On the Use of Modern Portfolio Theory in Public Utility Rate Cases: CommentAuthor(s): Stewart C. MyersReviewed work(s):Source: Financial Management, Vol. 7, No. 3 (Autumn, 1978), pp. 66-68Published by: Wiley on behalf of the Financial Management Association InternationalStable URL: http://www.jstor.org/stable/3665014 .

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On the Use of Modern Portfolio Theory in Public Utility Rate Cases: Comment

Stewart C. Myers

Stewart C. Myers is Professor of Finance at the Sloan School of Management, Massachusetts Institute of Technology. He acknowledges with thanks the helpful comments of Gerald Pogue.

* Sometimes procrastination helps. In this instance it allowed me to read drafts of most of the other com- ments on the Brigham-Crum article [1] before writing my own. The others cover most of the specific issues I would have addressed had I started from scratch. Thus relieved, I will restrict myself to five general points that express my view of the proper role of modern portfolio theory in rate of return regulation.

1. Do not reward witnesses who bury assumptions in judgment.

My first appearance as an expert witness was on behalf of the Federal Power Commission staff in 1969. I estimated the cost of equity capital for Texas Eastern Transmission Company, a gas pipeline, based on a model of the firm's stock price. During cross- examination, the company's lawyer confronted me with a list of 21 distinct assumptions that I had made in my direct testimony. I defended all of them as reasonable, but I had to admit that some of the assumptions were not literally true and that others were only "probably" or "approximately" correct.

Then the lawyer gave a little speech about the 21 assumptions, arguing that, since they could not all be

® 1978 Financial Management Association

correct, my estimate of the cost of equity capital was worthless.

As usual, I thought of the perfect comeback too late. I should have said: "Think of your witnesses. They only made one assumption. They assumed the answer!"

Any competent witness who uses capital market data to estimate the cost of capital is forced to reveal his or her assumptions. This creates targets of oppor- tunity for opposing lawyers or rebuttal witnesses. Anyone who uses the Capital Asset Pricing Model (CAPM) is particularly vulnerable because that model has been the focus of so much theoretical and em- pirical work.

The CAPM's problems are well known. Who knows what secrets lurk in less formal and allegedly more realistic approaches?

2. Use simple models. The best estimates of the opportunity cost of capital

are still liable to measurement error. The errors come from noise in rates of return on common stocks, and from the difficulty of inferring investors' expectations from historical data. (The so-called comparable earn-

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MYERS/MODERN PORTFOLIO THEORY IN RATE CASES

ings method, which does not rely on capital market data, encounters equally severe measurement problems. The method is also logically unsound. See Myers [3], esp. pp. 61-63.)

The likelihood of measurement error is why honest estimates of the cost of equity capital are normally given in whole percentage points - occasionally tenths of a percent, but never hundredths. That is also why economists usually stick to relatively simple models. Many refinements, although they look as if they might capture more of reality, just lead to arguments over insignificant digits.

I believe this is why the so-called DCF model is so widely used in rate cases.' The model assumes that in- vestors forecast a perpetual and steady growth of dividends. I doubt that investors have that simple a view of the future. The model nevertheless seems to give reasonable answers, at least for the traditional public utilities in telecommunications, electric power, gas pipelines, etc. Evidently firms in these industries move slowly enough, yet at the same time have enough financial momentum, for the DCF model to work.

Those who use beta as a risk measure do so because it is simple, objective, makes common sense, and is consistent with modern portfolio theory. They cannot say that the theory is the whole truth. They avoid fan- cier measures of risk, not out of laziness but because they try to stick to a simple measure whose properties are well understood.

3. Use more than one model when you can. Because estimating the opportunity cost of capital is

difficult, only a fool throws away useful information. That means that you should not use any one model or measure mechanically and exclusively. Beta is helpful as one tool in a kit, to be used in parallel with DCF models or other techniques for interpreting capital market data.

4. Modern portfolio theory is more than the CAPM.

The usefulness of beta as a measure of security risk does not depend on the strict validity of the CAPM. The measure can be based on the following logic.

1. Portfolio risk can be measured by ap, the stan- dard deviation of portfolio return.

2. The risk of any security is its marginal contribu- tion to ap. For security j, the marginal contribu- tion is proportional to ojp or to /jp, j's beta with respect to portfolio p.

1The model states that stock price equals D,, next year's dividend, capitalized at k-g, the difference between the opportunity cost of equity capital and the growth trend of dividends. Thus k can be es- timated at dividend yield plus growth: k = D,/P + g.

3. Of course ,jp is different for each possible com- bination of portfolio and security. But the returns on any well-diversified portfolio are highly correlated with returns on the market portfolio. The bulk of capital invested in securities is invested via diversified portfolios. Thus we take the market (portfolio M) as a "standard" portfolio to proxy for investors' ac- tual portfolios, and #j = ajM/aM2 to proxy for /jp.

The CAPM goes further. It says that /j is a com- plete and sufficient risk measure, that the expected risk premium demanded by investors is zero when /j is zero, and that this risk premium is linearly related to fj. Roll shows how difficult these statements are to prove or disprove [5]. Therefore, the CAPM remains controversial. The general, qualitative tenets of modern portfolio theory are more widely accepted.

5. Beta is most useful for qualitative risk com- parisons; the CAPM is also useful.

There is an unfortunate tendency to refer to any use of beta as "an application of the CAPM." Actually, one can get a good deal of mileage out of modern port- folio theory without ever using the CAPM formula for cost of equity capital estimates.

My testimony in two cases before the FCC il- lustrates this point [4,6]. In the 1971 AT&T case, beta was used to confirm 1) that AT&T stock was less risky than the market portfolio or a sample of large industrial companies, and 2) that AT&T's stock was just about as risky as a sample of electric utilities. The cost of equity capital estimates were obtained primarily from DCF models applied to AT&T and to the utility and industrial samples.

In the Comsat case, Gerald Pogue and I argued that Comsat common stock was significantly riskier than the typical stock in the market portfolio and afortiori riskier than AT&T. Comsat had already requested a 12% equity rate of return, above the 10.5% the FCC had allowed in the prior AT&T case. The extra return had to be justified by showing that Comsat was riskier. Pogue and I showed that Comsat's beta was more than double AT&T's and that the difference was significant. We did not attempt to translate this difference into a numerical estimate of the cost of equity capital. (In both cases, the risk comparisons were repeated in terms of standard deviations of stock rates of return. The conclusions were unchanged, which I think will be the typical result in rate cases.)

As these examples illustrate, there are many ways to use betas that do not depend on the CAPM for- mula. Incidentally, the FCC relied on my approach in

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FINANCIAL MANAGEMENT/AUTUMN 1978

their AT&T decision but dismissed the Myers-Pogue study with essentially no explanation.

The CAPM could have been used to generate cost of equity capital estimates for both AT&T and Com- sat. That would have required stronger assumptions, although not necessarily unreasonable ones:

First, we have to accept the CAPM. This is naturally controversial. I nevertheless believe the CAPM is a reasonable theory so long as the numbers it generates are not treated as exact or conclusive. It is a rule of thumb - something worth leaning on if you don't have to lean too hard.

Second, we do not know exactly what the expected rate of return on the market portfolio is, although re- cent research gives an improved picture of "normal" rates of return in the U.S. economy. (See Holland and Myers [2] for evidence on "normal" rates of return and also for references to other work in this area.)

Third, standard errors of beta estimates are large for individual securities. For example, Comsat's beta was estimated at 1.69 from 6 years of monthly data, with a standard error of .30. A confidence interval in- cluding ± 2 standard errors would be 1.09 < d

2.29.2 Estimates of industry betas are more ac- curate, providing that it is possible to obtain a sample of reasonably similar firms.

The distinction between industry and firm betas is important in rate cases. It is hard to estimate a regulated firm's cost of equity capital if data on only that firm are available. This is true regardless of the approach taken. It is necessary to broaden the sample.

2Yet Comsat's beta was so far above 1.0 or AT&T's beta that Pogue and I were able to establish our point despite the high standard error of the estimate. The Comsat case was a rare opportunity because there was such a dramatic spread between its risk and AT&T's.

(See Myers [3], pp. 70-71.) Fourth, beta may not be stable. It can be dangerous

to project it from historical data. However, I believe much of the concern about instability is misplaced. Assuming a stable beta is usually no worse than assuming a constant compound growth rate for future earnings.

Conclusion

Risk comparisons are inevitable in rate of return testimony. So far, beta is the only risk measure we have that is sensible, objective, and consistent with modern portfolio theory. Clearly it should be used carefully; but so what? Any application of finance theory should be careful.

References

1. E. F. Brigham and R. L. Crum, "On the Use of the CAPM in Public Utility Rate Cases," Financial Management (Summer 1977), pp. 7-15.

2. D. M. Holland and S. C. Myers, "Trends in Corporate Profitability and Capital Costs," Working Paper 999-78, Sloan School of Management, M.I.T., 1978.

3. S. C. Myers, "The Application of Finance Theory in Public Utility Rate Cases," Bell Journal of Economics and Management Science (Spring 1972), pp. 58-97.

4. S. C. Myers and G. A. Pogue, "An Evaluation of the Risk of Comsat Common Stock," in U.S. Federal Com- munications Commission, Prepared Testimony S. C. Myers, F.C.C. Docket 16070, 1973.

5. R. Roll, "A Critique of the Asset Pricing Theory's Tests, Part I," Journal of Financial Economics (March 1977), pp. 129-76.

6. U.S. Federal Communications Commission, American Telephone and Telegraph Company, Prepared Testimony S. C. Myers, F.C.C. Docket 19129, 1971.

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