APPENDIX

THE MEASUREMENT OF RISK

Risk measurement is one of the most difficult and perplexing problems of modern mathematical economics and econometrics. The contributions of insurance actuarial science are but tangentially related to the problem of measuring socioeconomic risk as used in our study. Hofflander and Mason make some very sweeping condemnations of our risk measurement. These condemnations do not appear to be in keeping with any of the on-going research in finance and economics and seem more to be the reviewers' personal opinions. Further, the reviewers do not in any systematic or scientific way address the substantial body of econometric results we obtained during our study instead they ignore it.

In the following we will show why the comments made by Hofflander and Mason are without merit and purely ex cathedra. Even if all the objections Hofflander and Mason raised about our risk measure were true, our results and conclusions would not be changed. The reviewers admit this in their final statement:

"Finally, while not stated in the Arthur D. Little report,
it is clear that the managements of most insurance companies
believe the non-life insurance industry to be both risky and
unprofitable. From this apparently universal belief, one
may draw the conclusion that the insurance industry is not
earning a rate of return commensurate with the associated
risks; but, if so, this study has not demonstrated that
fact." (Hofflander and Mason, op. cit., p. 13)

In his analysis of Hofflander and Mason's review Professor Webb summarizes and evaluates the objections raised by the reviewers as follows:

"While the relationship between risk and rate of return
is generally accepted, the methods used to measure yield
and risk are open to some question.

"The A.D. L. study measures risk by the variance of rates
of return about their mean value. The use of this unit
of measure is based on the definition of risk as uncer-
tainty. The greater the variance of the rates of return
the greater will be the uncertainty as to the rate of
return which will actually be realized by a given firm.
"Hofflander and Mason question this measure of risk on
the basis that '. . most of the differences in insurer
operating results are due to differences in: (1) compo-
sition and performance of investment portfolios, (2) the

mix of business underwritten, (3) geographical
diversification of business, and (4) management
philosophies and goals.' That is, they believe that
variations in rate of return are due more to conscious
decisions of management than to chance variations.

"While the composition of the investment portfolio is
largely under the control of management, the performance
of that portfolio is not. Investment analysis is not an
exact science. Many errors in judgment are made in
portfolio selection. Also, the performance of a portfolio
after it has been selected is subject to many chance influ-
ences: the death or sickness of a president, rumors of
war (or peace), devaluation of a major foreign currency,
changes in stock market fads, and others too numerous to
mention. To attribute to management the power to control
the performance of their investment portfolios is to endow
them with omniscience and omnipotence which few (if any)
of them possess.

"The influence of geographical diversification upon the
results of the study is not likely to be large for two
reasons. First, the more severe fluctuations are spread
over the entire industry through the mechanism of
reinsurance. For example, the losses from a major hurricane
on the Gulf coast are not borne only by companies writing
direct business there, but are spread by reinsurance over
the insurance industry of the United States and most of the
free world. Second, the A.D.L. study covered a period of
eleven years.
The influence of regional losses, particu-
larly after the effects of reinsurance, should be quite
small over such a long period.

"Furthermore, the variance is used as a comparative measure,
to permit the comparison of the insurance industry with
other industries. The presence of some influences which
are under the control of management would not affect the
comparison unless it is assumed that such influences are
not present, or are present to a substantially lesser or
greater degree in the other industries."

(Webb, op. cit., pp. 213-214)

Professor Webb's final point bears emphasizing. While our measure of risk is far from ideal (as we note below), it is free of systematic bias among the various industries. For example, the inclusion of capital gains does not affect it. It is, therefore, a good comparative measure, and it was only as a comparative measure that we employed it.

We comment on the measurement of risk as follows:

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"Management bases its risk evaluation and investment decisions on its experience within its own industry. A way of picturing and quantifying an important part of that experience is by considering the scatter of returns earned by firms in that industry. Industries characterized by highly dispersed profit distributions will be considered by management and investors as riskier industries than those characterized by compact distributions of profit rates. Stated in this way, this concept of risk is believed to be amenable to fairly straightforward statistical measurement, employing well-established and well-understood mathematical relationships. The statistical and mathematical details appear in the A.D. Little Report. It relies on statistical techniques that flow naturally from these considerations of the way management perceives risk, as well as from the implications of the economist's theory of utility maximizing behavior.

"While this paper discusses primarily a cross-sectional (inter-spatial, inter-company) risk measure, the intertemporal aspects of risk were not ignored in the research. Measures for the year-to-year fluctuations in rates of return were derived for both the industry's values and the individual companies' values.

"Researchers who have concentrated on temporal measures of riskiness have generally found them unsatisfactory, both theoretically and empirically. The inability of these temporal measures to 'explain' rates of return is attributed to the fact that they confound predictable with nonpredictable changes. It is suggested that the inter-spatial risk measure better captures the allimportant nonpredictable element. This feeling is borne out in the multiple regression equations (reported in the Little Report) which show that neither 'industry temporal variance' nor 'average company temporal variance' (see definitions in the Little Report) possesses much independent explanatory power with respect to return, once the inter-spatial variance is considered. For these reasons, this paper concentrates on the simple, two-variable regression model using interspatial risk measures.

"It is obvious that this risk measure would not be valid if (1) the individual company returns did not vary in time, or (2) the company rankings did not vary in time.

"Studying the temporal variances of rates of return together with rank-order correlation coefficients,

however, allowed the conclusion that both individual
company returns and ranking do indeed vary over time.

"It should be emphasized that inter-spatial variance
is not an ideal measure of risk, for it, like any
other scalar, does but an imperfect job of describing
the various dimensions of the risk problem. In the
insurance business, differences in investment port-
folio composition, in mix of business, in geographical
areas may all affect this distribution.

"The same types of factors are at work in other in-
dustries, together with the universal factor of dif-
ferences in management. As shown in the Little Report,
a multiple regression approach which allows inter-
temporal, inter-spatial and various other risk quan-
tums to enter the explaining equation is preferred.
Nonetheless, the single best scalar measure of risk,
as derived from these econometric investigations, is
the inter-spatial measure being used here. A scalar
measure has the advantages of allowing the results
to be shown on a two-dimensional graph. It is inter-
esting to note that of all the proposed measures of
risk, this one tends to minimize the risk of being in
the insurance business. Relative to other industries,
insurance has higher temporal variance than cross-
sectional (inter-spatial) variance." (Plotkin, op.
cit., pp. 12-14)

In summary, the criticisms of our risk measure appear to be made by persons unschooled in modern risk theory and econometrics. Neither are they valid theoretically nor do they address the evidence supporting our procedures. Finally, by the reviewers' own statement they are nonessential to an evaluation of the issue.

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NATIONAL ASSOCIATION

OF

INSURANCE COMMISSIONERS

REPORT OF THE SPECIAL COMMITTEE ON
AUTOMOBILE INSURANCE PROBLEMS

1969 ANNUAL MEETING OF THE NAIC

June 16, 1969

Bellevue-Stratford Hotel

Philadelphia, Pennsylvania