2. a Highly Personal Comment on on the Use of the CAPM in Public Utility Rate Cases

7/29/2019 2. a Highly Personal Comment on on the Use of the CAPM in Public Utility Rate Cases

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A Highly Personal Comment on on the Use of the CAPM in Public Utility Rate Cases

Author(s): Willard T. CarletonReviewed work(s):Source: Financial Management, Vol. 7, No. 3 (Autumn, 1978), pp. 57-59Published by: Wiley on behalf of the Financial Management Association InternationalStable URL: http://www.jstor.org/stable/3665012 .

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A H i g h l y Personal Comment o nO n t h e U s e o f t h e C A P M i nP u b l i c U t i l i t y R a t e C a s e sWillard T. Carleton

WillardT. Carleton is WilliamR. Kenan, Jr., Professor ofBusiness Administration at the University of North Carolinaat Chapel Hill.

* ProfessorsBrigham nd Crum hereafterBC)haveperformed valuable ervice n their article[3].Theyhavebrought o the attentionof academicians con-troversy hat since the Breen/Lerner 1] and Myers[10] nterchange ad beenarguedoverprimarilynthetrenches utility rate hearings.The focus of BC'scriticismis quite narrow, calling attention to theeffects of risk non-stationarity n measuredbetas,hence on estimatedcosts of equity. BC appeartoacceptas valid the underlyingheory,a subjectof in-creasingdispute n itself. The purposeof my note isnot to findfault withthe BC analysisandexamples;surelymuchfault-findingnk willbe spilled n Finan-cial Managementwithoutmy help.1RatherI shouldlike to add to the menu of CAPM problems, n the'Indeed, BC's prose has the evangelical tones of the reformedsinner. Professor Brigham and I were adversaries in the Comsatrate case [2, 8, 9], where non-stationarityof beta was a majorpointof contention. It is gratifying to observe a heightened sensitivity toCAPM implementation issues in the BC article. 1978 FinancialManagementAssociation

samegeneralspiritas BC.2The first temonthismenu s theeffectof monetaryphenomena.Therateof return xpressednthetypicalutilitycase is an annualrate, presumably pplicableprospectivelyoranindefinitelyongfuture.TheGor-donvaluation ormula,k = D/P + g, reflects,amongother things, similar assumptions:k, the cost ofequity, normally s estimatedusingannualdata;it isthen by construction an internal rate of returnassumed onstant orall future ime. Sucha construc-tion obviously s invalid if the term structureof in-terestrates has a significant lope,forthen weshouldfind a k1foryear 1,a k2 oryear2, and so forth in-stead of forcingan averagek by (usually) mplicit2For a description of statistical specification and estimationproblems that afflict regulatoryuses of the CAPM beyond both thescope of the BC paper and the limited purposesof this note, see [4].Also, misapplication of Bayesian methods can now be added to thelist of horrorstories on regulatoryuses of the CAPM. For a highlyadversarial discussion of one of these, see [7].

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FINANCIALMANAGEMENT/AUTUMN978

assumption. Now let us examine the manner in whicha "riskless" nominal rate of return, RF, has to beemployed in order to implement the CAPM in a rateof return application. If / is derived using as RM(thesurrogate for rate of return on the market portfolio)annual data, then RF should be the rate on an ap-propriate one-year security in the formula

E(RC) = RF + 3C [E(RM)- RF],where E(Rc = one-year estimated cost of

RF

cE(R RE(RM)- RF

equity capital for company C(i.e., E(Rc) = k);one-year "riskless" rate ofreturn;company C's estimated beta;estimated spread of average,annual rate of return on themarket over RF assumed sta-tionary.

The use of any other RF, of either shorteror longermaturity than the data interval that generated $candE(RM), in the presence of a yield curve slope, is for-mally incorrect. How much damage can result can beappreciated once we contemplate that 1) monthly orquarterly data intervals are usually employed in betaestimation, to secure degrees of freedom, and 2) thecorrect use of a short term Treasury bill yield as RFwould then lead, ceteris paribus, to frequent wideswings in E(Rc).3 For a hypotheticalexample, assumethat c = 1.0 and E(RM)- RF = .005 (correspondingto an annualized rate spread of .0617). Also assumethat on Treasury securities we observe, at twodifferent dates, the following: Observation ObservationDate1 Date2ase1. Monthly yieldon one-month bill

Annualized yield2. Monthly equivalentyieldonone-yearbillYieldonone-yearbill3. Monthly quivalentyieldonten-yearbondAnnualized yield

.005 .0076

.0617 .095

.0057 .095.07 .09

.0072 .0072.09 .09The results, in terms of estimated E(Rc), in an-nualized units are:

3The correct use is in the compound interest formula, E(Rc) =[1 +ERc)Mo]12 - 1, where E?RC)Mos the one-month CAPM-derived cost of equity capital for company C. Casual inspection ofCAPM-based testimony [7] gives me the impression that dis-ingenuous errors are frequently made in the adversarial setting ofutility rate hearings.

Observation ObservationDate 1 Date 2ase123

.127.136.157.162.157.157

The only correct assertion on date 1, given theassumptions, is that company C's cost of equitycapital is at an annual rate of 12.7%for the nextmonth and on date 2 it is 16.2%. Any other con-clusions would be attributable to the spirit of advocacythat infuses expert witness testimony in public utilityrate cases. This includes the intuitively reasonableproposition that the "long-term (annual) cost ofequity is 15.7%at both dates" - a proposition that isboth misleading and incorrect in terms of statistics,the arithmetic of compound interest, and the for-malisms of the CAPM. The range and shift of interestrates depicted are well within the range we haveobserved in recent years. It is also true that am-biguities in the regulatoryuse of the expression, "rateof return,"make it uncertainjust what maturity yieldand shifts are importantto regulation. Nonetheless -and the point of this note - the CAPM is sufficientlyformalized so that the data interval and hypothesizedinvestor holding period are co-specified. If this leadsto rate of return estimates that are revised substan-tially with every shift in Treasury bill yields, by im-plication requiring continuous rate hearings, there isnot much we can do about the matter without scuttlingthe CAPM framework.I suspect that this problem with CAPM use will beappreciatedby any thoughtful student of finance. It isin fact the CAPM-specific illustration of what is en-countered when any formal framework is employed todetermine the "cost of equity capital." My seconditem on the problem menu shares this characteristic,but its appreciation requires a subtler understandingof what rate of return regulation tends to produceeconomically and what it is intendedto do legally. Bynow it is commonplace [5] that rate of return-ratebaseregulation tends to drive a company's stock price,ceteris paribus, up or down toward book value. Itwould seem necessary that any stock price-basedcostof capital model used to estimate utility rates of returnbe modified explicitly to incorporatethe effects of in-vestor knowledge of this result. The Gordon modelhas been so modified [6] but, to the best of myknowledge, the CAPM has not been.In the same spirit, the famous Hope case decisionrequires that rate of return allowances protect thecredit standing and financial integrity of the enter-

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CARLETON/COMMENTN THEUSE OF THECAPM

prise. On occasion, for example, it may be necessaryfor a utility commission to permit a company -because of bond indenture provisions - to earn anoverall rate of return that bears no obviousrelationship to the conventional weighted cost ofcapital, in which equity cost is estimated by any one ofour market-basedtechnologies. If one wishes to adoptCAPM terminology, the Hope criteria require regula-tion to take into account the downside part of non-systematic risk.The question before the house in this note is: Canthe known-to-investorscircumstancesof regulationbeincorporated within both the equilibrium propositionand market model of the CAPM? At the risk of beingprovocative, I would assert the answer is no, and thereason is straightforward. If one contemplated themarket/book value of equity tendencies and financialintegrity implications of utility regulation in theabstract, one would likely conclude that utility in-vestors face trivial risks, so the choice of the CAPMor some other frame of reference to estimate cost ofequity is so much small change. On the other hand, theimpact of changing technology/cost considerations,income distribution influences over utility pricing, en-vironmentalquestions, and above all volatile inflationand interest rate experiences have produced gapsbetween what we generally think regulation does andwhat it actually does. In particular,the periodbetweenthe emergence of a spread between investor-requiredand company-realized rate of return and its dis-appearance- regulatory lag - can be both long anduncertain. To many students of utility regulation,regulation itself has been the main source of investorrisk in recent years. And no situation of actual lag is astationary one; it implies non-constant expected ratesof return to the firm and to investors over futureperiods. Yet the CAPM would appear to require, forimplementation, that there be no external force(regulation) systematically shifting the firm's profitopportunities through time in a fashion intimately tied

to the investor valuation process.Brigham and Crum finish on a conservative ad-visory note: "Yet, at present, the CAPM should beused in utility rate cases, if at all, only with a greatdeal of caution." Without necessarily subscribing toall of the BC analysis, I wonder whether they didn'tstop short of the more appropriaterecommendation.References

1. WilliamJ. BreenandEugeneM. Lerner,"OntheUseof f in Regulatory Proceedings,"Bell Journal ofEconomicsand Management cience(Autumn1972),pp. 612-21.2. Eugene F. Brigham, Testimony, Federal Com-municationsCommission,DocketNumber 16070 Oc-tober 1971).3. EugeneF. Brigham ndRoy L. Crum,"On the Use ofthe CAPM in Public Utility Rate Cases,"FinancialManagementSummer1977),pp. 7-15.4. WillardT. Carleton,"A Note on the Use of the CAPMfor Utility Rate of Return Determination," orth-comingin Applicationsn Finance(TIMS StudiesinFinance),eds. EdwinJ. Elton and MartinJ. Gruber.5. WillardT. Carleton,"Rateof Return,Rate Base andRegulatoryLagUnderConditions f ChangingCapitalCosts,"Land Economics May 1974),pp. 145-51.6. WillardT. Carleton,Testimonyon CarolinaPower&LightCompany'sFair Rate of Return,NorthCarolinaUtilities CommissionDocket NumberE-2, Sub. 297(April1977).7. WillardT. Carleton,TestimonyorCommunityPublicServiceCompany,New Mexico Public ServiceCom-mission,Case Number1378(December1977).8. WillardT. Carleton,Testimony or the FederalCom-munications Commission, Docket Number 16070(February1972).9. WillardT. Carleton,Testimony or the FederalCom-munications Commission, Docket Number 16070(September1973).10. Stewart C. Myers, "On the Use of 3 in RegulatoryProceedings: Comment,"Bell Journalof EconomicsandManagement cience(Autumn1972),pp. 622-27.

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2. a Highly Personal Comment on on the Use of the CAPM in Public Utility Rate Cases