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ON ESTIMATING THE GROWTH TERM FOR USE IN THE DISCOUNTED CASH FLOW MODEL OF DETERMINING THE COST OF EQUITY: FORECASTS BY HISTORICAL METHODS VERSUS SECURITY ANALYSTS' FORECASTS By STEVE VINSON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 1i Qa Copyright Steve 1988 Vinson For Elizabeth and Elizabeth Claire ACKNOWLEDGMENTS This research been conducted over rather extended period of time, through many phases of my life and career. There are so many people who have contributed large small ways that is doubtful that can recall thank them all. would and like everready thank Eugene assistance Brigham throughout his guidance academic professional career. Without Gene's encouragement support would never have had the opportunity pursue interests in corporate finance. From first time read one textbooks, long before met him personally, during period when were actively working together, I have gained continuing through from him a distinct body present day, of knowledge and an immeasurable number of insights. also thank the members of the finance and economics faculty the University Florida, especially Sanford Berg, Arnold Heggestad, and Robert Radcliffe who serve dissertation committee. I have greatly enjoyed and benefited from their teaching, friendship, and wisdom. Over course of preparing this study, numerous AT&T, including Eric Lindenberg, Mark Stumpp, Bill Ford, George Lee, and Sue PerlesGoldberg. have benefitted from number conversations with members academic community who also practice rateofreturn consulting. In addition Gene Brigham, these include Bill Carleton, Jim Vanderwiede, Irwin Friend, Dick Bower, Fred Pettway, Weston, and Chuck Linke. .tzenberger, Several m Bill Avera, members Dick security analysts community provided valuable information on their profession and methods. would especially like thank John Bain, Mark Luftig, Charles Benore, Charles McCabe, Leonard Hyman. This assistance study of my also good benefits friends, from Dilip Shome, advice Lou Gapenski, Pietra Rivoli, Brad Jordan, who on more than one occasion buoyed my failing spirits. Finally, lovingly and gratefully acknowledge continuing moral, financial, and spiritual support Elizabeth Vinson, from whom all the good things in my life flow. TABLE OF CONTENTS Page . iv ACKNOWLEDGMENTS................. ................... LIST OF TABLES. . . ................... ... .x ABSTRACT. ................ ......................... .xv CHAPTERS EARNINGS REGULATION, CASH FLOW METHOD, AND ESTIMATION........... THE DISCOUNTED METHODS OF GROWTH ..I ....... .. .1 Intr The The Fina The Comm 1.6. 1.6. oductio Economi Cost of Common Establ ncial a of Ret Discoun For Es only Us 1 2 Grow Secu n.... .. c Princ Common Regula fishing nd Lega urn.. ted C timat ed Gr th Es Hist rity ing owth tima oric Anal f Regul and It ocedure ards e Co stim s De Acc ts' ethod st of ators. rived ountin Growth Fair Equity * . 1 Rate ....1 S21 00.0...... from g Data.... Forecasts S . THE THEORETICAL FORECASTS IN THE ROLE OF SECURITY ANALYSTS' FORMATION OF INVESTOR EXPECTATIONS............ .. . .. .. . .34 Introdu A Model In The Rol A Model Op Diverge A Simul In rket ion P onsen forma and Opin Analy Effi rodu sus tion Cons ion sis Consensus * ...... . cie ncy on. ect qui us a R the ana Expectat ions..... tion, Div pectation k Factor. fighting ion...... ... .36 . .40 s...44 . ..55 * ....63 .......... .34 A REVIEW OF THE EMPIRICAL LITERATURE............66 Int The 1 s i Li ' S eld Car and Gr Stu Li terature o h e u d t reduction Empirica Analyst .1 Baref .2 Basi, .3 Brown .4 Elton .5 Other Empirica Analyst .1 Cragg .2 Malki .3 Cragg ortTer and Com y and T Roseff ber, an ies.... erature ngTerm Malkiel d Cragg Malkiel m is wa (1 d Securi recast y (197 (1976 8).... Itekin ty s. . 5). ). . (1c curity a; .. .. 66 ......7 ...... 7 981)..8 ......9 sts. ..... .93 ..... ...... 93 ......... ...99 . . . 105 AN INTRODUCTION TO THE DATA...... . . .....115 Overview.. Long Term Histo Comparison Withi Comparison Metho By Se Comparison Metho Indus Value Line ........... Growth Fore rical Accou of Forecas n Industry of Forecas ds with For curity Anal s of Foreca nd IBE Clas Forecasts casts Deri nting Data ts by Hist Classifica ts by Hist ecasts Mad ysts...... sts by His Forecasts ifications of Growth. orical tions. orical e .... 115 Dm S. ....120 Methods S... 129 S. . .137 torical Within S........ ..140 S. . 147 AN EXAMINATION OF FORECAST ACCURACY............151 Introduct Computati Fore Forecast Forecast Cate Forecast Decomposi Diag Industry Error Dec The Corre The Pric ion. on o cast f Actual Growth Errors......... racy............ racy Within Indu Rate: .........151 s and trial cy Within Utility f Forecast Errors actors id Err rror Decomposition..... ion By Utility Sector.. of Forecast Methods to ectional Structure of earnings Ratio ..1 ..1 .168 .187 r . .2 . 2 s..... ... . . s' Lo and el an and . 1 . . .231 SUMMARY AND CONCLUSIONS........................ 238 Introduction.......... Findings.............. An Explanation For the Performance of Security Analysts .......Superior Superior .. .. ....2 ..........2 Forecasts.......... 257 BIBLIOGRAPHY.............. ... ................ .... 269 APPENDICES SECURITY ANALY ESTIMATES CONTRIBUTING THE IBES DATA BASE ............280 INDUSTRY SIC CATEGORIES AND ASSOCIATED CODES...... ...... ...... ........ ......282 FORECASTS BY PEARSON HISTORICAL CORRELATION METHODS: COEFFICIENTS...........284 FORECASTS BY HISTORICAL METHODS AND IBES FORECASTS: PAIRWISE COMPARISONS OF FORECAST AGREEMENT. COMPUTED VALUES OF FRIEDMAN STATISTIC......299 FORECASTS BY PAIRWISE HISTORICAL COMPARISON METHODS AND OF FORECAST IBES FORECASTS: AGREEMENT..314 DECOMPOSITION OF FORECAST ERROR: DECOMPOSED BY BIAS, EFFICIENCY, ERROR. FORECAST ERRORS ASSESSED ACTUAL EARNINGS GROWTH.......... DECOMPOSITION OF FORECAST ERROR: DECOMPOSED BY BIAS, EFFICIENCY, ERROR. FORECAST ERRORS ASSESSED ACTUAL DIVIDEND GROWTH.......... AND RANDOM AGAINST . . .321 AND RANDOM AGAINST . ...331 ACCURACY OF FORECASTS IBES FORECASTS. BY HISTORICAL METHODS WILCOXON SIGNED RANKS: Tl rnrTITm a nnrifT r r.,1Tn ^Trtrnn VERSUS ACCURACY OF FORECASTS IBES FORECASTS. ERRORS ASSESSED GROWTH.......... BY HISTORICAL METHODS WILCOXON SIGNED RANKS: AGAINST ACTUAL EARNINGS VERSUS BIOGRAPHICAL .......... .354 SKETCH. ...............................366 LIST OF TABLES .1 Average .2 Average .3 Analysis Annual Forecast E Industry Forecast of Turning Point rror.... Error.. Errors. . . . . .73 . . . . .73 S. .. . . ..74 Theil' UStati stic . . . .75 .5 Representative .6 Specification Forecast E of Forecast rrors....... Horizons... . . . .78 ...... .... 80 TValues Associated with Forecast Errors . . .83 Rank Order Average Correlation Cumulative Coefficients. Excess Returns . . . .88 .............. .88 Other Studi ............. ....... .. .... .92 Theil' UStatistic. .. .. .............. .. ... .98 Regress Estimated Asymptotic Result S . Parameter tStatisti ................103 Values............ CS.... . .....104 . . . .111 .1 Forecasts criptive storical storical Statistics Methods Methods.. : Growth . . . .123 Forecasts ....125 Agreement Pearson Among Forecasts Correlation Historical Coefficients and Methods Number Common Observations........... .130 Agreement Pairwise Among Forecasts Comparisons Historical of Forecast Methods Agreement... .131 .6 Forecasts Agreement Historical within Methods: Industrial Forecast ass cations . .135 .7 Descriptive Stati cs: IBES Forecasts (Full Sample)..... criptive Stati stics : IBES Forecasts (Reduced Sample) Agreement Among Forecasts storical Methods and IBES Forecasts Pearson Correlation Coefficients. .139 Agreement Among Forecasts Historical Methods and IBES Forecasts Pairwise Compari son Forecast Agreement...... IBES Forecasts : Intraindustry Summary Statistics. . . 143 .12 Forecast Forecast ssifi Historical Agreement cations... Methods Within Indus IBES Forecasts trial ...144 Descriptive Stati CS: Value Line Forecast .149 Value Line Forecasts Agreement with Forecasts storical Methods and IBES Forecasts . . .150 Accuracy of Forecasts storical Methods IBES Foreca sts: Errors Assessed Against Actual Growth Earnings per Share.. .157 Accuracy of Forecasts Historical Methods and IBES Forecasts : Errors Assessed Against Actual Growth Dividends per Share... ....158 Accuracy of Forecasts Historical Methods And IBES Forecasts Mean Square Forecast Error... . .158 Accuracy And IBES of Forecasts Forec asts by Thi stori Methods UStatistic.. . .161 5.5 Accuracy of Forecasts storical Method IBES Forecasts: Errors Assessed Growth......... Wilcoxon Against A Signed ctual Ranks Tests Earnings .164 . . ..138 . . ..138 S . .141 5.6 Accuracy Forecasts Historical Methods IBES Forecasts coxon Signed Ranks Tests Errors Assessed Against Actual Dividend Growth... ...167 Median A Methods Against ctual and Errors IBES F Actual Forecasts forecasts Earnings : Errors Historical Assessed Growth.. ....174 5.8 Median Absolute Percentage Errors Forec asts Historical Methods and IBES Forecasts: Errors Asses Against Actual Earnings Growth. ....177 .9 Median Actual Methods and Against Median Errors IBES Actual Absolute Forecasts Forecasts: Dividend Perce Errors storica Assessed Growth... ntage S. .180 Errors Forecasts Forecasts: stori Errors Methods Asses and Against IBES Actual Dividend Growth. . 183 summary Industry Vs. IBES of Wil coxon Forecasts Forecasts: Signed Ranks Histori Errors Assesse Test Methods d Against Actual Earnings Growth.......... ..188 Summary Industry Vs. IBES Actual Median Median of Wilcoxon SForecasts Forecasts: Dividend Actual Absolut Signed Ranks Histori Errors Assess Growth Forecast Test Methods ed Against .............189 Errors..... Percentage Errors .15 Wil coxon Signed Ranks Tests Telephone Companies coxon Company Signed es. Wilcoxon Signed Ranks * ... Ranks Tests Tests Electric Servi . . .197 Natural Gas Transmi ssion Companies .....*198 Wilcoxon Signed Ranks Tests Natural Gas Distribution ra4 1 n ^ Companies C nn v rJ Tr'1 anr^^ i r. . ..199 I . . . .191 . . . .192 . . ..196 *D a'M'b rplaeC+E r, c Decomposition Aggregation: of Forecast Errors Asse Error ssed Level Against Actual Earnings Per Share . .206 5.21 Decompos ition Aggregation: Dividends Per of Forecast Errors Share Asses Error sed A Level against Actual . .206 5.22 Decomposition Error. Errors y Bias, Assessed Efficiency, Against and Actual Random Earnings Growth. . . . . ................. Decomposition Error. Errors Bias Assessed , Efficiency, Against and Actual Random Dividend Growth.. .210 5.24 Evaluation of Linear Bias and Inefficiency . ... 212 .25 Compari son of Sources of Error: Forecasts Historical Differences Methods Linear . IBES Bias Forecasts Tests Contribution MSFE. ...220 .26 Decomposition of Forecast Error : Telephones ...223 Decomposition of Forecast Error : Electric Service Companies . ..224 Decompo Gas sition Transmiss of Forecast on Companies Error: Natural . . .225 Decomposition of Forecast Error: Natural Gas Distribution Companies...... . . .226 Decompo sition of Forecast Error: Electric And Gas Evaluati Combination on of Linear Compani Bias es. and .....227 Ineffi ciency: Forecasts Telephone Historical Methods and IBES Forecast s. . 5.32 Evaluation of Linear Bias and Inefficiency Forecasts Electric Historical Service Company Methods es..... and IBES Forec asts .229 Evaluation Forecasts Natural Gas of Linear Bia Historical Transmi ssion and Methods Compani Inefficiency: and es. IBES Fore casts. Growth.......... Growth................ . Evaluation Forecasts Natural of Linear Bias Historical Distribution and Methods Company Inefficiency: and es. IBES Foreca Evaluation Forecasts of Linear Bias Historical and Methods Inefficiency: and IBES Forecas Electric and Gas Combination Companies.. .. .2 5.36 Correlation Between Forecast Methods and Earnings Ratio S.... .234 5.37 Correlation Earnings Between Ratios Forecast Industry Methods Category and .235 Average Return. Earnings Retention and Earned Rates .258 6.2 Compari son of Analysts' Revi sions Pre and Post Rate Author zation....................... Abstract of Dissertation Presented the Graduate School the University Requirements f of Florida the Degree Partial of Doctor Fulfillment of of Philosophy ON ESTIMATING IN THE THE DISCOUNTED GROWTH CASH TERM FLOW FOR USE MODEL OF DETERMINING THE COST OF EQUITY: FORECASTS BY HISTORICAL METHODS VERSUS SECURITY ANALYSTS' FORECASTS STEVE April . VINSON 1 1988 Chairman: Eugene Brigham Major Department: The cost Finance of capital , Insurance, of critical Real Estate importance in almost financial economic deci sion making. Nowhere that importance more observable than the process setting prices regulated public utilities. Over the twenty years the counted cash flow (DCF) model of estimating cost of equity capital has become the most popular method ascertaining the cost capital regulated public utilities However, implement the DCF model necessary estimate the longterm growth rate cas flows. this study, several methods of estimating growth accounting data with estimators taken from security analyst forecasts. Institutional Security Brokers analysts' Estimate forecasts System ( are IBES) taken data from ase represent the consensus view a number of professional security analysts. addition direct examination growth also estimators examines regulated large cross utility section companies non the study regulat industrial firms. Historically based and security analyst forecasts systematic are contrasted biases, and measures strength of foreca relationships accuracy to stock price earnings ratios. The study' findings indicate that the consensus security analysts ' foreca most reliable estimator longterm growth utility company es. For most other industrial sectors , the consensus security analysts' forecasts properties generally storically equivalent based growth desirable estimator estimators. The study also demonstrates that estimators of growth taken from security analysts' forecasts are more informationally efficient than growth estimators based solely on historic time series data. CHAPTER ONE EARNINGS REGULATION, THE DISCOUNTED CASH FLOW METHOD AND METHODS OF GROWTH ESTIMATION Introduction explicit critical knowledge importance the many cost capital economic decisions. Capital budgeting choices require estimates Cos capital screening hurdle investment rates cutoff opportunities. The points valuation closely held firms with untraded stock, valuation of divisions projects within firms that have traded stock will normally call estimate cost capital. Nowhere, however , does determination the cost capital receive more attention, more scrutiny, and more debate than the process of regulating prices and earnings public utility companies. The reasons such close examination are straightforward. 1986, example , the total invested capital maj or domestic electric , gas, telephone utilities was about $593 billion. A change the cost of capital that averaged only one percentage point across this total investment would have changed annual revenue anticipated requirements, cost the that aggregate the consumption total of these regulated goods and services , by almost billion. That equivalent wealth annual of about per capital event such redistribution immediate immense economic impact on society must obviously examined carefully Yet determination the cost capital, including consideration of how and when does change not are an exact used science. evaluate The methods cost and p capital Procedures are that evolving dynamically point time, the methods are neither unanimou accepted nor subj ect to universally consistent application. many respects, regulatory proceedings have served many years testing development a new 1iteratur witness laboratories of cost concept financial of capital or theory somewhere appearing there before economists methods. Almost introduced in th will a regulatory an expert body at the soon academic financial tempting introduce that concept in estimating the utility' cos capital And because the stakes are high and the regulatory process the United States has become increasingly adversarial, these innovations rarely unchallenged. fact, as Harrington (1979) , IS process, the ensuing debate provides valuable feedback the academic community at large, stimulating vast amounts of empirical and theoretical research. within this regulatory environment that questions about appropriate estimate of growth use determining discounted cash flow cost equity capital have received significant attention, especially within producing the recent growth several estimates years using the when consensus method of security analysts' forecasts emerged as a direct challenge more traditional estimating technique that relies on the extrapolation of historical time series data. The that purpose regulatory this environment, chapter discuss is to briefly the describe importance cost of capital the det ermination of regulated ces and set the stage the specific analy ses the later chapters Section 1.2, introduction underlying economic principles price and earnings regulation is presented. Thi followed Section a simple used model rate that setting explains how procedures cost that are of capital followed almost regulatory jurisdictions. Next, Section sets the economic and legal standards that qualify fair rate of return. In Sections 1.5 and the basi concepts the counted cash flow model are reviewed The Economic Principles of Regulation The justification regulatory control intervention ses out alleged inability marketplace to deal with particular structural problems. Kaysen and Turner (1959) suggest that regulation exemption from competition may appropriate when one more three situations are found within industry: Situations cannot exist which or survive competition, long, an as a practical d in which, th matter erefore an unregulated results. market will not produce competitive Situations which active competition exists , but where does because not produce of imperfections one or more the competitive market, competition results Situations exist, and competitive cons iderations has which produced results, but compete itiv competition or may D where in e results e exp light are exists, ected of ot unsatis or could to produce her policy ;factory one or more aspects. a public utility, the first situation the most traditional and persistent rationale regulation the firm' pri ces and profits. For these firms, technology the industry creates the existence "natural monopoly. In other words, claimed many basic types services, that the market cannot efficiently support more than one firm. For example, a point, electricity producers find progre ssively cheaper 1 nt's 1 to supply a 1 1 an1 ,1  extra units nnmn J i W a e of electricity. Ii stta l atrvn m nn l Similarly, nf Cen 1 o S.',' * one telephone company attempted to supply service in a particular area. Thus, traditional rationale has been that more efficient grant one firm monopoly a service territory. And , in order protect the consuming public from abuses that monopoly, the firm' prices and earnings become subject government regulation This market traditional failure view due holds existence that case of economies of scale and natural monopoly, the aim price and earnings regulation perfectly emulate competitive the results market. That that is, exist ere perfectly competitive market, firms would expand output the point where price equals marginal cost, unregulated monopolist, the other hand curtails production in order to raise prices. While higher price means lower demand, the monopolist will willingly forego quantity sales the extent that lost revenues are compensated higher revenues on the units does more Panzar, (1975), recent and holds sufficient unless production may engage view, Willig that ass (1986) the produce market costs, in "hit ociated , Bailey potential f competitive is truly the and primarily (1971), with and F competition results. characterized possibility run" entry that and a compe exit Baumol, aulhaber may That subadditive ting firm is sufficient cause the competitive incumbent manner. *S firm that *  price event, exogenous * S goods in a regulatory Ti Ur a  q I X q~ ~ X u X q m sell the higher price. The result waste; consumers end buying more cheaper but less preferred products , even though costs society ess in real erms produce more the monopolized product Thus , where economic scale create natural monopoly, regulator will attempt to set regulated monopoly pri ces (rates) near the prices that would obtain a compe titive market, and thereby induce the monopolist to expand output the socially desired level and to reduce the amount ineffic ient consumption substitution buyers. The price that is set the regulator , however, generally production not eq as would uivalent be required marginal standard cos model perfect competition. Faulhaber (1975) more recently, Baumol (1986) have pointed out, economic scale preclude the financial viability of a rule requiring equality between pri ces and marginal costs Prices which cover only covering marginal any the costs fixed do not costs general of production. contribute Thi because economies scale often occur the presence substantial fixed investment stri adherence the priceequal smarginal cost standard would not allow the owners the regulated firm recover these fixed costs. a consequence, regulators have most often adopted a policy that equates price with the average the fixed plant investment) plus return investment. that process and procedures how regulated prices 1.3. are And determined as will that be shown, are one subjects primary Section elements setting pri ces the determination the return allowed equity investors the firm. concept, regulator can achieve at 1 eas one outcomes perfect competition of eliminating monopoly profits that allowing equivalent a fair the return marginal on the cost equity i of equity investment capital. The Cost of Common Requlatorv Eauitv Procedure and Use Establishing In A Common Prices The most common system establishing ces regulated ratemaking. monopolies It is currently known being cos used tof to set service ces electricity generation, transmiss ion, stribution companies, gas local distribution and and interexchange transmiss telephone companies companies , water sewage companies and until recently was used price setting mechanism such industries airline transportation, bus and livery transportation, and trucking and cartage. Costof service ratemaking essentially a two step operating costs include, where appropriate, direct costs production such fuel, labor salary and fringes, supervi sion, and indirect cos such maintenance, general administration, marketing, finance and accounting, and other overheads, as well as taxes. Added the basic operating costs of production are the capital cos depreciation fixed which investment, represents and the a reasonable periodic level recovery earnings that allows firm pay debt interest expense and afford return equity putting their investors money a compensatory at risk rate productive endeavors firm. The total of operating costs service and capital costs of servi call the revenue requirement (RR), RR = OC + D which equivalent amount money the firm needs collect production, from customers recover fixed pay investment and expen ses provide investors with a fair rate return. The second step in costof servlice ratemaking establish unit price the firm' goods servi ces dividing the total revenue requirement anticipated number of output units that will be sold, =RR / + E Thi has effect of setting unit price equal average total unit cost of production. Through service, through that certain the investigation investment, setting societal and prices, the management, regulators objectives are utility' and seek achieved. cost ultimate ensure Breyer (1982) has noted that while the precise objectives cost ofservice ratemaking vary from jurisdiction jurisdiction, regulators would generally agree that such system should ordinarily seek prevent excess profits hold prices down to costs, avoid economic allocative waste minimizing shortages surpl uses eliminate ineffi cient production methods, assure admini strative ease. The first four objectives are generally believed occur a competitive marketplace, thus often stated that the ultimate goal earnings regulation through the mechanism cost service ratemaking is to replicate a competitive market. Although costof simple service in concept ratemaking the can actual become application burdensomely description difficulties multiproduct offering whose t stinct abstracts encountered multi several otal cus different output demand tomer intentionally establishing class regulated taken characteristic firms. goods or customers , it from prices For service with the for firms s. or highly necessary allocate r.WI aI A.rA nr. the costs at. aI YA a servi a1. ces  a a F among ml.. 4.4 those .n goods ^ 1 a .4 4~ a 3Thi complex. Prices are generally being set for consumption that will occur the next and several immediate future periods Thus, the measurement underlying costs production should, theory, reflect the costs that are expected incurred during those future periods. Similarly, the output quantities that are anticipated sold must also forecast. Regulators seek establish a base time period, called the test year, from which reasonable forecasts costs and output can made. The test year may an actual historical period time, perhaps the most recent twelve months preceding the filing of a request a rate change. When storical test years are used, pro forma adjustments to reported accounting data are often made to make the test year results representative as possible the expected economic environment that will apply when the new rates into effect. the general economy has become more volatile, and with dramatic rapidly impacts changing inflationary of uncertain fuel expectations capital costs, both nature and magnitude these adjustments have become more important and contentious issues during rate case proceedings. In other regulatory jurisdictions, the test year may a hypothetical future twelvemonth period. In that case, the costs of service are based budgets projections. When a future test year is used, Other areas debate include accounting conventions that are used to record expenses revenues. many instances, there are legitimate, prof ess ional disagreements periods over deferring or recognizing them certain as costs expenses u of service ntil future during the test year. some extreme circumstances, costs may deemed disallowed imprudent from or unnecessary, inclusion and totally cost or partially service. For example, management salaries may deemed excess there fore only an amount of salaries acceptable regulator would be allowed the cost service. the regulator may feel inappropriate firm advertise goods because monopoly, therefore disallow entirely marketing expenses. Concurrently with estimation operating costs service, the amount of assets required to produce the expected output must ascertained. These assets, termed the rate base (RB) , represent the dollar investment land, fixed plant equipment material supply inventories , fuel stock, and other productive assets. In addition, an allowance working capital used to provide timing difference between the rece and disbursement of cash often included the rate base. discussion, assumed that rate base financed total the capital supplies Thi investment must generate enough earnings pay interest debt, provide dividends preferred stock, their and money compensate at risk. the The equity return investors that putting is required called the cost of capital. Within the framework of cost service regulation, the cost of capital, or the overall rate of return (ROR) , is measured as the weighted sum the cost existing debt (Kd) the cos sting preferred stock (Kp), and fair rate of return common equity capital (ROE). The weights are det ermined the relative proportions the sources of capital used to finance rate base, ROR The = Kd actual (D/RB) dollar (PS/RB) earnings + ROE (CE/RB) requirement then computed multiplying rate of return time rate base = ROR x RB 4There are other sources of capital that can finance rate base including deferred income accumulated taxes cus cash tomer inflows depos provided ts, and investment tax credits. With minor modification, current SCUSS can extended to accommodate ose types of capital. 5It rate may base the case ess that than the or total great dollar value r than the of sum investor implicit supplied in rate capital. case However, proceedings treat generally rate base i c rit i nfl orma 1 .rn t nti 1 r i 4 11 I ciiltA or^ tnr ~aiiitC+tmfc + Kp I 1 and the dollar revenue requirement equivalent sum individual cost components, RR = OC + D x ROR), and finally after substituting the complete cost capital expression, revenue requirement can be stated as a function cost of capital through RR = OC + D + RB (D/RB) (PS/RB) + ROE (CE/RB)].. In assessing the importance the cost of capital ultimate revenue requirement, should be noted that many regulated utilities use highly capital int ensive produce tion technologies These firms often invest dollars in rate base assets in order to produce output that can be sold revenue. at all unusual to find that that the required earnings investment these capital intensive regulated firms can constitute percent the total revenue requirement. a fair Thus, rate the of return linkage and between revenue the determination requirements and ultimately prices paid consumers quite direct when costof service ratemaking employed. Financial Leaal Standards Fair Rate of Return Generally, the costs debt (Kd) of preferred stock (Kp) are measured embedded or average costs + Kp contractual agreements that exist between company debt and preferred stock holders. The fair rate return (ROE) on common equity capital not formally contracted. Rather, with common equity investments, the return common equity represents residual only claim after on the prior earnings claims the have firm been that met. paid However, inves tors will not make an equity investment unless they anticipate that this residual return will, over time, offer them fair compensation the risks they bear. the province cos of capital experts determine the minimum level return required investors that will induce them to make a common equity investment in the regulated firm. To offer more than the minimum level would generate excess profits the shareholders and unduly burden ratepayers. offer ess than minimum required level would penalize existing investors have the effect of confiscating their investment. Gordon (1974) has demonstrated that under certain assumptions the about economic the reactions environment, regulators fair rate to changes of return equity capital will cause the market value the firm' common the equity equity to just portion equal its the rate accounting base book investment value of In other words, regulators allow the firm earn a fair rate corresponding risk, the opportunity excess or monopoly profits will be eliminated. In turn, the market value the firm' common equity will equal regulatorydetermined value earnings base , that the equity portion ratebase. see , let the accounting book value equity portion the ratebase be defined = RB (CE/RB) , then e equity expected annual (ignoring the pool impact earnings available of dividend policy for and common future investment) given ROE x B. Gordon' standard determining fair rate return follows from assuming that the equity investors are purchasing future stream earnings with expected will annual be willing value pay (ROE x B). an amount The just marginal equal the investor present value this stream earnings where the present value determined discounting the earnings stream the appropriate riskadjusted cost of equity capital, For the sake of simplicity but without loss of generality, the stream definition assumed fair rate to be a perpetuity of return can , Gordon' expressed algebraically (ROE x B) / Ke. ROE = Ke, then = B, and monopoly profits will have been eliminated. Thus, the goal of regulators setting utility pri ces should be to determine the marginal, market required as a fair cost rate of equity of return capital, on the and book to utili value that the value common equity portion of the rate base investment. Gordon's work provided direct opportunity cost linkage and between the the economic estimation concepts fair rate return ratemaking common purposes equity that As such, his was appropriate approach was largely responsible shifting the focus of regulatory attention away from book accounting results and toward the capital markets for determining the cost of equity. Although Gordon' conceptualization the regulatory problem estimatin provided a the economic cost guidance of equity measuring capital, the controlling regulatory principles standards fair established two rate of return Supreme Court are deci legal sions, Bluefield Water Works Improvement Company Public Service Commission West Viraina (262 U.S. 679, 1923) and Federal Power Commission Hope Natural Gas Company (320 U.S. 391, 1944). In Bluefield, the court determined the standard against which just and reasonable rates (prices) are measured: A public tri l n a v utility m 4 entitled a a ~ Y.n rn~lrrr o such ank rates tr~ 1 ii n r l r undertakings risks and be reason in the fi should b economical its cred necessary duties. ( U ab na e it fo Pa which are uncertainties le, sufficie ncial soundn adequate, management, and enable r the proper ge 116) attended *. * nt ess u to e di The to ass of th under e maintain it to charge corresponding return should ure confidence e utility, and efficient and n and support raise money of its public In Hope, the court expanded guidelines to be used assessing reasonableness the allowed rate return. The court again reemphasized comparable risk nature the return made special note that costs of service include a fair amount earnings, ratemaking fixing a bal intere Pipeli insure re co a in re of re fo in st eq on co sh fi ma 25 of " ancing sts. ne Co t venues. nsidera legit tegrity gulated view venue n r the clude s ock.... uity ow inves rrespon would be nancial intain ) ust of Thus ca hat th " 315 tions imate of th . Fro it is ot only capital process and the we se e as c e m im f c i C under the act, .e.y reasonable" rates, inv investor and the con stated in the Natural that "regulation does busi U.S. de, ncer ompa the por or ost service on t By that ner should tments in ding risks sufficient integrity its credit ness sh p. 5 the inve n with ny whose nvest nt th erati of t debt ndard n b C oth to of and or at ng he an all p 90. stor i the rate or c there expen busin d divi the re reduce But nteres fina s are ompan be ses b ess. dends turn y e ut t commensurate with r er enterprises That return, mor assure confidence the enterprise, so attract capital. on o et ha eo in a ( the lives umer Gas not net such has cial eing oint ough also hese the the urns ving ver, the s to Page Morin (1984) has termed both the economic and legal standards fair rate return transparent and stated that the real difficulty determining a fair The precepts of Hope and the financial concept the cost capital, or presc public ription utility for statutes what give no detailed constitutes formula "just reasonable" rate return equity. The applicable legal standards permit public utility commissions choose among variety analytical techniques procedures setting allowed rate return equity. Kolbe, Read and Hall (1984) reviewed the hearing transcripts and testimony of a number of rate cases found that five general cost of capital methods have been commonly used to implement concept determining fair rate of return on common equity capital6 They are order the quency their total storical use Comparable Earnings, Discounted Cash Flow (DCF) Capital Asset cing Model (CAPM), Risk Premium Risk Positioning), and Marketto Book Ratio. comparable earnings method was the mos t prevalent method establishing rate return until the mid 1970s. According Kolbe, Read and Hall, the time publication their study, the Discounted Cash Flow 6Morin (APT) a capital. indicates use. identify method However, that Other to date methods the Arbitrage estimating review the Pricing cos regulatory has received that have extremely received t of Tneory equity testimonies limit limit use S,, a a a A. Z  .3,'a; A. he   ,,,,,,,~,: C1 U A I method had become the predominant methodology in terms current usage. Although the choice of method extremely important, should standard not a fair forgotten rate that of return the is the ultimate socalled legal "end result" test In effect, while the rate of return that used set rates mus compensatory and must confiscate the wealth investors must equitable consumers. Striking a balance between competing interests investors consumers political not an economic decision. However financial economic cost may may of capital, be predicated be able so that upon improve ultimate stronger the estimation judgements evidentiary fairness support The counted Estimating the Cash Flow Cost Method Equity The cla ssical value theory of Irving Fisher (1907) and J.B. Williams (1938/1956) holds that value asset determined earnings power ability generate future cash flows. That theory states the fundamental value an asset is the discounted sum of all future cash flows that are expected to be received the owner of that asset. The Discounted Cash Flow (DCF) model C_ L * Ak~~^ ffT nf ia^ nr^aae r~~11 da nabnarriC an~ , 4 4 (rl~i vf nx nara r J security valuation has emerged the direct application that classical theory. The most general form the DCF model developed first expected noting cash that flows the come holder the common form stock, of dividends the and changes the the dividend price the the stockholder stock. expects Letting represent to receive Year represent price the stock the end of Year and required rate of return the stock. the shareholder anticipates receiving dividends periods and then selling the stock the period the pres value the stock can determined from + Pn) . + (1+K (1l+Ke)2 (1+Ke)3 (1+Ke)n this equation, the pattern dividends unspecified through time. That , dividends may increase, decrease, become zero or quite large and model may still used assess value stock. imposing structural assumptions upon the time path dividends and earnings changes, simplified, eas solved version of the model may developed. Gordon (1962) has shown that dividends are expected grow at a constant rate over an infinite number periods, ess than and the firm either (3a) , g, loss when new shares are issued, the model reduces This known as the Gordon or constant growth version the DCF method. rearranging the terms the equation, the constant growth model may be solved the required rate of return on the stock, While more complex and less restrictive versions the DCF are sometimes employed, the above equation forms the basis the most commonly used DCF technique estimating the cost of equity capital. further assumed that the observed market price the stock equilibrium and that reasonable estimates anticipated next period dividend and longterm growth rate can be made, then is a straightforward computation arrive an estimate the required rate return common equity the firm question. The commonsense logic the model that equilibrium, sum required expected rate dividend of return yield on the and expected the capital appreciation possess growth algebraic simplicity Moreover, the easily model explained. Most likely, these properties that have made constant growth model the currently most often used method of determining cost of equity capital 1.6 Commonly Used Growth Estimators While simple form, DCF model does have a maj or implementation problem: order use DCF procedures estimate an independent estimate must first made and then used as an input the equation. That actual application while not always generally agreed upon, the measurement the stock price and anti cipated dividend pose less problems than the estimation long run growth rate. According to Morin (1984), The princ required ipal return ascertaining the difficulty DC growth rate calculating F approach which inves tors in are currently infallible rate its the expecting. method is precisely, magnitude growth While in assessing an explicit cannot component there what the assumption avoided. the most growth about Estimate difficult controversial inve step a quantity wh stores. (Page ich in implementing lies buried in DCF the since minds 123) their review of rate case testimonies , Kolbe, Read, and Hall (1984) found that the popular methods growth estimation may placed three general categories th Energy recently com e industries pleted that Regulatory generic they rate regulate, Commission of return both and the the dockets Federal Federal Communications Commission specifically adopted rcnnne* m rirnr.r+ 1 nTrlnl 4 r n * ,m m r rt mn^hnA n~F Trnr]T Use over so Sometime per sha growth, in disc growth r starting of historical me past s past re is because rete j ate can and period growth used e divid umps, change ending gr, , o in S nd no no points owth ften f earni a pr s are that ticeab rate ive ngs oxy chan the ly w of the of dividends data ten y book r div by esti the seri ars. alue dend irms ated xact s. Use inve of forecasts of stment services. growth These rates public forecasts shed are sumed to be investors. representative of the expectations 3. Use "retenti as the times retained paid ou growth i recognize its cos for exis overall instead the on" ra the w t a s e es t o tin re of or te o pr ithi s di qual tha f ca g eq turn bein "sustainable" "plowback") f return oport n the viden to ( t if pital uity to g pai ion of firm, ds. Tha b x BRO the firm , future can only invest d out. growth on book (also called rate, measured equity, BROE, earnings b, instead t is, an E). Thi is earn growth i come if rs is p (Page 55) tha d of estim s ap ing e n div part lowed a is eing e of coach ctly ends the back the discussion below, some characteristics each the first two these growth estimator methods are described. First, standards however, assessing useful the to list quality some reasonable growth rate estimators. These standards allow, essentially, third computati appr fore sepa peri the coach cast rate od r sust trending fn ra ror" e c +a onal may data and tent inab of nf approach method be imp an di ion le d will stinct ratio growth history is less ology. lemente not be foreca s and b method ical d Iir/ a competing method The sustainable d u tr sti ook is ata ntrn sing e eated i ng meth rates simply If P rav 1 either his n this st odology. of return a variat security caF *t1, tor udy I ar ion a 1h than a growth o na v prior used, n the lysts Rnnn 9The I ( ( formulation empirically testable later c hypotheses which hapters. this will be examined stage the study the standards provide basis for logical prioril reasoning about the relative strengths weaknesses the competing estimator methods. evaluate the Brigham, appropriateness Vinson, Shome of growth (1983) estimating methods, identified four desirable properties of a growth rate estimator, Estimates should unbiased Valid procedures that than inter techn tend techn are the est. ique to ique should, either "true" Thus, can be be too fails a on ave system value if a shown t high critic 0 a rage, produce ically higher of the var growth rate produce esti r too low, 1 test. estim nor 1 able estima mates then ates ower of ting that that 2. est inf dis est exi aff Es imati ormat regar imati sts ect g ti ng io d ng an ro mates should method sho in; that is, information growth fai ,d which can wth, then the be uld tho efficient. utilize al actimate If a Is to utiliz logically be method fails m e ex t A 1 rel should ethod data pecte his t val eva d n which d t est. 3. Estimates should produce highly sensiti particular samp value. Thus, different estim given company seemingly slight method fails the should be consis growth estimate ve to the s le of data used if a method pr ates of the gr in a given tim changes in inpu consistency tes tent. es that electric to est oduces owth r e peric t data, t. )n :i r *a >d A method are not of a mate the adically te for a due to then the 4. opi cri bec opi and Est ons cal se on ts c inmates should of market parti in a DCF cost it is the rep that determines ost of capital. be reflect cipants. of capi resentativ a company' (Page 2) tive This tal e i s st 0 po ana nve ock f th int i lysis stor' price 1 . .6.1 Growth Estimates Derived From storical Accounting Data Cost capital analysts have often bas their historical computations on earnings per share , dividends per share and book value per share. While theory states in the clearly form that the of dividends that expected future constitute value, cash flows a case can be made using other quantities as well. First, the ability pay dividends stems from company' ability generate earnings, therefore growth earnings per share can expected influence the market' dividend growth expectations major disadvantage using directly dividend growth the discretionary nature the firm' dividend policy. That historical dividend growth may be biased because short run changes in the payout rate the firm. Over the pace longer for run, future growth dividend earnings growth per and share thus, may the expec station earnings dividend growth growth. may more A drawback representative to using historic future 1 time series earnings per share to derive expected growth the relative volatility earnings When earnings per share become negative very small, historically based growth estimates may become highly started computationally infeasible. In addition, firms are known r' ar'rnniiT i nfl *rtI II in/I n h /* rt"l II ~h~ra th rrnninh 6oma vn ^nr nar reflective the expected the ongoing level earnings. The use of historical growth book value per share as a proxy the expected dividend growth of a regulated utility may be justified under certain conditions Book value a principal determinant of earnings utiliti original cost rate base jurisdictions. Because earnings return per and share book are value the per product share, the the earned storical rate growth book value per share may provide indication the growth growth of earnings per earnings share. per share turn may , as noted pace above growth dividends the per share. usefulness of b However, ook value two per assumptions share are crucial growth, the future earned rate of return must be expected remain stable, stable and about the unity. market The to book later ratio must assumption remain ecially important because book value per share will increase decrease with the issuance new shares when the market to book ratio different from one. The type growth that attributable to book value accretion dilution generally transient and serves produce biased proxies longterm expected growth. After selecting historical seri of data, time period over which growth to be measured must current economic conditions. the same time the data period should long enough avoid short term influences. Selection of a time period depends largely judgement, but customarily historical based estimates rely the most recent five ten years of data, although some series analysts , and o have others used as short long a period a twenty as the year most time recent single year rate of growth. The analyst must also choose a computational form extracting Numerous the methods growth have rate been from employed raw accounting including the data. root the ratios (geometric averages, averaging weighted the least averages, beginning squares centered and trend ending fitting, averages values moving simple averages. These computational methods are more or 1 ess highly sensitive the choice of beginning ending values are not generally cons istent when the data period changed slightly. More sophis ticated computational methods such as Box Jenkins or extrapolation with intervention are not generally used due the large 10it among For would an understatement those example apple seeking , in fo v to to compute rmulating 1400 that historical cost firms confus rates of capital that provide exists of growth. rules that interstate telecommunications Commi ssion coefficient recently derived services the proposed from Federal the simple Communic use linear the regre nations slope sslon rr i ri orn^/ rv 3 + ITT1 SM v rman r xr "t c!k~ra nnr rviroy J r~ n data input requirements that are necessary establish the base model. The choices of data seri , computational form, data period are examined more detail Chapter However, general, can be said that historical data reflect the economic conditions that prevailed prior periods. economic structure has changed there is an anticipation that may change, the use historically based growth rates can not reasonably expected produce quality estimates the current growth expectations investors It has been said that the naive extrapolation of historical data determining expected growth very much like driving a car only looking rear view mirror While criti cism certainly historical valid, data the seri use are growth popular rates because derived the from ease data acquis ition and the presumed factual character data themselves. 1.6.2 Security Analysts' Growth Forecasts alternative to the use of historical data base growth estimates on security analysts' forecasts. Most large investment banking firms, some large institutional investors, and many investment research firms employ security analysts who produce forecasts 1^ 1+.fa a1 ne AI rAa e f h ~JTn nnc 1* ana t \TC Cn+n ^r r^ F M CHi C? stm dividends, or the implicit growth rate may be extracted from the underlying earnings and dividend forecasts The analysts who make these forecasts often special particular financial industry analysis and profession they with often come substantial experience from previous employment in the particular industry which they analy ze. any given time, several different analysts may making forecasts about the same company. Because has been recognized market participants that the composite consensus of these forecasts might more informative than any single analyst forecast, information service companies that collect forecasts and publish them summary form have come into operation. The oldest such service the Standard and Poor' Earnings Forecaster which provides information on the one year ahead and two year ahead earnings per share forecasts many security analysts. different inadvertently, 1968. type Burton service Malkiel, began, then almost of Princeton University and John Cragg of the University British Columbia, cooperation with the Institute Quantitative Research Finance, collected both short run earnings per share forecasts and the longterm earnings growth forecasts of several investment firms order to conduct research nature and accuracy purposes over for the several Wall years Street until firm maintenance Lynch, Jones was and taken Ryan. Lynch, Jones and Ryan began marketing the consensus (mean) one year ahead and two year ahead earnings per share forecasts the mid 1970s under the name Institutional Brokers Estimate System (IBES). They expanded the number companies covered to include almost New York Stock Exchange listed firms and a number of firms the American and overthecounter exchanges. They also increased the number analysts that contributed forecasts the consensus value. In late 1981, Lynch, Jones and Ryan began systematically collecting longterm earnings (five or more years ahead) growth forecasts January of 1982, first ongoing , well maintained data base security analysts' longterm growth forecasts became publicly available. Lynch, Jones and Ryan intended the data base provide used subscribers valuing with security growth es. estimates That that could subscribers were generally known to be using growth estimates inputs the model received future computing periods, the and expected then dividends discounting to be that stream of dividends the cost of capital they felt to be appropriate the security' sk in order to determine their intrinsic value the stock. That intrinsic value Although cos capital analysts had been using individual security analyst' forecasts growth several years, mos t notably the foreca Value Line many cost of capital analysts were quick recogni improvements to be gained through the use of a broad based consensus forecast. Not only was there immediate improvement the representation of differing opinions embedded the consensus, but there was also a gain from using standardized consensus forecasts from an independent source. That , the availability the IBES consensus forecasts removed an element of judgement and potential selection bias that had plagued the evidentiary quality the use of analysts forecasts that point While the use IBES long term growth fore cast data has spread quickly since their introduction, questions remain about the appropriateness use the reported consensus measure. Morin (1984) has suggested most that reliable "one could forecasts decide and then which a confine analysts the make analy S1S those forecasts" (page , although goes on to note that approach securing the may b track e impractical records due the the difficulty individual forecast agents. Litzenberger (1985) suggested that only analysts who have been recognized their investment clients providing superior information, such as those analyst who suggested that the median the individual forecasts use the consensus measure as opposed using the mean forecast because the median ess influenced outlying and, presumably , 1 ess influential opinions about the growth prospects the stock. Those opposition the use of security analyst or the analysts' investment forecasts houses t have hey argued represent that are the often friendly the firms whose earnings are being regulate and if would, they therefore, felt they bias could their growth influence forecasts outcome upwards author zation rate of return level Still others relying upon anecdotal evidence, dismi the usefulness the foreca because their poor forecast accuracy More complaint than criticism observation analysts that are the not precise generally forecasting known. methods Because used proprietary nature the analysts' services they rarely acknowledge how they actually about making forecasts. reasonable assume, however, that they often begin with historically based extrapolation and then supplement the that industry information or the with company their under private analysis. knowledge This consi stent with some results Chapter where the correlations historically based growth rates analysts' forecasts are shown to be generally positive but Finally , during the initial period introduction the IBES forecasts into regulatory arena, the IBES values have tended to be greater than the growth estimate values derived from storical time seri es. This condition created a clientele of cost of capital witnesses who opposed the use of IBES values apparently because the security analysts' forecasts generated cost of capital estimates that were higher than the cost of capital estimates produced historical growth estimates CHAPTER TWO THE THEORETICAL THE ROLE FORMATION OF SECURITY OF INVESTOR ANALYSTS ' FORECASTS EXPECTATIONS .1 Introduction Most existing research that important the study security analysts' forecasts empirical nature. This apparently so because existence security analysts their longrun equilibrium employment and obvious demand their costly servi ces provide sufficient economic justification scientific observation and analyst without the necessity establishing formal theoretical basi noted Stanley, Lewellen, and Schlarbaum (1981), The question payoff from whether devoting there resources truly a producing those been [security addressed analysts'] n a number outputs occas , however, ions has the literature date are of finance decidedly . [and] the reviews mixed. Clearly, large q directly individual quantitiess through investors this >scriptior are paying research, is to i] either investment sory commissions though private services charged. product enterprise characteristic economy, thought indirectly . Thus, it the appears demandwhich, IS be not generally possessed item having no value. (Page Thi observation, however, inconsistent with advi reflect perfectly instantaneously available information. firms, This implies industries, the that a economy analysis cannot individual contribute returns, and therefore such analysis, while having a cost, has payoff. Further, rational markets characterized strongform efficiency, security analysis would cease exist. When taken logical extreme, strongform efficiency implies that prices are fully revealing information, and therefore, investor expectations are endogenously determined, conditional only upon the pri ces themselves. other words, information like security analysts' forecasts which comes from an exogenous source other that security prices would play no theoretical role the formation investor expectations. This support chapter the is concerned function with of security developing analysts theoretical as producers useful information within efficient market context. Section 2.2, the notion market efficiency expanded allow exogenous information such security analysts' formation models forecasts investor growth potentially expectations. incorporating diversity impact Sections and opinion and information specification production the are consensus derived expectation that allows way that specifically demonstrates why the expectations of wealthy, basis the analysts' observation forecasts may that diversity positively security related the riskiness securities. Section 2.6, simulation analysis using empirical estimates the relevant parameters reported attempt quantify weight classes market participants formation the consensus expectation. A Model of Market and Information Efficiency Production Fortunately, the working security analyst concerned about the longterm viability of her job and the empirical researcher with significant data to analyze, the strongest form the efficient markets hypothesis been generally rejected. For example, Grossman and Stiglitz (1980) , have demonstrated under plausible conditions that even theory when prices that cannot reflect information perfectly costly information obtain. keeping with Akerloff (1970), they show that price system were fully informative, there would differences expectations (that expectations would determined endogenously from prices which are freely observable market participants), and there were differences expectations then there would trade, and markets would collapse. trading their endowments, no trading would take place. alternative, Grossman and Stiglitz have constructed an alternative notion of market efficiency that allows some private information production and some endogeny information prices. Competitive market efficiency viewed process instead fixed equilibrium, where the force driving prices toward their efficient level the their prices production model only of an private equilibrium partially information. degree reflect the sense, disequilibrium: information investors who choose become informed, there may always incremental gains acquiring private information. The following presents stylized version the GrossmanStiglitz model. There are two assets, one safe and one risky. risky asset has uncertain return, which depends random variable, which can observed cost, and another, unobservable random variable, so that K Both and are independent and normally distributed. Knowing reduces but does eliminate the risk associated with the asset. Some investors choose become informed about therefore their per capital demand, will depend both the price asset and u, Di=Di (P,u). Demand assumed increasing decreasing The per capital demand the uninformed, , depends only on P, Dj=Dj (P). Equilibrium each period requires that supply, equal demand f[Di(P,u) ] f) [Dj (P)], where the fraction the individuals who are informed. Given these basic conditions it follows immediately that the uninformed can infer there are other sources uncertainty the model fixed supply and deterministic demand). That since the informed will exhibit higher demand associated with higher values corresponding there any price. will precisely This price one system fully revealing, conveying information from informed the distribution uninformed, given the since same the the conditional conditional distribution of K given However, additional sources uncertainty are admitted (e.g. stochastic demand and uncertain supply), prices will convey some but not information. That may when also high may be due be because supply the high, risky but ass possible values The price system conveys some information, because average, when high, return high are correlated), but the price signal noisy that and not convey same information about This outcome leads demand information production about Note that when one informed, price system does not convey any information, and value incremental information about high. other hand, when almost everyone informed, the price system with very precision informative, small. the The result value knowing equilibrium which the price conveys some information but does fully reveal information. The fraction investors who opt become informed contrasted with those who infer something about the information from prices) determines how fully the information reveal Further, equilibrium would predicted that the marginal informed investor equal finds the expected expected utility utility being remaining uninformed. These results provide form market efficiency efficiency, that where weaker expectations than are d pure determined strongform completely endogenously. Strongform efficiency not appealing information. other hand, these results provide escape from complete exogeneously formation expectations, which would not be rational pri ces reveal some useful information. other words market characterized prices that are only partially revealing , an individual will utilize endogenous variables such pri ces forming expectations, because benefits from the bits impounded information that have been collected others. the same time, because prices are not totally revealing there remains incentive This function formation otherwi to collect argument private investor efficient. question private creates whether information. theoretical information expectations then security production market becomes analysts that empirical outputs the information outputs other agents methods better explain the actual structure prices. The Role of Consensus Expectations Although theoretical justification the for security analysts producers private information) the formation investor beliefs expectations has been established, still necessary show that security prices might actually imbed r.,%a nen el 'mn ellrnr r nrtr l a 1 4a 1 19 4 1, a n 1 airal , in CkV 1I h Although individual investors independently in holc arriving i deci sons their the individual observed buy market sell, price stock reflects the consensus view investors regarding future growth. Therefore, 1 is embodied argument investors consensus market depends do actually analysts' pric es. the use fore Or course, assumption analysts forecasts casts that and market However, majority forecast numbers c adequate forecasts until its valuation analysts. The prices is not are based required investors information: ,f large financial , then t market and, (Page purpose on these that utilize there institutional backing, hey price hence thi will who are forecasts or even analyst suffi investors use trade reflects , the their the cient , with analysts' security intrin sic foreca section develop theoretical underpinning seemingly plausible argument. begin thi analysis, assume, addition the conditions the GrossmanStiglitz model the prior section, that there only one source information about thi case, would highly redundant inefficient any investor, other that the first, become informed because they would receive the same piece information. With only one source information, the GrossmanStiglitz model reduces polar example asymmetric information, investors are either informed uninformed, but there are degrees informational accuracy diversity beliefs. the GrossmanStiglitz model prices can not aggregate diversity beliefs expectations, simply because that order obtain role consensus beliefs, first necessary construct richer model prices and the formation expectations that incorporates both asymmetric information and diversity of opinion, and yet, still retains the notion of market efficiency. imposing structure of preference functions over the marketplace and allowing investors engage process acquiring private information beyond that contained stock prices, possible derive analytic expression the consensus expectation and determine the necessary conditions that would embed that consensus into the market clearing price. Before beginning development such model simple example will used establish where the analysis should lead. First , assume that market composed two investors who are identical respects except the following. One investor has formed expectation say, growth dividends, over a highly optimi stic information set, The other investor formed her expectations over highly pessimis 1This The analysis analysis is cas similar t in t erms that of of the Verrecchia expected (1980) rate c return risky expectation. uncertainty growth expected rate those then rate security ; assumed and that expectations would return a . with the the is variance primary the ar appropriate t rn expression 0 that source iticipated replace expected OYT a n LL ,,,'1 E LLI ~L ~L ~ 1L ~L 1 L A information set, Assume further, that trading between the two investors results price that reflects "average" expectation. The average information the union of 0 and Next, allow entry third investor who knows information The third investor clearly better informed than the other two since his information the contains the relevant bits information each others. same time , there way can earnan excess the return equilibrium from this price informational been determined advantage on the because basis consensus belief. this notion pursued. informational Rubenstein (1975) efficiency has that suggested, necessary and sufficient condition informational efficiency information that fully individual reflected perceive prices. that In other of his words, even investor possesses additional information compared the information possessed other individual market participants there will not possibilities gains his informational advantage, his additional information reflective the consensus expectation. However, also possible that the optimistic investor held a vastly superior expectation, the sense that had devoted significant time and expense , A, process between those two investors would take place. Instead, driven superior knowledge, optimistic investor could buy the security from the pessimist bargain price and earn excess returns. Therefore, critical condition the market clearing price reflect consensus expectation that inve stor have "better" consensus. information That ex than that ante, contained informational the effi ciency obtain, the consensus expectation must least accurate any individual' personal expectation, will possible that investor capture excess returns from private information. A Model Diverse Opinion of Information and Consensus Acouis Expe ition stations The analytic following framework notation examining used the role develop the consensus expectations determining equilibrium pri ces: the periodic rate return risk free security. .s the e: security is the p expected before rnor periodic private expected rate return information value held the obtained risky 1. It investor the risky obtained variance security the expected before rate private of return on the information the security aL 1.. .6. a expected periodic indicated n  a .8 a  rate the *a trh return private J1~ a I aI  the sky information s4c A ~ nl  k L obtained sample o investor the variance f information. investor return s posterior on the information. expectation risky It with is the belief security formed private about after comn expected obtaining ] binina the  J rate private prior information. investor the expected s formed private s posterior rate belief return combining the about i the prior the risky belief variance security. with the information. Ui (W) investor s utility function of wealth, investor risk aversion PrattArrow It is coefficient absolute defined U" (Wi) U' (Wi) where ' and " denote first and second derivatives the utility function with respect wealth, respectively. the number in acquirir of sample ig private observations information. taken investor P is the equilibrium price the risky security. C(n) the function cost of of the obtaining number o private information observations taken cost function assumed common investors. the (unlimited) supply the risk free security. the fixed supply the risky security. investor' DiR DiK investor demand the s demand risk the free risky security. security. the true but unknown mean the distribution random rate of return on the risky security. the the true random and u rate known variance of return on the the risky distribution security. Investors enter the market with unequal endowments wealth, They are offered the opportunity purchase either the risk free security, or a risky security, The the risk free end security some offers future certain period. Before return trading information acquisition activities begin, the random return the risky security believed investor normally distributed with mean return, ' and with variance, Before opportunity engaging acquire trading, additional, investors private have information about the risky security. The information acquisition process will described sampling process, with samples drawn from normal probability distribution. This additional information characterized sample predetermined size observations, Xil, *.,in , which are known independently and identically normally distributed with mean, and variance, Under the conditions described above Raiffa Schlaifer (1961) have shown that investor i will have posterior (after obtaining private information) beli that the rate of return on K distributed normally with 3In acquire more descriptive information from terms, the security investor analyst A at might some     first dollar S 3 3*L*   1 ~II _I ^_ __ __1  __  mean variance, where following definitions apply: nik" where t =1 (ii.) and (iii The posterior expectation weighted average the prior mean the sample mean, with the weights being the reciprocals distributions. variances The weight received the the the sample two mean also depends size the sample. Thus, amount more of sample influence information the increases, sample the results. posterior The mean reciprocal the posterior variance the sum the reciprocals the variance the prior and sampling distributions. This implies that the posterior variance smaller than either the prior sample variance. other words, there ess uncertainty posterior distribution than either the other two. Investor i wishes to maximize her expected utility future the wealth posterior choosing expectation holdings ns forme of R and d over K based her upon private sample observations she takes, the more strongly held will be her beliefs about the expected rate of return. statistical sense, the smaller will her posterior expectation information the costly return variance. obtain. However, assumed that that the cost acquiring information can be described the function, where increasing twice differentiable Thus, formal problem facing investor 1 is Maximize (ni,DiR, DiK) U(Wi) dF (kis2i)dF(k,s2) m K subject to Wi = DiR +PDiK+C(ni) assumed that investors have exponential utility functions form ai(W)Wi U(Wi) = ai(W)e tractable closed form solution the maximization can problem explicit because determined formulation well the known which turn consensus economic results belief This property 4The as primarily permits. ;sumption due When of the investors exponential ease have utility algebraic m heterogeneous function manipulation it expectations, I* A n f a  A s an e tIC 1Al t a e Al aT a r1w i n n a 5 nT C(n), exponential utility function constant absolute risk aversion, a3je ai(W) ai(W)Wi ajie or that the coefficient of ri sk aversion independent wealth. Substitution into allows explicit formulation of the maximize ation problem ai(RfDiR + mDiK) Maximize (ni,DiRDiK) aie dF(ki,s2i)dF(k,s2), m K subject = DiR + DiKP +C(ni) The price the risk free security taken numeraire. That price normalized one. Conditional upon value say n*i, optimal holdings the risk free and the risky security can determined from the solution the following LaGrangian equation: ai(RfDiR L(DiR ,DiK aie + mDiK) dF(ki, [DiR + DiKP + C(n*i)]}. Taking derivatives with respect DiR n.K *a * 41A #4 4 ai(W)Wi = ai ,li) EI~n/ 3 *: ' AY~3AY A A A A 9lIl *Y1 expression determined the investor price optimal the risky demands security then given ai(RfDiR /me ai(Rf DiR dF(ki, + mDiK) dF(ki, Integrating and simplifying results  (s2iaiDiK) And rearranging terms results determination individual investor' demand for the sky security  RfP) DiK Summing over investors yields the total demand the risky security  RfP) DKTOTAL Then equating total demand with supply, DKTOTAL allows specification the equilibrium price function the aggregate expectations of all investors the form Vgki + mDiK) SKVo The term, E(VOki can thought type geometric weighted average individual investor expectations the risky security' rate of return, where the weights are the product individual preferences risk and the posterior variance estimate each investor brings the marketplace. Note that constant, and that (Vo thus confirming that those terms are weights and their sum can can be normalized unity. Next, multiply both numerator and denominator 1/V0, and define ais2i (10) Then the consensus expectation can be written Voki (11) Inspection (11) indicates that the expectations investors with smaller coefficients risk aversion (more risk tolerant) will have greater impact the consensus expectation. Similarly the expectations investors with beliefs a smaller variance of returns will also receive greater weight consensus. 5Note that PrattArrow risk 1 ntxWctnrM sai is premium nrnnnr* a 4 equivalent [v2/2] [U"/U functionally and r'nn~r4 huI+ 4 n i r repres *ho Tn the ents 'Tarofc 1 ' C: the same sense that the union the information sets the optimistic and pessimistic investors represented the consensus expectation the simple example presented above, the term Voki also a consensus expectation. demonstrate that this also the consensus expectation that informationally contained efficient a price market, determined sufficient to show that that individual investor has expectations that are more accurate than the consensus. Under Rubenstein' definition market efficiency, sufficient demonstrate that, ex ante, the consensus expectation least accurate any individual expectation. This equivalent showing that no one can earn excess returns from their private information. the statistical framework this model, determination the relative accuracy respective information variances equivalent individual' comparing posterior distributic consensus the expectation. variance The the formal distribution condition the stated more formal justification using the variance as a measure (1948) ths nnti nr informational Thiel f nf (1971) accuracy . For i n fnrmnart i nnAl can nonsymmetric sntrnnv 1SC5 found Shannon distributions, mnre general  I follows: Var s2i, Si' to I. (12) Noting that the variance of ki simply and assuming that each investor' expectation independent other investors' expectations, the variance the consensus expectation given Var (13) Which must less than equal the variance individual investor' sterior distribution expected returns for market efficiency obtain. Inspection (13) indicates that the variance the consensus expectation will tilted favor variances investors with small coefficients risk aversion. This because the investors the variance with weight the large given their summation coefficients will risk posterior estimate greater aversion. than And general, investors better the with (more condition less precise, aversion lower v stated risk variance) (12) must assessmei hold, contribute nts toward determining the market clearing price than those investors with greater risk aversion. basic i nriiui iuinal assumption the analysis that Sn o ncr ~n i any ri 1 *nty~car h1 avhi ki1 + ah rrll11" among investors, those with more wealth will ess risk averse than those with lower wealth. Thus, smaller coefficients aversion should, general, associated with investors with greater wealth . These ess risk averse investors will, most likely, allocate proportionately more their wealth investments the risky security, which turn implies they will hold larger absolute amounts the risky security. this indeed reasonable depiction the characteristic market participants, investors with greater risk tolerance (lower risk aversion) may expected safeguard their greater investments risky assets demanding more information about those assets. The implications thi analysis are ear, there increasing cost obtaining information, then degree of risk aversion will determine how much additional information investor acquires. situation, most risk tolerant investor will acquire the most 7Following thi economic logic, Verrecchia (1980) shown the that under development condition the the demand information) risk aversion. assumptions this weak equivalent model, inequality information I decreasing But this (the the size, function condition the coe simply those formal made suffic to hold ient that sample ffi the cient same saying that investors act their own best interests protecting seeking j . their acquire S, investments private the risky information security beyond that  0 f [ ' k I A additional information. Thi further implies that most risk tolerant investor will, in general , be best informed the sense that holds the smallest expectation the variance expected returns the risky security. Finally, thi implies that the market clearing price and the consensus expectation that impounded will weighted favor individual expectations the more informed inves tors with greater risk tolerance, presumably the large institutional investors with large wealth endowments. And from thi theoretical perspective, the bases the intuitive arguments Brigham, Vinson, Shome (1983) appear to be justified. .5 Divergence of ODinion as a Risk Factor Several authors, including Miller (1977), Cragg Malkiel (1985) (1982), have Peterson noted that and Peterson market (1982) where , and Varian diverse and heterogeneous opinions aggregate determine prices, measure the amount diversity may important determinant security' riskiness. this observation correct, and accepting the theme this thesi that security analysts' forecasts are important determinants investor expectations, then follows that measure that might highly correlated with SA.. . 1 ~ i _* * I^ L m __~~___ * the review the empirical literature that follows Chapter Three, this topic examined. this point, Section however, the model goal was somewhat developed more that abstract. I demonstrates under plausible stock prices conditions, that equilibrium reflective determination consensus individual expectations. That model is now to be extended way that permits prediction how stock prices will respond the diversity the consensus expectation increases. More specifically, can shown comparative static analysis that the equilibrium stock price declines when the diversity the consensus Increases, then increasing diversity can theoretically associated with increasing risk. The first consideration this analysis determine how change the individual posterior variance estimates expectation and u impacts Itimately the the diversity equilibrium the consensus stock price. Note that equilibrium, the price given supply the risky asset and known value the risk free rate interest, largely function variables, and where a function and s2i, VOSK (14) Recalling that and are the parameters the posterior distributions of expectations and are determined under the definitions given [iii.] allows a writing as follows: i + ni( Clearly increase information the , leads variance increase sample the posterior variance as shown ds2i ds2" i(ni) i(ni)) similar fashion, increase the prior variance for a given sample variance and sample size would lead Increase the posterior variance Thus, general, any increase the uncertainty the prior beliefs diminution the quality private information will lead increased uncertainty about the posterior expectation. This would turn lead increase given dqi aiV0 ai2s (V0)2 because Because expectations terms the are are weights the rec. positive applied iprocals and the the aiVo > ai individual return an increase leads decrease the weighting . For xed ds2i expectation Thus , in aversion will lead almost and reduced trivial increase sense, the equilibrium constant individual price. risk posterior variances that does not alter the individual beliefs about the posterior mean, the stock price will unambiguously decline. examination (13) indicates that increase will also lead increase the variance the consensus distribution. Thi because the consensus variance will directly increase with increases in s but will only indirectly decrease through proportionately smaller decreases the weights Under the assumed structure preferences and distributions expectations, beliefs . consensus. increase eads Therefore, the increase either dispersion the event, individual dispersion increased individual uncertainty increased consensus uncertainty leads lower equilibrium stock price. The analysis becomes ess clear when the assumption constant case explicitly absolute longer and risk possibW therefore aversion to evaluate a closed dropped. e the in form that Itegral expression the consensus expectation and the variance the consensus can not derived. Heuristically, the coefficient becomes function expected terminal distribution. Thus, the assumption constant absolute risk aversion dropped and no restrictions are placed the manner in which posterior distributions can change, analytical prediction the risk effects increasing d If changes diversity the of opinion posterior can be made. distributions returns are restricted changes that alter the posterior variance but leave the posterior mean unchanged, some additional assumption implications of constant can absolute obtained risk relaxing aversion. begin, redefine =(ai(wi) i)/V0 , where now Zai(wi) Note that now assumed function terminal wealth and will more generally, constant value assumed previously. obtain decrease find his posterior necessa variance, acquire more investor sample will observations. However, with increasing marginal cost obtaining that information, expected terminal wealth will decrease with each additional unit information obtained. coefficient risk aversion increases "too fast" with 8At this consensus under point it it expectation conditions assumed that equivalent constant risk the to basic the aversion. I form form That derived the consensus weighted generally at least average true determination the analysis of can can the also a positive individual derived consensus beain from function expectations. from the g That Litner' expectation. the Pratt This (1964) geometricc this is (1967) part of or Arrow decreases terminal wealth, possible that reductions aversion. the other variance words 4 will even not though offset h the increased returns risk the security become more certain, the investor becomes proportionately risk averse. this the case, stock prices will decline with reductions the consensus variance instead rising. that event, change the the diversity the consensus expectation cannot be directly associated with Algebraically, ai(wi)s2i and letting = ai(wi) i + YO, where Eaj (wj)s2j, then ai(wi) ai(wi) i + Yo And letting indicates ai(wi) i + YO (15) ai(wi) Defining this way allows a more direct inspection the the changes that occur when a variable takes new value. effect the weight each investor brings the consensus expectation. The goal to determine how changes s2i that are brought about increased acquisition information =1/qi previous analysis, ai(wi) will also change with but generally in an opposite direction from s2 i Utilizing (ri)ki. given (15), The rewrite total change the consensus differential the number the sample expectation expectation observations acquired d(ri) ds2mi ds2 \ dni/ d(ri) dai(wi) dai(wi) dwi dwi dC(n) dki nidni {dni dC(n) dni dni/ (16) Manipulation (16) indicates that order a change brought about change offset the countervailing effect change ai(wi), that the consensus expectation increases, the following must hold as a necessary condition, ds2i (17) ai (wi) where the first derivative the coefficient risk aversion with respect wealth, the first derivative the information cost function with respect and dni has been normalized unity. From Pratt (1964) Arrow (1971) well known that ai(wi) positive. Further, positive economically acceptable, and the left hand side (17) negative. Therefore, (17) will always hold positive. The a'i a'1 quadratic utility function exhibits this property The negative exponential utility function has will fulfill such as the the requirement logarithmic and . For power functions functions, with certain additional restrictions must be imposed ensure that the consensus expectation will increase with increased sampling that brings about decreased variance the expense decreasing wealth. These restrictions are relative and somewhat interdependent, and may, hold either singularly some combination: the incremental cost of additional information small the large. sample Note data that informative a'i/ai (wi) that reduces logarithmic and power functions , which turn will very close zero most investors with ese types utility functions general, finance most literature utility supported functions empirical assumed studi the will 9See, example, Alexander and Franci (1986) page SCUSS functional forms assumed the p: utility properties functions various 10The ai(wi) The g ai(wi) =1/ generic w4. and eneric  1/wi. log a'i= positive The g and * eneric function, l/wi2 , power a'i=(l U=ln(wi), therefore function, c)/wi2 negative power indicates wi)= a'i/ai( U=wic, therefore function 1/wi indicates a'i/ai (w) , U=wi ,  n  , so therefore, 1/wi =(lc)/wi, ( I I exhibit the properties of risk aversion a manner which will cause (17) hold. summary, from theoretical perspective, increase the diversity the expectations individual investors may increase decrease equilibrium value the security utility prices function. depending However upon , the the most likely effect to decrease security pri ces A Simulation Analysis the Weichtina in the Consensus Expectation Utiliz equation (11) , the algebraic expression consensus expectation that was developed Section values and risk taking aversion point from estimates the studi the relevant Blume Friend (1975), Grossman and Schiller (1971) , and Litzenberger and Ronn (1986), and point estimates security Ibbotson returns and and Sinquefield associated (1982) variances studi from , simulation analy the m ses the market individual clearing consensus investor' expectation contribution were toward performed. Investor expectation the return hypothetical risky security was generated taking the simple mean twenty random observations drawn with replacement from 11The empirical res each Blume and Friend (197 Gro ssman I, nnrt and Schiller (1971) and Lit zenberger and Ronn   *1 .1  r e!1  .u 2  I ,I i, I 4m . Ir _ normal distribution reference to Ibbotson with and parameters Sinquefi established eld, ki= Sxin/20 Investor coefficient risk aversion was obtained coefficients the random based above draw from references studies. distribution the Several empirical different such results types distributions the risk simulations, aversion including coefficients were distributions utilized that were symmetric about mean coefficient and those that were skewed toward lower and higher values. Next, estimated posterior variance was calculated variances for were each expectation. ranked from this point, smallest however, largest and disassociated from any particular expectation. The smallest greatest variance risk was tolerance assigned coefficient, the and investor with until investor with the lowest risk tolerance coefficient was assigned the greatest measure variance. This keeping with the inference the self interest nature the model. Using aversion consisting different coefficients types with 10,000 distributions hypothetical investors, risk markets numerous simulations were performed. The consensus expectation weights, shown (11) are the product individual variance aversion estimates coefficients multiplied Normalized by to the their individual total risk weighted sum. The remarkably impact market results stable, the participants the indicating choi simulations little stributions For example, were differential number representative simulation indicated that the individual expectations the 40 percent investors with the highest risk aversion contribute slightly ess than percent the weight towards the consensus expectation. Whereas , the individual expectations the percent investors with the least risk aversion contribute almost percent the weight the consensus expectation. Noting that the simulation results not account poss differences wealth and the trades the market participants, conservative the terms results the true are impact most large, likely ris tolerant investors actually have consensus expectations . As crude rule thumb, gen erally stated that percent stock market activity attributable institutional investors. that ratio mapped into the simulation results, would indicate that more than percent the weight the consensus CHAPTER THREE A REVIEW OF THE EMPIRICAL LITERATURE Introduction The existing empirical literature and research that important study security analysts' forecasts generally fall into two categories. The first topic, which literature of short1 covered that term examines values. Thi Section security research the analysts' can empirical forecast decomposed into three distinct types comparative studi , (1) evaluations shortterm forecasts against naive extrapolations historical time series evaluations security analysts' forecasts against forecasts made management, and evaluations shortterm forecasts among security analysts. Often , thi research accuracy characterized security tests analysts the other forecast foreca agents or methods, the diagnosis forecast error or the influence of unexpected changes shortterm forecasts share prices. literature There thi extremely area; therefore, large this body review concentrates on the more recent, representative article es. avi study, includes the examinations security anal forecasts longterm growth. contrast studi about resear shortterm fc ch attention, recasts, fact thi most area likely has due received the little limited types and small amount data that have been available analysis The focus section literature review will the work Cragg and Malkiel who have provided the seminal (1968) and most comprehensive (198 examinations long term forecasts and the recent extensions to Cragg and Malkiel. Chapter security individual consensus Two, analysts' fc investor E expectation theory recasts was might expectations developed how incorporated and embedded the ultimately market into into clearing price. This chapter explores the question security analysts' forecasts might important formation keep investor mind expectations. reviewing general literature point security analysts' forecasts, that either one two distinct theori the can actual be invoked formation as a basis their expectations The importance older theoretical views can traced the celebrated beauty contest profe John M ssional newspaper :aynard Keynes investment competitions (1935/1964), may ne .n which likened the cc where those mmpetitors have pick out the prettiest faces from  . _.  why I _ 1 JtL.  A I A  ., I l_ .. ...  _1 _ finds pr likeliest ettiest, but catch competitors, from the same point those the f whom ar of view. which "ancy e he the looking at (Page 132) thinks other problem The theory emanating from this view indicates that more important know what the market thinks expects, say, earnings per share earnings growth will than know precisely what actual earnings growth are realized. Under this theoretical specification, security analysts' forecasts are tested against forecasts from other sources determine which type forecast methodology best explains the crosssectional structure share prices the crosssectional structure price/earnings ratios. The forecast that provides best explanation the structure then inferred representative the market expectation. This view holds that not the ultimate accuracy forecast methods that important but rather how strongly particular type forecast influences the formation investor expectations The more recent theoretical view a product rational expectations literature. Brown and Rozeff (1978) claim that rational investors incorporate into their expectations only the most most useful information which, extension from the definition rationality, the most accurate information. A  I This theoretical perspective _  L_  _ J    _ IL errors produced security analysts' forecasts with errors produced alternative forecast methods date, the empirical results from the tests security distinguish analysts' between forecasts the cannot existence used marketplace dominated investors forming expectations about what they believe the best forecasts future values (rational expectations) investors forming expectations over what they believe other market participants forecasting (Keynesian beauty contest). Empirical results tend indicate that the structure security pri ces best explained security analyst forecasts and that security analysts forecasts tend have the small est forecast error. Note, however, that under theory rational expectations, forecasted values that are derived from best forecasting method should also expected offer the best explanation cross sectional variation price structure, that method used formation expectations. the other hand, theory the formation investor expectations keeping with the Keynesian beauty contest does not rule out security analysts forecasts being the best predictors future necessary values. nor That , forecast sufficient accuracy support neither that theory from implications hypotheses formed under the other theory. knowledge investor e determining the expectations the correct would usefulness model be of the valuable security formation asset analysts' longterm forecasts the discounted cash flow model estimating that the model cost would capital. allow That , a prediction knowledge benchmark measure security neither longterm analysts' growth forecasts observations expectations could actual against measured. expectations which However, nor sound theoretical predictions are possible, thus thi study will necessity rely statistical inference coupled with reasoned economic logic. such, the literature review focuses equally logical assumptions, data sources, application statistical empirical methods, studies . and For resulting the conclusions dual of exi purposes sting this study identify and offer correction methodological infirmities existing studies well extend the lone Malkiel forecast accuracy scriminating (1982). They methodology and consistently necessary a] explains over Although an I not test has claim both been that t produces suggested :he crosssectional extended period sufficient for Cragg showing superior price of the time and that forecast structures would be existence l . * q A * f 'I 1~ L * I t body knowledge regarding security analysts' forecasts of longterm growth. The Emoirical Literature Security Analysts' Shortterm Forecasts 3.2.1 Barefield and Comi skev (1975) This article reports study analyst forecasts oneyearahead earnings per share (EPS) company sample New York Stock Exchange firms. Barefield and Comiskey (BC) analyze forecasting performance relation addition investigate year naive and industry mechanical the examination analysts' ability classification forecasting forecast predict error, "turning points" in a company' earning series. source analyst forecasts, used Standard and Poor' Earnin.s. Forecaster The forecasts are provided Standard and Poor' brokerage houses, and other Wall Street researchers and analysts reported two three forecasts per company was the norm , although the number forecasts varied positively with the size the firm and the volume trading activity . Barefield and Comi sky drew company sample that satisfied December three fiscal constraints: yearend; the the company company was had sted the New York Stock Exchange; and the company was consisted observations, forecasts the next year' EPS companies each of 6 years. Each average forecasts year the were I forecast individual measured a was analyst defined forecasts approximately ten the provide months simple d. The prior the end the respective fisal year Barefield and Comiskey absolute defined value annual the forecast percentage error difference (FE) between actual and forecasted EPS, FEt = FtAt /Ft, where forecast EPSt year and actual EPSt for year They also defined average forecast error (AFE) over the six year period AFE (1/6) FEt. In addition to computation forecast error, BC al investigated analysts ' abilities to predict turning points company' earnings stream over the six year period. For example, suppose that analysts are predicting year overyear positive changes three years, symbolically the predicted series would +++. actual earnings changes turn out two years positive changes follow a decrease EPS, which pattern given then the analysts have failed predict one turning point. reported the crosssectionally following year over forecast their errors firm averaged sample Table Average As Reported Annual Forecast Barefield and Error Comiskey Average Year Forecast Error Average 1967 1968 1969 1970 1971 1972 1967 14.14% 13.92 13.31 14.22 16.07% They also reported average forecast errors industry over the same period: Tabl Average As Reported Industry Barefi Forecast eld and Error Comiskey Average Industry Forecast Error Utiliti Banking Drugs Food/Beverage/Tobacco Other Chemical .49% 6.05 7.71 15.29 Oil Manufacturing Transportation The examination turning point predictions produced the following results Table Analysis As Reported of Turning by Barefi e Point Id and Errors Comiskey Predicted Turning Point No Turning Point Turning a. c. Point 132 67 No Turning b. d. Point 37 164 Cells and represent the two types turning point errors: actually (b), materialize turning s, and point (c) , predicted turning  but point none does occur but was not forecast. The number correct forecasts the sum and or a total out 400. Finally, BC compared the forecasts of analysts the prediction naive, mechanical forecast. The naive forecast change" prediction, that EPSt+I EPSt Utilizing Theil' Ustatistic, where the difference  Ai)2 {Ai2} 1/2 of predicted year actual EPS year for company and the difference actual year t1 and year company Coefficient approaches zero lower boundary when predictions are correct, and takes S(Pi And greater than unity when the predictions are ess accurate naive than model the , BC naive, report no change the benchmark. following Against distribution computed Uvalues: Table Theil' UStatistic As Reported Barefield and Comiskey UValue Number of Companies 0 .26 .51 .76 1.00 1.26 1.25 1.50 >1.50 Total Barefield and Comiskey conclude that fore cas errors forecast security errors analysts management compare favorably reported other with studi They find the average forecast error about percent reported their study about the same the average the percent Financial forecast Analysts error Federation managers 1973 reported study. also note that security analysts are very successful forecasting earnings turning points, having accurate ely predicted the direction of change almost 75 percent time. comparisons against naive, change" predictions , security analysts forecasts were more nn '*/*i' v +A aiIm Eamrn% nA mha7r t,,+ rrhmn~~~ dE kY  , ^^ I I I I comparison decline and that more analyst sophis forecasting ticated, performance mechanical model might were employed as a benchmark. .2.2 Bas Carev . and Twark (1976) Basi , Carey, and Twark (BCT) consider two questions forecast accuracy: How well does management forecast EPS? What the relative accuracy security analysts' forecasts as compared the forecasts of managers? From the Wall Street Journal, BCT gathered annual earnings forecasts made managers over the period 1970 to 1971. ese forecasts were of four general types: . Point . Range estimates estimates of EPS EPS. Point from the estimates previous year' percentage s earnings. Increases decreases Range from the estimates previous year' percentage Earnings. increases decreases the forecast was made the form of a percentage change, the BCT computed percentage the the dollar prior EPS year' forecast EPS. the applying forecasts were the form a range, used the midpoint the range the point comparative estimate. accuracy order managers construct and analysts test , it was also required that analysts forecasts  nan .1. 'tw C~ a  lfcI k * ___ __ ~ A *L ; r CkA <'/ an rl w rr LnA were able construct sample firms having necessary data. The tests designed BCT actually address four hypotheses regarding forecast accuracy: Forecasts for utilities are more accurate than those nonutilities. Forecasts firms are Exchange more listed accurate firms.3 New than York Stock those Exchange American listed Stock Company than those (manager's) of security forecasts analysts. of EPS are more accurate 4. Forecast approaches accuracy the end improves of the the date accounting the period fore when cast the actual results are computed. order following test measures these hypotheses computed both , BCT the utilize managerial forecast and the analyst forecasts (Forecast  Actual) Mean Percentage Error Actual Forecast Actual Mean Absolute Percentage Error Actual (Forecast Mean Square Percentage  Actual) Error Actual considering the simple mean percentage error, BCT are able determine the average direction forecast error and considering the mean square error, * outliers are given proportionately more weight the final analysis. Average representative results the BCT study are shown in the table below: Table Representative Forecast Errors As Reported Basi , Carey , and Twark Mean Mean Absolute Mean Squared Percentage Error Percentage Error Percentage Error Utilities NonUtiliti NYSE AMEX Firms Values errors columns security .005 .095 .018 .211 .060 under .003 .134 .029 .303 .088 columns r company labeled S analysts' .045 .131 .065 .231 .101 labeled forecasts are the .052 .185 .088 .321 .138 are and average .009 .072 .016 .172 .050 the values .009 .123 .025 .293 .083 average under errors forecasts. After computing the error values, BCT rank ordered the errors, and created cumulative distributions error values Using the method stochastic dominance, forecast method was claimed dominate more accurate) cumulative distribution function was never ess than that of another, competing forecast method and was greater than the other method least one point. order dominance determine statistically the significant distributional , BCT employ KolmogorovSmirnov two sample test. general, BCT find a ,. a4.a anae anf  4a t  p1rI ~ Ckrn Ckh*n1./. CklrC ~~I~~~~LI~CA ~ AIIIYI ~ YLII ~yA 'III~LYA security analysts but the difference not significant. Finally , to test Hypothesis BCT correlat mean percentage errors with the length time between publication the forecast and the reporting actual results. They found that both company and security analysts forecasts showed significantly smaller errors the nearer the actual reporting date the fore cas was made. For example , the average correlation coefficient between the mean percentage error company forecasts and the length time until actual results were known was .275, which stati stically significant .001 level Bas company analyst errors Carey, forecasts Forecasts and and were both stochastic Twark conclude slightly on the dominance better basi criteria. that than size Furth average security average ler they find that both companies and security analysts forecasted for utility better than nonutiliti , and NYSE listed firms better than AMEX listed firms. Brown and Roz eff (1978) Arguably the best and most to date the studies security analysts' shortterm forecasts , Brown Rozeff (BR) examine relative forecast accuracy i, proxy for the average forecast security analysts, use primarily the published forecasts the Value Line Investment Service. The study examines several forecast horizons Their choice horizons reflected considerations microlevel information obtained security analysts often impacts earnings projections one five quarters ahead, the effects on corporate earnings of changes fiscal and monetary policy often take eighteen months wind through the economy and the available published forecasts are mainly for short horizons. They chose investigate point estimates quarterly EPS for forecast horizons one five quarters advance, over the period 1972 1975. Specifically, they took forecasts several points time that were conditional the knowledge different sets past results. For example, the the year 1973, they investigated the following quarterly forecasts: Table Specification of Forecast Horizons As Employed by Brown and Rozeff 1 Quarter Ahead Quarters Ahead Quarters Ahead F(73Q1 F(73Q2 F(73Q3 F(73Q4 72Q4) 73Q1) 73Q2) 73Q3) F(73Q1 F(73Q2 F(73Q3 F(73Q4 72Q3) 72Q4) 73Q1) 73Q2) F(73Q2 F(73Q3 F(73Q4 72Q3) 72Q4) 73Q1) Quarters Ahead 5 Quarters Ahead F(73Q3 F(73Q4 72Q3) 72Q4) F(73Q4 72Q3) that had the necessary earnings forecast data published Value Line. addition those constraints, was also necess ary include only firms that had available, public shed source quarterly the period 1951 through 1972. This time series historical data was necessary implement the BoxJenkins technique. insufficient earnings data utility were excluded from the sample population. In addition the evaluation of quarterly forecasts also annual investigated forecasts annual were forecasts obtained EPS, summing where the the four quarterly forecasts that were conditional on knowledge the prior year' For example, the annual forecast 1973 the sum F(73Q1 72Q4), F(73Q2 72Q4), F(73Q3 72Q4), and F(73Q4 72Q4). The BoxJenkins technique makes very effici use the available data. Under the BoxJenkins procedures , BR estimated different forecasting model each the fifty firms their sample . In implementing BoxJenkins, the analyst chooses model structure from among numerous alternatives that satisfies one more predetermined diagnostic conditions such the structural form with highest Rsquare, most significant tstatisti and forth. making priori assumptions about the process that generates EPS, the BoxJenkins approach researchers. effect, the BoxJenkins technique selects the best forecasting model available given the historical data utilized, other words, BoxJenkins lets data speak itself. noted earlier, the source security analysts' forecasts were the quarterly EPS forecasts Value Line. The measurements these forecasts were taken way that made the historical information available the security analyst approximately coincident with the data available the BoxJenkins forecast method. test the relative accuracy the two forecast methods, employ the Wilcoxon Signed Ranks test. For each forecast period, forecast errors from each method are paired company. The members each pair are reduced to a single observation taking the absolute differences the assigned paired ranks errors. from Next, these to n according differences the relative are size the actual difference. difference Then, the dependent errors, upon the the rank sign given the the same sign. Finally, a test statistic computed ] Rank SRank where the ranks and the squared ranks are summed over companies for forecast horizon thus the critical region can be read directly from a table areas the normal distribution. reject the hypothesis that the BoxJenkins forecasts are more accurate than Value Line' forecasts requires Tvalue greater than 2.326 the percent significance level and Tvalue greater than 1.644 the percent significance level. Brown and Rozeff report the following Tvalues the quarterly forecasts: Table TValues Associated As Reported with Brown Forecast and Errors Rozeff Forecast Hori zon (Number of Quarters Ahead) Year 1972 1973 1974 1975 1.75 2.48 1.16 4.09 3.34 1.45 1.62 1.04 0.22 3.93 0.92 0.08 0.45 , the Value Line forecasts were more accurate comparisons, and stati stical significance occurred 11 of those For the annual forecasts, report Wilcoxon Signed Rank Tvalues 3.45, 2.17, 0.61, and 1.28 years 1972, 1973, 1974, and 1975, respectively. Thus, based the BR analysis Value Line' forecasts were more accurate than the BoxJenkins forecasts each the four years, and were significantly in 2 the four years Brown and Rozeff provide strong conclusions based their analyses. The following tend to capture the essence significantly seri model better The predictions statistically than time significant experiments the remainir Wilcoxon t additional overwhelmingly ig experiments :ests favor support the favor the m Value Value Line. majority Line hypothesis In the , providing of analyst superiority. If market earnings follows tha forecasts sh earnings exp expectations, t the expectations best used lould ,ectations. our are available measure rational of Given evidence rational, earnings market market analyst superiority analysts firm (Page over time Forecasts valuation [anc series should d] cost model be use : of means studi that capital .2.4 Elton. Gruber , and Gultekin (1981) Whil Brown and Rozeff construct explicit hypothe ses about forecast accuracy under the theory rational expectations, Elton, Gruber, and Gultekin (EGG) examine the importance expectations determination share price. Implicitly, the study EGG more keeping with the Keynesian beauty contest than rational expectations. That , irrespective forecast accuracy itself, EGG are concerned with determining the type expectational data that has the greatest influence share price. their tests , the type expectational data that known individual could produce excess returns. acknowledged EGG, the testing expectations the determination share price was poss ible before the development large, consistent data 