an investigation into the efficacy of beta as a risk ... - …
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AN INVESTIGATION INTO THE EFFICACY OF BETA AS A
RISK DISCRIMINATOR IN PUBLIC UTILITIES
by
DALTON LEE BIGBEE, B.A., M.B.A.
A DISSERTATION
IN
BUSINESS ADMINISTRATION
Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for
the Degree of
DOCTOR OF BUSINESS ADMINISTRATION
Approved
May, 1981
ACKNOWLEDGMENTS
I am indebted to Professor William P. Dukes for both
his able guidance of this dissertation and his original
suggestions which determined the direction of my research. I
am also indebted to Professors Oswald D. Bowlin, William J.
Conover, and J. William Petty for their timely contributions
and helpful criticisms. Ms. Cindy Adkins and Mrs. Sue Jordan
provided invaluable typing assistance, for which I am deeply
grateful. Finally, I must acknowledge the faithful support
and encouragement of my wife, Anita, and my children, Amy,
Nathan, and Aaron, from whom much time has been taken and to
whom it must now be repaid.
ii
CONTENTS
ACKNOWLEDGMENTS ii
LIST OF TABLES vi
I. INTRODUCTION 1
II. HISTORICAL DEVELOPMENTS 5
The Development of the Capital Asset Pricing Model 5
The Application of the CAPM to the Cost of Capital Problem 15
The Application of the CAPM to the
Regulatory Process 18
III. CRITICISMS OF THE CAPITAL ASSET PRICING MODEL . . 28
Empirical Problems 28
Validity of the Assumptions 28 The Problem of Equilibrium 30
Empirical Findings versus Model
Specifications 30
Measurement Problems 34
The Investment Horizon 34
The Relevant Risk-Free Rate 35
The Number of Holding Periods 36
The Proper Market Index 37
The Choice of Estimating Equations . . . 38
Misleading Shifts in Beta 38
Problems in Applying CAPM to Public Utilities 40
iii
nimm^ ui n
Summary 41
IV. METHODOLOGY 44
The Risk Variables 45
Xij: Vulnerability of Product Demand . . 46
X2j: Regulatory Environment 46
X3j : Inflation 47
X4j : Operating Leverage 49
X5j: Financial Leverage 49
X5j : Firm Size 50
Xyj: Growth in Operating Earnings . . . 51
Xgj: Growth in Earnings per Share . . . 51
X9j: Interest Coverage 52
Xioj: Trend of Interest Coverage . . . . 52
Xiij: Liquidity 53
Xi2j and Xi3j. Variability and Trend of EPS 53
The Creation of Risk Classes by Clustering 55
The Need for Principal Components
Analysis 60
Testing the Hypothesis 64
V. RESULTS AND INTERPRETATION 65
Principal Components Analysis 65
Interpretation of the Principal Components 70 The Results of the Clustering 74
IV
VI. SUMMARY AND CONCLUSIONS 82
Conclusion 87
BIBLIOGRAPHY 90
APPENDIX: PUBLIC UTILITIES IN THE DISSERTATION . . . . 96
itv
LIST OF TABLES
TABLE PAGE
2-1 Determination of Required Revenue 21
5-1 Eigenvalues for Principal Components 66
5-2 Initial Variable Loadings on the Principal Components 68
5-3 Rotated Variable Loadings on the Principal Components 69
5-4 The First Twenty Iterations of the Clustering Process 75
5-5 Composition of Multiple-Firm Clusters at M = 115 76
5-6 Selected Iterations of the Clustering
Process 78
5-7 Results of Elton-Gruber Stopping Procedure . . 80
5-8 Results of Stopping at Selected Iterations . . 81
VI
CHAPTER I
INTRODUCTION
One of the most innovative developments in the field
of finance in recent years is that of the capital asset
pricing model. The derivation of the model and the extent of
its application will be discussed in detail in the next
chapter; put simply, the model attempts to describe or pre
dict the relationship between risk and return. The rela
tionship is assumed to be one in which firms with high levels
of risk generate returns higher than those of firms with low
levels of risk.
This dissertation examines the ability of beta, the
slope of the regression line between a security's return and
a "market" return, to discriminate adequately between public
utilities with varying levels of underlying risk. In the
course of the examination, the role of the capital asset
pricing model in public utility regulation will be discussed.
Additional discussion will focus on the nature of risk
itself, and the critical assumptions about risk that are
implicit in the use of the model. Theoretical acceptance of
the capital asset pricing model has led to widespread
attempts to apply the model to business situations which
have obvious risk/return relationships.
1
r
The utility regulatory commissions in several
states as well as other agencies such as the Federal Power
Commission and the Interstate Commerce Commission have
sought ways to utilize the model in the regulatory process.^
Their attempts have been encouraged, in part, by the desire
to simplify the complexities which surround the rate-making
process. If the capital asset pricing model is applicable,
the target rates of return could be established on the basis
of the firm's risk level. The model should identify a
unique rate of return for each firm, provided that each firm
has unique risk characteristics. The success of regulatory
proceedings, as measured by realized rates of return com
pared to target rates of return, depends upon the efficacy
of the methods used in the rate-making process. If the
capital asset pricing model is to be applied to regulatory
or rate-making procedures, then the regulatory agencies,
utilities, and consumers must be confident that the model is
effective in differentiating among firms of varying risk.
The academic and business communities have not been
unanimous, however, in their enthusiasm for the model. As
will be pointed out in Chapter III, some researchers have
^Cooley [15] provides a detailed breakdown of the source of advocacy of 3 as a regulatory tool. On eighteen occasions, expert witnesses advocating the use of 3 were members of commission staffs; on twenty-five occasions, they were academicians; comparatively few advocates were from consumer groups, consulting firms, or from the utilities themselves.
ITv
3
raised questions concerning both theoretical and practical
limitations to its use.
The purpose of the dissertation is to test the
model directly as to its ability to categorize one public
utility as being riskier than another. Briefly, thirteen
variables are identified as describing a substantial portion
of the firm's risk. These variables are then calculated for
as many of the Compustat utilities and telephone companies
as have complete data. Any effects of multicollinearity
among variables are then eliminated through principle com
ponents analysis. Risk classes based on these underlying
risk components are established by means of cluster
analysis. These clusters should then differ from one
another according to the level of risk inherent in each
class. The firms within each risk class should have similar
betas, and the betas of one risk class should be different
from the betas of another risk class.
This relationship between risk classes and betas forms
the basis for the hypothesis to be tested, which is formally
stated in Chapter IV. The dissertation will examine direct
ly the degree to which the relationship holds. Chapter IV
also discusses the methodology for testing the hypothesis,
and the results of these tests will be presented in Chapter
V. If the clusters are composed of firms with similar
betas, and if clusters differ from one another in terms of
their firms' betas, then one can assume that the capital
asset pricing model is correctly identifying the risk levels
of public utilities. If this relationship between beta and
risk classes cannot be demonstrated, then no conclusion
about the model's effectiveness can be made. Thus, if the
capital asset pricing model does, in fact, identify a firm
or a particular group of firms as being in a different risk
class than another firm or group of firms, then the users
can be confident that the application of the model is
appropriate for the regulatory process. If, on the other
hand, no conclusion can be drawn as to its effectiveness,
the use of the model as a regulatory tool should probably be
discarded, or at least used with extreme caution. Chapter
VI will conclude the discussion with implications of the
results and suggestions as to the appropriateness of the
model.
CHAPTER II
HISTORICAL DEVELOPMENTS
The Development of the Capital Asset Pricing Model
This chapter traces the development of the capital
asset pricing model and discusses its application to various
aspects of financial management. The most fruitful area of
application has been sho\>7n to be in the area of the firm's
cost of capital, and the use of the model to that end in the
regulatory proceedings of a publicly-held utility will be
discussed.
yiost of the credit for developing the capital asset
pricing model (CAPM) has gone to Sharpe [53], Lintner [35],
and Mossin [41] , who published similar models almost
simultaneously. Jack Treynor also developed a pricing
model, to which Sharpe alluded, but the model was not
published.2 The work of all these writers, however, was
based on the research of Markowitz [36, 37] and Tobin [56]
concerning the relationship between risk and return and the
efficient construction of portfolios.
^Credit is generally given to Sharpe, Lintner, Mossin, and Treynor for independent development of the model. Subsequent research has been based on their collective results. For the purpose of the dissertation, Sharpe's development will be examined in more detail.
Markowitz first attempted to develop a portfolio
selection process based on rational investor behavior; such
behavior would necessitate the consideration of the risk
characteristics of any potential investment. One rule of
financial theory previously asserted that investors allo
cated assets in such a way as to maximize the discounted
value of expected returns.^ Markowitz pointed out that such
a policy would never lead to diversification, and, there
fore, the theory must be discarded since diversification was
both empirically observable and theoretically sensible. He
then went on to develop a diversification system by which an
investor could rationally evaluate the risk and return
characteristics of a given security and their anticipated
effect on his portfolio.
Defining "risk" per se as the variance of a
security's return around its expected value, Markowitz
demonstrated that the variance of a portfolio is affected by
the degree of correlation between one security and another.
The higher the degree of correlation between securities, the
less reduction in variance that will occur through the
combination. Thus diversification is effective only to the
extent that securities do not exhibit high positive correla
tion. The key to his method was the realization that the
3Markowitz [37, p. 77].
7
covariaince between securities determined the real risk of a
portfolio. To assemble a portfolio, one needed to examine
the covariance between those securities already in the port
folio and the one under consideration for addition to the
portfolio. "Efficient" portfolios then were those which
maximized return at any given level of risk or minimized
risk at any given level of return.
Tobin's contribution to the theory was the proof
that dominant sets of investments could be demonstrated, for
combinations of cash and risk-free investments, and for com
binations of cash and risky investments. He, too, used the
idea of covariance to identify those combinations of assets,
or portfolios, that dominate others. The idea which may
have affected the CAPM more than any other was his proof
that "...the proportionate composition of the noncash assets
is independent of their aggregate share of the investment
balance."^ In other words, the individual's utility pre
ferences affect only the amount invested; they do not affect
the composition of the portfolio. This "separation theorem"
leads to the idea of a "market portfolio", since it is pos
sible to describe investment decisions "...as if there were
a single noncash asset, a composite formed by combining the
multitude of actual noncash assets in fixed proportions."^
^Tobin [56, p. 84] .
5lbid.
8
The market portfolio becomes crucial in the development of
the CAPM.
Sharpe's [52] first article on this subject was
ostensibly an attempt to develop an algorithm which would
simplify Markowitz's methodology. His "diagonal model" was
stated simply as
Ri = Ai + Bil + Ci (2-1)
where Ai and B^ are parameters, C^ is a random variable with
an expected value of zero, and I is the level of some index.
The index "I" was not yet identified with the market port
folio, but was allowed to be "...any factor thought to be
the most important single influence on the returns from
securities."6 One of the obvious advantages to the diagonal
model was the gain in computational efficiency. To
illustrate, Markowitz's method requires estimates of the
expected return and variance of returns for each security
under consideration, and the covariance between each pair of
securities. The number of pairs of covariances is given as
^(^"^) where n is the number of securities under consider-
ation. Thus to examine only 100 securities would require
estimates of 100 means, 100 variances, and 4,950 covariances,
for a total of 5,150 estimates. An examination of 2,000
securities, roughly the number of listed securities, would
require 2,003,000 estimates, clearly a prodigious task for
6sharpe [52, p. 281].
man or computer. Sharpe's method requires only estimates of
"A" and "B" for each security, as used in equation (2-1),
the variance for each security, and the expected return and
variance for the index itself. Thus, the examination of ICO
securities would require 302 estimates; 2,000 securities
would require 6,002 estimates.7
Sharpe's contribution was by no means finished. He
developed in a subsequent article [53] an equilibrium
theoretical model for the pricing of risky assets. He began
by demonstrating that in equilibrium, the expected return
and standard deviation of return for efficient combinations
of risky assets have a simple linear relationship. However,
the relationship between risk and return for undiversified
holdings is not so clearly defined. By regressing over time
the returns for security i with an efficiently diversified
portfolio g, the relationship between their returns can be
examined through a linear equation similar to equation (1).
Here Sharpe identified B^g^ the slope coefficient in the
equation, as
Big = ^ig 'i (2-2)
g
where o^ and Og represent the standard deviations of returns
on security i and combination g, and r^g is the correlation
coefficient. This term, Big, in equation (2-2) corresponds
7The numbers used in the illustration are taken from Sharpe [52, p. 282].
10
to Bi in equation (2-1), but the "index" would be provided
by the efficiently diversified portfolio g. Sharpe called
this part of a firm's risk "systematic" since it was
described by its relationship to the index. This portion of
the risk "...which is due to its correlation with the return
on a combination cannot be diversified away when the asset
is added to the combination."8 But, by implication, the
remainder of the risk, termed "unsystematic", can be diver
sified away; thus the relevant portion of a firm's risk is
described by the slope coefficient, Big.
Generally, two forms of the model appear in the
literature: the market model and the equilibrium model.
Although the slope coefficient has the same meaning in both
models, the development of each is different. The market
model, very similar to Sharpe's diagonal model, is generally
expressed as
Ei = ai -»- 3iEni + ei (2-3)
where the variables are analogous to those in equation (2-1),
except that Em is understood to be the return on the market
portfolio. It is, of course, simply a regression equation.
This version of the model appears in various forms by Black,
Jensen and Scholes [2]; Blume [6]; Breen and Lemer [10];
and others [32, 33, 42, 45, 46, 51].
The development of the equilibrium form of the CAPM
Ssharpe [53, p. 440].
11
as opposed to the market model in equation (2-3) is based
upon Tobin's assertion that there exists a market portfolio
and that it consists of all marketable assets in proportion
to their value weights. Using Sharpe's notation (with some
minor changes), the relationship between risk and return in
well-diversified portfolios is illustrated in Figure 2-1.^
A combination in which QLL of an individual's assets
are invested in risky asset i and (1-a)7o are invested in
H
Rf
Capital Market Line
'g
Figure 2-1: The opportunity set provided by combinations of risky asset i and efficient portfolio g
efficient portfolio g would have the following expected
return and standard deviation:
E = aEi -I- (l-a)E g (2-4)
= [a2a i2 + (1-a)2o22 + 2 r i e a ( 1 - a) oiOa] 1/2 (2-5) g
^The following discussion is based upon a similar development by Copeland and Weston [16] which in turn was based on Fama [19].
12
where: ai2 = the variance of risky asset i
Og- = the variance of efficient portfolio g
rig = the correlation coefficient between i and g
As a, the proportion invested in the risky asset,
is allowed to vary, the change in expected return will be
as follows:
dE = Ei - Eg (2-6)
and the change in standard deviation will be as follows:
do = 1/2 [a2oi2 + (i-a)2ag2 + 2riga(1 - a) oiOg] " 1/2
X (2aoi2 + 2aog2 _ 2 ag2 + 2rigaiag - 4rigaaiOg)
(2-7)
Now, in an equilibrium condition, excess demand for
security i would not exist-, therefore, a = 0. Reevaluating
in the above cases, equation (2-6) is valid for any value of
a since it is not in the equation. However, equation (2-7)
can be greatly simplified, where a = 0.
da = l/2[og2]-l/2 X [-2rg2 + 2rigaiag]
= l_[-ag2 + rigoiog]
g
= n oOi Oo - a. ig"i"g -2 (2-7a)
g
But, since rigOiOg is equal to the covariance of i and g,
given as oig.
Gig - Og' do = ^ Og (2_8)
13
Thus, the slope of the boundary of the opportunity set igi'
at point g, given in Figure 2-1, is
dE /do = Ei - Eo
ig - V (2-9)
g
But, the point g also lies on the risk-return tradeoff line,
or capital-market line, whose slope at any point is given by
dE = Eg - Rf (2-10) do
g
Since equations (2-9) and (2-10) both describe the slope of
the respective functions at the same point, and since the
two curves are tangent (not crossing), the slopes are equal.
Setting the two equations equal,
Eo - Rf Ei - Eo _~ = (2-11)
Og 'ig - 'g-
g
Rearranging, and solving for Ei, the equation can be
restated as follows:
Ei = Rf + ig (Eg - Rf) (2-12)
Given that the well-diversified portfolio g is in fact the
market portfolio, equation (2-12) is the common equilibrium
form of the CAPM.
Replacing the subscript g with the subscript m, the
measure of nondiversifiable risk is
14
aim GOV (EiEm)
0^2 VAR (Eni) (2-13)
The graphic representation of the model is given in Figure
2-2 as the security market line.
m
Rf
Security Market line
'im
am-1 om2
Figure 2-2: The equilibrium CAPM or the security market line.
The risk-free portfolio with a return of Rf would have a
beta of zero since its covariance with the market portfolio
is zero; the market portfolio itself would have a beta of
one because its covariance with itself is by definition the
variance of the market portfolio. Thus, the riskiness of
any asset can be described by the level of its beta.
This form of the model, although based on the works
cited earlier, was first given expression by Jensen [29].
However, one must assume the following conditions in order
for the equilibrium conditions to hold:
(1) Every investor is a one-period expected utility
maximizer and exhibits diminishing marginal utility of ter
minal wealth;
15
(2) All investors have the same one-period time
horizon;
(3) Every investor feels that he can evaluate a
portfolio of one-period returns;
(4) No transactions or information costs exist, the
borrowing and lending rates are equal, and investors will
select only those portfolios with optimal combinations of
risk and return. The capital market is a perfect market;
(5) All investors hold identical or homogeneous
expectations about the distributions of future returns.
(6) The capital market is in equilibrium.!0
After the model was developed in the general
theoretical framework, its application to corporate finan
cial theory was the next logical step.
The Application of the CAPM to the Cost of Capital Problem
Hamada [24] was one of the first to link the asset
pricing mechanism of Sharpe-Lintner-Mossin to corporate
financial theory.1^ In his 1969 article, he used the CAPM
framework to support the famous Propositions I and II of
Modigliani and Miller [40], first in the no-tax case and
then in the case where corporate taxes are applied. The
lOSee Friend and Blume [20].
11 Perhaps the very first was Lintner himself who had pointed out [35, pp. 28-30] that the model applied to the selection of portfolios of business projects as well as to security portfolios.
16
value of the firm was expressed in terms similar to those
of Modigliani and Miller, but because return was described
through the use of the capital asset pricing model, the need
for the assumption of homogeneous risk classes was
eliminated. He demonstrated that the value of the firm was
dependent only on its expected earnings, its risk (as
expressed by the covariance of its returns with market
returns), and two market factors: X, the price of risk, and
Rf, the risk-free rate. The financing mix was irrelevant,
thus supporting Proposition I. In a similar manner, the
rate of return demanded by investors was shown to be a
linear function of the debt-equity ratio, supporting
Proposition II with a CAPM framework.
Both Rubenstein [50] and Weston [60] made signifi
cant contributions to financial theory in their explanations
of the application of the capital asset pricing model to
capital budgeting. Rubenstein used a mean-variance approach
to the theory, with covariance between security returns and
market return as his relevant risk measure. Weston built on
this framework to develop acceptance criteria in capital
budgeting decisions. The relationship is illustrated in
Figure 2-3.
In Figure 2-3, 3j represents the level of systema
tic risk for firm j, WACCj represents the cost of capital
for firm j and its traditional hurdle rate for project
acceptability. The criteria as illustrated by the graph are
17
WACC J
Security Market Line
Figure 2-3: Illustration of the Use of Investment Hurdle Rates
to accept those projects which plot above the market line,
such as projects A and B, and reject projects which plot
below the market line, such as C and D. Managers seek to
find new projects such as A and B whose returns are in
excess of those required by the equilibrium relationship of
the market line. Once the projects are accepted, the
expected return on common stock increases causing the price
of the stock to rise until the equilibrium relationship is
restored.
Using the traditional hurdle rate, WACCj, project B
would have been rejected and project C would have been
accepted, obviously conflicting with the CAPM approach.
The capital asset pricing model has been shown to
be applicable to valuation theory and to investment decision
18
theory. The remaining major aspect of corporate finance,
the cost of capital, has proven to be a very fruitful area
for the application of the capital asset pricing model. The
model, of course, measures the cost of equity capital
directly. Examining equations (2-12) and (2-13), the 6i is
calculated on the basis of the covariance of the return on
firm i's common stock with the return on the market
portfolio. Thus, if estimates of firm i's systematic risk
and estimates of the market return are known, the cost of
equity capital can be estimated directly:
Ei - Rf + 0i (Em - Rf) (2-14)
Ei is then the cost of equity capital for a firm.
The Application of the CAPM to tne Regulatory Process
One of the first to advocate the use of the CAPM in
regulatory hearings was Stewart Myers [42] . He suggested
that much of modem finance theory was being ignored by uti
lity regulators and could be applied readily. Regulated
firms provide an attractive laboratory for the application
of finance theory because of the fact that so much of
regulation is concerned with the firm's rate of return.
Regulation in general is held to be a substitute for com
petition according to Aversch and Johnson [1] since the
regulated firm has been given a monopoly position in its
market. The presence of regulatory commissions permeates
every level of government: the Federal Power Commission,
19
the Interstate Commerce Commission and other agencies have
regulatory authority over many firms operating across state
lines such as operators of gas pipelines; all fifty states
have public utility commissions which regulate utilities
within those states; counties and cities regulate waterworks
companies, garbage collection agencies and other small
utilities.^ 2
The legal basis for the regulation of utilities'
rates is attributed to two landmark Supreme Court cases:
Bluefield Water Works and Improvement Company vs. Public
Service Commission of the State of West Virginia (262 U.S.
679) in 1923 and Federal Power Commission vs. Hope Natural
Gas Company (320 U.S. 591) in 1944. In the Bluefield
decision, the Court stated that "...A public utility is
entitled to such rates as will permit it to earn a return on
the value of the property which it employs...equal to that
generally being made at the same time and in the same
general part of the country on investments in other business
undertakings which are attended by corresponding risks and
uncertainties...The return should be reasonably sufficient
to assure confidence in the financial soundness of the
utility, and should be adequate...to maintain and support
its credit and enable it to raise the money necessary for
12Robichek [47, p. 693] .
20
the proper discharge of its public duties." (Bluefield,
692-693).
The decision stated explicitly what had already
been a principle of regulation, that is, that the returns
should be commensurate with the risk undertaken. What the
decision did not address was the proper manner in which
those returns were to be determined.
The Hope decision specifically addressed the issue
of the return to the investor: "From the investor or com
pany point of view, it is important that there be enough
revenue not only for operating expenses but also for the
capital costs of the business. These include service on the
debt and dividends on the stock...By that standard the
return to the equity owner should be commensurate with
returns on investments in other enterprises having
corresponding risks. That return, moreover, should be suf
ficient to assure confidence in the financial integrity of
the enterprise, so as to maintain its credit and to attract
capital." (Hope, 603)
The decision of the Supreme Court appears to be
simple and straightforward - the regulatory agencies need
merely to set rates that allow public utilities to earn a
rate of return that is appropriate for firms with the same
degree of riskiness. To illustrate one manner in which the
decision has been implemented, assume that an electric
utility has total assets of $1,000,000 which are financed
21
with $400,000 in bonds and the remainder in common stock.
The bonds have an average coupon rate of 8%, the firm's
income tax rate is 407c,, and analysts have determined that
the appropriate rate of return to stockholders is 107o.
Furthermore, operating costs and depreciation are expected
to be $368,000. Since the book value of the common stock is
$600,000, the earnings available to equity holders are 107o x
$600,000 or $60,000. Next, the pre-tax earnings necessary
to generate $60,000 after taxes would be $60,000/(1 -.40) or
$100,000. The interest on the firm's debt is 87o of $400,000
or $32,000. Thus, total earnings before interest and taxes
are $100,000 + $32,000 or $132,000. The firm must also
TABLE 2-1
DETERMINATION OF REQUIRED REVENUE
Dollars Proportion
Debt $ 400,000 .40 Equity 600,000 .60 Total Capital $1,000,000 1.00
Return to Equity (107o of 600,000) $ 60,000 + Income Tax (at 407,) 40,000 =Earnings Before Taxes 100,000 +Interest (87o of 400,000) 32,000 =Earnings Before Interest and Taxes 132,000 +Operating Costs and Depreciation 368 ,000 =Total Revenue Needed to Cover Expenses and Service Capital $500,000
22
cover its other costs, so total revenue would be $368,000 +
$132,000 or $500,000. The regulatory commission then must
set rates sufficient that at expected levels of usage, the
resulting revenue would be $500,000. These calculations are
summarized in Table 2-1.
An alternative approach is to weight the various
capital costs by their respective capital proportions to
determine an overall allowed rate of return. This rate is
then multiplied by the "rate base" to determine the dollar
amount of allowed return. Using the same example, the
overall rate of return is determined to be (.40 x .08) +
(.60 X .10) or .092. Since.total assets are $1,000,000,
total dollar return is .092 x 1,000,000 or $92,000. This
figure can be verified from Table 2-1, in which the dollar
return to stockholders and interest payments to bondholders
total $92,000.
In reality, however, the actual proceedings are far
from simple and straightforward. Achieving the goals
defined by the Supreme Court is often illusive. Robichek
[47] points out that almost every item which impacts upon
the final allowed rate is a subject of controversy to some
extent.
Differences of opinion arise over whether the cost
of debt should be the embedded, or historical, cost or
whether it should approximate current market rates. From an
economic point of view, the marginal cost of debt would be
23
considered the most relevant; if capital must be raised, the
firm will have to pay rates that may differ from historic
rates. However, a regulatory strategy based on current debt
costs would require market weights for the capital component
proportions to compute the overall cost of capital. Regula
tory commissions are often reluctant to use market weights
as compared to book weights because the market weights are
constantly changing. If the cost of debt is constant, or
if no regulatory lag occurs (i.e., if the firm is able to
pass along increases in debt costs immediately) the embedded
cost of debt may be appropriate.^^ In a period of rising
interest costs with regulatory lag, embedded costs are less
appropriate. Estimates of future changes should impact upon
the decision to use embedded or current debt costs.
However, regulatory commissions have almost always used the
embedded debt cost in determining levels needed to service
capital.
The rate base is likewise a point of controversy.
Since the allowed rate of return is calculated as a propor
tion of the capital base, the value of that base necessarily
affects the resulting revenues. Two problems must be faced
in establishing a program value for the rate base. The
regulatory commission must first decide what assets are to
be allowed as part of the basis. An investment in a manu-
13Myers [42, pp. 92-93].
24
facturing subsidiary may justifibly be excluded; on the
other hand, non-productive assets (idle capacity) may be
included on the basis that future demand will justify their
use. After the proper assets have been identified, the com
mission must choose the valuation method. Historical costs
have often been used, but in times of rapidly rising costs,
utilities have been pressing for the use of replacement cost
or "fair value" valuation bases.^^
The level of operating expenses that should be
allowed, the proper ratio of debt to equity, the setting of
rate structures (as opposed to rate levels) and the
establishing of base years are all other areas that have
given rise to controversy. Each of these items of
discussion has had, and probably will continue to have, its
moment of relative importance as situations change. No area
has generated as much controversy, however, as the problem
of determining the proper level of return to stockholders.
The Hope decision clearly states that the return to the
stockholders should be equal to that of other firms with
similar risks. Much of the debate has centered on the
question of what constitutes equivalent risk. Classman [22]
and Hyde [27] imply that an equivalent risk class would be
composed of other similarly regulated utilities. But since
those utilities' performance is to a large extent influenced
l^See Robichek, op.cit., Hope.
25
by prior years' regulation, using it as a standard means
that the regulators ultimately must set an arbitrary stan
dard for return. Hayes [26] suggests that large, stable,
well-diversified, but non-regulated firms should be the
benchmark. Myers [42], however, states that these firms are
by definition riskier since they are not regulated, and
therefore, the idea of "commensurate return" cannot be based
on the company point of view. Myers defines commensurate
return as the "rate of return investors anticipate when they
purchase equity shares of comparable risk." This measure
anticipates return in the form of dividends and capital
gains, rather than the book rate of return expected by the
firrn on its own investments. This return has been described
for regulatory purposes as the earnings-price ratio,
reflecting the market expectation of rate of return.
Alternately, by combining the expected dividend yield and
the expected growth rate in dividends, an appropriate cost
of capital can be determined. Hayes [26] points out that
the former method has been persistently advanced in rate
hearings, and has resulted, where it has been accepted, in
average rates of return lower than what might otherwise be
expected. The latter method, also known as the Gordon
model, has its problems as well. Although it does take into
consideration the future growth possibilities of the firm,
it suffers from circular reasoning. The growth in dividends
26
is assumed to be a function of growth in earnings--theoreti-
cally the growth rates should be identical, and if the firm
has a constant dividend payout, they will be identical. But
the growth in earnings depends upon the rate of return
allowed by regulators, so problems arise in trying to gauge
what the rate of return should be.
Against the cacophony of differing opinion among
the commission staffs, the utilities, their respective
expert witnesses, and the increasing militance of consumer
groups, the relative simplicity of the capital asset pricing
model appears to be the solution to many of the problems.
As presented in the preceding section, it measures the cost
of equity capital directly, and the beta of the model
defines the risk class quantitatively. Additionally, the
argument of regulated versus nonregulated risk classes
becomes irrelevant since all nondiversifiable risk is bound
up in the beta.
Since Myers first recommended the CAPM for public
utility regulations, the model has aroused much controversy
in its application. The basis for this controversy is both
theoretical and practical and will be explored in depth in
the next chapter. Despite the controversy, regulatory com
missions have increasingly begun to study the capital asset
pricing model. Vandell and Malernee [58] wrote in 1978 that
at least 15 jurisidictions had seen it proposed as the main
theory by regulatory commission staffs or their experts.
27
Brigham and Crum [12] mention seven states and two federal
agencies before whom it was used. Since the model is
growing in acceptance, the need is imperative to understand
the problems associated with its usage and construction, and
to determine the ultimate usefulness of the model.
CHAPTER III
CRITICISMS OF THE CAPITAL ASSET PRICING MODEL
The problems associated with the capital asset
pricing model can be categorized roughly into three groups:
those problems discovered as a result of empirical tests of
the theoretical model, denoted herein as "empirical pro
blems"; those arising out of a lack of normative theory con
cerning the data base used to generate the model parameters,
denoted herein as "measurement problems"; and those asso
ciated with attempts to apply the model to the regulatory
process. Although the categories are not mutually
exclusive, each problem will be discussed under its most
general characteristics.
Empirical Problems
Validity of the Assumptions
The first problem has to do with the relationship
between theory and reality in the assumptions of the model.
These assumptions were listed in Chapter II and are obvious
ly simplifications of reality, as are the assumptions of any
other model. The assumptions may, in fact, be incorrect
but, as Vandell and Malernee [58] point out, their realism
is not the issue. The power of a model does not lie in the
28
29
validity of its assumptions, but in the accuracy of its pre
dictions. However, various combinations of the assumptions
are critical to the model's several proofs. If material
misspecification occurs, does the model remain valid? If
the model is consistently accurate in its predictions, even
material variation from reality should not affect the deci
sion to use the model. However, the success of the model as
to its predictive ability is hardly exemplary. Friend and
Blume [20] found, using performance measures developed by
Sharpe [54], Treynor [57], and Jenson [28], that the risk-
return relationship specified by those measures had unex
plained results. In all cases, the relationship was
inverse, and highly significant. The adjustment of rate of
return for risk reversed the relationship normally expected.
All of the performance measures were based on derivations of
the capital asset pricing model. "Until the accuracy of the
specific CAP model is established ..., a model with many
questionable hypotheses is suspect."^5 Thus, when the model
is recommended in a regulatory proceeding, numerous
questions are raised about the assumptions themselves, and
their validity.
As an example of a violation of an assumption,
Blume and Friend [8] found that a large proportion of port
folios were highly undiversified. The results of their
15vandell and Malernee [58, p. 24].
30
research implied that either investors held heterogenous
expectations about future returns or that they did not pro
perly aggregate the risks of individual assets to measure
the risk of the portfolio.
The model upon which we based our conclusion of constant proportional risk aversion may yield a poor description of investors' behavior. In this case, our conclusion about the form of investors' utility functions and by inference the aggregate demand function for risky assets is suspect. [8, p.603]
Either of these interpretations, if true, implies serious
shortcomings in the model.
The Problem of Equilibrium
Another problem with the model is that it is a
single-period equilibrium model. The market, however, is
not static, but is continually shifting. Perhaps one could
argue that it shifts from one equilibrium condition to
another; nevertheless, the model does not reveal how the
market gets from one equilibrium to another. Dynamic models
are not currently developed to the stage of the single-
period model.
Empirical Findings versus Model Specifications
Some of the more serious empirical problems may lie
in the fact that market behavior does not seem to comply
with the specifications of the model. That is, the capital
market line has parameters which vary from those predicted
31
by the model. For example, Black, Jensen and Scholes [5,
pp. 133-114] found that:
The time series regressions of the portfolio excess returns on the market excess returns indicated that high-beta securities had significantly negative intercepts and low-beta securities had significantly positive intercepts, contrary to the predictions of the traditional form of the model...we therefore concluded that the traditional form of the model is not consistent with the data.
Friend, Westerfield, and Granito [21] tested the capital
asset pricing model for portfolios of common stocks, for
portfolios of bonds, and for combinations of the two. Their
results, in all cases, implied that the actual capital market
line was flatter and had a higher intercept (risk-free rate)
than was predicted by the model. Risk-free rates of 10.07,,
6.47o, and 8.87o respectively were predicted, higher than is
normally observable in the market on the securities con
sidered to be surrogates for that rate. "These findings are
inconsistent with Sharpe-Lintner theory if it is appropriate
to use for empirical testing the one factor return-
generating function relating actual to expected return and
[the] empirical construct for the market portfolio."[21, pp.
910-911] These results (in general) are described in Figure
3-1. The graph demonstrates the flatter market line using
the results of Friend, Westerfield, and Granito. This
misspecification in the theoretical model can be dangerous
for firms with low betas (such as public utilities with
measured betas typically around 0.7) because it materially
R-
B
32
.7
Theoretical market line
Empirical market line
1.0 Beta
Figure 3-1: Theoretical versus Empirical Market Line Source: Vandell and Malernee [58, p. 25]
understates the cost of capital to the firm. This under
statement would be the vertical distance from point A to
point B.
A similar problem arises from the fact that neither
the market line nor characteristic lines for individual
firms remain constant, but exhibit shifts from one period to
the next. Blume [6] found that beta coefficients of single
securities were not good predictors of the next period's
beta, i.e., beta shifted unpredictably from one period to
the next. Predictability improved with increases in port
folio size, and the direction of the shift could sometimes
be predicted. High betas tended to shift downward; low
betas tended to rise. Klemkosky and Martin [33] improved on
the predictability through combinations of large portfolios
33
and Bayesian statistics. Naturally, if beta can be
predicted, the fact that it is not stationary is of less
importance. However, Pettway [45] had mixed results:
(1) There were periods when the estimated structural parameters were stable enough to provide good estimates of the subsequent observed values.
(2) There were some periods of significant disturbance when the parameters were not good estimates of the observed values. This period of instability lasted for in excess of one year.
(3) The period of instability, although somewhat long, was transitory as the values of the observed 3's returned to the former levels such that they were insignifantly different from those of previous estimates. [45, pp. 247]
The problem with these results, which Pettway ac
knowledges, is that one cannot forecast a period of instabi-
lity or its termination, and "there is no ex post test that
can assure regulators that past relationships will be valid
in the future." [45, pp. 247].
Pettway's observation reveals the major fundamental
problem of beta: it is an £x ante concept constructed on ex
post information. For regulators to be able to identify
correctly the risk class of the firm requires knowledge of
how the firm's stock price will react to market forces in
the future. The relationships that resulted in a calculated
level of beta may be completely irrelevant as far as future
performance is concerned. The real beta may never be known
ex ante.
34
Measurement Problems
The problems of instability, lack of predictability
and misspecification are all serious problems. However, the
real problem may not lie in the characteristics of the
parameters, but in the attempts to measure them. All of the
problems discussed above may exist only in the measured
values. In situations where the underlying risk exposure of
the firm is changing, one would expect shifts in the real
beta, but for ordinary conditions, the measurement of true
beta may be unstable because of measurement error. This
fact, however, does not reduce the severity of the problem,
and may even make the application of the model more
difficult. Several of these measurement problems will be
discussed, keeping in mind that the boundary between
measurement problems and empirical problems is somewhat
amorphous.
The Investment Horizon
The first of these problems deals with the interval
over which beta is to be computed. In the regression model,
the returns of the firm are compared to the returns on the
market index over successive intervals of an arbitary size.
The assumption of the model is that all investors have the
same investment horizon, the length of which is unimportant
as long as it is identical for all investors. However, the
return for a particular security is affected by the length
35
of time it is held. Levhari and Levy [34] discovered that
the beta is affected as well.
Specifically, betas of defensive firms (0 < 1)
generally decreased as the investment horizon increased;
betas of aggressive firms (3 > 1) tended to increase as the
investment horizon increased. The authors contended that
the "investment horizon for which data are collected plays a
crucial role and has a great impact on both the regression
coefficients and the performance indexes." [34, pp. 103]
They point out that many of the empirical problems in
measuring beta are the result of assuming investment hori
zons shorter than are actually held by investors.
The Relevant Risk-Free Rate
Carleton [14] brings up a similar, though more
theoretical problem. The surrogate for the risk-free rate
used in most rate hearings is the annualized rate of return
on short-term treasury bills.
"If Bi is derived using as Rm (the surrogate for rate of return on the market portfolio) annual data, then Rf should be the rate on an appropriate one-year security . . .The use of any other Rf, of either shorter or longer maturity than the data interval that generated Bi and E(Rni) , in the presence of a yield curve slope, is formally incorrect." [14, p. 58]
Since the data interval and hypothesized investor holding
period are co-specified in the model, the implication is
that rate of return estimates should be revised with each
shift in Treasury bill rates, clearly an impossible task.
36
since each would require new hearings. He draws the conclu
sion that the model should be scuttled.
The Number of Holding Periods
Another measurement problem related to the invest
ment horizon has to do with the number of periods • included
in the regression equation. This problem is closely linked
to the preceding one because the longer the investment
horizon, the longer the period of time over which obser
vations must be gathered. Ideally, researchers would want a
large number of intervals in order to fairly represent the
ex ante distribution. Yet, periods remote in time may be of
no value in the model. Cooley [15] found that the most com
mon number of monthly intervals used in rate hearings was
60, but others ranged from 12 to 120 months. When weekly
intervals were used the number was almost always 52. This
lack of uniformity does have an impact on results, as
demonstrated by Baesel [2]. He found that betas were very
unstable, as might be expected, when the number of periods
was low, but improved as the number of periods was in
creased. Greater stability was exhibited for 108 months
than for 12 months; Baesel did not, however, indicate that
this was the proper number of intervals, or what the proper
number of intervals should be. For rate cases most estima
tes of beta probably use a number of intervals for which the
data is conveniently available, such as over a five-year or
37
ten-year period, a speculation supported by the findings of
Cooley mentioned above; apparently, little consideration is
given to a theoretically correct number.
The Proper Market Index
The next category of measurement problem involves
consideration of the market index used. The model specifies
that the risk premium is the difference between the risk-
free rate and the expected return in the market. Unfor
tunately, the "return in the market" is impossible to
measure. Most advocates of the CAPM in a rate case use some
broad value-weighted common stock index, usually the New
York Stock Exchange Index or the Standard and Poor's
500-Stock Index.16 Others have used narrower indices such
as the Standard and Poor's Utility Index.^7 Fisher's Link
Relative Index has been used by some [2, 7, 32] to try to
achieve the effect of a true market index, but in reality
Rni cannot be measured since all possible investments would
have to be known. If one assumes that the indices are
fairly representative of total market behavior, then the
absence of a market index is not a serious problem. Breen
and Lerner [11] found that changing the index in the model
from the New York Stock Exchange Index to an index made up
16see Cooley [15, p. 13].
17ibid.
38
of all firms listed on the Compustat tapes caused' signifi
cant shifts in model parameters. One can draw the conclu
sion that since the indices generate different results, one
or the other (or both) is not accurately describing true
market returns. Thus, the choice of an index can have
significant impact on the computed cost of capital.
The Choice of Estimating Equations
The potential for differing results exists in the
choice of the estimating equation used. The market model,
according to Cooley [15], is used by about sixty percent of
the CAPM witnesses. Estimation of the parameters is done by
ordinary least square regression, with generalized lease
squares used in a few cases. The equilibrium, or risk-
premium, form of the model is used in thirteen percent
of the cases. In those instances where the two were
compared, the results were not significantly different.
Misleading Shifts in Beta
Finally, Brigham and Crum [12] identified a problem
of measurement that had not appeared previously in the
literature. They showed that it was possible for a shift in
the firm's systematic risk to result in a simultaneous oppo
site shift in beta'." That is, a sudden increase in the risk
exposure of the firm would result in a sudden reduction in
the observed beta. If true, this phenomenon would certainly
39
be misleading to investors, as well as to the regulatory
procedure.
The problem they identified is that beta is "a
biased estimator of the true beta whenever a company
undergoes a basic change in its systematic risk position and
its expected earnings do not immediately rise to offset this
increase in risk." [12, p.8] The problem results from the
way in which beta is estimated with the market model, where
the returns from the stock are regressed against the return
in the market. If a sudden increase in perceived risk is
detected by investors, and if that shift is not accompanied
by a corresponding shift in expected earnings, the price of
the stock will fall. The reduced return results in a data
point below the one which would have otherwise resulted and
leads directly to a reduction in calculated beta.
They go on to show that the same results occur even
if the change in risk is gradual. Such a shift could happen
to utilities because of the growing awareness that they
experience difficult problems during periods of rapid
inflation, or because of increases in debt ratios, or other
gradual changes in perceived risk. Evidence is presented to
show that the problem is more than just a hypothetical one.
First, the situation of the real estate investment trusts
(REITs) is cited during the period 1973-1975, during which
many REITs failed. Their risk exposure increased dramati
cally during that period, while their observed betas (as
40
published in Value Line) were dropping. Secondly, three
business failures - Penn Central, W. T. Grant, and Franklin
National Bank - were examined. As each progressively
approached bankruptcy, its respective beta declined. Final
ly, the case for the utilities is presented. Although their
condition has not been so severe as the other two examples,
they have certainly experienced an increase in risk.
Fuel shortages, environmental problems, and uncertainties about future demand have raised the investment risk of the electric, while actual and potential increases in competition and a rising debt ratio have increased the risks inherent in telephone stocks. Both groups have suffered from regulatory lag, inflation, and earnings quality declines...In spite of the utilities' increasing risks, their beta coefficients remained essentially unchanged from 1964 though 1975. [12, pp. 12-13]
Brigham and Crum concluded that historic, calculated betas
did not reflect the risk inherent in utility stocks. Any
further use of the capital asset pricing model was to be
undertaken with extreme caution.
Problems in Applying CAPM to Public Utilities
Not only does the model exhibit theoretical and
measurement problems, but it may have less application to
utility firms than it does to firms in other industries.
The Hope decision required that the allowed rate of return
be high enough to protect the credit standing and financial
integrity of the firm. Carleton [14] points out that a
public utility commission may occasionally find it
necessary--because of bond indenture provisions--to allow a
41
rate of return that is not related obviously to the cost of
capital, in the sense that equity cost is determined by
market-based measures. In that case, "if one wishes to
adopt CAPM terminology, the Hope criteria require regulation
to take into account the downside part of systematic risk."
[14, p. 59]
Brigham and Crum [13] question the model's applica
bility to utilities for the same reason. The distribution
of possible rates of return for utilities is skewed to the
left due to the upside constraints imposed by regulation.
Thus, random losses on one security cannot be offset by ran
dom gains on another. The capital asset pricing model
assumes that returns are at least symmetrically distributed.
This random distribution makes it theoretically possible to
diversify away the nonsystematic risk, but when the distri
bution is skewed, the model breaks down. Diversification no
longer eliminates the nonsystematic risk, so beta does not
serve adequately as the proper measure of risk. "Risk pre
miums must now reflect total risk, or at least some of the
unsystematic risk." [13, p. 74]
Summary
This chapter has attempted to delineate some of the
problems that have appeared in the literature as obstacles
to the application of the capital asset pricing model.
Some of the empirical problems were based on violations of
42
critical assumptions, misspecifications of model parameters,
a lack of compliance in empirical research with the predic
tions of the model, the instability and nonstationarity of
beta, and the basic problem of trying to predict the future
with historical measures.
Problems in the measured values of the parameters
were then discussed, including such variables as the rele
vant investment horizon, the period of time over which the
returns are calculated, problems relating to the choice of
an index, and the choice of the estimating equation. A
measurement problem resulting from shifts in true betas
described by Brigham and Crum [12] was seen to.have caused
misleading shifts in calculated betas. Finally, the argu
ments of Carleton [14] and Brigham and Crum [13] were pre
sented asserting that non-systematic risk must be considered
in the utilities' case.
Despite all these enumerated problems, the number
of hearings in which the capital asset pricing model is in
troduced keeps growing. Cooley [15] identified forty-nine
separate rate cases involving the use of beta, either in the
capital asset pricing model, or for forming comparable-risk
groups. This latter usage is precisely the subject of the
hypothesis to be tested in this dissertation. The methodo
logy for doing so is discussed in the next chapter.
The problems of beta were summarized succinctly by
Stewart Myers, one of the first to advocate applying the
43
model to the regulatory process. He writes
The real problems in using beta in a regulatory proceeding .. .are as follows: First, beta cannot be measured precisely. The possible errors in beta limit the precision of the conclusions that can be drawn. Second, beta may not be stable. This may also limit the precision of any conclusions, unless ways can be found to explain and predict shifts in beta. Third, the capital asset pricing model may not be the whole story about risk and return, on either a theoretical or an empirical basis. [43, pp. 626-627]
CHAPTER IV
METHODOLOGY
The fundamental question to which this dissertation
addresses itself is, "Does beta adequately identify dif
ferences in levels of risk among public utility firms?"
Given that risk varies from one firm to another, one is
interested in whether or not beta effectively quantifies the
risk that is there. The variables discussed below will be
used ultimately to create risk classes whose betas will be
analyzed. The question behind the analysis is "Can a regu
latory agency or an individual use beta to assess the risk
characteristics, or to identify the risk class of the firm?"
If the firms within a given risk class have similar betas,
and if the betas are different from those in another risk
class, the answer would be affirmative; if not, the betas
would not be useful to classify firms. The hypothesis to be
tested in the dissertation is
HQ: " 1 « "62 = ia = • •• = "Bk
where "s is the mean of the betas in the k^^ risk class.
The hypothesis would be rejected if the various risk classes
have significantly different betas.
44
45
The Risk Variables
The risk classes will be constructed on the basis
of various factors that would be expected to affect a firm's
exposure to business and financial risk. These factors are
the underlying basis for thirteen risk variables which have
been identified as being relevant to the public utilities
industries. Beaver, Kettler, and Scholes [3] and Bildersee
[4] demonstrated that a significant degree of correlation
exists between various accounting risk variables and syste
matic risk, specifically, the firm's beta. Their variables
are not identical to those used in the dissertation, but are
sufficiently similar that the underlying factor relation
ships should still hold. Some factors are exogenous; the
firm would exhibit little control over their magnitude.
Such factors would include the vulnerability of product
demand to cyclical variations in the general level of econo
mic activity, the regulatory environment in which the util
ity operates, and the presence and severity of the effects
of inflation upon the firm.
The measurement of these factors is an approxima
tion at best; nevertheless, variables have been identified
in an attempt to quantify the effect of each factor. These
variables will be calculated using the data available on
Compustat tapes. Some of the data are available by quarters
over ten years, and some are available as annual data over
twenty years. The degree of availability will sometimes
46
determine the form the variables take. Unless otherwise
noted, the variables are computed over the ten year period
1969-1978.
Xi j: Vulnerability of Product Demand
The vulnerability of product demand is measured by
the variance around a log-linear trend in gross revenue per
share. The trend equation is estimated using ten years of
quarterly data, with 1978 as the most recent year. The
following model is used:
log (Gjt) = aj + bjTt + ejc (4-1)
where log (Gjt) = the logarithm of gross revenue per share for firm j in quarter t
Tt = the time variable for quarter t
ej t = the error term associated with firm j in quarter t
and a and b = parameters.
The standard error of the estimate is the metric
used to measure the vulnerability so that
Xij = Var [ej] (4-2)
X2j: Regulatory Environment
The second factor to be included considers the
effect of the regulatory environment in which the firm
operates. Value Line Investment Survey includes an eva
luation of regulatory risk for each electric utility
included in its survey. This Regulatory Agency Rating
47
(RAR) is given simply as "above average", "average", or
"below average". For purposes of the study, these terms
will be assigned the values 1, 2, and 3 respectively. These
ratings are not a quantification of regulatory environment
risk, but merely serve as a proxy for that risk, which is
probably non-quantifiable. Therefore, the second variable
would be
X2j = RARj (4-3)
where RAR takes on value 1, 2, or 3. Non-electric utilities
will be assigned a rating based on their location.
X- j : Inflation
The third external risk factor is inflation and its
effects on the firm. The presence of sizable rates of
inflation in the environment of regulated prices can be
devastating to a utility unless the firm has ready access to
regulatory relief or has the authority to pass along cost
increases to customers. Even in those cases, "regulatory
lag" can reduce possible returns.
To quantify the effects of inflation, the ability
of the firm to raise prices relative to overall rates of
inflation will be examined, weighted more heavily for
current years, since later price adjustments could compen
sate for earlier deficiencies. The percentage change in the
firm's overall price level divided by the percentage change
in inflation, represented by the GNP Implicit Price
48
Deflator, would yield an index whose expected value would be
1.0 if the firm has been able to fully adjust prices to
account for inflation. The index of the effect of inflation
on firm j in year t will be
7oaP
where P = average price per unit sold, adjusted for product mix
and D = GNP Implicit Price Deflator.
The third variable will be a weighted average of the S's
from equation (4-4), the weighting to be such that recent
years have heavier weights then earlier year-s, given as:
10 . tStj
X33 = '-' 10 (4-5) I t
t-1
In the equation, the most recent year (1978) has a weight of
10, while the earliest year (1969) has a weight of 1. The
denominator is simply the sum of the weights.
Other risk factors are endogenous; that is, they
arise as a result of forces within the firm and are typi
cally used to evaluate management's effectiveness. Such
variables would include the firm's use of operating
leverage, the firm's use of financial leverage, the firm
size relative to the industry, the growth rate in operating
income, the growth rate in earnings per share, the ability
49
to meet interest payments, the ability to meet short-term
liquidity requirements, the variability in earnings per
share, and the direction or trend of earnings per share.
X4j: Operating Leverage
The first of these variables quantifies the firm's
use of operating leverage over the ten-year period. The
variability of the ratio of the firm's net operating ear
nings (earnings before interest and taxes) to total revenue
will be examined. The relevant index is
X4J = Var EBITj
- T R - J (4-6)
where EBIT = earnings before interest and taxes
and TR = total revenue.
The higher the variance of the ratio, the greater the fluc
tuations in the ratio, the less consistency in the use of
fixed costs in the operations of the firm, and the greater
the risk present. Even if a firm operates with high fixed
costs, the consistency of that level might indicate that the
firm was effectively coping with those costs (or even using
them to its advantages through the beneficial effects of
leverage) .
Xt; : Financial Leverage
The financial leverage factor is analogous to the
operating leverage factor. That is, the degree to which
50
financial leverage affects the firm's risk will be measured
by the variability of the ratio of net income to net
operating earnings. The index is, therefore.
X5T = Var Net Incomej
EBITj (4-7)
Again, the higher the value of X5, the greater the risk due
to financial leverage.
X6j: Firm Size
The variable which accounts for firm size examines
the degree to which the size of the firm affects its risk.
Intuitively, a larger firm should be more successful at the
rate hearings because of its ability to retain more highly
skilled (or at least more expensive) counsel, and to attract
a larger and better trained staff. The smaller firms, which
would be less able to influence the direction of a rate
hearing would suffer lower returns. The appropriate measure
of firm size is
TRj
X6i = -TT (4-8) ITRj
j = l
where n = number of firms in the industry, and TR= total
revenue for firm j. Since the denominator is the total
industry revenue, the index expresses each firm's size as
its proportion of total industry revenue. Higher values of
X^ would indicate lower levels of risk.
51
X7i: Growth in Operating Earnings
Growth often has been linked to risk; growth
industries or firms are often identified as being of higher
risk. The Gordon valuation model specifies that higher
rates of growth result in higher rates of required return,
implying greater risk; Beaver, Kettler, and Scholes [3] use
growth in total assets as a risk variable. In this disser
tation, "growth" will be defined as growth in operating ear
nings and growth in earnings per share."
The growth rate in operating earnings is simply the
geometric mean of the annual growth rate over the 10-year
period 1969-1978. Thus,
X7j = TfCi - gtj) t=1
1/9 - 1 .
where g M = ^^^'^^'^^ >j - 1 .
(4-9)
(4-10) EBIT tj
Xftj: Growth in Earnings per Share
Similarly, the growth rate in earnings per share
(EPS) is expressed as a geometric mean over the same 10-year
period.
X8j = TTd + gtj) t»i
1/9 - 1 .
where gtj » ^^^^-H ,j - 1 .
(4-11)
(4-12) EPS tj
52 X9i: Interest Coverage
The ability of the firm to meet its interest
requirements is normally measured by the interest coverage
ratio. This ratio exhibits the financial strength of the
firm by calculating the number of times the firm could have
paid its interest charges in a given year. The variable to
be used is the arithmetic mean of the last ten years'
ratios:
10 I
t=l
EBITtj
(4-13)
^91 = 10
where EBIT^j = earnings before interest and taxes for firm j
in year t,
and Itj = interest charges for firm j in year t.
The higher the ratio, the greater the financial strength of
the firm, and the risk of default or bankruptcy would be
lower.
X-j nj : Trend of Interest Coverage
In addition, the :rend of such a variable would be
of interest, since it would indicate whether the ratio is
improving (getting larger) or worsening (getting smaller).
The model to compute such a trend line is given as:
FEBIT'I = aj + bjTt + ejt (4-14)
where Tj = the time variable for year t
ejt = the error term associated with firm j in year t
53
and aj and bj = parameters.
The variable of interest is the slope of the regression
line, so that
XlOj - bj . (4-15)
Xl1j : Liquidity
Another factor impacting upon the risk exposure of
the firm is its ability to meet cash needs on a day-to-day
basis. Because data for cash levels are not available, a
surrogate liquidity measure will be used. Although
imperfect, the metric that will be used is the variance of
the current ratio, using quarterly data adjusted for stock
splits and dividends over the ten-year period:
Xiij = Var CAj
j_CLy_j (4-16)
where CAj = Current Assets for firm j
and CLj = Current Liabilities for firm j.
Xl 2j and Xi- j : Variability and Trend of EPS
Finally, the variability and direction of the
firm's earnings-per-share will be measured by the use of
another trend line. The trend equation uses quarterly data
over the ten-year period and is given by
EPSj - aj + bjTj + ejt (4-17)
where the regression variables are analogous to those in the
trend equations (4-1) and (4-14). The variance around the
54
error term serves as the measure of variability in earnings,
since changes in a positive direction are assumed.
Xi2j = Var [ejt]. (4-18)
The trend is given by the slope of the equation and
Xl3j = bj . (4-19)
Thus, thirteen variables will be computed directly
in the construction of the risk classes. As mentioned
above, these thirteen are thought to be particularly rele
vant to public utilities. The variables found by Beaver,
Kettler and Scholes [3] to be associated with systematic
risk included such variables as growth, financial leverage,
liquidity, firm size, and earnings variability. To include
other similarly-derived variables as risk-indicators would
seem to be defensible in light of these previous studies.^8
Most of the required data are found on the Compustat
Industrial tapes (quarterly or annual) or the Compustat
Utilities tape, or can be calculated directly from the data
found there. The only variables which require data sources
other than Compustat are X2, which requires the Value Line
Investment Survey, and X3, which requires the GNP Implicit
Price Deflator, the necessary values for which are contained
in monthly issues of the Federal Reserve Bulletin.
The firms under study will be the entire number
I^See also Bildersee [4] and Bowman [9]
55
listed on. the tapes in the Telephone Communication, Electric
Services, N atural Gas Transmission-Distribution, Natural Gas
Distribution, Electric and Other Services Combined, and Gas
and Other Services Combined industries, for which the
necessary data are available.
The Creation of Risk Classes by Clustering
To assign a firm to a risk class, grouping will be
done on the basis of the thirteen variables that were pre
viously identified. If n variables are used for the purpose
of grouping, then a firm can be represented as a point in
n-space. Groups can be constructed, or clustered, on the
basis of Euclidean distance between points. Cluster analy
sis is a group of algorithms for partitioning points in n-
space into groups according to some explicit or assumed
objective function.
In previous applications of clustering analysis in
financial and economic research, Jensen [30] attempted to
classify through cluster analysis those stocks which would
be high performers. He found that the results indicated
"that many of the best performing companies ex-post were
reflected in differences among companies with respect to the
...characteristics examined [in the cluster analysis]."^9
Elton and Gruber [18] found that the ability to predict
earnings-per-share on the basis of regression equations was
19jensen [30, p. 42] .
56
enhanced when the observations were clustered into groups
beforehand, and a regression equation computed for each
cluster. Martin, Scott, and Vandell [38] used cluster ana
lysis to demonstrate that traditional industry groupings
(based on the SIC four-digit codes) were not equivalent to
risk classes as had been traditionally presented.
The objective function of the clustering algorithm
used in this dissertation is to minimize the sum of the
squared distances between each point (firm) and its cluster
centroid. The squared distance between any two points in n-
space is given as:
Djk^ = ! (Pji - Pki)2 (4-20)
i=l
where Dji = t:he Euclidean distance between firms j and k
P j i_ = the value of variable i for firm j
and P^i = the value of variable i for firm k.
The algorithm to be used was developed by Ward [57] and is
based on the premise that the greatest amount of information
as specified by the objective function is available when a
set of n members are unclustered. The clustering process
begins by combining the two closest points into one group,
resulting in n-1 clusters. (Each individual point can be
imagined as a single-member cluster.) At the next
iteration, either of two events could occur: another pair
of single-member clusters could be combined into a group, or
another point could be combined into the two-member group.
57
In either case, n-2 clusters result. The procedure
continues, reducing the number of clusters by one at each
iteration, until all n points are combined into one cluster.
Since the number of clusters is systematically reduced by
one at each iteration, the procedure is termed
"heirarchical".
At each iteration, the decision must be made as to
which of the clusters should be combined. As long as the
clusters are single points, the grouping is not difficult to
conceptualize. Those points which are "most alike", that
is, nearest, or for which the Dj^ is a minimum, should be
joined. Once clusters exist with two or more members,
however, the decision is not so obvious. How does one
measure the distance between clusters when the cluster con
sists of multiple points?
Additionally, recall that the objective function is to
minimize the squared distances between each point and its
cluster centroid. This "within cluster" distance can be
expressed as:
V m G(g) _ , X
Wt + Z I I (Pij - Pi^^O ^ ( -21) i=1 q=1 j=l
where v = the number of variables upon which the clustering is performed
m = the number of groups or clusters
G(g) =• the number of points in group g
58
Pij = the value of the i b variable for the jth object in group g
p^vg;= the mean of the i b variable for group g
and Wt ~ ^be value of the pooled sum of squared distances at iteration t. (t = n - m)
Ideally, one would now want to examine every
possible combination of new clusters to see which one met
the criterion of the objective function most successfully.
However, to examine the value of the objective function
after each possible combination at each iteration would
possibly require an astronomical number of calculations.
The number of ways in which n entities may be assembled into
p mutually exclusive clusters is given as^O
N n P
P .i- I (-DP'Sg^'nl/gKn-g)! (4.22) •p! g»0
where the variables are analogous to those given in equation
(4-21). For example, the number of ways 50 points could be
assembled into 10 clusters is equal to 2,827,208,275,104 X
10^^. Clearly, massive amount of computer time would be
required. To hurdle this barrier, simplifying techniques
are employed so that the possible number of combinations is
reduced . '
20see Jensen [30, p. 51].
21 For further discussion of simplifying techniques, see Elton and Gruber [17, pp. 598-599].
59
The simplifying techniques usually take the form of
examining the values of Dji rather than the values of wt at
each iteration. Because of the hierarchical nature of the
clustering, two points cannot be separated once they have
been joined in a cluster. That is, they cannot be regrouped
into two separate clusters. Thus, the number of distances
to be computed can be reduced dramatically by limiting the
calculations to only a (relatively) few points. For
example, one clustering algorithm computes DJ\Q as the
Euclidean distance between cluster centroids. No matter how
many points are in the cluster, the centroid is represented
by only one point.
Another algorithm, termed "nearest neighbor", com
putes Djic as the Euclidean distance between the two closest
points. The algorithm used in this dissertation, "farthest
neighbor", is similar except that the distance between
clusters is the distance between the two points in the
clusters farthest away from each other. The advantage of
this method is that if the distance between clusters is the
distance between the two farthest points, all the remaining
points in the two clusters are no farther apart than that
distance. At each iteration the two clusters having the
smallest "farthest neighbor" distance are combined. The
solution, is an excellent approximation of the optimal solu
tion with substantial gains in computational efficiency.^2
22see Jensen [30. p. 52].
60
The Need for Principal Components Analysis
One encounters two fundamental problems in the use
of cluster analysis. The first of these problems is that
clustering, no matter which algorithm is used, is sensitive
both to the unit of measurement in each variable and to the
degree of correlation between variables. The variables used
in this dissertation are of various scales: variable X2,
for example, will be either 1, 2, or 3; variable X5 would
never be greater than 1.0; variable X]Q could be any posi
tive number. Unless the numbers are adjusted, the influence
of XT0 could be many times that of X7 or X3, simply because
of the differences in scale. Final groupings will also be
affected by the degree of correlation between variables.
Because of the way in which distances are calculated, if
variables X-) and X2 are perfectly correlated, their
influence is double counted. The greater the correlation of
one variable with another, the greater the effect of the
common influence.
In most economic problems, not only is the scaling
arbitrary, but the variables are often multicollinear. The
variables in this study are likely to exhibit some multi
collinearity as well. The most obvious pair are Xg and Xi3,
both of which are measures of growth in earnings per share,
and should be highly correlated.
If no solution existed to overcome this problem, the
uses of cluster analysis would be limited indeed. However,
61
principal components analysis provides a means for trans
forming the data into a new set of variables that are
orthogonal, and thus free of the problems of intercorrelated
measurements. Principal components analysis is one of the
subsets of the class of multivariate statistical methods
known as factor analysis. In general, it has as its purpose
data reduction and summarization. It simultaneously con
siders the relationships am.ong all the variables, and then
attempts to explain the variables in terms of their common,
underlying dimensions. Each factor, or component, is simply
a weighted linear combination of the original variables, the
weights being determined by an algorithm similar to linear
„ ^ - u- u ^ •«,• -u •». variance of PCI programming which maximizes the quantity total variation> giving the proportion of total variance captured by PCI,
the first principal component. The total variance of the
data is simply the sum of the variances of the original
variables. The first principal component, then, is that
weighted linear combination of variables which accounts for
a greater amount of the total variance than any other
component.
...The first factor may be viewed as the single best summary of linear relationships exhibited in the data. The second factor is defined as the second best linear combination of the variables subject to the constraint that it is orthogonal to the first factor. To be orthogonal to the first factor, the second one must be derived from the proportion of the variance remaining after the first factor has been extracted. Thus, the second factor may be defined as the linear combination of variables that accounts for the most residual variance after the effect of the first factor is removed
62
from the data. Subsequent factors are defined similarly until all the variance in the data is exhausted. [23, p.226]
Each variable is assumed to have a prior estimate of
variance equivalent to 1.0. The total variance for n
variables would then be n. The variance of each extracted
principal component is its latent root, or eigenvalue. In
general, any component with an eigenvalue smaller than 1.0
is considered insignificant and can be discarded.23 Those
with eigenvalues greater than or equal to 1.0 will remain
and form the basis for a reduced problem. These reduced
components will give the weights for calculating the com
ponent scores and will be used for the clustering.
Principal component scores for each observation are
calculated as a linear combination of the weights for each
principal component and the observed values for each
variable. These new scores are divided by their respective
eigenvalues to eliminate differences in dispersion among the
resulting component scores. And in conformity with accepted
procedure, they are then standardized.24 Thus the problems
of scale are likewise eliminated. These values then in
effect become the new variables for clustering.
23For a good non-mathematical discussion of principal components analysis, see Hair, Jr., et al [23, pp. 215-283] and Kleinbaum and Kupper [31, pp.~3"7^413] . For a rigorous, mathematical development, see Harris [25, pp. 155-204].
24see Elton and Gruber [17, p. 590].
63
The second fundamental problem in cluster analysis
is determining the point at which to stop the procedure.
Discriminate analysis, like cluster analysis, is a technique
which attempts to group observations according to common
characteristics, but the number of groups is known in
advance. The problem usually lies in determining the boun
daries of the groups and in correctly assigning a given
observation to a previously determined group. In
clustering, however, unless the researcher has some reason
for determining a particular number of groups, the critical
number of clusters is unknown. Elton and Gruber [17]
suggested that the clustering procedure should be terminated
when further combination would increase the within-group
distance (Wt) to an extreme value. Recognition of this
value remains a matter of judgment, however. To try to eli
minate the need for arbitrary decisions, Martin, Scott, and
Vandell [38] developed a "pseudo-F" to test for significant
changes in Wt. Their test is based on an F-ratio consisting
of the observed percentage change in Wt divided by the
expected percentage change in Wt where the expected percen
tage change in Wt is given by
Wt - Wt-1 P (4-23) '"t - ^t-l . pn - (m - 1 ) 1 r _m_ "I 2/ Wt _ |_ n - m _ _ ^ " ^ J
where n = the number of observations
m « the number of clusters in iteration t
64
and p « the number of variables used in the clustering procedure.
Unless one knows a priori that the ratio of two percentages
approximates an F distribution, the value of such a test may
be open to debate. The procedure in this dissertation will
examine clusters at the iterations based on the recommen
dations of both Elton-Gruber and Martin-Scott-Vandell.
However, additional iterations will be examined for possible
variations in the results.
Testing the Hypothesis
Once the risk classes have been constructed, the
next step will be to compute the value of beta for each firm
in the study. Betas will be computed by regressing each
firm's monthly holding period returns against the holding
period return of the Standard and Poor 500-stock index over
the period 1969-1978.
The test itself will be a one-way analysis of
variance of the betas in the risk classes. If the variance
among clusters is significantly greater than the variance
within clusters, the hypothesis would be rejected, and one
could conclude the beta varies according to the risk class
of the firm. The results of the analysis are discussed in
the next chapter.
CHAPTER V
RESULTS A:1D INTERPRETATION
The firms used in the dissertation were those uti
lities on the Compustat tapes for which all the information
was available. Out of the 177 firms on the tapes, 124 had
complete data available. These firms are listed by industry
grouping in the appendix.
Principal Components Analysis
As outlined in Chapter IV, the first step in the
dissertation was to perform a principal components analysis
on the variables. The purpose was to eliminate the problem
caused by multicollinearity and by differences in scale.
The results of the analysis are presented in Tables 5-1
through 5-7. Table 5-1 shows the eigenvalues for each of
the principal components. As explained in Chapter IV, the
eigenvalues are analogous to that portion of total variance
for which the principal component accounts. The total
variance for 13 components would be 13.0. The fact that the
first principal component has an eigenvalue of 2.495 means
that it accounts for 2.495/13.0 of the total variance or
19.27o. By examining the eigenvalues, one can determine
whether to eliminate any of the components for purposes of
further analysis. As a rule-of-thumb, those components
65
66
TABLE 5-1
EIGENVALUES FOR PRINCIPAL COMPONENTS
Cumulative Principal Explained Explained Components Eigenvalues Variance Variance
1 2.495 .192 .192
2 2.245 .173 .365
3 1.700 .131 .495
4 1.306 .100 .596
5 1 .020 .078 .674
6 .978 .075 .749
7 .734 .056 .806
8 .634 .049 .855
9 .583 .045 .900
10 .465 .036 .935
11 .447 .034 .970
12 .252 .019 .989
13 .141 .011 1.000
67
which do not have eigenvalues equal to or greater than 1.0
are normally discarded, although the decision must be tem
pered by judgment. For purposes of this dissertation, prin
cipal components one through six were retained and the
remainder were discarded. (Although principal component six
has an eigenvalue of .978, the rule-of-thumb mentioned above
is not seriously violated, and that component accounts for
7 .57o of the variance.) Reducing the number of components
not only saves considerable amounts of computer time, but
facilitates interpretation of the results. Reduction of the
number of components is normally advisable since the latter
components contain much of the random effects of the vari
ability in the data. With six principal components about
7 57o of the variation was captured in this dissertation.
Table 5-2 shows the variable loadings on the six
retained principal components. The loadings represent the
correlation between the variables and the principal
components, and, after rotation of axes, provide the basis
for interpretation of the results. The loadings resulting
from the rotated axes are shown in Table 5-3. Interpre
tation of these results will be discussed below. The
variable loadings were divided by their respective eigen
values before computing principal component scores. This
division was accomplished in order to reduce the dispersion
in the scores; the greater the dispersion, the greater the
effect of that component on the clusters. The principal
68
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70
component scores are the values that were used in the actual
clustering, but before they were used, they were standar
dized as is the customary procedure.
Interpretation of the Principal Components
As mentioned above, the variable loadings of Table
5-3 provide the basis for attributing meaning to the prin
cipal components. The axes of the matrix have been rotated
to facilitate interpretation. As stated earlier, the ini
tial factor solution extracts factors in order of their
importance, with the first factor accounting for the largest
amount of variance. The effect of rotation is to redistri
bute the variance from early factors to later factors in
order to achieve a simple, more meaningful pattern. (The
factor scores for clustering, however, are drawn from the
initial solution.) Although the exact meaning is probably
unknowable, perhaps some interpretation can be made. Each
of the six retained components will be discussed.
The first principal component (PCI) exhibits high
positive correlation with variables Xg and X-| 3 , a lesser
degree of positive correlation with variable X^Q, and lesser
degrees of both positive and negative correlation with the
other variables. Xg and Xi3 are both indicators of growth
in earnings-per-share, and Xi 0 i-s the trend (or growth) in
interest coverage. One might infer that as a firm's earn
ings grow, its ability to meet interest payments is
71
improved. One might, therefore, deduce that PCI is a growth
factor.
PC2 is more complicated in its composition. It
exhibits strong negative correlation with X9, the interest
coverage ratio, and positive correlation with X3, inflation;
X5 financial leverage; and X-| Q , the trend in interest
coverage. In terms of absolute values, the correlation
coefficients are largest for X9 , X5 , and X-; Q , all of which
are related to the concept of financial leverage. The signs
of the relationship seem to be correct: high values of X5,
financial leverage, would imply relatively lower values for
X9, interest coverage. The inverse is also true. The fact
that PC2 is negatively correlated with X9 and positively
correlated with XiQ implies that X9 and XIQ are negatively
correlated. The inference is that firms with low levels of
debt have capacity to add more debt; thus, over the ten-year
period, the addition of more debt causes the interest
coverage ratio to deteriorate. Firms that are highly
leveraged may tend to "work off" their debt over time,
leading to an improving interest coverage ratio, or a trend
with a positive sign. As mentioned above, PC2 also captures
much of the variation in X3, the inflation variable. Recall
that high values of X3 indicated an ability of the firm to
offset the effects of inflation through price increases.
The relationship of this variable to the financial leverage
variables would seem to indicate that debtors indeed benefit
72
from inflation, the fixed interest costs associated with
debt becoming relatively less important as inflation
adjusted revenues rise. PC2, therefore, appears to be
related to financial leverage.
The third principal component exhibits positive
correlation with Xi, the vulnerability of product demand;
X3, inflation; and Xi2, the variability in earnings per
share. Negative correlation with X7, the growth rate in
operating earnings, is also present. The negative correla
tion with X7 and the positive correlation with X3, implying
X7 and X3 are negatively correlated, would seem to indicate
that firms with low rates of growth are better able to cope
with inflation than firms with high rates of growth, since
low values of X7 would tend to be associated with high
values of X3. However, since the highest correlation coef
ficients are those Xi and Xi2, PC3 seems to be related most
directly to demand and earnings vulnerability to cyclical
variations in the general level of economic activity. The
fact that these variables have signs opposite that of
X7 would imply that firms with little variability would have
high growth rates, and those with high variability would
have low growth rates, an implication that runs counter to
traditional theory. One would infer that PC3 captures the
risk attributed to cyclical variation.
PC4 is highly correlated with X4 and Xi1. X4 and
Xl 1 are the variance of operating leverage and the variance
73
of the current ratio respectively. X4 was constructed as an
attempt to measure the impact of operating leverage risk,
and Xl 1 was derived as a measure of liquidity risk.
Operating leverage is the degree to which a firm uses fixed
costs, apart from interest charges, in its operations. The
higher these costs are, the higher the risk that is said to
exist. Liquidity problems would be involved as these costs
rose, because greater amounts of cash would be required to
service the accounts. In this case, both variables relate
directly to operating leverage risk, and PC4 should be so
identified.
PC5 exhibits high negative correlation v/ith X2 , the
regulatory environment variable, and a smaller, but
positive, degree of correlation with X3, the inflation
variable. Since the magnitude of the coefficient for X3 is
so much smaller than that of X2, the impact of X3 upon PC5
is less important than it would be otherwise. PC5,
therefore, probably captures the risk attributable to the
regulatory environment, with a slight effect of inflation
due to regulatory lag (the inability to "pass along cost
increases due to imposed rate structures.)
PC6 is highly correlated with variable X5, the
measure of firm size, and exhibits very little correlation,
either positive or negative, with any other variable. Thus,
PC6 could be said to capture the risk attributable to the
size of the firm within its industry.
74
In summary, the preceding section is subject to
differences of opinion; no single description could ade
quately cover the true meaning of any of the components.
Those variables with small correlation coefficients were
ignored in the analysis; in reality, the correlation,
although slight, might impart some shade of meaning.
However, the meaning of the components is irrelevant to the
construction of the risk classes, a procedure which is
discussed below.
The Results of the Clustering
The procedures for the clustering analysis were
discussed in the preceding chapter. Using the Martin-
Scott-Vandell "pseudo-F" test, the clustering was halted
after nine iterations. Table 5-4 displays the results of
the first twenty iterations of the clustering process. The
pseudo-F became significant (at 57o) on the tenth iteration,
an indication that the increase in total sums of squares was
greater than would be expected on chance alone. Therefore,
the clustering procedures should be halted prior to that
significant change in error. Thus, the appropriate number
of clusters would be 115. As can be observed from the
table, most of the iteraations following that one also
result in statistically significant increases in error.
A problem exists, of course, in the assessment of
the results of the clustering. Of the 115 clusters, 107
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consist of one-firm clusters, 7 are composed of two firms,
and 1 is made up of three firms. The multiple firm clusters
are exhibited in Table 5-5. For all practical purposes,
these results are not interpretable unless one is willing to
accept that at least 107 utility companies are risk classes
unto themselves. The hypothesis that these risk classes
have equal betas is testable, however. The one-way analysis
of variance with 114 and 9 degrees of freedom yields an F-
value of 1.379, not large enough to reject the null
hypothesis. Thus, using the Martin-Scott-Vandell pseudo-F
test as a stopping rule, no significant difference exists in
the betas of the risk classes.
TABLE 5-5
COMPOSITION OF MULTIPLE-FIRM CLUSTERS AT M = 115
HE CER TE KGE
CNR COC RGS DPL
DTE
NGE CIP NMK IPC
SDO GTC VEL IDA
77
However, the question arises as to the validity of
the pseudo-F test, specifically as to the distribution of
the ratio of the percentage changes. An F-ratio is ordi
narily considered to be the ratio of two variances, but it
is unlikely that the distribution of the ratio of percentage
changes in those two variances would also be an F-distribu-
tion.25 Because of this fact, one must examine other iter
ations before the results can be generalized.
An alternative stopping rule which suggests itself
from the preceding discussion is to use, instead of the
ratio of the percentage changes, the ratio of the changes
themselves. This F-ratio T.ight be an improvement on the
previous ratio because of the former's inherent distribution
problem. As a result of this test the clustering procedure
was stopped after sixty iterations, moving from sixty-six to
sixty-five clusters. Table 5-6 displays the results of the
iterations immediately preceding and following that
iteration.
Testing the null hypothesis with sixty-six
clusters, the F for 65 and 58 degrees of freedom is 1.650
which is not significant at a = .05. Thus, the null
hypothesis cannot be rejected using this rule for stopping.
Again, one could fault this F-test for the same
25More exactly, an F-ratio is the ratio of two chi-square variables, each of which is divided by its respective degrees of freedom.
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shortcomings of the Martin-Scott-Vandell test: the ratio of
the changes in variance is not necessarily distributed in
the same manner at the ratio of the variances themselves.
The method mentioned in the previous chapter, recommended by
Elton and Gruber, was to terminate the clustering when
further combinations would increase W^ to an extreme value.
This "extreme value" is of course relative to the scatter of
the points being clustered. Extreme values were treated as
those resulting from larger than normal additions to W^ at
any iteration. Thus, the percentage change in W^ which was
extraordinarily larger than those immediately preceding it
was considered to result in an extreme value. Large contri
butions to Wj occurred in iterations 44, 50, 77, 83, 84, 95,
99, 105, 106, and 109. These ten iterations, if correct,
would have stopped the clustering process at 81, 75, 48, 42,
41, 30, 26, 20, 19, and 16 clusters respectively. The
results of testing the hypothesis at each of these ten
levels are displayed in Table 5-7. Eight of the ten tests
failed to reject at a = .05. One (with 48 clusters) failed
to reject at a = .025 and one (with 81 clusters) failed to
reject at a = .01. While these tests are not conclusive
proof, the results seem to indicate that the risk classes
do not have significantly different betas.
Finally, one could arbitrarily stop the clustering
process at some predetermined level of significance. For
example, if one knew, a priori, that there were ten risk
80
TABLE 5-7
RESULTS OF ELTON-GRUBER STOPPING PROCEDURE
81 clusters: F(80,43) = 1.783 significant at a = .05 not significant at a = .01
75 clusters: F(74,49) = 1.378 not significant at a = .05
48 clusters: F(47,76) = 1.587 significant at a = .05
not significant at a = .025
42 clusters: F(41,32) = 1.090 not significant at a = .05
41 clusters: F(40,83) = 1.131 not significant at a = .05
30 clusters: F(29,94) = 1.208 not significant at a = .05
26 clusters: F(25,98) = .907 not significant at a = .05
20 clusters: F(19,104) = .823 not significant at a = .05
19 clusters: F(18,105) = .838 not significant at a = .05
16 clusters: F(15,108) = .955 not significant at a = .05
classes in the group of firms, the procedure could be halted
after 114 iterations. Since this kind of information was
not known, one could arbitrarily choose a level that might
lend itself to a "proper" number of risk classes. One might
test the hypothesis at, say, five, ten, or fifteen risk
classes. No significance could be attached to these levels;
one could as logically select any other number of clusters,
but for analytical purposes, one would hope to see a some
what lower number of risk classes than selected by the
81
previously mentioned methods. Thus, the hypothesis was
tested at levels of five, ten, and fifteen clusters with the
results given in Table 5-8.
TABLE 5-8
RESULTS OF STOPPING AT SELECTED ITERATIONS
15 clusters: F(14,109) = 1.030 not significant at a = .05
10 clusters: F( 9,114) = 1.141 not significant at a = .05
5 clusters: F( 4,119) =« 1.431 not significant at a = .05
Summarizing the results, fifteen analyses of
variance were performed, at iterations consisting of 5, 10,
15, 16-, 19, 20, 26, 30, 41, 42, 48, 66, 75, 81 and 115
clusters. In thirteen tests, the F-values were not large
enough to cause a rejection of the null hypothesis at a =
.05. Of the two which did cause the hypothesis to be
rejected, one would have failed to reject at a = .025 and
the other at a = .01. The evidence all seems to support the
hypothesis that the betas of the various risk classes,
varying from as few as five to as many as 115, do not signi
ficantly differ between risk classes. As much variation
exists within risk classes as exists between risk classes.
CHAPTER VI
SUMMARY AND CONCLUSIONS
The capital asset pricing model has, since its
development by Sharpe [53], Lintner [35], Mossin [41], and
-Treynor [57], been demonstrated to be applicable to many
areas beyond its original use in portfolio theory. As
discussed in Chapter II, it has been applied, to those
situations involving the relationship between risk and
return, including valuation theory, investment decision
theory, and the cost of capital. This latter field of
application, particularly in the area of the cost of capital
to publicly held utilities, provided the basis for this
dissertation. The cost of capital to public utilities has
been of special interest to academicians and others because
of the fact that the utilities are so closely regulated.
This environment provides a mechanism for the application of
methods and controls which would be impossible to investi
gate in a more competitive atmosphere. Since regulatory
agencies at federal, state, and local levels set target
rates of return for the utilities they regulate, a
"laboratory" setting is created in which the results of
various activities can be monitored.
The legal basis for regulating utilities' rates of
82
83
return is found in two U.S. Supreme Court decisions. The
Bluefield decision26 in 1923 codified what had already
become a principle of regulation, that is, that the returns
should be commensurate with the risk undertaken. The Hope
decision27 in 1944 extended this view to the investor
himself. Thus the regulatory agencies are required to con
sider the risk of the particular firm when setting the
allowed or target rates. The capital asset pricing model
seemed to be readily applicable to the rate-setting
procedure. In the late 1970's, many rate hearings involved
recommendations that the model be used.28 At the same time,
numerous articles appeared urging caution and pointing out
possible shortcomings in the model.
The kinds of problems that were identified involved
those of theory and those of measurement. The model is
based upon a set of assumptions of questionable validity.
If these assumptions are sufficiently weak, or if the model
has little predictive power, the basis for the model's use
fulness may be of little worth. Several studies [5, 19, 20]
revealed that empirical attempts to derive the capital
^^Bluefield Water Works and Improvement Company vs. Public ServTce Commission of the State of West Virginia (26"2" U.S. 679).
^^Federal Power Commission vs. Hope Natural Gas Company (320 U.S. 591).
28see Vandell and Malernee [57], Brigham and Crum [12], and Cooley [15].
84
market line results in significantly different parameters
than those specified by the equilibrium form of the model.
Problems of stability and stationarity were noted; these
problems, if severe, limit the usefulness of the model's
predictive power. These are closely related to the basic
problem of predicting future events on the basis of histori
cal data. After all, beta is an ex ante concept; the
theoretical beta may not be predictable on the basis of
historical returns.
However, historical returns are currently the only
practical basis for forming predictions of future betas.
The accuracy of the procedures is, therefore, crucial.
Measurement problems make up a category unto themselves;
these involve studies of the effects on estimated rates of
return resulting from the way in which the parameters are
estimated. Allowing the length of the investment horizon to
vary, for example, causes great differences in beta.
Similar studies were concerned with the size of the period
of time encompassing all the intervals, the proper risk-free
rate as it relates to the investment horizon, the choice of
market index and the choice of estimating equations. In
most cases, different measures resulted in different betas
(or different estimates of the rate of return).
Some writers thus questioned the ability of the
model to measure adequately the impact of the risk of public
utilities [13, 14]. Unsystematic risk was thought to be of
85
significance in utilities due to distortions introduced by
the regulatory process. Beta was said to be an incorrect
measure of the relevant risk.
To determine whether or not a firm's level of risk
is related to its beta, the dissertation attempted first to
create risk classes. Based on methodology first used by
Martin, Scott, and Vandell [38], groups of firms with simi
lar risk characteristics were identified by means of cluster
analysis. This technique groups firms in n-space by com
bining those which are nearest each other, as measured by
Euclidean distance. Termed hierarchical in nature, the pro
cedure begins with a number of clusters equal to the number
of points (observations) and systematically agglomerates
them, decreasing the number of clusters by one at each
iteration, until all points are contained in one cluster.
At any iteration between the first and last, clusters of
varying sizes will exist, i.e., the sizes of the clusters
will not necessarily be uniform at a given iteration.
The risk factors upon which the clustering is based
were derived from thirteen risk variables. These risk
variables were either commonly accepted metrics of business
and financial risk or were especially created to attempt to
measure aspects of risk that may uniquely affect utilities.
Incomplete data required eliminating several firms from the
Compustat lists of utilities; one hundred twenty-four firms
were included in the study. (See appendix.)
86
To eliminate the effects of multicollinearity and
to adjust for the effects of differences in scale, a prin
cipal components analysis was performed on the raw data.
Aside from the benefits just mentioned, principal components
analysis allows the user to reduce the numbers of variables
under consideration. The risk variables are thus trans
formed into underlying risk factors and reduced in number.
The principal components analysis revealed that six factors
(components) should be retained. The clustering was per
formed on these six components.
The null hypothesis was stated as:
Ho: 3 i = 3^= D 3 = •••= 0^
where k is the critical number of clusters as identified by
one of several cluster procedure stopping rules. The
hypothesis was tested at levels where the number of clusters
was 115 (Martin-Scott-Vandell "pseudo-F"); 66 (another
"pseudo-F"); 81, 75, 48, 42, 41, 30, 26, 20, 19, and 16 (all
Elton-Gruber extreme-value test); and 15, 10, and 5
("proper-number" measures). Rejection of the null would
indicate significant differences between the mean betas of
the various risk classes. Failure to reject would indicate
that no significant difference could be detected. The test
was the one-way analysis of variance.
87
Conclusion
The results of the fifteen tests were detailed in
Chapter V. Briefly, at each iteration resulting in the num
bers of clusters listed above, all tests failed to reject
the null hypothesis at a =.05, except at 81 clusters and at
48 clusters. However, at a = .025, the test at 48 clusters
failed to reject, and at a = .01, the test at 81 clusters
failed to reject. These results would seem to indicate that
very little difference exists between the average betas of
the risk classes. What little conflicting information
exists is at cluster levels higher than one can readily
accept as being meaningful. That is, in a group of 124
public utility firms, one would assume that for all prac
tical purposes, fewer than 20 distinct risk classes would be
detectable. All of the analyses of variance at 20 or fewer
risk classes resulted in F-ratios with a-levels greater than
57o. Thus, one would have great difficulty assigning a firm
to a particular risk class on the basis of its beta. One
could not say with any degree of certainty that two public
utility firms with different betas would necessarily be in
different clusters. On the other hand, neither could
one say that two public utility firms with the same beta
would be in the same cluster. Beta, then, does not discri
minate adequately between public utilities of different risk
levels, as determined by the variables examined in this
dissertation.
88
Admittedly, beta is not a measure of total risk,
but a measure of systematic, non-diversifiable risk. Total
risk is more likely to be measured by the variance of
holding period returns. However, Miller and Scholes [39]
and Klemkosky and Martin [32] found beta was highly and
positively correlated with nonmarket risk in individual com
mon stocks. The studies mentioned in Chapter IV by Beaver,
Kettler, & Scholes [3] and Bildersee [4] found that
accounting risk variables displayed significant correlation
with systematic risk. Thus, a test of beta through the use
of accounting variables which address both market and non-
market factors influencing risk is not inappropriate.
Additionally, the use of beta in regulatory proceedings
often fails to address the issue of systematic versus total
risk. To the non-diversified investor (such as many public
utility investors may be), or to the non-diversified firm
(such as a public utility) total risk may indeed be the
relevant measure. If such is the case, beta would be
misused to set rates. However, that issue is a subject for
further research.
The Supreme Court cases do not address the issue of
non-diversifiable risk. Whether or not some risk can be di
versified away depends not only on the characteristics of the
available set of investments, but upon the accuracy of the
information about them, including the calculations of beta.
89
One might raise the issue as to whether or not all
relevant variables have been included. Certainly, addi
tional accounting variables could be calculated which could
possibly address some risk factor ignored in this disser
tation. Those variables that were used, however, were
attempts to capture those factors that are widely accepted
as indicators of risk, i.e., the extent to which a firm is
affected by leverage, the ability to meet current obli
gations, etc. Other variables could be included, but none
are likely to change the results. A regulatory agency is
unlikely to identify additional variables of such importance
that they would generate clusters more homogeneous (in terms
of beta) than those in the dissertation. However, addi
tional research should be directed toward isolation of fac
tors or variables that are truly indicative of the level of
risk. Regression analysis used with principal component
analysis could prove to be a useful tool.
In light of the problems with beta discussed above
and in Chapter III, and in light of the results of this
paper, the use of the capital asset pricing model in the
regulatory process should be discouraged. Only when the
measurement of risk becomes much more precise, and the abi
lity to discriminate between that which is diversifiable and
that which is not becomes more refined, will the model's
usefulness be enhanced.
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APPENDIX
PUBLIC UTILITIES IN THE DISSERTATION
Company Names (by industry) Ticker Symbol Beta
Telephone Communication
American Telephone and Telegraph T .614 Cincinnati Bell, Inc. CSN .534 Mountain States Telephone and Telegraph MOU .557 New England Telephone and Telegraph NTT .502 Pacific Northwest Bell Telephone PNB .391
Pacific Telephone and Telegraph Company PAC .424
Natural Gas Distribution
Cascade Natural Gas Corporation CGC .677 Indiana Gas Company IGC .647 Michigan Gas Utilities Company MCG .504 National Fuel Gas Company NFG .503 Nicor, Inc. GAS .614 Piedmont Natural Gas Company PNY .651 Public Service Company of North Carolina PSNC .536 Southern Union Company SUG 1.018 Natural Gas Transmission-Distribution
Arkansas Louisiana Gas ALG .866 Columbia Gas Systemn CG .630 Consolidated Natural Gas Company CNG .556 Enserch Corporation ENS .851 Equitable Gas Company EQT .662 Mississippi Valley Gas Company MVAL .527 Oklahoma Natural Gas Company ONG .756
Electric Services
American Electric Power ^ P -^24 Atlantic City Electric ATE ./iJ Bangor Hydro-Electric Company BANG .DZb Black Hills Power and Light Company BHPL .654 Boston Edison Company BSE .639 Carolina Power and Light GPL .»iD Central and South West Corporation CSR .875 Central Maine Power Comany CTP .429
96
97
Electric Services (continued)
Central Vermont Public Service Cleveland Electric Illuminating Columbus and Southern Ohio Commonwealth Edison Community Public Service Detroit Edison Company Duke Power Company Duquesne Light Company Eastern Utilities Association Edison Sault Electric El Paso Electric Company Empire District Electric Company Florida Power and Light Florida Power Corporation General Public Utilities Gulf States Utilities Company Hawaiian Electric Company Idaho Power Company Indianapolis Power and Light Kansas City Power and Light Kansas Gas and Electric Kentucky Utilities Company Maine Public Service Middle South Utilities Minnesota Power and Light Nevada Power Company New England Electric System Northeast Utilities Ohio Edison Company Oklahoma Gas and Electric Otter Tail Power Company Pennsylvania Power and Light Potomac Electric Power Public Service Company of Indiana Public Service Company of New Hampshire Public Service Company of New Mexico Puget Sound Power and Light Savannah Electric and Power Southern California Edison Company Southern Company Southwestern Electric Service Southwestern Public Service Company Tampa Electric Company Texas Utilities Company Toledo Edison Company United Illuminating Company Upper Peninsula Power Utah Power and Light Virginia Electric and Power
CPUB CVX COC OWE CMM DTE DUK DQU EUA ESE ELPA EDE FPL FDP GPU GTU HE IDA IPL KLT KGE KU MAP MSU MPL NVP NES NU OEC OGE OTTR PPL POM PIN PNH PtTM PSD SAV SCE SO SWEL SPS TE TXU TED UIL UP EN UTP VEL
.683
.558
.764
.794
.630
.713
.844
.532
.672
.122
.599
.449
.902
.872
.837
.935
.769
.593
.848
.656
.757
.645
.422
.968
.680 1.086 .698 .638 .611 .809 .502 .612 .589 .868 .552 .840 .648 .688 .851 .856 .444 .726
1.025 .708 .756 .557 .523 .678 .956
Electric and Other Services Combined 98
Arizona Public Service Company AZP .754 Baltimore Gas and Electric BGE .634 Central Hudson Gas and Electric CNH .583 Central Illinois Light CER .700 Central Illinois Public Service CIP .684 Central Louisiana Energy Corporation GEL .732 Cincinnati Gas and Electric GIN .630 Consolidated Edison of New York ED .773 Consumers Power Company CMS ^804 Dayton Power and Light DPL !667 Delmarva Power and Light DEW .783 Fitchburg Gas and Electric Light FGE ^361 Illinois Power Company IPC .749 Interstate Power Company IPW .515 Iowa Electric Light and Power lEL .730 Iowa-Illinois Gas and Electric IWG .675 Iowa Power and Light lOP .720 Iowa Public Service Company IPS .407 Iowa Southern Utilities Company lUTL .828 Kansas Power and Light KAN .516 Lake Superior District Power Company LAKE .458 Louisiana Gas and Electric LOU .593 Madison Gas and Electric Company MDSN .520 Missouri Public Service Company MPV .721 Montana Power Company MTP .636 New England Gas and Electric NEC .656 New York State Electric and Gas NGE .748 Niagara Mohawk Power NMK .567 Northern Indiana Public Service NI .816 Northern States Power NSP .642 Northwestern Public Service Company NWPS .626 Orange and Rockland Utilities ORU .624 Pacific Gas and Electric PCG .684 Pacific Power and Light PPW .621 Philadelphia Electric Company PE .609 Public Service Company of Colorado PSR .687 Public Service Electric and Gas PEG .769 Rochester Gas and Light RGS .777 San Diego Gas and Electric SDO .706 Sierro Pacific Power Company SRP .787 South Carolina Electric and Gas SCG 1.079 St. Joseph Light and Power SAJ .639 Washington Water Power WWP .368 Wisconsin Electric Power WPG .589 Wisconsin Power and Light WPL .627 Wisconsin Public Service WPS .373
Gas and Other Services Combined None
