as the possibility of loss

from some particular hazard, as fire risk, war risk,

credit risk.7

In the McGraw-Hill Dictionary, risk has been de-

fined as the exposure of an investor to the possibility of

gain or loss of money. Machol and Lerner defined risk as

the cumulative probability of the return falling below some
level of ruin. And, in the state-of-nature approach to

evaluating risk, it is implicitly defined as the possibility

that the desired, rather than the expected, return will not

be achieved.10

Although all of these definitions suit their own

places, there is need for some definition which fits the

context under study. For that purpose, risk is here

defined as the possibility that actual outcome of a

random variable will deviate from that which is expected.

The random variable can, of course, represent such di-

verse factors as cash-flow, rate of return, expenses,

bad debts, or even the business activity level.

Common YMeasjres of Risk

Having risk thus defined, then, a measure of risk

is a means by which the extent of risk is ascertained.

There is, however, no single measure of risk which can well

explain the actual risk associated with any factor under

consideration. Facing this difficulty, the authors in the

field of economic and business, and especially in the por-

folio literature, have adopted various means as measures

of risk, each with its own virtues and limitations. So

far, the most popular measure of risk has been variance

(or standard deviation) of a random variable around its


Variance or standard deviation of a single

variable. Tobin, in adopting the standard deviation as a

measure of risk, although in a portfolio context, made the

following statement in his celebrated paper on "Liquidity

Preference as Behavior Towards Risk:"12

The risk attached to a portfolio is to
be measured by the standard deviation of R,
OR. The standard deviation is a measure
of the dispersion of possible returns
around the mean value uR. A high standard
deviation means, speaking roughly, high
probability of large deviations from uR,
both positive and negative. A low standard
deviation means low probability of large
deviations from u; in the extreme case,
a zero standard deviation would indicate
certainty of receiving the return 4R. Thus
a high-oR portfolio offers the investor the
chance of large capital gains at the price
of equivalent chances of large capital
losses. A low--R portfolio protects the
investor from capital loss, and likewise

gives him little prospect of unusual gains.
Although it is intuitively clear that the
risk of a portfolio is to be identified with
the dispersion of possible returns, the
standard deviation is neither the sole mea-
sure of dispersion nor the obviously most
relevant measure....

The variance of a random variable is the expected

value of the squared deviations from the mean:

n -2
V(R) = Z (R. R) P. (12)

where V(R) is the variance of the random variable R, n is

the number of possible outcomes, R. is the i-th possible

outcome, R is the expected value of all possible outcomes,

and Pi is the probability or the relative frequency,

whichever is appropriate, of occurrence of the i-th event.

The standard deviation is simply the square root

of the variance:

oR = \V(R) (13)

The variance obtained by equation (12) is in an

absolute term. For comparing the variability of different

distributions, however, there is need for a measure of

relative dispersion. This need is met by forming the

coefficient of variation as expressed below:

CV(R) = V(R) / R (14)

Semi-variance. Markowitz, who pioneered the modern

theory on portfolio selection, considered the standard

deviation, the semi-variance, the expected value of loss,

the expected absolute deviation, the probability of loss,

and the maximum loss as candidate measures of risk.1

Among these measures, however, he concentrated more on the
first two measures. One of the reasons for considering

semi-variance as a candidate measure of risk is its ability

to measure the skewness of the probability distribution of

the random variable, say, return.

Unlike the variance, which ignores the shape of the

probability distribution, semi-variance takes into account

the downside or upside tendency of the probability distri-

bution. Since most economic units associate risk with the

possibility of loss, downside fluctuations in return, and

not dispersion per se, have considerable importance. A

distribution skewed to the left, as indicated by semi-

variance, would involve more chance for low or negative

returns than a distribution skewed to the right, all other

things being the same.

Semi-variance can be expressed in the same way as

variance was stated in equation (12) with the exception

that n and i now represent, respectively, only total num-

ber of those outcomes and the i-th outcome whose values

are smaller (or greater, according to one's purpose) than

R, the overall mean value:

SV(R) = E (Ri R)2 P, (15)

Markowitz suggested the ratio of V(R)/23V(R) as a
measure of relative skewness. For symmetric distributions

this ratio equals one, but it is greater or less than one if

distribution skewed to the right or left, respectively.

Third moment. The measure of skewness is not limi-

ted, of course, to semi-variance. Skewness, in absolute or

relative sense, may be measured also by the third moment of

the probability distribution of the random variable. The

third moment about the mean may be expressed by:

m3 = (Ri -R) P (16)
S i=l1

which is similar to equation (12), with the exception that

the deviations from mean, the term (R R), is now cubed

rather than squared. Cubing the term does not change the

sign of the deviations, but it magnifies the extreme devia-

tions, thus making the risk measurement possible. Against

this advantage, the third moment has the same disadvantage

that other moments have, i.e., it is greatly affected by

a few extreme deviations. In fact, since the absolute

amount of skewness depends on the dispersion of data, a

given value of m3 could be the result of slight asymmetry

together with large dispersion, or great asymmetry with

small dispersion. Its usefulness cannot be doubted, how-

ever, especially when it is combined with other moments.16

Arditti, in an empirical study, "Risk and the

Required Return on Equity,"7 employed second and third

moments along with some other risk factors, and concluded,

among other things, that the market required return had

direct relation with third moment, as was expected from a

measure of risk.

Third moment may become more useful in comparing

among several distributions if it is expressed in a rela-

tive term. This is done by dividing the moment by the cube

of the standard deviation of the random variable and is

called standardized third moment:

a3 = m 3/o (17)

Rate of growth. It was discussed in previous para-

graphs that third moment about the mean is greatly affected

by a few extreme deviations. In fact, the sign of the

moment may be largely attributable to a single large nega-

tive (or positive, as appropriate) deviation. Further-

more, what a measure of skewness shows is the existence of

asymmetry in the frequency distribution. It can not iden-

tify how this asymmetry occurred, i.e., whether it was due

to regular or irregular changes in the values of the random

variable. It is obvious that a steady trend in one direc-

tion removes most of the uncertainty (or risk) associated

with predicting a certain value for the variable, whereas

irregular fluctuations make such prediction very difficult.

In order to detect the regular changes in one direc-

tion, the concept of rate of growth, whether positivee or

negative, can be utilized. There are two ways to get the

rate of growth: the first one is through applying a geo-

metric mean method. The second is through utilizing the

regression analysis concept. The latter method, which is

discussed below, seems to have more advantage than the

former. This is due to its ability to provide some addi-

tional information, such as R the coefficient of deter-

mination of the regression line.

The model which is discussed here has originated

from that which is used for computing the continuously
compounded rate of interest.9 It is expressed as:

V = Aert (18)

where Vt is the value of the variable after t years, A is

the initial value, e = 2.71828, r is the instantaneous rate

of growth, and t is total years under consideration.

To calculate r, first take the natural log from

both sides of equation (18):

In Vt = In A + rt (19)

Then, by utilizing equation (19), regress In Vt
against t, and obtain r as well as In A and R the coef-

ficient of determination, of the regression line. R

which is bounded between zero and one, is a useful measure

of the goodness of fit of the regression line. The closer

is R2 to one, the better is the fit.20

In analyzing risk, it seems more useful to use R

along with r, the rate of growth, and both R2 and r in con-

junction with other measures of risk such as variance and

semi-variance, because each of these measures captures only

a portion of total risk associated with the variation of the

random variable.

Confidence level. Baumol, who was also concerned

about the downside fluctuations of a random variable, such
as return, proposed still another measure of risk.2 His

measure of risk resembles a lower bound or confidence

limit on the expected outcome and is expressed by:

L = R kaR (20)

where L is the suggested measure of risk, R is the mean of

the random variable, k is a positive parameter that re-

presents the number of standard deviations below the mean

value, and oR is the standard deviation. Unlike the

previous measures of risk, however, this one is not in-

dependent of the evaluator's preferences. That is,

before any value can be found for L, a value should be

assigned by the evaluator to k. The dependence of this

measure of risk on the evaluator's utility function detracts

from its usefulness for the purpose, here.

Covariance. One of the useful measures of risk is

covariance between two random variables, say, the firm's

net income and the changes in business activity. It is a

measure of the extent to which the value of the two vari-

ables tend to move up and down together. It can be ex-

pressed by the following equation:

COV(R,Q) = Z (Ri R)(Qi Q) P. (21)
i=l 1

where R and Q are two random variables with expected values

of R and Q, respectively, R. and Q. are the i-th possible

outcomes of R and Q, n is the total possible outcomes of

each variable, and P. is the joint probability that R. and

Q. will occur simultaneously. As is seen from equation

(21), when both Ri and Q. are above or below their related

means for most of the times, the covariance becomes posi-

tive, whereas, when one of them is above its mean more

frequently while the other is below its mean for most of

the times, the covariance becomes negative.

Correlation coefficient. Although the covariance

formula is a good mean to explain the relative movements

of the random variables, its absolute value is difficult

to interpret. A better measure which is directly related

to covariance and can be easily interpreted is correlation

coefficient. It may be expressed by:

COR(R,Q) = COV(R,Q) (22)
CR "' Q

If the two random variables move up and down in

perfect unison, the correlation coefficient is one (they

are perfectly correlated). A correlation coefficient of

zero, on the other hand, indicates that their movements

are completely independent from each other (they are uncor-

related). If the two variables move in reverse direction

in perfect unison, the correlation coefficient is minus

one (-I). Any other imperfect correlation lies somewhere

between +1 and -1.

Variance of a group of variables. In the port-

folio context, where the return on portfolio is dependent

upon the returns on the constituent securities, it has

long been known that the variance of the portfolio return

is a function of the variances of the comprising securities

as well as the correlation coefficients between every pair

of these securities. More exactly:

n n
V(P) = E E X. X. COR(i,j) o. o. (23)
i=1 j= 1 3

where n is total number of securities in the portfolio, X.

and Xj are the percentages of funds invested in securities

i and j, COR(i,j) is the correlation coefficient between

these securities, and oi and .q are standard deviations of

securities i and j.

The concept may be extended to contexts other than

portfolio, where determination of a variation of a single

random variable, such as operating revenue of a firm, in

terms of variations of several other random variables, for

example, revenue from each line of product, is also

desirable. All elements of equation (23) can then be

easily redefined to fit such cases, except for X. and X.
1 3

which should be interpreted in a slightly different way.

In retrospect, when past series data are used, one may

interpret X. and X. as the shares of random variables i

and j, respectively, in the overall picture. For example,

if talking about the variation in the company's revenue,

one may interpret X. and X. as average proportions of the

total revenue which are contributed by product lines i and

j, respectively.

Computation of the collective variance by equation

(23) is easy when the number of constituent random vari-

ables is small. For a large number of such variables the

computation in this way becomes cumbersome. The diagonal
model presented by Sharpe2 has solved this problem. In

the portfolio context, the following steps should be taken

to calculate the variance of portfolio:

First, a suitable market index such as GNP is

selected and then by using the following linear equation

for each security, individually, various returns of each

security are regressed against the corresponding value

of the index:

R.. = A. + B.I. + e.
13 1 1 3 1

where R. is the j-th observation of the randcr variable

i, I. is the j-th observation of the index, A., B. and e.

are y-intercept, slope, and random error related to the

regression line of the variable i, respectively.

Then, by using the results obtained from this

step in the following equation, variance of the portfolio

is calculated:

n 2 2 2 2
V(P) = Xi i + Xn+ln+l (25)
i=1 1 n+ n+

where n is the total number of securities in the portfolio,

X. is the percentage of funds invested in security i, a.

is the standard deviation of e. in (24), a+l is the stan-

dard deviation of the index, and Xn+ is a "pseudo" secu-

rity defined as

X+1 = E X. B. (26)
n+l = i (26)

The expected value of the portfolio, which is

needed for computing the coefficient of variation, is cal-

culated by the following equation:

E(P) = E XiA. + X A1 (27)
i=l 1 i n+l n+l

where A n+ is the expected value of the index. The co-

efficient of variation is:

CV(P) = V(P)/E(P) (28)

Again, these formulations may be applicable to

contexts other than portfolio, as will be shown later.

The probability of disaster level. In the economic

world where the outcomes of most activities are subject to

uncertainty there is always a range of outcomes for each

activity over which the economic unit is drastically af-

fected. The upper bound of the range where the vulner-

ability to the chance event just begins may be referred to

as disaster level.

Examples of disaster level can be found abundantly

in the firm's various facets. If the firm's net cash-flow

drops below a certain point, for example, the firm may

face a hard time. When the sales shrink to a specific

level, it may experience large losses. Or, if the total

asset value declines to a level which is less than the

total liabilities, the firm becomes insolvent.

If a means can be found to show the chance of a

random variable being at the disaster level or below,

then it can be used as an appropriate measure of risk for

dealing with such cases. Fortunately, following Roy,2

one can apply Tchebycheff's inequality in obtaining such

probability. This, of course, assumes possession of in-

formation about the mean and variance as well as the

disaster level of the random variable. The Tchebvcheff

inequality may be expressed as the following in this


P( R El E d) u2/(E d)2 (29)


P(R d) $ 22/(E d)2 (30)

where P is the probability operand and R is a random vari-

able whose expected value, variance, and disaster level

are, respectively, E, o and d.

One of the advantages of the Tchebycheff inequality

is that it does not require the probability distribution of

the random variable to be normal. There is, however, a

difficulty in applying equation (30) in the context used

here. This difficulty is due to the unavailability of

disaster level (d) in any of the related cases. For-

tunately, however, a designated d need not be very exact,

because firms usually are able to manage their affairs over a

range of each variable. And this range may not be rela-

tively too narrow.

A sufficiently close approximation of d may be

obtained by averaging the variable over all available

firms of similar size and nature which have actually ex-

perienced the financial distress. The implied assumption

here is, of course, the dependence of the financial dis-

tress upon the disaster level of the variable.

If data unavailability precludes grouping the

firms of similar size and nature for this purpose, one may

resort to some appropriate ratio of the variable. The

ratio could first be averaged over all available firms

which have experienced financial distress and the average

could then be transformed to an absolute value for each

firm by a simple calculation. As an example, suppose that

the average disaster ratio of sales to assets turns out to

be 0.5, then the disaster level of sales for a firm having

a total assets of one million dollars can be obtained by

multiplying one million by 0.5 which equals $500,000.

Risk Factors

Risk associated with cash-flow (RSKCF). The im-

portance of sufficient cash inflow in meeting the firm's

obligations cannot be over-stated. Since cash-flow is a

random variable, at any point of time, it may take some

value between two possible extreme points relevant to the

firm. But, at some level of cash inflow which is of

course different for each firm, the firm may not be able

to run the business smoothly. The possibility that the

cash inflow falls below this disaster level, then,

constitutes a risk factor which may play an important

role in determining the possible financial distress of

the firm.

If it is possible to estimate such a disaster

level for each firm, it may then be possible to estimate

the probability of its occurrence by resorting to the

Tchebycheff's inequality, as reproduced here.

P(ACF : d) oCF/(ACF d) (31)

where P is the probability operand, ACF is the available

cash-flow variable whose mean value and variance are ACF

and o2 respectively, and d is the disaster level for
available cash-flow.

To find the disaster level of each firm it is

highly desirable to have access to data of as many failed

firms as possible which have the same characteristics,

particularly with respect to size and business nature, as

those of the firm under consideration. But, since finding

such firms is not always possible, a reasonable approxima-

tion may be obtained by first averaging the ratio of ACF

to total assets of all failed firms in the same industry,

and then transforming this average ratio to an absolute

value through its multiplication by total assets of the


To find the probability that the cash-flow of the

firm may fall below this calculated disaster level, it is

necessary to calculate the mean value and variance of

cash-flows of the firm over a recent period of time to be

used, along with the calculated disaster level, in the

Tchebycheff's inequality. The probability obtained in this

way :s a conservative one, yet it may be a useful approxi-

mation to risk assumed by the firm with respect to its

cash-flow procedure.

Donaldson has proposed that the main concern of a

company is to see whether the cash balances fall below

zero or not, and to determine such possibility, he suggests

examining the cash-flows under recession condition.24

If that is the case, ACF in equation (31) may be

redefined to be net cash-flow. Then, the disaster level,

d, changes to zero, and the probability that the net cash-

flow falls below zero becomes equal to or less than the

ratio of the coefficient of variation to the mean value of

the net cash-flow:

P(ACF 5 0) 5 CV(ACF)/ACV (32)

The preference of (31) to (32), or the other way

around, as a determinant of the firm's risk exposure

depends, of course, on the results of empirical checks.

Risk associated with revenue (RSKREV). Risk

associated with revenue is the possibility that actual

revenue will deviate from that which is expected.

Following the discussion above of the measure of

risk section with respect to the properties of the variance

of a random variable, one measures the risk associated with

total revenue by finding the variance of the values taken

by revenue variable over the period under consideration.

Equation (33) may be used for such purpose:

1 2
V(REV) (REV. REV) (33)
n i

where V(REV) is variance of revenue, n is total number of

observations on revenues, REV. is the i-th observation, and
REV is the mean value of total observations on revenue.

This equation provides an absolute value for the vari-

ability of revenue. Its relative value, however, which

is obtained by coefficient of variation, may be more useful

in discriminant analysis:

CV(REV) = V(REV)/REV (34)

As was discussed in previous section, however, the

variance alone does not capture all the risk associated

with revenue. If the frequency distribution of revenue is

skewed to the left, there is higher possibility of loss,

and as a consequence, higher possibility of financial

distress. It may, therefore, be helpful to supplement the

coefficient of variation with a measure of relative skew-

ness. For this purpose it is possible to use either semi-

variance or third moment of revenue. But to choose between

them by detecting the discriminatory power of each of them,

it seems appropriate to use both in this analysis. The

semi-variance of revenue may be expressed by:
1 n
SV(REV) (REV. REV) (35)
n i=l I

where n represents the number of values below the mean,

REV, and REV. is the i-th observation of such values.

The relative skewness, using semi-variance, is

thus obtained by the following ratio:

CSV(REV) = V(REV)/2SV(REV) (36)

The third moment about the mean of the frequency

distribution of revenue may be expressed by:

1 3
m (REV. REV) (37)
3 n i=l I

where right-hand symbols are the same as those in equation


The standardized third moment which indicates the

relative skewness of revenue frequency distribution is

then obtained by:
a3 = m3 / V(REV)2 (38)

For the reasons explained in the measures of risk

section, it may be useful to consider the rate of growth

of revenue in conjunction with the above-mentioned measures

of revenue dispersion and skewness. It is necessary to re-

define the variables in equation (19), first:

In Vt = In A + rt (39)

where A is the initial total revenue, Vt is total revenue

after t years, r is the rate of growth, and t is the t-th

year of T, the total years under consideration.

Then.a regression line is fitted to the points

obtained by plotting the natural log of total revenue of

each year (Vt) against the time (t). The rate of growth

and R2 obtained from this line is then used in the analysis.

Risk associated with product lines (RSKPL). The

risk associated with revenue changes with the number of

product lines that the firm offers. The reason is based on

the same principle applied to diversification in investment.

Indeed, having several product lines may be necessary but

it is certainly not sufficient to reduce risk. If all the

product lines are perfectly positively correlated, with

respect to revenue, with each other, then there accrues no

benefit from such diversification. Their collective per-

formance resembles that of any constituent individual line,

except on a larger scale.

Negative correlations between revenues generated by

each product line, on the other hand, reduce the risk as-

sociated with revenue. The higher is the degree of diver-

sification of product lines with such properties, the lower

is the related risk. The recent great wave of conflomera-
tion seems to be partially, at least, in pursuit of such


Existence of some negative correlations, however,

does not guarantee that the collective risk is changed

significantly. If the analysis of the historical data

indicates that the product line with negative correlation

contributes only a small percentage to the total revenue,

its risk-reducing effect would be minor, and vice versa.

All the above points are accounted for if, follow-

ing the portfolio concept, the variance of total revenue is

expressed by the following function:

n n
V(REV) = Z E X. X. COR(i,j)c. o. (40)
i=l j=l

where n is the number of product lines, Xi, Xj are the

historical average proportions of total revenue which come

from lines i and j, respectively, COR(i,j) is the correla-

tion between revenues from lines i and j, and ai, oj are

standard deviations of revenues from lines i and j,


Under a certain condition, it may be possible to

calculate the risk associated with product lines. This

condition is that the firm should either have only one

store, or else, if it is a multi-store firm, all the stores

should be, revenue-wise, perfectly positively correlated

to each other. If this condition is not met, however,

the calculated risk represents the combined risks of both

product lines and stores.

To find the risk associated with product lines,

assume first that all the lines are perfectly positively

correlated with each other; then all correlation terms in

equation (40) would, by definition, be equal to one. This

constitutes the unper limit of the variance of total reve-

nue. On the other hand, if all the product lines were

perfectly negatively correlated to each other, all correla-

tion terms in equation (40) would, by definition, equal

minus one. This constitutes the lower limit of the vari-

ance of total revenue. For any imperfect correlation,

either positive or negative, between product lines, each

correlation term in equation (40) assumes a value between

-1 and +1. The weighted average of these correlations

then determines the position of the variance of total

revenue between its upper and lower limits.

Bearing in mind the above discussion, one may

express the upper limit of the variance of total revenue

by the following equation:

n n
V(REV) = Z E X. X. a. J. (41)
i=l j=l 1 3 l 3

The case for any position between upper limit and

lower limit could, of course, be expressed by equation

(40) itself. The deduction from variance of total revenue

which resulted from imperfectly correlated product lines,

or equivalently, the risk (although negative) associated

with product lines, is then equal to the negative of the

difference between equations (40) and (41).

n n n n
L =- [ : X. X. . :: X X. COR(i,j) i oj]
i=l j=l 1 1=1 j=l

The first term in the bracket can be rewritten as:

n n n
n X + z E X. X. a. a., for all i/j
i=l 1 i=l j=l 1

The second term in the bracket can be rewritten as:

n n n
E X o. + E X. X. COR(i,j) o. o., for all i/j
i=l i=l j=l 1

Replacing the terms in brackets with their equivalents,
n 2 2
omitting E X o, and factoring common factors, there
is obtained

n n
RSXPL = 2 F X. X. c. o. [1 COR(i,j)] for all ifj
i=l j=l1 1

The negative sign in front of the E notation

indicates that multiple product lines have a risk-reducing

effect, but to compare the effects of various product lines

one should compare their negative effects on reducing risk

associated with total revenue. The larger is the absolute

value of RSKPL, the larger is the deduction from the vari-

ance of total revenue as a result of such diversification,

and vice versa. Therefore, the larger is the absolute

value of RSKPL, the more desirable is the product line, and

in the discussed risk context, the smaller is the risk

associated with it. Conversely, the smaller is the absolute

value of RSKPL, the larg'-r is the risk associated with

product line. The lower bound of the absolute value of

RSKPL is zero, and it occurs just when all the product

lines are perfectly positively correlated, i.e., correla-

tions between all product lines are equal to one and thus

all [l-COR(i,j)] terms in equation (42) become zero. This,

of course, means that no benefit is accrued from such di-


The risk expressed in equation (42) is in an absolute

term. In order to make it in a relative term, and bring

it into a line with the coefficient of variation, divide

both sides of (42) by the mean value of total revenue.

Thus, denoting the relative risk associated with product

line by RRSKPL, there is obtained:

n n
RRSKPL = --- XX. o. o. [1 COR(i,j), for
REV i=l j=l 1 3 1 3
all i / j (43)

If the product lines are many and calculation of

the covariance terms is cumbersome, it may be helpful to

apply the indexing method in computing the risk associated

with product lines. In that case, GNP or another suitable

market index is selected and variables in equations (24)

through (27), which are reproduced here, are redefined to

fit the revenue context. Thus:

REV.. = A. + B.I. + e.
13 1 1 ] 1

where REV.. is the j-th observation of the revenue gener-

ated by product line i, I. is the j-th observation of the

index, and A., B., and e. are y-intercept, slope,and random

error related to the regression line of the product line

i, respectively.

n 2 2 2 2
V(REV) = X + X+1 on+ (45)
i=l n+l n+l
where V(REV) is variance of total revenue,o is the vari-

ance of ei, an+ is the variance of the index, and Xn+ is

"pseudo" product line defined as

Xn+1 = Xi B. (46)

And the mean value of total revenue is obtained by:

REV = E X Ai + Xn+ An+ (47)

Where An+1 is the expected value of the index.

Now, if it is assumed that all the product lines

are prefectly positively correlated to each other, then B

B2 = ... = B = B*, where B* is the slope of the regression

line fitted to past series data on total revenue and the

index values. In that case:

n n
Xn+= X.B. = B* Z X. = B* (48)
i=l i=l1

Replacing (48) in (45), gives the risk associated with

total revenue in the absence of any advantage from diversification.

n 2 2 2
V(REV) = X o2 + B* 3 (49)
i= 1 n+

Reduction in this risk as a result of combining product

lines which are not perfectly positively correlated to

each other is obtained by calculating the difference be-

tween equations (49) and (45). Again, the negativeof this

difference is the risk associated with product lines.

n n
RSKPL= [ o + B*2 2 (z X2 + 2+
i=l =n+l il n+I n+

2= (*2 2n
_n+B -n+l


2 2 n 2
n (50)
RSKPL =-n+ [B*2 ( E XiBi)2] (50)
n+ i=

To get the relative risk associated with product

lines, divide both sides of equation (50) by the mean

value of total revenue.

o2 n
RRSKPL = n+ [B*2 ( X.B.) 2 (51)
REV i=l

Risk associated with places occupied (RSKPO).

Another factor which may have risk-reducing effect on the

firm's position, is the number of places that it occupies.

The effect comes through the same principle as applied to

product lines. Over any period of time, many factors,

such as changes in the competitive forces, changes in the

buying population, and changes in the purchasing power of

the inhabitants of the location where the firm has its

business act and react on the firm's overall performance.

Supposedly, diversification into several places

deducts from the dependency of the firm's performance on a

set of factors peculiar to a certain location. This may

mean reduction in the business risk of the firm, but this

reduction may not materialize if some conditions, similar

to those of product lines, do not exist. To name only a

few, these conditions include existence of negative corre-

lations between each pair of stores, as well as the rela-

tive importance of the contribution that the stores with

negative correlations make to total revenue.

It seems also plausible to expect that the reduc-

tion in risk through multiplication of stores is, ordi-

narily, in addition to that which is resulted from

diversification in product lines. Otherwise, the mul-

tiplication of stores would have a negative effect.

The provision for calculating risk associated with

number of stores is similar to that for product lines.

That is, the firm should either have only one product

line, or else, all product lines should be perfectly

positively correlated to each other.

To calculate RSKPO, the procedure is the same as

that applied to the product lines case. First, suppose

that the stores in different places are perfectly

positively correlated wiLh each other. Thus:

n n
V(REV) = E E Y Y.QQ. (52)
i-1 j=l 1

where V(REV) is variance of total revenue, n is the number

of stores, and Y. and Y. are the historical average pro-

portions cf total revenue which come from stores i and j,

respectively, and Q. Q. are standard deviations of reve-

nues from stores i and j, respectively.

Then, consider the case in which the stores are

not, revenue-wise, perfectly positively correlated with

each other. In that case:

n n
V(REV) = Z Y.Y.COR(i,j)QiQ (53)
i=1 j=l 1

where COR(i,j) is the correlation between revenues from

stores i and j.

The deduction from variance of total revenue as a

result of the imperfectly correlated stores is the differ-

ence between equations (53) and (52). Thus, the risk

associated with stores (although negative) is the negative

of such difference:

n n n n
RSKPO = [ 7 Y.Y.Q.Q. E Y.Y.COR(i,j)Q.Q.] (54)
i=l j=l 3 i=1 j=1l 3

This expression, after some manipulation similar to that in

the product lines case, can be rewritten as the following:

n n
PSK- O - 2 Y.Y.Q.Q. [1 COR(i,j)1, for all i-j (55)
i=l j=l 1

Which can be put in a relative form by dividing by the

mean value of total revenue:

n n
PSKPO = Y.Y.QQ .[l-COR(i,-)], for all i/j (56)
R V i=l j= 1

At this point, it should be noted that when the

firm has more than one product line, or, otherwise, when

the product lines are not perfectly positively correlated

to each other, the calculated RSKPO above represents the

total risk associated with diversification in both dimen-

sions, product lines and stores. For such companies, the

value of this combined risk should conceivably equal that

obtained through product lines analysis.

The risk associated with places that the firm

occupies is not limited to the one calculated above. It

can be extended to cover firms which operate internation-

ally. Companies which are multi-national in nature, are

constantly facing changes in exchange rate, changes in

foreign governments' policies, and changes in the eco-

nomic conditions of these countries. The risk associated

with some of these factors can be quantitatively accounted

for in the analysis, but for other factors qualitative

measures may be more applicable.

Risk associated with eox:oanle rite (RSKXR) The

risk associated with exchange rate is suitable for treating

quantitatively. A part of this risk comes through the net

income before taxes contributed by the firm's divisions in

foreign countries. Another part comes through assets of

these divisions physically placed in such countries. Ac-

cordingly, we may express this risk by the following equa-


n n
RSKXR1 = E X.CV(XR). + Z Y.CV(XR). (57)
i=l i=1

where n is the number of countries in which the firm has a

division, X. is the proportion of net income before taxes
which comes from the division in i-th country, CV(XR) is

the coefficient of variation of the exchange rate in the

i-th country over some period of time, and Yi is the pro-

portion of the assets placed in the i-th country.

The first term in equation (57) is a weighted

average of coefficient of variations of exchange rates of

the related countries, whose weights are the relative

importance of the contribution of each division in foreign

countries to total net income before taxes. The second

term is another weighted average of such coefficients whose

weights are proportions of assets placed in each country.

The more is the company's dependency on the income provided

by a foreign division, and the more it has engaged its

assets there, the higher is its risk with respect to the

exchange rate. From equation (57), it follows that, for a

firm which operates only domestically, X 's and Y 's are

equal to zero, and thus it does not bear any exchange rate


It may be more useful to supplement the above

measure with the relative measure of skewness, the stan-

dardized third moment about the mean of each of the ex-

change rates. The negative sign of the moment may indicate

depreciative tendency of the changes in the exchange rate,

whereas a positive sign may signify appreciative propensity.

Since there are no positive correlations between all ex-

change rates at all times, some component parts of the risk

may be cancelled out, if the weights are in appropriate

proportions. To express the above points in another way:

n n
RSKXR2 = Z X (a3 i + Z Yi(a )i (58)
i=l i=1

where (a3,) is the standardized third moment of the exchange

rate frequency distribution of the i-th country which can

be obtained by applying equations (16) and (17).

The risk associated with exchange rate is then a

function of equations (57) and (58). Thus:

RSKXR = e(RSKXRl, RSKXR2) (59)

Risk associated with age (RSKAGE). The relation-

ship between age and revenue of a firm was discussed

previously. This relationship can now be extended to the

extreme, the firm's financial distress. It has been an

observable fact, as shown by any listing of failed com-

panies, that business failures occur mere frequently in a

certain age group. Conceivably, this age group differs

from industry to industry due to the peculiarities and the

complexities involved in and the experience required by

each industry. In general, however, younger firms are more

apt to fail than older ones. But the relationship is not

linear. In fact, over a certain range of the earlier years

the function is increasing until it reaches a peak point

and then it diminishes. Age, thus, seems to be a rela-

tively important determinant in business failures.

The possibility that a firm faces financial dis-

tress is, therefore, partially dependent upon its abso-

lute age as well as its relative age position in a popula-

tion of failed firms in its industry. To find the risk

that a firm bears by being in a certain age group is, then,

to find the probability that the age of the firm is the

age of failure. To find this probability, take advantage

of the Tchebycheff inequality:

P(A : d) $ 2/(E d)2 (60)

where A is defined here as failure age variable whose mean
value and variance are E and a respectively, and d is

any specified level of age within the range of A.

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