Download On the Usefulness of Financial Ratios to Investors in Common Stock

On the Usefulness of Financial Ratios
to Investors in Common Stock:
A Comment
A. Rashad Abdel-khalik
N the April, 1973 issue of THE ACCOUNTING REVIEW, O'Connor reported
the results of an interesting study on
the association between financial ratios
averaged over a period of time and the rate
of return on common stocks averaged
over a subsequent period of equal length.^
A major part of the testing was based on
regressing average rate of return on the
averages of financial ratios. The analysis
was repeated after adjusting the average
rate of return only for the market and industry effects. The parameters generated
by the regression sample of 64 firms were
applied to a hold-out sample of 63 firms
in order to predict the rate of return of
the firms in the second sample. The association between the rankings of the predicted and of the actual rates of return
has revealed no significant relationship.
The author then concluded that his research "provides evidence that commonly
discussed financial ratios based on published data are not useful to investors interested in ranking common stocks by future
rate of return" (p. 341; italics in the original).
This note is aimed at the readers who
might consider this conclusion as a definitive evidence. In this comment, issues will
be raised concerning (1) the propriety of
the testing procedure used, and (2) the
I
difiiculties associated with the specification and the measurement of relevant
attributes.
DIFFICULTIES WITH THE TESTING
PROCEDURES
Since the parameters of the regression
of the primary sample have been used to
predict the rate of return of the hold-out
sample, the reliability of the prediction
becomes a direct function of the reliability
of the parameters and the regression
equation itself. It is my belief that the
regression equation and the parameters
estimated were not valid for predictive
purposes for three primary reasons: (1)
the choice of the explanatory ratios was
peculiar, (2) the issue of the ratios' multicoUinearity, and (3) the use of unadjusted
R^ as a measure of the explanatory power.
The author designated the rule adopted
The author would like to thank Carl L. Nelson,
Dennis Frolin, and V. Jaikumar for commenting on an
earlier draft.
1 Melvin C. O'Connor, "On the Usefulness of Financial Ratios to Investors in Common Stock," THE ACCOUNTING REVIEW (April 1973). pp. 339-52. Future
reference to this study will be made by specifying the
page number in the text.
A. Rashad Abdel-khalik is Assistant Professor, Graduate School of Business, Columbia University.
547
548
for retaining some financial ratios as explanatory variables in the following hianner:
Next, a step-wise addition linear multiple regression of the rate of return on the explanatory
variables was conducted from the firms in the
analysis subsample until one of the lO-ratios
entered the regression equation with a coefficient
that was not significantly different from zero at
the 0.05 level, (p. 347).
That is, the retention of the ratios as explanatory variables was based on the significance of the /-ratios of the estimated
parameters. This rule, however, is not in
conformity with the procedures recommended in econometrics. Two procedures
appear to be acceptable, each under different conditions. First, Haitovsky has
provided a nice proof showing that, if the
absolute value of the /-ratio of a coefficient
in the regression equation is greater than
one, then dropping that variable might reduce the explanatory power of the remaining variables.^ Second, in a subsequent article, P. Rao has shown that this rule is
valid only when one variable is being discarded, but does not apply in successive
selection of variables. In the latter case, a
suggested rule is to retain an explanatory
variable in the regression equation if its
exclusion will alter the coefficients of the
other variables, even if that variable has
a very small /-ratio.' Unfortunately,
O'Connor did not use either method, and
his rule of significance has most likely reduced the explanatory power of the ratios
by eliminating them. The author seemed
to have followed the rule to its end to the
extent of apologizing for the inclusion of a
financial ratio whose /-ratio is 1.76 (footnote to last table, p. 352).^
It should be mentioned that the extent
of the bias introduced by the choice rule
discussed above would depend to a great
extent on the multicolhnearity of the
financial ratios. Although the author has
acknowledged the presence of multicol-
The Accounting Review, July 1974
linearity, he discounted its significance
since the intercorrelation of the 10 ratios
was about 0.25 (p. 343). But under these
considerations, the estimated variance of
the coefficient of any collinear variable
will be overstated. This bias in estimate of
the variances would render some estimated
coefficients nonsignificant. Accordingly,
any decision rule based on the significance
of the estimated coefficients becomes invalid. Furthermore, the relatively small
size of the intercorrelation coefficient between the ten financial ratios is not a sufficient indication that the bias in the variance estimate will be small since this will
depend on the magnitude of the bivariate
correlations.
Thus, even if the choice rule was apphed properly, mutlicoUinearity would forbid the use of individual parameters as a
basis for the selection of indpendent variables.
The third difficulty with the testing
stems from the use of the unadjusted R^
for the measurement of the explanatory
power and for the evaluation of the statistical significance as measured by the Fratio. Since the greater the number of
explanatory variables, the smaller the
number of degrees of freedom, the unadjusted R^ will increase as independent
variables are added even if the added variables do not have any additional explanatory power. In this situation, the summary
statistic "R^, the adjusted R^, would be the
proper measure to use since it is not influenced by the number of explanatory
variables and is therefore comparable.*
_ ' Y. Haitovsky, "A Note on the Maximization of
R'," American Statistician (February 1969), p. 20.
' Potluri Rao and Roger LeRoy Miller, Applied
Econometrics, (Wadsworth Publishing Company, 1971),
pp. 36-8, and pp. 65-7.
•* The author writes, "Explanatory variable X, is
included in this equation because it noticably improves
R^, and its inclusion maintains the group of explanatory
variables established in the exponentially weightedmarket adjusted returri_S-year equation."
J
5 Adjusted R^ (or R') = 1—(variance of Residual/
Total Variance): see J. Johnston, Econometric Methods
(McGraw-Hill, 1972), p. 130.
Abdel-khalik: Financial Ratios: A Comment
O'Conner's analysis has, therefore, left
us in a quandary. On the one hand, the
use of the unadjusted R^ as a measure of
the explaned variation has probably improved the explanation as five variables
were used instead of a smaller number.
On the other hand, using the significance
of the ^ratio as the rule for the retention
of some explanatory variables and the
deletion of others in conjunction with the
use of unadjusted R^ has probably resulted
in deleting ratios that would have added
more explanation and including ratios that
have added no explanation. The extent
of the effect of each type of bias on the
results would be very difficult to assess indeed.
Before leaving this point some apparent
typographical errors must be corrected.
Usually, the F-ratio is computed from
i?2 as follows:
F={Ryk-l)/[(l-R')/
(n—k)], where k is the number of estimated parameters and n is the number of
observations.' Accordingly the F-ratios for
the four tables in Appendix I, pp. 351-352.
should have been as follows:
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ation does not necessarily mean any predictive power. Do decision-makers use the
ratios in the manner described in this research? Without this link, the strength of
explanatory power of a regression equation is of a questionable value in evaluating
usefulness or in predicting behavior.
DIFFICULTIES WITH THE SPECIFICATION
OF RELEVANT ATTRIBUTES
In adjusting for industry and market
effects, the method followed by Fama,
et al. was adopted. There are two issues
involved in this adoption: First, the
method was initially used to measure the
effect of new information, such as splits
and dividends, on the returns to common
stocks. Since there is nothing unique about
publishing the financial ratios data base,
the information displayed by the trends
and the changes in the ratios should have
been considered the relevant attribute in
applying the diagonal model. In one of the
methods used in computing the average
ratio, O'Connor applied an exponentially
weighted average method which "involves
a nonarbitrary weighting procedure that
Table #
1
2 . 3
4
attaches greater weight to more recent
Reported F-ratio 25.615 24.395 5.1144 5.3166
annual ratio values" (p. 344). Although
The correct F-ratio 5.615 5.048 5.081 5.046
there was no reason as to why this weightWith degrees of freedom 5 and 59, Fing procedure is nonarbitrary, this was
ratio is statistically significant at alpha
later confused with trends. The author
= 0.05 if it is greater than 2.40, which
states "There was very little change in
render all of the above F-ratios statisticaleither the explanatory relationships or the
ly significant. O'Connor, however, does
R^'s when exponentially weighted average
not attach importance to this fact as he ratios were used in place of simple average
states:
ratios as the explanatory variables. This
indicated that over the 1950-1954 period
In fact, even though the F-value associated with
each explanatory relationship indicated that the
there were no significant trends in the repexplanatory variables have some ability to ex- resentative ratios", (p. 348; italics proplain the varia,bility in the explained variable, it
vided. The statement is incorrect since
appeared unlikely that there was enough extrends may be taking on a pattern differplanatory ability to justify any expectations that
ent from the weighting procedure. Since
the explanatory relationships would be useful as
predictive devices (p. 348).
trends and deviations were ignored, was
the diagonal model adaptation approThis is an apparent fall into a methodpriate?
ological trap that we all sufifer from: Without causal relationships, significant associ' Ibid., p. 143.
550
Furthermore, the adjustment for the
market and industry effects was done only
for the dependent variable, average rate
of return. Would the results have been
different had the explanatory variables,
the financial ratios, also been adjusted?
A second problem lies with the unclear
usage of two criteria: decision-effects and
the predictive-ability. Relying on Beaver,
Kenelly, and Voss' argument, the author
states that making a decision requires
making a prediction and if a piece of data
has a higher predictive power, then it
should be more useful to decision-makers.
The dependent variable, however, was not
the prediction of an event. Rather, it was
the prediction of the magnitude of the
average rate of return over a period of
time in the future. Thus, it was the within
variability of average rates of return that
was the subject of explanation and predic-
The Accounting Review, July 1974
tion. In turn, this variability, which is
infiuenced by the collective behavior in
the market, was used as a surrogate for
decision-effects. It is not clear then if the
usefulness of the financial ratios would be
ascertained (1) if they affect decisions or
(2) if they can predict the ranking of the
decision-effects.
CONCLUSION
A brief review of the study by O'Connor
shows that the strong conclusions made
regarding the lack of usefulness of financial
ratios may not have been warranted. The
research design and the testing procedure
are not quite appropriate for drawing a
definitive statement about the usefulness
of financial ratios. The study, however,
provides a good base for future efforts in
the area.