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ALFRED P. SLOAN SCHOOL OF MANAGEMENT
A RISK/RETURN PARADOX FOR STRATEGIC MANAGEMENT
Edward H. Bowman
WP 1107-80 March 1980
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A RISK/RETURN PARADOX FOR STRATEGIC MANAGEtffiNT
Edward H, Bowman
WP 1107-80 " March 1980
To be published in the Sloan Management Review
A RISK/RETURN PARADOX FOR STRATEGIC MANAGEMENT
by Edward H. Bowman
The total set of industries from Value Line is used to
demonstrate that business risk and return are negatively correlated
across companies within industries. Some empirical questions
about industries themselves are also raised. The concepts of
income smoothing and corporate strategy are utilized to explain
this apparent paradox. Further work is both suggested and
A Risk/Return Paradox for Strategic Manc.gement
by Edward H. Bowman*
Strategic management is concerned with choosii g environmental
domains, determining the nature of the interaction:; with these domains,
and making the internal adjustments suggested or required by these choices.
An organizational and hierarchical way of capturing these activities, and
differentiating among them, is to analyze the issues of corporate
strategy, of business strategy, and of functional strategy. 
One of the major elements present at all three stages of strategic
decision making is resource commitment in its various generic investment
forms. Examples would be a) acquisition of a company in an unrelated
product/market - at the corporate level, or b) mounting a substantial
research and development program to reposition a product line - at the
business level, or c) beginning a different promotion and advertising
program for a product in the mature stage of its life cycle - at the
Ideas about the risks and returns associated with strategic resource
commitments, or generic investments, at all three organizationa] levels
supply the motivation for this research paper, one of a series dealing
vith the study of company differences within industries, 
A great deal of both theoretical and empirical analysis has recently
been addressed to the relationship between financial risk and return. Most
* Many colleagues and students at both M.I.T. and Ohio State University
have helped with this research; most helpful have been Dan Skrzypek,
Barbara Barnhart, Michael Treacy, Professor Andrew Chen, and anonymous
of this work has dealt with security markets, thougli some has also addressed
the corporation itself. Such analysis has both intjrest in its own rijjht
as well as influencing approaches to public policy questions like concern
for capital formation and its associated effects.
This paper explores some recent empirical vjork at the level of the.
firm and the industry, rather than the more popular stock market domain.
Though paradox may be in the eye of the beholder, some interesting
associations between risk as currently measured and profits at the level
of the firm are explored here.
An academic interest in the associations between risk, uncertainty and
profit goes back many years. Professor Paul Samuelson in Economics  both
describes profits and elaborates their possible misspecif ication, e. g.
inflation effects. He includes uncertainty associated profits in his
discussion citing Professor Frank Knight's early work. Professor Frank
H. Knight in Risk, Uncertainty and Profit  while discussing misspecifi-
cation of profits and dwelling on the uncertainty aspect makes the extremely
interesting comment, "The writer is strongly of the opinion that business
as a whole suffers a loss." While perhaps oversimplifying the case here,
and contrary to some popular impressions. Knight does not appear to say that
uncertainty ex ante either causes or justifies profit, though it may in
part explain some profits ex post . As Knight indicates "Profit (when
positive) is not the price of the service of its recipient, but a 'residual,'
the one true residual in distribution. " 
From current economic theory and from recent theoretical and especially
empirical work in finance one gets the impression that risk must carry its
own reward. The argument of/for economic rationality suggests that because
the typical business executive is risk averse the higher risk project/
investment will require a higher expected return, at least ex ante , or
it won't be undertaken. The following are typical quotations to this
a) Samuelson states, "Many economists think that businessmen on
the whole act as if they dislike mere riskiness and hence they
must on the average be paid a positive premium or profit for
shouldering risks. " Also, more recently, he "worries that
businessmen could find themselves in a 'risk trap.' 'An
increase in uncertainty could lower the expected value of an
investment, when corrected for risk. . .below the rate required
by investors with a resulting fall off in capital spending.'"
b) A Harvard Business Review article by Conrad and Plotkin states,
"And in considering capital and other investments, managers in
the industrial sector of the economy as a matter of course
weigh risk and return together. "
c) A standard textbook in finance by Solomon and Pringle states,
"For a typical (average-risk) project undertaken by a firm,
the required risk premium equals the firm's risk premium...
For projects involving higher or lower risks the risk premium
equals the firm's risk premium. .. times the ratio of project
risk to firm risk..,. "
d) Caves, in American Industry: Structure, Conduct, Perf ormance,
states under the topic, Risk Avoidance , "they (the managers)
might go for the quiet life. This could mean that they avoid
risky projects that could turn out to be very profitable,
settling instead for a smaller but more certain profit" and
later, "The evidence seems to show that equity capital does
demand a somewhat higher rate of return where risks are
higher - where firms' fortunes vary wildly, or where profits
fluctuate a lot from year to year. "
e) Armour and Teece in a Bell Journal of Economics article state,
"...economic theory suggests that the rate of return associated
with a particular asset is a function of the risk inherent in
the asset, and (assuming risk aversion) the greater the risk,
the greater the expected return. "
f) Christensen, Andrews, and Bower in Business Policy: Text and
Cases write, "Is the chosen level of risk feasible in economic
and personal terms? Strategies vary in the degree of risk
willingly undertaken by their designers. For example, a small
food company in pursuit of its marketing strategy, deliberately
courted disaster in production showdowns and in erratic behavior
of cocoa prices. But the choice was made knowingly and the
return was likely to be correspondingly great. "
Wliile both business administration and economics theory and
literature, such as that quoted above, laaintain that there is a positive
association between risk and returns, this paper discusses some evidence
which throws this association into question, \fhile undertaking some
previous empirical work it appeared that not only is risk not associated
with higher profits/returns, it is actually ( ex post ) associated vjith
lower profits/returns. Here then is the apparent paradox which will be
further developed in this paper. The earlier work referred to centered
on several comparative studies of companies within an industry (e.g. food-
processing and computer peripherals) .  Taking one industry at a
time has the great advantage of "controlling for" the many between
industry differences of which growth, cyclicality, capital intensity,
regulation, and concentration/market structure are some of the more
Risk is the concept which captures the uncertainty, or more partic-
ularly the probability distribution, associated vjith the outcome of
resource commitments. Aggregating the results from these resource
commitments will produce variance in returns both cross-sectionally and
longitudinally. While the risk may be regarded before the resource
commitment (i.e. ex ante ) , the effects and the aggregation of numerous
commitments can only be observed over time (i.e. ex post ) . Therefore
(variance) of profit is used here as a measure of risk. Research and
professional practice accept this measure of risk.
a) Solomon and Pringle state, "Firm risk.. .is defined as the
standard deviation of the after-tax operating return of a
typical (average-risk) project. "
b) Hurdle explains, "Recent, numerous studies have tested the
relationship between market structure and rate of return...
several of these authors have included a risk variable or
a financial structure variable or both in a linear regression
model. They have commonly representee the degree of risk
by variability of profits over time."! 16]
c) Armour and Teece define "RISKit= the -/ariability
(variance) of the dependent variable (rate of return on
stockholders' equity, book value) associated with the
ith firm in the j-th period calculated on the basis of the
observations in the five previous years. "
d) Shepherd states "Yearly profit variance has become a
standard index of such risk, especially for empirical
Profits are represented here as after-tax profit divided by stock-
holders' equity, labeled return-on-equity (ROE). Since ROE each year
is used rather than some measure like earnings per share, it is less
necessary to posit some kind of trend line, to normalize the variance
calculation. Dividing yearly earnings by that year's equity offers a
reasonable surrogate for this. Not only does ROE tend to normalize for
trends, but it is^ the variabje of interest here. Return on equity is
not only the profit measure of primary interest to most managers and
strategic planners, it is one of the more common measures of profits used
in economic research, i.e.:
Fisher and Hall explain, "The term profit as used here is probably
equivalent to net business income, i.e. the difference between revenues
and costs. To adjust for differences in firm size, profit is usua] ly
expressed as a percentage of some base. . .Among the many possible measures,
rate of return on net worth appears the most appropriate for studies
of the risk-profit relationship. "
Armour and Teece state, "A performance measure that appears to be
capable of reflecting superior performance is the rate of return on
stockholders' equity (after-tax profits divided by stockholders' equity) .
(See their convincing argument - p. 109 footnote - for why market value
and return should not be used for their study.) 
Hall and Weiss argue, "Ve prefer the rate of return on equity to
that on total capital, partly because this is the profit rate reported
in Fortune, but also because it seems theoretically correct. It is
what managers acting in the owners' best interests would seek to
The Empirical Results
The essence of our findings is that it was determined in the
majority of industries studied that higher average profit companies
tended to have lower risk, i.e. variance, over time. The empirical
results from the first two industries studied (for strategic management
purposes) are shown in the first tables. The number of companies are
shown in each quadrant of the 2x2 contingency tables, based on the
company's average profit and the variability of profit over the five-
year period, 1972 to 1976. The split between "High" and "Low" in the
2x2 contingency tables is not arbitrary, but simply divides the
total data set in half for both rows and columns. That is, a rank
order of all companies for each characteristic - ROE and variance - was
constructed and then divided at the median. Each company was then high
or low on each characteristic, placing it in one of the four quadrants.
Such table construction will always appear symmetrical, and the null
hypothesis, i.e. no association, calls fcr equal numbers in each of
the four quadrants.
(1) Food Processing Industry Companies
/0\ T^^vi t ^» o T^-i f-«n t n f» /p.-^7*Jri^'*'^ j*o 1 Tr> r?^ t r»<- t^ • ^^#-*•rr^r^'^v^ ^ of
Nine additional industries were arbitrarily chosen from the Value
Line  survey to show a test of these results, for the same period,
1972 to 1976, and in the same form showed the same relationship.
Container and Packaging Industry
Et.;ild5x';^ Jjiv yjiry
Pa!5or and Forest Products IriCiiGtry
Metals & Mipinq (2)
Only the Metals & Mining Industry seemed to show a positive association
between average profits (over a five-year time period) and profit vari-
ability/risk. However, this is due to the fact that gold mining, of which
there were four companies, all had relatively high profits and high vari-
ability. IVhen these four were removed from the table and the table
recalibrated with the medians recomputed, (and in a sense treating Gold
Mining as a separate industry), the remaining companies did not show this
relationship. This effect of a different industry is an interesting one
and reappears shortly in this paper.
Tho lest two of tha nino bidastries chccen are the E;-.8ic Chsinical iuid hxtzQxi'Xc-d
Both of these lsd-antric3 alao cupport tho basic hyr»othsr.is, tho'jfjh of courss
the Chamical Industry barely so. Ralhsr thtn applying the usual statiotical testa
(e.g. clii-squars) to the qur.drants of each industry tabis, v/hich would yield rather weak
elgnalfl glvaa tha number of comp:aiies in each tablo, rxd tlie closeness of some of tho
results to tha null hypothesio, i.e. completely equal distrib-jtions across quadrants, It
makes nxo>:^ o^ise to treat tho tc3ta oiherwiGe. The paradox batog dsmonctrated horo
is tho negative corrQiatioa of risk and return v/ithln induBtries, and this la capturod by
the sura of low/high and high/low quadrants (5 + 5 = 10 in the Steel
Industry) being larger than the sum of high/high and low/low quadrants
(2 + 1 = 3 in the Steel Industry). If there were no correlation, random-
ness would result in an expectation that half of these tests would be
favorable/ l:rue and ha].f would be unfavorable/false. The binomial is
the statistical test to use in this regard, (i.e. null: p = 0.50) but
one hardly needs it because the eleven industries support the hypothesis
10 to 1 here (or 10 and I/2 to I/2 depending on one's taste in methods).
A much larger and complete test was made of these exploratory in-
dustry studies in order to confirm or refute these findings. All in-
dustries from the set of 85 covered by Value Line  and including
1,572 companies have additionally been analyzed, and these using a nine
year period (1968-1976) for ROE mean and variance rather than five years.
Of this total set of 85, 56 support the hypothesis of a negative risk/
return correlation, 21 refute it, and 8 are ties. See Appendix I for this
list of industries and results. The additional industry tests offer the
added advantage of the longer nine year time period for ROE mean and
variance calculation eliminating any brief and confounding transient
phenomena. In sum, both five year periods and nine year periods support
the negative correlation hypothesis/paradox beyond the statistical pa]e.
The statistical usage of contingency tables and more particularly
nonparametric tests are chosen here as the basic methodology for their
clarity and simplicity and in order to cope with, rather than eliminate,
some of the companies with strange data points, i.e. very large measures
for negative ROE where equity, E, is almost zero and/or especially
sizable variance, which would tend to dominate and distort traditional
("least squares") regression/correlation/parametric tests. Similar
methodology is used by others in this field for the same reasons. 
Soraewhat more powerful nonparametrir procedures of rank orders and
Spearman tests have been used in a study which replicated and substantiated
our findings. Treacy in a currently unpublished paper both supports
and extends the paradox findings reported here. His study has the
advantage for a second test that it is from a different source (Standard
and Poor Compustat Tapes) , with a somewhat different configuration of
industries (54 industries vv?ith 1,458 companies), for a slightly different
ten year period (1966-1975), using a different and perhaps more powerful
methodology (rank orders comparison a la Spearman) , and including and
controlling for a third variable which would be in the minds of many
analysts (size of firm, average assets).
Treacy reports, (p. 17), "The effect observed by Bowman
that level and variance of return on equity are negatively
associated, is evident from the data. Forty-three of the 54
industries had a correlation coefficient that was negative
(Spcarr.an rank order correlaLiuu coeiricleni.) . . .a binomial
test... at the .00001 level of significance." Twenty of the
industry correlations were significant at the 10% level, and
eighteen of the twenty had negative coefficients. Contrclling
for size only drops the number of negative partial correlations from
43 of 54 to 39 of 54. Treacy (abstract) writes, "Results confirm
that there is a strong negative correlation between firm size and
variance of return on equity and a moderate correlation between
firm size and average level return on equity, but the evidence
does not support the hypothesis that firm size is the major
intervening (i.e. "explaining") variable between level and
variance of return on stockholders' equity."
The next intermediate step in this analysis was to mix the approxi-
mately three hundred companies from the nine demonstration/test industries
arbitrarily chosen. This undifferentiated mixture showed the following
Comoanies from Nine InduEtries
This large set of mixed companies showed no real relationship
between corporate risk and return, (correlation either positive or negative
between ROE average and variance) . This result is supported by a number
of studies of an undifferentiated group of companies across industries.
Shepherd reports (p. 275), "Many models and groups of firms were tested,
using data from 245 large U.S. firms. Yet profit rates and variation
were not related in any of them.... the "risk premiums" estimated in some
earlier studies have probably instead reflected market power. "
However, the negative correlation demonstrated within industries
while apparently significant is modest, and this mixed group of companies
shows no real correlation mixing within and between industries. Therefore
the betv7een industries correlation for risk and return must not be as
strongly positive as both received theory and previous empirical work
Taking all 85 of the Value Line industries at their company averages
(ROE and variance), i.e. the industries themselves, shows a surprising
non-correlation (or even nonsignificant negative correlation) between
risk and return.
This is contrary to the positive correlation findings Conrad and
Plotkin reported in the Harvard Business Review cited earlier here. And the
reason for this apparent discrepancy can now be made clearer. Conrad
and Plotkin argue: 
"A corporate manager bases his risk evaluation and investment
decisions to a large degree on the experience of his industry.
A way of picturing and quantifying an important part of that
experience is by considering the scatter of returns on invest-
ment earned by the companies in the industry. We contend that
industries characterized by highly dispersed profit distributions
are judged by management and investors to be riskier than those
characterized by compact distributions of profit rates.
We developed our measure of risk for each of 59 major
S.I.C. fields of business (primarily industrial and nonf inancial)
by calculating the dispersion (or variance, in mathematical
terms) of return on capital of individual companies around the
average return fcr that industry... The average of the yearly
dispersions then became the 'typical risk quantity' for that
industry for that period of time."
In summary, their calculation of variance (for the measure of risk) has
been cross-sectional. They compute the variance between companies within
an industry for one year at a time, and then average the sixteen yearly
figures. A rather similar group of companies could each show enormous
swings between years, and the industry by this calculation could show
a very small variance - and by substitution therefore risk.
The calculation for variance in this paradox paper on the other
hand has been longitudinal, A variance for each company ROE has been
computed between years, and then these company figures have been averaged
within each industry. Therefore, for instance, a very dissimilar group
of companies which each showed mild swings between years would represent
an Industry with small variance.  This longitudinal treatment of
variance is both more consistent wi th other analyses of risk found in the
literature, and more pertinent to the questions addressed here - starting
with the differences in variance between companies within industries.
A number of other studies touch on the paradox explored here, but
usually not using methodologies to probe the relationship between firms
industry by industry. Shepherd, and Samuels and Smyth in a study
of 186 British companies, show no correlation, though their studies are
not within industries. Armour and Teece in their petroleum industry
organization structure study. Hall and Weis in one version of their
firm size study, Hurdle in part of a leverage study, and Neumann,
Bobel, and Haid in part of a West German industry study show results,
some not statistically significant, which support the apparent paradox
of a negative association between risk and return; yet virtually all ignore,
reject, or transform the results because they are a minor part of their
studies - and unexpected. Cootner and Holland and Hall and Fisher
show results which refute our findings,  though there are numerous
differences in their questions, data, and methods from ours.  and 
To summarize the empirical findings here, neither the companies
within industries nor the industries themselves show a positive correlation
between risk and return as the initial quotations supplied in this paper
imply. Companies within industries show a negative correlation (significant,
but by-and-large usually modest) , and the industries show no significant
correlation (or negative and non-significant) .
Explanations, Speculations, and Discussion
The risk/return paradox described here deals essentially with the
behavior of the firm and its managers, while it is perhaps only obliquely
linked to capital and securities markets, (which are used here for both
contrast and analogy) .  It seems clear that there is an apparent
contradiction (the paradox) between the posited risk aversion of a firm's
managers with the implied necessary coupling between risk and return on
the one hand, and the empirical results within industries of the negative
correlation of risk with return on the other hand.
There would be much less agreement that the paradox described here
is a puzzle in the context of securities markets and the "Capital Asset
Pricing Model," (CAPM) . Here the free, open, sizable and relatively
"efficient" market place for securities can and does (at least seems to)
compensate for anomalies in the behavior of firms. It is a well documented
phenomenon that securities with a high variance in their market returns
(at least the variance which is correlated with total market variance) will
yield (require) higher returns to investors. 
To put it differently, the anomaly or paradox at the level of the
firm described here car be eliminated in the shareholder markets by the
pricing of securities. The firm with lower risks and higher returns
(to the firm) can have its securities priced relatively higher by the
securities market place, thus lov;ering its return to the securities buyer,
which then eliminates the paradox at the level of the securities
owner/buyer. In other words, market returns to the investor (gains plus
dividends) will probably not capture the phenomena explored here. Thc;
"perfect" market will both compensate for and mask the effects demonstrated
in this paper. It may be argued that equilibrium conditions will tend
to eliminate this discrepancy, but clearly equilibrium within the capital
market place cones much more rapidly than equilibrii.im between the capital
market place and the firm, if it comes at all.
Another equilibrium concept associated wd th the capital asset
pricing model, that of theoretical indifference to the amount of the firm's
leverage, should be dealt with here.  An increase in leverage, i.e.
debt to equity ratio of the firm, would presumably both increase the
profits (ROE) and also perhaps increase the variance of the profits over
time. This would tend to counteract the empirical findings here. The
paradox findings presented are all the stronger then for this latent
confounding effect of leverage. Hurdles' work on leverage and risk
obliquely touches on this possibility.
The explanation for the negative correlation between risk and return
may be that, once within an industry, good management will bring about
higher returns (for that industry) and lower variance (again for that
industry) . Another explanation which seems less plausible is that
managers aren't risk averse and in fact are risk favorers. They'll
take higher risks even with lower returns in contrast to the opposite,
because they prefer them - though this is rather unlikely and contrary
to most thought on the subject. However, some economic thought on the
penchant for lotteries going all the way back to Adam Smith even casts
doubt on this. And Professor Knight adds, "To this bias must be added
an inveterate belief on the part of the typical individual in his own
'luck,' especially strong when the basis of the uncertainty is the
quality of his own judgment ." 
As with Sutton's push/pull theory of diversification, where
empirical economic analysis seems to support the pnsh theory, (companies
leave unfavorable positions for otlier positions) , there may be some
justification for a push/pull theory of risk/return, a version of
behavioral theory's "problemistic search. "[4A] It may be that longitu-
dinal analysis would show that the less profitable firms (and in some
cases the unprofitable firms) are pushed into making the more risky
resource commitments. The more profitable firms "need" not take these
risks, i.e. they are not pulled .
That "good management" will be associated with both higher profits
and lower risk (longitudinal variance) may seem questionable to some.
This idea is in part derived from the large and growing literature on
"income smoothing" found in accounting iournals, [A5] which interestinslv
enough does not seem to note the paradox explored here. Income smoothing
is simply the apparent reduction of the differences between periods in
reported income (profit) . A distinction is frequently made in the
literature beti^een real and artificial smoothing - and both would tend
to support the concept (and empirical finding) of a negative correlation
within an industry between return and risk ( ex post ) .
"Real" income smoothing is due to economic/physical/organizational
(but not accounting) decisions made. These could include timing of
particular investments like machinery and equipment, new venture
expenditures, advertising, and a host of other activities. The smoothing
literature makes the case that 1) this activity is in fact economic and,
well done, can raise long run average profits, and that 2) successful
managers have the flexibility to engage in such smoothing. Strategic
management at all three levels discussed in the literature, i.e. a)
choice of domain, b) interaction with tht: domain, and c) internal
adjustment, or a) Corporate, b) Business, and c) Functional, may
directly address the economics and profit advantages associated with
real income smoothing. Probably more work, both theoretical and empirical,
has been done at the Functional level of production to demonstrate the
advantages of smoothing than in virtually any other field. 
At the corporate strategic management level, Ansoff et al [A7]
demonstrated in early work that planners (as distinct from their absence)
and planning associated with acquisition and merger activities lead to
(or were associated with) more profitable company experience. Integration
and lack of surprise (risk) should both increase/maintain the profit and
reduce the profit variance.
"Artificial" income smoothing is due entirely to accounting adjust-
ments of various kinds. This could be due to one-time type decisions
like changes in accounting treatment of inventories. However, it
can also be due to continuing and "flexible" treatment of reserves,
i.e. bad debt, obsolete inventory, business closing, etc. Both the
New York Times , and the Wall Street Journal  have reported
highly publicized investigations into unusual accounting treatments
of income between periods by such companies as Gulf and Western
Industries and H. J. Heinz Company. ^sTiile the two sets of alledged
company behavior dramatize artificial income smoothing, much milder
examples are possible which are less subject to raised eyebrows by the
accounting and regulatory communities. Something above a minimum level
of profitability would normally be required to indulge in this "artificial"
income smoothing,  (especially ex ante ) and hence the positive
correlation between profits and profit stability or, in the terms of this
paper, the negative correlation between profits and risk.
Wliile perhaps too big an umbrella, strategy, addressed to the
management of risk rather than income smoothing, may also help explain
the negative correlation between profit and risk within an industry.
Market dominance within an industry deriving from an earlier strategy,
which is not the same thing as either total size or traditional
monopoly/profit, may permit both higher profits and lower profit variance.
The big competitor drives the industry - IBM, not Honeywell (or RCA) •
GM, not Chrysler (or Packard) . The implication here is that market
dominance may simultaneously increase profits and decrease profit
variance (risk). Product reputation, customer base, employee loyalty,
supplier service, banker accomodation, and even government relationships
could all enhance the performance of the market-dominant firms. 
Many actions of the firm linking higher profits with lower risks
may be closer to strategic management rather than "income smoothing"
per se . By focusing on "value added" in the food processing industry, 
"good management" both increased the more successful companies' profits,
and provided the niche which protected against society's, markets', and
nature's vagaries. By the strategy of strong "customer orientation"
in the minicomputer/peripheral industry ,  "good management" both in-
creased profits and protected against costly variation in new product
acceptance and competitive effects. In both industries, the more profit-
able companies had more activity in international markets, which as a
form of diversification may have reduced the variance exposure, as well
as offered a wider variety of investment opportunities.
Good management, and an effective Board of Directors, can address
and cope with risk and variation both inside and outside of the corporation.
While the effect inside the corporation may come from activities and
choices, the effects outside the corporation may come from negotiations and
cooptationf;, to produce the "negotiated environment" discussed by Cyert
and March. [5A]
Still another possible explanation for the negative correlation
within an industry - the "paradox" - between risk and return (i.e.
variance and average return on investment) is an asymptotic concept.
If there is some maximum ROE feasible in an industry, then perhaps most
variance is really variance down from this upper bound (asymptote) . The
larger variance is then automatically associated with a lower mean.
Similarly, though rot quite the same thing, certainly the occasional
loss (negative ROE) would for most companies simultaneously both increase
the variance and decrease the mean - something approaching a mathematical
Finally, it is possible that the "real" investment decisions both
ex ante and ex post are as theory suggests, i.e. high profit means high
variance and vice versa. But this may be a "long run equilibrium"
phenomenon, and there may be sufficient strategic management, both planning
and control, income smoothing activities, problemistic search, capital
market decoupling, "aggregation effects," and measurement anomalies, some
of which are described above, that they tend to overwhelm the long run
investment decision effects. This overwhelming is not simply "statistical
noise", however, since the negative correlation - the paradox - still
In order tc explore the apparent paradox described in this paper,
a number of further investigations can be made:
a) A more detailed look at one or several industries, and company
behavior within the industry, can be undertaken. \-Jhat explains
or is associated with the placement of companies in one of the
four quadrants in the risk/return table? Using methodology
more akin to the intensive annual report investigations in
the food industry and the minicomputer/peripheral industry,
it may be possible to throw more light on the "paradox."
The choice of operational surrogate variables derived from the
discussion in the previous section of this paper, combined
with the appropriate metrics for empirical investigation,
should help in understanding these phenomena. Implications
or policy recommendations for managers might then follow. For
Instance, if one could believe that there were a causal link
between the characteristics of lower risk, or at least lower
variance, and higher profit within an industry, which character-
istic should strategic management first seek instrumentally ?
Would such a search be better directed at operating decisions,
or administrative decisions, or institutional decisions?
b) An investigation of the approximately one-quarter of the industries
(less if "coefficient of variation" is usefl) with an apparent
positive company correlation between risk and return might prove
useful. What distinguishing characteristics mark these industries?
Relatively few of these industries are in manufacturing. Many
of them seem to be in sectors such as utilities and service
industries, (i.e. Fast Food, Insurance, Natural Gas, Electric
Utilities, Railroads, Retail and Specialty Stores, Medical
and Health Services) . There is some evidence that regulated
industries are more prone to show this company positive
correlation between risk and return. Perhaps utilities
which must return to the market place frequently for equity
capital show this tendency. Characteristics like phase of
industry life cycle or levels of industry concentration
may also help explain or identify this minority category.
c) A more traditional (i.e. since the 1960 's) extension of the
empirical findings described here would be still another test
of securities markets and the "efficient market hypothesis."
Given that a negative correlation between risk and return (to
the firm) within industries is established here, in what way,
if any, does this idea/concept carry over into the capital
markets? It is unlikely - though not impossible - that a
"market imperfection" would be discovered. However, it may be
useful to find the appropriate place within the growing capital
asset pricing model (CAPM) literature for the empirical findings
d) The important linkage between the descriptive theory of security
markets and the normative theory of corporate capital budgeting
may still be rather poorly understood, and the not insignificant
proportion of corporate capital needs served by retained earnings
tends to obscure this linkage. The empirical findings of this
paradox paper may threw into some question the simple connection
that economists, financial analysts, and strategic planners may
currently draw between capital markets and capital budgets.
Both the theoretical questions and the measurement problems in
the relationships between ex ante "expectations" and ^x post
"realizations" may add tc the difficulty c;f productively exploring
these connections/linkages. Further work on theory, methodology,
and practice associated with this linkage should prove useful.
All of these theoretical and empirical questions can be explored by
additional analysis. For both the manager and the scholar, further questions
of validity, generality, and operationality must be answered by future
Value Line 1968 - 1976 Company Average ROE and vjriance,
85 Industries Ranked bv Negative Assoeiaticn Ratio"
** A B C
Auto & Iruck (7) 6.0
Distillins (7) 6.0
Finance (14) 6.0
Advertising (7) 6.0
Cement (12) 5.0
Machine Tool (17) 4.7
Aerospace Divers. (27) 4.4
Broadcastin'?, (10) 4.0
Real Estate (10) 4.0
Air Trans. (18) 3.5
Grocery Store (26) 3.3
Integ.' Steel (13) 3.3
Maritime (8) 3.0
Brewing (8) 3.0
Reit (3) 3.0
Real Estate (11) 2.7
Multifom (33) 2.7
Mobile iiome (11) 2.7
Personal Serv. (11) 2.7
Const. & ^'ining
Mach. (14) 2.5
Special Chem (17) 2.4
Trucking & Bus (23) 2.3
Industrial Srv. (18) 2.0
Meat Pack. (6) 2,0
Tobacco (") 2.0
Railroad (^.ast) (9) 2.0
Agric. Louit). (6) 2.0
Toys & Cchool
Supplies (9) 2.0
Computer (42) 2.0
Specialty Steel (6)
Integ. Petroleum (47)
Food Processing (50)
Drug Store (16)
Paper/Forest Prod. (25)
Securities Broker (10)
Travel Services (10)
Coal & Uranium (10)
Drug (Ethical) (14)
Proprietary Drug (7)
Home Appliance (14)
Midwest Bank (11)
Savings & Loan (15)
Basic Chem. (27)
Precision Instr (32)
C A B
2.0 Tire & Rubber (12)
2.0 Auto Parts (Rep.) (16)
1.9 Lead, Zinc,
1.9 Minor Metals (14)
Auto Parts (Orig) (12)
1.7 Soft Drink (8)
1.7 Sugar (8)
1.7 Recreation (24)
1.7 Retail Stores (38)
1.5 Elect. Equip. (35)
1.5 West. Utility (13)
1.5 Fast Food (19)
1.5 Insurance/P C (10)
1.4 Natural Gas (55)
1.3 Oilfield SRV/
1.3 Equip. (20)
1.3 Home Products (10)
1,3 Health/Hosp. (15)
1.3 Midwest Elec. Util. (51)
1.3 West. Railroad (11)
1.2 U. S. Shoe (11)
Oil Producing (11)
1.2 Gen. Metals/
1.2 Medical Services (6)
1.1 General Steel (13)
1.1 Diversified Ins. (20)
1.1 Ind. Gas/Fertilizer (7)
1.07 Retail (Spec.) Stores (16)
1.04 Life Insurance (17)
1.0 Railroad Equip. (6)
* Two by Two Contingency table; High/Low plus Low/High divided by High/High
plus Low/Low; (Less than 1.0 is Positive Association)
** (A) Industry Name, (B) Number of Companies in Industry, (C) Negative Association
 Peter Lorange and Richard F. Vancil, St rategic Planning Systems ,
Prentice Hall, 1977
 E. H. Bounnan, "Epis temology , Corporate Strategy and Academe",
Sloan Management Review , Winter 1974, pp. 35 - 50; E. H. Bo\^^nan
and M. Haire, "A Strategic Posture Toward Corporate Social Responsibility,"
California Management Review , Winter 1975, pp. -49 - 58; E. H. Bo^'jman,
"Strategy and the VJeather," Sloan Management Review , Winter 1976, pp. 49 - 62,
E. H. Bo\<7man, "A Risk/Return Paradox," College of Administrative Science,
Ohio State University, Working Paper, 1977, E. H. Bowman, "Strategy , Annual
Reports, and Alchemy," California Management Review , Spring 1978, pp. 54 - 71.
Paul Samuelson, Economics , McGraw-Hill 1951, pp. 639 - 647
Frank H. Knight, Risk, Uncertainty and Profit , Harper Torch Books, 1965
(from 1921), p. 365
Knight, op. cit . , page Ixii, Preface for the Reprint of 1957.
Samuelson, 1961, op. cit. , p. 666.
"The Slow-Investment Economy", Business Week , October 17, 1977, p. 62
Gordon R. Conrad and Irving H. Plotkin, "Risk/Return: U. S. Industry
Pattern," Harvard Business RpyTPy ^ Marrh - ApT-ii 1968^ n. 90.
Ezra Solomon and John J. Pringle, An Introduction to Financial Management,
Goodyear Publishing Co., Inc., 1977, p. 367 .
Richard Caves, American Industry: Structure, Conduct, Performance,
4th Edition, 1977, p. 4 and p. 69.
Henry 0. Armour and David J. Teece, "Organization structure and economic
performance: a test of the multidivisional hypothesis," The Bell Journal
of Economics , Spring 1978, p. 106-122.
C. Roland Christensen, Kenneth R. Andrews and Joseph L. Bower, Business
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Boumian, (1976), (1978), op. cit.
William G. Shepherd, The Economics of Industrial Organization , Prentice-
Hall Inc., 1979; and Caves, op. cit .
Solomon and Pringle, op. cit . , p. 367.
Gloria J. Hurdle, "Leverage, Risk, Market Structure and Profitability",
Review of Economics and Statistics , November 1974, pp. 478 - 485.
Armour and Teece, op. cit. , p. 110.
References - page 2
 Shepherd, op. cit. , p. 275
 J. N. Fisher and G. R. Hall, "Risk and Corporate Rates of Return",
Quarterly Journal of Econonilcs , February 1969, pj . 79-92. (p. 8A)
 Armour and Teece, op. cit . , p. 109.
 Marshall Hall and Leonard Weiss, "Firm Size ai-;.d Profitability", Review of
Economics and Statistics , August 1967, pp. 319 - 331. (p. 320)
 The Value Line Investment Survey , Arnold Bernhard & Co. (October 14, 1977).
 An additional three or four industries which do not include ROE or are
not "industries" have been excluded, such as Japanese companies and Dual
 Level of significance for the binomial test (p = 0.50) is 0.01 for the
5 year tests, and beyond 0.001 for the 85 industries nine year tests.
Grouping the companies by quadrants from the nine industries, (60, 88,
60, 87), and 'using the chi-square test, yields a level of statistical
significance of 0.018. If the normalized relative variance of ROE,
labelled "coefficient of variation" and computed by dividing each
variance by its mean, had been correlated with the mean ROE, this
automatically accentuates, by additional empirical checking, the
negative correlation which has been demonstrated here. Using solely
5 year tests rather than 9 year also accentuates the negative correlation -
something also tested by additional empirical checking.
J. M. Samuels and D. J. Smyth, "Profits, Variability of Profits and Firm
Size," Economica , May 1968, p. 127 - 139.
Michael Treacy, "Profitability Patterns and Firm Size", (Unpublished, ■
MIT Sloan School), January 1980, pp. 1 - 44.
Sidney S. Alexander, "The Effect of Size of Manufacturing Corporations
on the Distribution of the Rate of Return," Review of Economics and
Statistics , August 1949, pp. 229 - 235, and Shepherd, op. cit .
Shepherd, op. cit .
Conrad and Plotkin, op. cit .
The differences in results between the tv/o studies attributable to
differences between return on equity (ROE) and adjusted return on total
investment (RCI) would be negligible.
Samuels and Smyth, op. cit . and Shepherd, op. cit .
Armour and Teece, op. cit .
Hall and Weiss, op. cit .
Hurdle, op. cit .
References - pa;;e 3
 Manfred Naumann, Ingo Bobel, and Alfred Haid, "Profitability, Risk
and Market Structure in West German Industries," The Journal of
Industrial Economics , March 1979, pp. 227 - 242.
 Paul H. Cootner and Daniel M. Holland, "Rate of return and business
risk," Tlie Bell Journal of Economics an d Manag ement Science , Autumn
1970, pp. 211 - 226, and Fisher and Hall, op. cit.
 The difference in results may be accounted for in some combination
of a series of differences in either or both of the refuting studies:
(1) different time periods (earlier periods including the unusually
profitable decade ending in the mid '60s - Holland and Myers 
demonstrate the atypical profits for this period) , (2) different
industries and companies of more restricted domain (smaller number
of industries, i.e. 11 and 39, much smaller numbers of companies,
i.e. 88 and 315, and only larger companies, i.e. Fortune 500), (3)
aggregation of all company information in the same regression, using
dummy variables for industries, (4) different measures for profits
and computation of variance around a trend line, and (5) reliance
on regression and parametric statistical methods which in relatively
smaller samples may be swayed by outlier or unusual companies.
 Daniel M. Holland and Stewart C. Myers, "Trends in Corporate Profitability
and Capital Costs," pp. 103 - 188, in The Nation's Capital Needs: Three
Studies , edited by Robert Lindsay, Committee for Economic Development, 1979.
 Baruch Lev and Sergius Kunitzky, "On the Association Between Smoothing
Measures and the Risk of Common Stocks," The Accounting Review , April 1974,
pp. 259 - 270.
George W. Douglas, "Risk in the Equity Markets: An Empirical Appraisal
of Market Efficiency", Yale Economic Essays , Spring 1969, pp. 3 - 45.
Ray Ball and Philip Brown, "Portfolio Theory and Accounting," Journal of
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W. H. Beaver, P. Kettler, and M. Scholes, "The Association Between Market
Determined and Accounting Determined Risk Measures," The Accounting Review ,
October 1970, pp. 654 - 682.
 Lev and Kunitzky, op. cit. , Shepherd, op. cit . ; Beaver, Kettler, and Scholes,
op. cit .
 Franco Modigliani and Merton H. Miller, "The Cost of Capital, Corporation
Finance and the Theory of Investment," American Economic Review , June 1958
pp. 261 - 297.
 Hurdle, op. cit . , the main effect of substituting adjusted return on
total assets (ROA) for return on equity (ROE) would be to dampen the
effect of leverage's contrary confounding. (p. 483-4) "Debt enters
the profit equation with a positive sign... that is, a firm with a
high debt, other things equal, does have higher return on equity."
 Knight, op. cit ., p. 235.
References - page 4
 C. J. Suttor, "Management Behaviour and a Theory of Diversification,"
Scottish Journal of Political Economy , February 1973, pp. 27 - 41, and
Richard M. Cyert and James G. March, A Behavioral Theory of the Firm ,
Prentice-Hall, Inc. 1963.
 Paul E. Dascher and Robert E. Malcom, "A Note on Income Smoothing in the
Chemical Industry," Journal of Accounting Research , Autumn 1970.
Gary E. White, "Discretionary Accounting Decisions and Income Normaliza-
tion," Journal of Accounting Research , Autumn 1970.
Lev and Kunitzky, op. cit .
 Charles C. Holt, Franco Modigliani, John F. Muth , and Herbert A. Simon,
Planning Production, Inventories, and Work Force , Prentice-Hall, Inc. ,
1960, E. H. Bowman, "Consistency and Optimality in Managerial
Decision Making," Management Science , January 1963, and Herbert Moskowitz
and Jeffrey G. Miller, "Information and Decision Systems for Production
Planning," Management Science , November 1975 and bibliography.
 Igor Ansoff, Richard Brandenberg, F. E. Portner, and H. R. Radosevich,
Acquisition Behavior of U.S. Manufacturing Firms , 1946-65, Vanderbilt
University Press, 1971.
 New York Times , Sunday, July 24, 1977, p. 1.
 Wall Street Journal , November 8, 1979, p. 1.
 White, op. cit , for some contra evidence, and Cyert and March, op. cit . ,
 S. B. Thomadakis, "A Value-Based Test of Profitability and Market Structure,"
Review of Economics and Statistics , May 1977, pp. 179 - 185, S. Schoeffler,
R. 0. Buzzell and D. F. Heany, "Impact of Strategic Planning on Profit
Performance," Harvard Business Review , March - April 1974, pp. 137 - 145,
and Michael E. Porter, "The Structure within Industries and Companies
Performance," Review of Economics and Statistics , 1978, pp. 214 - 227.
 Bowman, op. cit . (1976)
 Bowman, op. cit . (1978)
 Cyert and March, op. cit ., and Jeffrey Pfeffer, "Size and Composition of
Corporate Boards of Directors: The Organization and Its Environment,"
Administrative Science Quarterly , June 1972, pp. 218 - 228,
3 TQfiD D04 M"13 3MT