More on the use of beta in regulatory proceedings

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M/B/175

Faculty Working Papers

MORE ON THE USE OF BETA IN REGULATORY PROCEEDINGS

Charles M. Linke, Professor, Department of

Finance
John E. Gilster, Jr., Assistant Professor,

Department of Finance

#691

College of Commerce and Business Administration

University of Illinois at Urbana-Champaign

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FACULTY WORKING PAPERS
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
July 27, 1980

MORE ON THE USE OF BETA IN REGULATORY PROCEEDINGS

Charles M. Linke, Professor, Department of

Finance
John E. Gilster, Jr., Assistant Professor,

Department of Finance

#691

Summary

This paper analyzes the process by which security prices adjust
to new information and shows that the adjustment process itself can
lead to temporary non-stationarity of security return distributions.
The paper illustrates the serious effect this can have on security
returns and argues that the price adjustment process can have a
similar effect on expost measurements of beta. Some implications for
utility rate regulation are discussed.

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MORE ON THE USE OF BETA IN REGULATORY PROCEEDINGS
1. Introduction

Modern portfolio theory is sometimes used to measure the risk per-
ceptions of equity investors and thereby to determine an appropriate
allowed rate of return for a utility. Recent articles in this Journal
(Breen and Lerner, 1972; Myers, 1972a, 1972b; and Pettway, 1978) have
questioned whether utility betas display sufficient stationarity for the
return estimation logic of modern portfolio theory to be operationally
useful in rate regulatory proceedings.

Blume (1971, 1975), Levy (1971), Porter and Ezzel (1974), Pettway
(1978), Francis (1980), and others have reported significant non-sta-
tionarity in measured beta. These authors have generally argued that
the non-stationarity of measured beta is due to changes in the under-
lying "true" beta. This hypothesized non-stationarity of "true" beta
has been shown to generate unusual measured betas at the individual
firm level. Brigham and Crum (1977) have used simulated data to demon-
strate that under extreme conditions a drop in the price of a security
resulting from an increase in true beta could actually cause measured
beta to decline temporarily. Instability in measured beta as well as
the possibility of such divergent movements between "true" and measured
beta have caused Pettway (1978), Breen and Lerner (1972), Brigham and
Crum (1977), Carleton (1978), and others to suggest the £ framework, may
not provide a feasible approach to rate regulation.

This paper will point out that the process by which securities ad-
just to dramatic, unanticipated, new information can produce misleading
estimates of systematic risk. Section 2 presents a theoretical

-2-

description of the phenomena. Section 3 suggests this phenomena as a
possible explanation for the beta non-stationarity in the utility industry
observed by Pettway and the beta non-stationarity surrounding stock splits
observed by Bar-Yosef and Brown. Concluding observations comprise the
final section.

2. Measured Beta and A Variability Phenomenon

Modern portfolio theory does not require the 0 measure of security
risk be stable over time. Indeed, a firm's perceived systematic risk
characteristics and hence its g can be expected to vary with strategic
and tactical management decisions made in response to changing product
and factor market conditions.

This paper will point out that the price adjustment process by which
securities adapt to new information can produce misleading beta measure-
ments .

The potentially bizarre nature of this adjustment phenomena is best
illustrated by its effect on security returns. Consider a firm that ex-
periences a shift in its systematic risk from .5 to .75. If the risk free
rate, P-, is 6.0% and the expected return on the market, E(PO, is 12%,
then investors pre shift required return is 9.0%, while the post-shift
required return is 10.5%. Assume for convenience this firm earns 9.0% on
its $100 book value per share, pays out all earnings, and the pre 6
shift market price of the stock equals book value. The equilibrium
holding period return, R , in the (3 pre-shift period would be

r . ?t " Pt-1 * Dt $100 - $100 + $9 _ n„

e Pfc , $100 " y'U7°

pre t-1

-3-

where P is price in time t, and D is dividend in time t. Assuming no
change in expected return on book value, the only way the $9 annual divi-
dends can provide the required 6 post shift return of 10.5% is for the
price to decline to $85.71. This will produce an observed annual rate of
return, R , during the adjustment period of

_ _ $85.71 - $100.00 + $9.00 _ . 0Q_
o " $100.00 " ~5'23A '

An increase in required return has produced a temporary decrease in re-
turn! Such price adjustments are also triggered by changes in earnings
expectations or the prevailing risk-return tradeoff.

The effect of the adjustment process on beta is more subtle. The
effect can be analyzed by expressing the total observable return, R , as
the sum of an equilibrium return, R , and an adjustment return, R_, or

R = R + R . (1)

o e a

Beta is equal to

6o = Cov(W/aM (2)

- [E(RoV -EO^EOgi/c* . (3)

Expressing R as a linear function of R yields

R = a_ + a,R + e (4)

a 0 1 e

where e is the error term. Substituting equation (4) into (3) reveals

E[(a0 * alRe + e + W ' E(a0 + alRe + e + VE(V
eo = 2

°M

-4-
(1 + a1)[E(ReRM) - ECR^ECBjj)]

o2
m

- (1 + a^Cgg) (5)

where

al " (pa,eaa)/ae •

Equation (5) shows that if the correlation between the component
equilibrium and adjustment returns is positive (negative), measured beta
will be greater (smaller) than true beta. However, the direction of the
discrepancy between equilibrium and measured beta does not necessarily
depend on the direction of the adjustment price change. If, for ex-
ample, p is always positive, both positive and negative price changes
a,e

will result an increase in measured beta.

3. A Practical Example

In a recent Bell Journal of Economics article Pettway [18] examined
whether the estimated beta of a 36 electricity utility portfolio was
3table enough to provide good estimates of subsequent observed 3 values
during various subperiods in the 1971-1976 period. In the middle of the
test period (April 18, 1974) Consolidated Edison announced it was omit-
ting its second quarter 1974 dividend.

Prior to the skipped dividend, 1971-1973, the utility portfolio
beta was relatively low (approximately .40). For some time after the
dividend omission, 1974-1975, the portfolio beta was considerably higher
(approximately .70), and then it settled back to its original level in
the last three quarters of 1976. Pettway argues that the skipped

-5-

dividend may have changed the systematic risk of electric utilities for
the period immediately following the dividend episode.

Pettway's explanation of the data may be correct. However, this
section will offer an interesting alternative interpretation of the same
data based upon the adjustment phenomenon described in equation (5).

Unfortunately, a direct test may be impossible. The correlation

parameter (p ) in the model cannot be directly observed. However, it
a,e

is possible to work backward and infer what level of correlation between

R and R would create the 6 effect observed by Pettway. The reasonable-
e a

ness of the computed magnitude of the correlation coefficient will pro-
vide an indirect test of the adjustment beta concept.

A review of Pettway's findings [18, p. 244] shows that the beta of
his 36 electric utility portfolio was about .41 before the April, 1974
dividend announcement. The portfolio beta averaged above .65 following
the dividend announcement before returning to the original 1971-1973
level of .41 during the final three quarters of 1976. By substituting
these values into equation (5) we can see that

3o= <* + «!><»«>

.65 - (1 + a.) (.41)

where

P a

al = &'o a = *59 • (6)

e

Parts of the Pettway study were replicated in order to estimate the

variance of returns before and after the April 1974 dividend omission.

-6-

Thls analysis showed the standard error of returns increased over 80%
after the Consolidated Edison dividend shock and settled back to its old
value when the portfolio beta itself resumed its 1971-1973 value in the
final three quarters of 1976. Therefore,

o = 1.80a , or (7)

o e

= (a2 + a2 + 2p a o )1/2. (8)

e a e,a e a

Substituting (7) into (8) yields

(1.80c )2 - a2 + a2 + 2p a a (9)

e e a e,a e a

o2 2p

2 24 = — - + — ^^
Z.Z4 2 0

a e

e

2
Equations (6) and (9) can be solved to obtain a p estimate of .178.

e,a

This suggests that only about 18% of the variance of the price adjustment
return series for the utility portfolio would have to be explained by the

equilibrium return series for the adjustment phenomenon of equation (5)

2
to account completely for Pettway's findings.

2
We feel a p of .18 is reasonable. It suggests that the relation-
e,a

ship between the two component return series is lower than the relation-
ship discovered by King [11] between market and individual security re-

2
turns (p = 30% to 60%), but higher than the relationship between industry

2
and security returns (p » io%) .

Pettway's analysis illustrates the effect on a portfolio beta from

stock price adjustments to bad news. Studies of the effects of stock

splits by Fama, Fisher, Jensen and Roll (1969) , and Bar-Yosef and Brown

(1977) provide examples of stock price adjustments to good news.

-7-

FFJR point out that prior to a stock split a security exhibits a
relatively short period of intense upward price adjustments. Bar-Yosef
and Brown show that the average value of beta increases substantially

during this upward price adjustment period. However, as in the Pettway

3
bad news analysis, beta later returns to its original value. This time

pattern displayed by measured beta in both the "good news" and "bad
news" studies is consistent with the adjustment return phenomenon de-
scribed in equation (5). Specifically, if the price adjustment is not
the result of a change in equilibrium beta, measured beta may increase
during the adjustment period but it will eventually return to its orig-
inal value.

Conclusions and Implications

Occasionally a security's price must adjust to reflect unanticipated
new information. This paper points out that the adjustment process can
create measured betas having little relation to the final, post-adjust-
ment, equilibrium value. A model of a "0 variability phenomenon" has
been offered as a contributing source of beta non-stationarity in gen-
eral, and a plausible explanation of Pettway' s and Bar-Yosef and Brown's
findings in particular.

Ignorance of the phenomenon can produce serious errors when uti-
lizing ex post 3 estimates in rate regulatory proceedings.

(1) After substantial, unanticipated new information it is natural
to expect a new value for systematic risk. A researcher who
is unaware of the adjustment phenomenon might assume the tem-
porary adjustment beta Is the new equilibrium beta. This is

-8-

particularly serious (as indicated by equations 1 through 5)
because the adjustment beta does not necessarily bear any re-
lation to the final equilibrium value.

(2) A researcher might blindly compute betas using historic data
which includes periods of adjustment mixed in with periods of
equilibrium. This approach has serious heteroscedasticity
problems and may lead to serious misestimation of beta. The
recommended practice [14,15] of estimating a specific utility's
beta to be the beta measure of a portfolio of comparable firms
does not necessarily avoid the heteroscedasticity problem
posed by adjustment periods. Both individual firms and entire
industries can experience significant adjustment periods as
the Pettway and Bar-Yosef and Brown studies reveal.

(3) The researcher might drop adjustment periods from his data
base and ignore them entirely. This is also wrong. Occasion-
al violent adjustments in security prices are an integral part
of security performance. Moreover, while the price adjustment
phenomenon persists, a security's adjustment beta has the same
effect on portfolio performance as betas resulting from any
other cause. Adjustment betas must therefore be rewarded by
appropriate (market equilibrium) levels of expected return —
just like any other betas.

The adjustment phenomenon is probably best handled by:
(a) Adjustment and equilibrium betas should be calculated
separately to avoid heteroscedasticity.

-9-

(b) The researcher should estimate the likelihood that an
adjustment beta will occur during the period for which
predictions are being made. He must also assess the
probable intensity and duration of such an adjustment.
To make these predictions, the researcher should look at
historic data over an extended period so as to get a long
term feeling for the incidence, duration and intensity
of these adjustment periods.

(c) If beta is to be used to determine appropriate rates of
return for utilities, a market equilibrium expected
returns should be calculated for equilibrium and adjust-
ment betas. These different expected returns should be
averaged geometrically with weightings determined by the
probability assessments described above. This will pro-
duce an average return which compensates investors for
adjustment and equilibrium systematic risk.

-10-

FOOTNOTES

Modern portfolio theory is more than the CAPM, and the usefulness
of beta as a measure of security risk does not depend on the strict va-
lidity of the CAPM (Myers, 1978).

Incomplete lists of the application of modern portfolio theory in
rate regulatory hearings can be found in Myers (1972b, 1978), Carleton
(1978), Pettway (1978), and Peseau and Zepp (1978).

2
Believers in efficient markets will have trouble accepting the

idea of a non-instantaneous adjustment to new information. Yet, seme

of the more recent studies of market efficiency allege that the market

is very slow to adjust to new information. For example, Latane and

Jones (1979) find that prices don't adjust to unanticipated earnings

for 5 to 6 months after the end of the quarter and 3 months after the

actual announcement.

If this is the adjustment period for something as simple as a

change in reported earnings, what period of uncertainty (and adjustment)

might result from something as ambiguous in future implication as

Consolidated Edison's skipped dividend?

3
Unfortunately neither FFJR or Bar-Yosef and Brown present the

change in variance accompanying the change in beta making it impossible

for us to calculate the implied p as in the prior example. FFJR do

present the mean absolute deviation and it seems to indicate the same

general level of increase in variability as the Pettway example.

4
Bar-Yosef and Brown and Pettway dealt with the heteroscedasticity

problem differently, but both calculated betas which proxy to some ex-
tent the constructs of adjustment and equilibrium betas. Pettway used
the occurrence of major events to segment his study period into sub-
periods, while Bar-Yosef and Erown used a moving beta measure.

It is interesting to note the very different implications of past
changes in beta due to the adjustment phenomenon and past changes in
beta due to changes in equilibrium beta. A researcher has no reason to
expect past equilibrium values of beta to reappear and only the most re-
cent equilibrium betas should be used in prediction. The researcher
has every reason to believe that adjustment periods will occur in the
future. Therefore, such data must be used in prediction of beta.

Ideally, a prediction of future beta should include a pre-adjust-
ment equilibrium beta and an adjustment beta and a post adjustment
equilibrium beta. Unfortunately, although a researcher can be confident
that the future will contain periods of adjustment, he will not normally
know what the stock is adjusting to.

The methodology described here implicitly assumes the pre and post
adjustment equilibrium betas are equal. If the price adjustment is not
in response to a change in equilibrium beta (as seems to be the case in

-11-

Pettway's and Bar-Yosef and Brown's findings), this assumption will be
correct. If equilibrium beta has changed the assumption will, hopefully,
be reasonably unbiased.

The justification for the use of geometric mean is best illus-
trated by a simple example. Assume the capital market equilibrium ex-
pected returns for adjustment and equilibrium betas are ER and ER re-
spectively and assume the security is predicted to spend one period in
adjustment and one period in equilibrium. The capital market equilib-
rium two period return will be

ER„ = (1 + ER ) (1 + ER ) - 1
2 a e

the mean single period return will be

ER = [(1 + ER )(1 + ER ) - 1]1/2 - 1
n a e

ER will then compensate investors for both adjustment and equilibrium
betas.

-12-

References

1. Bar-Yosef, Sasson, and Brown, L.D. "A Reexamination of Stock Splits
Using Moving Betas." Journal of Finance, Vol. 32, No. 4 (September
1977), pp. 1069-1080.

2. Blume, M. E. "On the Assessment of Risk." Journal of Finance, Vol.
26 (March 1971), pp. 1-10.

3. . "Betas and Their Regression Tendencies." Journal of

Finance, Vol. 30 (June 1975), pp. 785-795.

4. Breen, W. J., and Lerner, E. M. "On The Use of b in Regulatory
Proceedings." The Bell Journal of Economics and Management Science,
Vol. 3, No. 2 (Autumn 1972), pp. 612-621.

5. Brigham, E. F., and Crum, R. L. "On the Use of the CAPM in Public
Utility Rate Cases." Financial Management, Vol. VI, No. 2 (Summer
1977), pp. 7-15.

6. . "Reply to Comments on 'Use of the CAPM in Public

Utility Rate Cases'." Financial Management, Vol. VII, No. 3
(Autumn 1978), pp. 72-76.

7. Carleton, W. T. "A Highly Personal Comment On the Use of the CAPM
In Public Utility Rate Cases." Financial Management, Vol. VII,
No. 3 (Autumn 1978), pp. 57-59. "

8. Fama, E. F., Fisher, L., Jensen, M. C, and Roll, R. "The
Adjustment of Stock Prices To New Information." International
Economic Review, Vol. 10, No. 1 (February, 1969), pp. 1-21.

9. Francis, Jack Clark "Statistical Analysis of Risk Surrogates for
NYSE Stocks." Journal of Financial and Quantitative Analyses,
December 1979, pp. 981-997.

10. Gilster, J. E., and Linke, C. M. "More on the Estimation of Beta
for Public Utilities: Biases Resulting From Structural Shifts in
True Beta." Financial Management, Vol. VII, No. 3 (Autumn 1978),
pp. 60-65.

11. King, B. J. "Market and Industry Factors In Stock Price Behavior."
Journal of Business, January 1966, pp. 139-190.

12. Latane, H. A., and Jones, C. P. "Standardized Unexpected Earnings —
1971-1977." Journal of Finance, June 1979, pp. 717-724.

13. Levy, R. A. "Stationarity of Beta Coefficients." Financial
Analysts Journal, Vol. 27 (November-December 1971), pp. 55-62.

-13-

14. Myers, S. C. "The Application of Finance Theory to Public Utility
Rate Cases." The Bell Journal of Economics and Management Science,
Vol. 3, No. 1 (Spring 1972a), pp. 58-97.

15. . "On the Use of b in Regulatory Proceedings: A

Comment." The Bell Journal of Economics and Management Science,
Vol. 3, No. 2 (Autumn 1972b), pp. 622-627.

16. . "On the Use of Modern Portfolio Theory In Public

Utility Rate Cases: Comment." Financial Management, Vol. VII,
No. 3 (Autumn 1978), pp. 66-68. "

17. Peseau, D. E., and Zepp, T. M. "On the Use of the CAPM in Public
Utility Rate Cases: Comment." Financial Management, Vol. VII,
No. 3 (Autumn 1973), pp. 52-56.

18. Pettway, R. H. "On the Use of b in Regulatory Proceedings: An
Empirical Examination." The Bell Journal of Economics, Vol. 9,
No. 1 (Spring 1978), pp. 239-248.

19. Porter, R. B., and Ezzell, J. R. "A Note On the Predictive Ability
of Beta Coefficients." Journal of Business Research, Vol. 3
(October 1975), pp. 365-372.

20. Rosenburg, B., and Guy, J. "Prediction of Beta From Investment
Fundamentals: Part One." Financial Analysts Journal, May-June
1976, pp. 60-72.

21. . "Prediction of Beta From Investment Fundamentals:

Part Two." Financial Analysts Journal, July-August 1976, pp. 62-70.

22. Sharpe, W. F. "On the Use of the CAPM in Public Utility Rate Cases:
Comment." Financial Management, Vol. VII, No. 3 (Autumn 1978),

p. 71.

M/E/192

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