IS FINANCIAL ANALYSIS USELESS?

The Proceedings of a Seminar on theEfficient Capital Market andRandom Walk Hypotheses

William F. Sharpe Franh E. Bloch

Edmund A. Mennis Jack L. Treynor

Michael C. Jensen Jerome L. Valentine

Neil Wr(fiht

THEFINANCIALANALYSTSRESEARCHFOUNDATION

10-digit ISBN: 1-934667-13-7 13-digit ISBN: 978-1-934667-13-2

CONTENTS

PREFACE

ABOUT THE AUTHORS

Efficient Capital Markets: A Review of the Theory-William F. Sharpe

Efficient Capital Markets-A Practitioner's View-Edmund A. Mennis

Tests of Captial Market Theory and Implications of theEvidence-Michael C. Jensen

Capital Market Theory and Implications of theEvidence-Frank E. Block

Long Term Investing-Jack L. Treynor

The Capital Asset Pricing Model From A Professional'sPoint of View-Jerome L. Valentine

Discussion of Capital Market Theory-Neil Wrz~iiht

vii

IX

1

19

29

49

53

61

81

THE FINANCIAL ANALYSTS RESEARCH FOUNDATIONAND ITS PUBLICATIONS

1. The Financial Analysts Research Foundation is an autonomous charitablefoundation, as defined by Section 501(c)(3) of the Internal Revenue Code.The Foundation seeks to improve the professional performance of financialanalysts by fostering education, by stimulating the development of financialanalysis through high quality research, and by facilitating the dissemination ofsuch research to users and to the public. More specifically, the purposes andobligations of the Foundation are to commission basic studies (1) with respectto investment securities analysis, investment management, financial analysis,securities markets and closely related areas that are not presently oradequately covered by the available literature, (2) that are directed toward thepractical needs of the financial analyst and the portfolio manager, and (3) thatare of some enduring value. Within the constraints of the above obligations,the Foundation cooperates with other organizations, such as The FinancialAnalysts Federation and The Institute of Chartered' Financial Analysts, that toa substantial degree share mutual interests and objectives.

2. Several types of studies and publications are authorized:

A. Studies based on existing knowledge or methodology which result in adifferent arrangement of the subject. Included in this category are papersthat seek to broaden the understanding within the profession of financialanaiysis through reviewing, distilling, or synthesizing previously publishedtheoretical research, empirical findings, and specialized literature;

B. Studies that apply known techniques, methodology, and quantitativemethods to problems of financial analysis;

C. Studies that develop new approaches or new solutions to importantproblems existing in financial analysis;

D. Pioneering and original research that discloses new theories, newrelationships, or new knowledge that confirms, rejects, or extendsexisting theories and concepts in financial analysis. Ordinarily, suchresearch is intended to improve the state of the art. The research findingsmay be supported by the collection or manipulation of empirical ordescriptive data from primary sources, such as original records, fieldinterviews, or surveys.

3. The views expressed in the publications are those of the authors and do notnecessarily represent the official position of the Foundation, its Board ofTrustees, or its staff. As a matter of policy, the Foundation has no officialposition with respect to specific practices in financial analysis.

4. The Foundation is indebted to the voluntary financial support of itsinstitutional and individual sponsors by which this and other publications aremade possible. As a 501(c)(3) foundation, contributions are welcomed frominterested donors, including individuals, business organizations, institutions,estates, foundations, and others. Inquiries may be directed to:

Executive DirectorThe Financial Analysts Research FoundationUniversity of Virginia, Post Office Box 3668Charlottesville, Virginia 22903

(804) 977-6600

w

THE FINANCIAL ANALYSTS RESEARCH FOUNDATION

1974-1975

Board of Trustees and Officers

David G. Watterson, C.F.A., PresidentBoyd, Watterson & Co., Cleveland

Jerome L. Vaientine, C.F .A., Vice PresidentTexas Commerce Bank N. A., Houston

Leonard E. Barlow, C.F.A., Secretary-TreasurerMcLeod, Young, Weir & Company LimitedToronto

W. Scott Bauman, C.F.A., Executive DirectorUniversity of Virginia, Charlottesville

Gordon R. Ball, C.F.A.Martens, Ball, Albrecht Securities LimitedToronto

Frank E. Block, C.F.A.Shields Model Roland IncorporatedNew York

Roger F. MurrayColumbia University, New York

Jack L. TreynorFinancial Analysts JournalNew York

Ex-Officio

William S. Gray, III, C.F.A.Harris Trust and Savings Bank, ChicagoChairman, The Financial Analysts Federation

Robert E. Blixt, C.F.A.Minnesota State Board of Investment, St. PaulPresident, The Institute of Chartered

Financial Analysts

C. Stewart SheppardUniversity of VirginiaDean, The Colgate Darden Graduate School

of Business Administration

Finance Committee

Gordon R. Ball, C.F.A., ChairmanMartens, Ball, Albrecht Securities LimitedToronto

Leonard E. Barlow, C.F.A.McLeod, Young, Weir & Company LimitedToronto

George S. Bissell, C.F.A.Massachusetts Financial Services, Inc.Boston

Calvin S. Cudney, C.F.A.The Cleveland Trust CompanyCleveland

William R. Grant, C.F.A.Smith Barney & Co. IncorporatedNew York

William S. Gray, Ill, C.F.A.Harris Trust and Savings BankChicago

Robert E. Gunn, C.F.A.Financial Counselors, Inc., Kansas City

Frank X. Keaney, C.F.A.G. H. Walker, Laird IncorporatedSt. Louis

George Stevenson Kemp, Jr., C.F .A.Paine, Webber, Jackson & Curtis Inc.Richmond

Staff

W. Scott Bauman, C.F .A., Executive DirectorUniversity of VirginiaCharlottesville

v

Richard W. Lambourne, C.F.A.Crocker Investment Management CorporationSan Francisco

James G. McCormick, C.F.A.Eppler, Guerin & Turner, Inc.Dallas

David G. Pearson, C.F.A.Blyth Eastman Dillon & Co. IncorporatedLos Angeles

LeRoy F. Piche, C.F.A.Northwest Bancorporation, Minneapolis

Morton Smith, C.F.A.Philadelphia

Raymond L. Steele, C.F.A.The Robinson-Humphrey Company,Inc.Atlanta

David G. Watterson, C.F.A.Boyd, Watterson & Co., Cleveland

David D. Williams, C.F.A.National Bank of DetroitDetroit

Gordn" T. Wise, C.F.A.First City National BankI-I':usion

Robert H. Trent, Project AdministratorUniversity of VirginiaCharlottesville

CF,A.of the

cen tra!

efficient market

financialWithm a mere

has become

and is

foundation or

lTJany Ls.

the

to the very

followed by

believe it will be benefiC!;t! for us tosubject in three dislinct sleps:

en this

lim! tal ions,

ErvIH as,wen),"t :mel sccun

ouldc

and concl usi ons[0

L

We should reView the

used bOlh tocviden ee :mel. research

fULl'

ofthesh ouldFincontributions and lim "",,!,,)U,;:'

3.

!s till eUve

their

e will

Uillquc

;m:l"ernent cxpen

1hat diversi ficatio!1

seeube more successful inand instil utionalexposure to risk. F",empi,'ical research ug,l',e';

portfolio turnovCl'

should be 1m at !'estricte!!

approaches should be considered in developing portfolio strategies andin selecting securi lles which appear undervalued, Undervaluedsecurities, in the jargon of IT10dern portfolio theory, arc securities whichoffer abnormal or excess retums, This is what the E:vIH game is allab Ol! t.

These papers provide us with extremely valuable insights intothese vitally im issues. We are indeed fortunate to have such ,illoutstanding coHee tion 0 I p,lpers presen ted by in ternationallyrecognized scholars ,Inc! pro!csS!OILd financial analysts.

vVe wish to express ;1 warm gratitude to our speakers and severalothers whose efforts made this new semillar senes such asuccess. Specialrecognition is extended to :\11'. Robert D. l\TiJne, C.1".I\., Dr. Edmund A.Mennis, C.F.A" and :vIr. Frank E. Block, C.F.A., who served on thegeneral planning committee; [vIr. Donald W. Jones, C.F.A., Dr. Jerome L.Valentine, C.1"./\., Professor James A. Largay, Ill, and Dr. GastonRimliner, who superbly planned the program and seminar arrangementsin Houston. IS expressed for the generous grantmade by Texas Commerce Bank in launching this first C,1".A. Seminar.Special thanks go to Rice University for its sponsorhip of the program andfor the use of its fine facilities.

I wish to thank the staff for its dedicated assistance in theadministration o!' this project, Mrs. Beatrice Gordon for handling theseminar registDtiol1,Dr. Robert II. 'rrent for editorial supervision ofthe proceedings issue, :\lrs, l\Iary D. Shelton for publication production,and Mrs. Miranda Collins for copy preparation.

LV'. Scot{ Ball1nan, c.F./1.Executive Director

VIll

ABOUT THE AUTHORS

All'. Franh E. Bloch, c.1'."1.

Mr. Block is a partner and Director of Research at Shields ModelRoland Incorporated. He is an Associate Editor of the FinancialAnalysts Journal and a member of the editorial board of The CTA.J)z/sest, and a member of the Board of Trustees of The FinancialAnalysts Research Foundation. Mr. Block is a past President of bothThe Institute of Chartered Financial Analysts ,md The FinancialAnalysts Federation.

Dr. Michael C. Jensen

Dr. Jensen is Associate Professor in the Graduate School ofManagement, University of Rochester. He has published numerousarticles and books, ,md received several io,'ran ts and fellowships,including ones from the Ford Foundation, National ScienceFoundation, and the American Bankers Association. He received hisPh.D. and M.B.A. from the University of Chicago.

Dr. Edmund /1. Mennz:\", CTA.

Dr. Mennis is Senior Vice President and Chairman of theInvestment Policy Committee of Security Pacific National Bank. Hewas a member of the Board of Trustees of The Institute of CharteredFinancial Analysts for six years and served two terms as President. Dr.Mennis is a frequent contributor to professional publications. In 1972he received the Nicholas Molodovsky Award from The FinancialAnalysts Federation. Dr. Mennis is Editor of The CF.A. Dz:,?est and anAssociate Editor of the Financial Analysts Journal. He received his B.A.from the City University of New York, his M.A. from ColumbiaUniversity, and his Ph.D. from New York University.

Dr. William 1'. Sharpc

Dr. Sharpe is Timken Professor of Finance in the Graduate Schoolof Business, Stanford University. He has written four books, includingPortfolio Theory and Capital Mar!{cts (1\!lcGravv-Hill, 1970), and his

IX

his IllllCYVativc uscreceived his Ph.D. in

works appear in theTheprofessionalApplieati ()nsIne I-Ie is

of the Greek

the Fillancial "1'[ative "j and other

Mr, L

Mr. Treynor haseXPOSl1llQ financial analysts to significant

le"Hnn" and stimulating. He iswhich are already

is a member 0 f the Board ofR.esearch Foundation.

As Editor of the Financial /1provided valuable !c;li(krslllOissues and th whichthe author of m,Ul)considered to be classics.Trustees of The Financial

Dr. Jerome L. ValentIne,

Dr. Valentine is Vice President ,md Trust Officer of TexasCommerce Bank. He is an author of several innovative publications,including a book entitled VI,!(I/I!U/IUZUCand an Occasional and CapItalNlarlu:t Theory. Dr. Valentine is a member of the Editorial Board ofThe C. F./L a member 0 f the Board of Trustees () l' TheFinancial Research Fo undati Oll.

Dr. Nell

Dr. Wright is a Professor in tilRice Univers . lIe' a

of Economics andscholar in the fidd of

finance.

EFFICIENT CAPITAL MARKETS: A REVIEW OF THE THEORY

William F. Sharpe

Recent years have seen the rapid development and considerableacceptance of the subject variously called efficient capital markettheory, beta theory, portfolio theory, random walk theory, etc. Alongwith this has come substantial hostility and widespread confusion. Thispaper is designed to provide a basis for a continuing discussion of themerits and drawbacks of this line of inquiry. Modifications of thetheory, criticisms, and empirical tests will be discussed little if at all.Instead, we will concentrate on the theory in its original form. l

Two ground rules need to be established. First, in the tradition ofmodern economic theory, the issue of the relevance of the assumptionswill not be considered directly. The very nature of theorizing requiresthe adoption of unrealistic assumptions, for the real world is toocomplex for careful analysis. Instead, one must abstract those fewaspects that appear to be most important. The test of success in thisendeavor is the consistency between the implications of the theory andthe relevant attributes of the real world. The most important questions,then, are whether the conclusions reached are reasonably consistentwith reality, and how the theory compares with alternative approachesthat are capable of guiding decisions.

Second, it is important to emphasize that in this discussion, onlysubjective estimates of the future, of the type that could be made bysecurity analysts will be considered. No assumption is made thathis toric data processed by comp utel'S are necessarily rclevan t, wi thou tmodification by human beings. Efficicnt market theory is almostcompletely dependent on the assumption that clever, wellin formedanalysts constantly review available in formation and process it inrelevant ways. This certainly requires computer analysis of past data,but undoubtedly much more is needed.

I () d "f" " (h" b" ")" I "1. I" 1 tn e mo I lcatlOn t e zero - eta verSlOn IS (eSCnUeCA In t le paper )"Michael Jensen included in this volume.

2 vVlLUANI F SHARPE

lu ture

th IS that of market . Thisalk" --a term that has un t connotations

Ie in a techn lcal sense. The term "market

and m ore correct. Definition ismarket is fficient if there are many very

cons tan tJy searching for securitiesas this force is operative, when informationit will lead to transactions that will shortly

information . As a result, the

C1 for long from itswhere the latter is defined as the certain present value of

assessed a clever, well-informed

is both morebut the idea < th

vl/ell-in formed

Thewas born asand lS noledifficubri t,

that arc IIlJiSplJLCUbecom es re;IS()lJ;lb ltvcause pnces toprice of a

intrinsic

the uncertain

analyst.

secun

There are, of course, shades and gradations of efficiency. A

hardline view would hold that the rnarket is so efficient that prices

virtually always reflect almost all available information. A moremoderate view \Aimlld hold that available information is reilected

in prices quite rapidly. In either case, the relationship between priceand value refers to the latler as assessed at the time. In retrospect, with

hindsigh t, it is to show that most securities have been"mispriced" in some sense. But this involves information not available

at the time. JVIarket e requires that currently available

information be properly reflected in price.

In the real of course, there arc differences of 0pll1lOn and

differences in circumstances situations, legal constraints, etc.). For

purposes of deriving a simple theory, most of these will be ignored.However, i l is worthwhile to consider briefly the possible interpretationof market in these circumstances.

'-0"""," h ted 0 l in a recen l issue of the Financialcan reasonably take the price of a

at any time as a given. In the absence of restrictions, eachher holdings until the marginal value of

After this everyone would

in the sense that one

same amount to each

investor

each prIceo

agree thal every as

more or one less share would be "worth" the

investor.

There are some needed qualifications to this statement. Most

importantly, institutional constraints and requircments for short sales

EFFICIENT CAPITA L AJA RK ETS: A Rr" VIEW OF TIlE 1HEOR Y 3

sorne differences

for the

n,""ynYJ('(',i" if he

in theif more

m circumstances (taxuseful

mer-priced) in it th,m would

the most rudimentaryto rnmkct swings, tc.).issuc IS not essen tial

to the semanlicists.

lead to a range of' prices over which a given investor should take neithera long nor a short position. Even without this, however, theproblem of' defining "mispriced" securities remains,

An investor t be said to consider a 'ty

or she chooses to invest less than a market-v,tluesecurity', and might be said to consider a securith,m a market-val JS invested.

111 holdings arc atlributablc to dilc constrain ts,

definition might a thatwith a decision to invest more oj'

have been invested had the an

facts about it (e.g" its yield, senFortunately, resolution oj this

material to folIoY'!. Let us leave it

Historical Development

mtl in lhe developmentli,t! tributiol1 or

!em of'Ls -; cst i n1 aIe:; ()r

can be traced back toand J. B Williams.

",'''''LU theory cxplicitlybeen accomplished only

Land

both risk andmethod Cor measuring bOlh,

relurns could be takenwith theinto account in th

constructing dn 'lpppossible fulure lTlurnsreturn be considered,and showed how rclat

Important aspects of efficicn t marketBachelier, Irving Fisher, Graham andHowever, non of these authors constructed ataking uncertain in to account. This task hasin the last 25 years.

Two rn,~ior approaches to the ,liT curren m usc. Themore general is the tim developed by,"-!TO\V ,md Debreu. This is being in the field offinance, crC::lSlll,0; out' or (JJcapiLlI structure, [he efficiency f finan(i~d rnarke etc. However,most work in investments has thus !"

4 WILL/A/vI F. SHARPE

question of appropriate estimates and the manner in which securityprices might be determined in the marketplace.

A series of subsequent contributions increased the practicality ofMarkowitz's procedures. Tobin, dealing with a somewhat different issue,showed that the ability to borrow or lend funds at a riskless rate ofinterest makes it possible to separate the portfolio decision into thedetermination of a preferred combination of risky securities and thenthe determination of an appropriate degree of leverage. Otherssuggested simpli fled III oe! cis 0 f the relationships am ong securities andcomputer algorithms to exploit them. But all this work remainednormative, directed towards actual decision-making by portfoliomanagers, and avoided the Issue of price determination in themarketplace.

The second major phase began in 1964 with papers by Sharpe,Lintner, and l\:lossin. The focus was pCJSltlve, rather thannormative-that devotee! to the question of "what is" rather thanthat of "what should be." Investors were assumed to be equallywell-informed and to be following Markowitz's recommendations. Givensuch a world, what could be said about security prices? What would bethe relationship between risk and return? What types of risk would berewarded and what types would not? The Capital Asset Pricing Modelwas in tended to provide answers to such questions.

The third phase is in process today. Given a market almost orentirely consistent with the implications of the Capital Asset PricingModel, what sorts of policies should an investment organization adopt?In short, what sort of normative rules make sense in the context of amarket consistent with a positive model of market efficiency? A keycontribution along these lines is the recent paper by Treynor and Black.In a broader sense, almost all informed discussion of investment policycan be considered part of this phase.

The remainder of this paper is designed to cover the essentialingredients of the Capital Asset Pricing Model. The approach will be farfrom rigorous, and a number of corners will be cut in the interests ofclarity and simplicity. But hopefully it will provide the desired base forfurther discussions.

The Capital Asset Pricing Model

To begin, we need to concentrate on some holding period. Forconcreteness, assume 90 days. We are going to focus on analysts'

EFFICIENF CAPITAL MAUKETS: RF~ TIiE'OR Y 5

.c.,tax

out of capital

in the an

h

withtreasury biJI would be

terms, but again, toto do v,;ith rea]will avoid the

of investmentrisldess investment,

holdingrse, this is riskless

expectations eoncerl1ln rate of rerurnyield plus price change. To mattersconsiderations, institutional restrictions ongains, etc.

TwoThe first IS

deal in exccss return ,the returnon a riskless investmen 10 To C"lf'''d3U.C

(if ) the in terest rate on,this measure.

When a investment, 11 is rememberthat there is a riskless alternative. l'hus the ;Ictuat return on a riskyinvestment should be ""nn"n'rr! to that ieh could have been obtained

l his usc ful toor below

will use

1'he second investment 1S termed "the market portfolio."

Formally, it represents a portfolio of all available investments, eachheld in proportion to its total dollar value outstanding (at market). As apractical matter, often use a measure such as Standard and Poor'sSOO-stock index as a surrogate. However, will deal v,ith the moreall ,inclusive here.

The Inm-ket portfolio is especicdly 0 t because It representsthe ultimate in attainable diversification. It follows that the riskassociated with the market portfoliu is all unavoidable-it cannot bediversified awayo And this suggests the kind of risk tint is unavoidablewhen consi dering sm stock: the risk that is attrib u table to marketswmgs.

These considerations suggest that it is lIseful to think about theprospects for a stock in terms of a ch(lraclen~\tc lzllCo Figure 1 shows anexample. This is not mtended be oC some that h'L'.;happened. Rather it a ;m about whatmight happen in the future:. I summarized inthree measures'

1.SCeLm

mthat

return on themarket excess

market portfolio

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EFFICIENT CAPITAL MARKETS: A REVIEW OF THE THEORY 7

2. Beta-the slope of the line: the extent to which the analystbelieves the security's excess return will be affected bychanges in the market's excess return. A value of 1 meansthat the stock is average; a value of less than 1, that it isdefensive; and a value of more than 1, that it is aggressive.

3. Non-market risk-the range around the line within whichactual results are likely to fall. This is a measure of theanalyst's feelings about all the uncertain factors that canaffect a stock's return in addition to any influence themarket may have. This includes "business risk" and"financial risk" as typically defined. And it is by far thelarger part of total risk for most securities (about 70 percenton the average).

It is important to note that with this procedure the analyst is notrequired to make an assessment of the likely return on the market.Instead, he or she makes a best guess aboLlt each of a number ofpossible returns on the market (the characteristic line) and indicates hisor ht:r confidence in that set of guesses (the extent of non-market risk).The task of estimating the likely future of the market can thus be leftto others.

Now, what of portfolios? Just as a security's prospects can besummarized with a characteristic line, so, too, can the prospects of aportfolio. In fact, given analysts' feelings about securities, theappropriate feelings about a portfolio can be calculated directly:

1. The alpha value for a portfolio's characteristic line is simply aweighted average of the alpha values of its componentsecurities, with market values used as weights.

2. The beta value for a portfolio's characteristic line is simply aweighted average of the beta values of its componentsecurities, with market values used as weights.

3. The non-market risk is more complex. In general, the morediversified a portfolio, the less its non-market risk. For thekind of portfolio held by the typical open-end mutual fund,as little as 10 percent of total risk may be attributable tonon-market factors.

WILLIANI F. SHARPE

This latter roin t indicates the importance of both alpha and beta.While they tell relatively little about the prospects for an individualsecuri , they tell quite a bit about the for a diversifiedportfolio. Thus it is important to good estimates of alpha and betafor securities, since are the componen ts from which portfolioalphas and betas are fOHnerL

Now let's tum to the matter of prices in an efficient market. Wewill deal with characteristic lines that reflect. a "consensus" opinion ofanalysts. Let's begin wit.h the possibilit.y that t.here may be some bondthat., like a treasury bill, is considered complc tely riskless. Imagine thatit is priced t.o ret.urn more t.han a t.reasury bill. What. will itscharacteristic line look like? Figure 2 provides an answer. No matterwhat the return on t.he market, this bond will give the same positiveexcess return. It.s characteristic line is thus horizont.al and lies above t.hecharact.eristic line for a treasury bill (which coincides with t.hehorizontal axis).

How long could this situation prevail? Not very long, for arbit.ragewould swiftly be brought. t.o bear. Investors would shun treasury billsand l10ck to buy this clearly underpriced bond. Prices would thenchange, under buying and selling pressure, unt.il the two prospects werebrought int.o balance. The two characteristic lines would then coincide.

A similar situation can be described for a risky security. Considerthe one whose characteris tic line is shown in Figure 3. The consensusopinion is t.hat this security has an alpha of -2% (per quarter) and a betaof .8, as well as some non-market risk. Is it underpriced, overpriced, orcorrect! y priced?

Let's compare it with a treasury bill, whose prospects arc shownby the flat characteristic line lying along the horizont.al axis. Treasurybills arc less risky, but if the market ret.urn is high enough, they will beout-performed by t.his secu . It. is not clear which is better.

Turn next to an investment in t.he market portfolio. It.scharacterist.ic line is a 45-degree line through t.he origin, since the excessreturn on the market portfolio (vertical axis) must., of course, alwayseq ual the excess ret.u rn on the market portfolio (horizon t.al axis). Thevalue of alpha must thll be zero, and the value of beta must be one.Moreover, as indicated earlier, the market. port.folio has no non-market.risk.

Now, is the hypothetical security in Figure 3 better or worse th~illinvestment in t.he market as a whole? The market port.folio's return ismore sensit.ive to market swings and could underperform t.he security if

FIG

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EFFICIENT CAPITAL MARKETS: A REVIEW OF THE THEORY 11

the market falls far enough. On the other hand, the market portfoliohas no non-market risk. Here too, it is not clear which is better.

But there is another possibility. An investor could split his fundsbetween the market portfolio and treasury bills in a manner designed togive the same level of market risk as that associated with the security.In this case the appropriate division would result in 80 percen t investedin the market portfolio and 20 percent in treasury bills. This strategywould have a characteristic line passing through the origin (i.e., an alphaof zero) with a slope (beta) of .8; and it would clearly dominate thehypothetical security. Why? Because it would have the same level ofmarket risk, no non-market risk, and offer an expected advantage oftwo percent per quarter, no matter what the market might do. In factthere is an interesting arbitrage strategy for a case such as this: (1) shortthe security and (2) go long the market portfolio and treasury bills. Inany event, no analyst holding the opinion portrayed in Figure 3 wouldrecommend holding the security.

The result is predictable. The security would be subjected to heavyselling pressure. Its price would fall, causing its characteristic line torIse.

A similar argument can be made if a security has a beta greaterthan one. In such a case, however, the appropriate strategy for purposesof comparison requires margined purchase of the market portfolio, thedrawing down of an investor's savings account, or some other action ofthis type. To keep the analysis simple, it is assumed (perhapsunrealistically) that this can be accomplished at a cost equal to thereturn on a riskless secun ty.

In either case, the conclusion is obvious. If the market is efficient,no security will be priced to have a negative alpha in the opinion of awell-informed analyst.

But what about the opposite possibility? Might a security have apositive alpha? Recall that the market portfolio as a whole must havean alpha of zero. But recall also that this is the weighted averageof the alphas of the component securities. have just established thatin an efficient market, no security will have a negative alpha. Then howcan the average value be zero? The ;;;:swer is inescapable: every valuemust be zero.

We thus reach the denouement: in an efficient market, allsecurities will be priced so that in the consensus opinion, theircharacteristic lines pass through the orIgin- -i.e., they will have alphas c11

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32 MICHARL C. JENSEN

its mean in such months, since if that were true all the points in thegraph would lie exactly on the regression line. The vertical distancebetween each point and the regression line represents the error term,ej t' in equation (1 )-also illu strated in Figure 1. The in tercept, a = .018,tells us that we expect Xerox to earn 1.8 percent per month on the average

when the returns on the market are zero. These coefficien ts, thus, havevery simple and intuitive interpretations. Furthermore, we also knowthat the average intercept and slope coefficients for all securities arerespectively zero and one given our definition of the market index. 2

Thus, securities with betas greater than one are more volatile or moresensitive to general market conditions than the average and vice versafor securities with betas of less than one. The market model given byequation (1) can be applied to bonds as well, and Sharpe [1973] showsthat the beta for bonds over the period 1946-1971 was .252. He usedquarterly returns on the Keystone B-2 bond fund and the Dow JonesIndustrial Average to obtain these estimates.

Several other examples of estimates of the Market Model forsecurities with widely different characteristics are given in Figures 2, 3and 4. The time periods used are July 1960-June 1970 or the period oflisting on the NYSE, whichever is shorter. The securities and theirregression statistics are also given in Table 1. As the reader can see theutility and gold stocks represented by Consolidated Edison andHomestake Mining are far less sensitive to market movements (i.e., lowbetas) than Xerox, and Teledyne is far more sensitive (i.e., high beta).

In addition, Figure 5 portrays the market model for a portfoliomade up of an equal dollar investment in the following 17 stocks, all ofwhich are contained in the Dow Jones Index:

U.S. SteelGeneral ElectricInternational PaperAmerican BrandsGeneral FoodsProcter & GambleTexacoInternational NickleJohns-Manville

Eastman KodakUnion CarbideAllied ChemicalSears, RoebuckGeneral MotorsGoodyearInternational HarvesterOwens-Illinois

The intercept and beta for this portfolio are respectively .001 and .672.The major difference between the model as applied to the portfolio and

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36 MICHAEL C. JENSEN

TABLE 1

Illustrative Regression Estimates of the Market

Model Obtained from Monthly Data

R. = a + (1.RMt + e tJt J J j. J

(Standard error of estimate in parentheses.)

"Security" Intercept Slope

a (3.J .1

Xerox .018 .974(.008) (J 70)

Consolidated Edison - .008 .438(.007) (.140)

Homestake Mining .003 .137(.008) (.163)

Teledyne - .015 1.789(.016) (.286)

17 Security Portfolio -.001 .672(.018 ) (.037)

Correlation Time PeriodCoefficient and Sample

Size

.488 8/61-6/70107

.277 7/60-6/70120

.770 7/60-6/70120

.675 6/66-6/7049

.860 7/60-6/70120

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38 MICHAEL C.

the scatter

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individual securitics. Thisthe correlation coefficient of

or 3 that [19711

very noticeable

IS also

the individual secuntiesaround the or characteristicthe flcc!s of diversification-the ermrs arcthan for individual s('cun while the ,',-,i/'n'er,l

of e coefficien for theaveragediversification ffect.86 vvhich is muchfinds for individual

Empirical Texts of the Market Model

'I'here has been considerable of the IVIarketlVIodel '3 and themajor conclusion of these ls that the model is ill wellspecified. Empirical estimates of the' and beta coefficientsof course, contain errors, but the evidence indicates that the betacoefficients are over time (especially forportfolios). This is an result since these coefficients animportant role as the measure of risk in thePricing l\!odel we shall see belovv). Blume 19701 demonstrates thatthe market model can be very useful m assessing the outcomes ofsecuri ty re turns; especially forecasts 0 I' returns condi tional onforecasts of future market conditions.

If the market is rising' vvouid be desirable to hold thosesecurities with and vice in in which the marketis faIling. In addition it would be desirable to find and use as investmentvehicles those securities whose were in bull markets and lowin bear markets. However, as indicate, there is no differencein the slope of the scatter between of positive andmarket returns. indicates thatthere are securities which possess this desirablecharacteristIC, . the to be In upand down markets.

In additIOn Blume examined th of theof the estimated beta coefficients over time in

some detaiL Table 2 gwes the correlation coefficients between theestimated beta coefficients for portfolios of size N = I, 4,7, 10,35, and 50 securities for pairs of year time intervals in the periodJuly 192G June 1968. used cLlta on

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40 MICHAEL C. JENSEN

six subperiods. He constructed the portfolios by estimating the betas ofindividual securities, ranking them from high to low and then formingportfolios containing the first N securities, the second N securities, etc.The portfolio returns were then estimated in the first period and in thesecond period noted in the column headings of Table 2. The portfolioreturns in these periods were then regressed on a market index toobtain a portfolio beta for the first period (for example 7/26-6/33) andsimilarly for the same portfolios in the second period (i.e., 7/33-6/40).These beta coefficients for each portfolio of size N were then correlatedwith each other to obtain a measure of the accuracy of the historicalbeta as an estimator of the future beta. As can be seen from Table 2,these correlations are quite high, ranging from .59 to .99-especially forportfolios containing 10 or more securities. Note that the squaredcorrelation coefficient measures the percentage of variation in thefuture estimates of betas explained by the historical betas. Thusroughly 36 percent of the variation in future individual security betas isexplained by the historical betas and 96 percent of the variation inbetas for portfolios of 50 securities is explained by the historical betas.Thus, simple extrapolations of past betas appear to provide very goodforecasts of future betas for large portfolios but somewhat poorerforecasts for individual securities and small portfolios.

Blum e [1971, 1974] also provides evidence that the betas tend toregress towards the overall mean beta of 1.0. That is, securities withestimated betas greater than unity in one period have betas greater thanunity in a future period but the future beta tends to be closer to unityand vice versa for low beta stocks. One can adjust for this regressiontendency in making forecasts of {J and Figure 6 provides a graphicalillustration of the accuracy of the historieal portfolio beta estimatedfrom three years of past monthly data (for portfolios of 30 stocks) as apredictor of the beta over the subsequent year. Levitz [1974] studiedthe predictability of future portfolio betas for portfolios of 30 and 40securities over the priod 2/63-1/71 for 800 stocks and Figure 6characterizes the results he obtained from using past betas adjusted forthe regression tendency for three different sub periods and twoportfolio sizes. Levitz used an approximation to Blume's [1971]estimates of the regression tendency to obtain an adjusted beta. Theequation used was: 4

1\

{Jt .30 + .75 {Jt-l

TESTS OF CAPITAL MARKET IHEOR Y

FIGURE 6

The Accuracy of the Adjusled Belas of 24 30-SlockPortfolios in Predicting Their Betas During the Subsequent Year

BETA(2/71 - 1/72)

2.6

2.4

2.2

20

18 -

16 -

1.4

1.2 -

1.0

.8 -

.6 -

.2

Source: Levitz [1974]

CorrelationCoefficient

= 0970

42 MICHAEL C. JENSEN

where ~Jt j 1S the beta estimated from the previous three years ofm and~, IS the Ousted forecast of the,

bela over the next (obtained from 6a plot of the actual beta for the period 2/71 - 1 2 (estimated

, P71072 vs.~ 8-71' the adjusted beta estimated ["rom

data in the 1/71. Perfect forecasts would, ofcourse, lie on the line and as one can see, the forecasts were very

wi th a correlation .97 wi th the fu ture beta.In add ilion to this eviden ce regarding the predictability of

individual security betas and the betas of portfolios of constantcomposition, Jensen [19691 and Pogue and Conway [19721 haveexamined the of the betas of managed portfolios such asmutual funds. Even If the betas of individual securities arc stationary

time there is no a . reason for the betas of managed fundsto remain constant. The manager can change it easily by makingsystematic changes in the portfolio composition. However, the evidenceindicates the systematic risk levels of portfolios are fairly constant overtiIne indicating that managers tend to follow relatively constant risk

7 is a 0 f the beta codficien ts estimated fromannual dataon 56 mutual funds in the ]Oyearperiod 1955-1964 versusthe betas for the same funds estimated in the period 1945-1954

Jensen f1969 J . The correlation between the tw 0 sampleswas CL74. Pogue and [1972] performed similar tests on a

of 90 mutual funds in the periods 6/70 10/71 vs. 1/69 - 5/70.estimated the betas over the two intervals on daily, and

fune! returns. The correlations between the betas were.915, .895 and .703 for the daily, weekly and monthly

betas. This is consistent with the Jensen results and also providesevidence of the benefits obtamed estimating the betas over shorteras opposed to longer differing intervals. As the frequency ofobservation of the returns mcreases' j as opposed to

for a total time interval, the number of returnobservatlOns Llsed in betas increases. This decreases themeasurement error in the estimates and thus increases the precision ofthe estimates. Since some of the error is due to this puremeasurement error, this increased precision will also increase thecorrelation of the estimates between present and future betas.

The assumption of the Market l'vlodcl which is notconfirmed the tests is the assumed independence of the error terms,ejt> among all securities. King [19661 demonstrates that these errors are

TESTS OF CAPITAL /VIARKET TlIEOR Y

HGURE

~ 1642iJ)

."..;

44 MICHAEL C. JENSEN

correlated across secuntles for a given time period and that thesecorrelations can be related to industry effects. Friend and Blume[1970], Black, Jensen and Scholes [1972], and Fama and MacBeth[1973] also present indirect evidence of the non-independence of theseerrors.

TESTS OF CAPITAL MARKET THEOR Y

NOTES

45

I

N (aj + iJj R M t + ej t )

L

2.

The data were obtained from the Center for Research in SecurityPrice (CRSP) monthly price relative file at the University ofRochester.

To see this note that the returns on the market index RM , formonth t are defined to be the average return for all securities(represented by N) for that month. Using this definition andsubstituting from (1) we have

J N NR - N ~ R - ~

Mt - j = 1 jt - j = J

where a, iJ, and et are respectively the average intercept and slopecoefficients and average error term. Since RMt must equal itselfwe see from this equation that amust be 0, F must be 1.0 and etmust be o. (See Fama [1968] for a more detailed discussion ofthis pain t.)

3. See, for example, King [1966], Fama, Fisher, Jensen and Roll[1969], and Blume [1970, 1971].

4. While the adjustment equation used by Levitz seems to work fairlywell it has the undesirable property that it will cause the adjustediJ for estimates slightly less than 1.0 to be greater than 1.0, andwill increase the iJ (and therefore move it away from the mean) fores timates in the range 1.0 to 1.2. This is inconsistent with theobserved evidence that the betas tend to regress towards the meanover time. In order to be consistent with this observation thecoefficients in the adjustment equation should sum to 1.0.

5. Note, however, that the degree of precision of the estimated meanreturn for a portfolio or security depends on the total length ofthe time in terval of observation and not on the frequency of theobservations within the interval.

46

REFERENCES

MICHAEL C. JENSEN

1. Black, Fischer; Jensen, Michael C.; Scholes, Myron. "The CapitalAsset Pricing Model: Some Empirical Tests," in Studies in theTheory of Capital lvlarhets, Michael C. Jensen (editor)(Praeger Publishers, 1972).

2. Blume, Marshall. "Portfolio Theory: A Step Towards Its PracticalApplication," Journal of Business (April, 1970), pp. 152-173.

3. Blume, Marshall. "On the Assessment of Risk," Journal ofFinance (March, 1971), pp. 1-10.

4. Blume, Marshall, "The Behavior of Risk and Rctum: AnEconometric Study," (Rodney White Working Paper, 1974,unpublished).

5. Fama, Eugene F. "Risk, Return and Equilibrium: Some ClarifyingComments," Journal oj Finance, Vol. 23, No. 1 (March,1968), pp. 29-40.

6. Friend, Irwin; Blume, Marshall. "Measurement of PortfolioPerformance Under Uncertainty," American EconomicRevzew (September, 1970), pp. 561-575.

7. Jensen, Michael C. "Risk, the Pricing of Capital Assets, and theEvaluation 0 f Investment Portfolios," J oumal oj Business,Vol. 42, No.2 (April, 1969), pp. 167-247.

8. Jensen, Michael C. "Performance of Mutual Funds in the Period1945-1964," Journal of Finance (May, 1968), pp. 389-416.

9. King, Benjamin F. "Market and Industry Factors in Stock PriceBehavior," Journal of Business, XXXIX, Part II (January,1966), pp. 139-90.

10. Levitz, Gerald D. "Market Risk and the Management ofInstitutional Equity Portfolios," Financial Analysts Journal(January-February, 1974), pp. 53ff.

TESTS OF CAPITAL MARKET THEOR Y 47

11. Pogue, Gerald and Conway, Walter. "On the Stability of MutualFund Beta Values," unpublished working paper,Massachusetts Institute of Technology, Sloan School ofManagement, June, 1972.

12. Sharpe, William F. "A Simplified Model for PortfolioManagement Science Oanuary, 1963), pp. 277-93.

13. Sharpe, William F. "Bonds Versus Stocks: Some Lessons fromCapital Market Theory," Financza! A na!ysts(November-December, 1973), pp. 74-80.

CAPITAL MARKET THEORY AND IMPLICATIONSOF THE EVIDENCE-CRITIQUE

Frank E. Block, C.F.A.

Professor Jensen has reviewed the market model and some of theevidence supporting it in a most concise and lucid manner. We have noquarrel with what he has said, but we do have some reservations aboutthe model itself.

Perhaps a good deal of the financial analyst's intuitive rejection ofthe academic model is a feeling that (1) the model is not expressed interms with which the practitioner can easily identify and (2) thesuspicion that academia is saying that the return from stocks is a resultof the return of the market itself (Professor Jensen is careful to avoidthis error in his paper). The truth, of course, is that market returns aresimply the weighted average of the returns of stocks, and not the otherway around. The association of a stock return with market returnsexists only to the extent that it is influenced by the same externalfactors that dominate stock returns generally-such factors as interestrates, inflation, confidence, demographics, tax rates, and the like.

Over a long period of history the stock market itself has provideda return of perhaps eight or nine percent. The market model for anindividual stock says that, on average, we will receive a return of betatimes whatever return the market offers for that period of time, plus(or minus) alpha. If the market does nothing (that is, provides a zeroreturn) then we are still entitled to a return of alpha.

The problem is that a stock with a beta of 1.5, seems to bepromising a long-term systematic return of 1.5 times, say, nine percent,or 13.5 percent. Yet when we review the list of companies having 1.5betas, we find a mixture of (1) volatile and cyclical stocks which havehad no history of such large returns and (2) growth stocks. Thecyclicals generally turn out to have large negative alphas, particularly ifthe betas were calculated properly-i.e., peak-to-peak ortrough-to-trough over one or more market cycles. Even the growth

50 FRANK E. BLOCK

stocks are likely to have negative alphas, although the pattern is lessclear. A good example is shown in Cohen, Zinbarg and Zeikel'sInvestment Analysis and Portfolio Management, on page 768. NinetyNYSE and ASE stocks having the highest 52-week betas are shown.Seventy-eight have negative alphas!

The .opposite phenomenon appears on low beta stocks. Positivealphas show up far too frequently. The problem is that market modelbeta magnifies the underlying market return as well as the variations inmarket returns. Conceptually, the risk adjustment should be from anormal return, rather than from a zero market return.

The market model can be expressed diagrammatically as follows:

Market Model

Expected Returnfrom a Stock

Specific +Return

Return forRisk Bearing

Random+

Noise

cx'J

+ + eJt

The specific return, of course, is alpha. Each alpha is unique to agiven stock, and the average of all alphas has to be zero. The secondelement on the right-hand side of the equation is the systematic return,or simply beta multiplied by the return from the stock market for theperiod. The final item is random noise with an average expected valueof zero.

We would like to suggest an amendment which would parallel thework that analysts do already and therefore makes the market modelintuitively more pleasing to practitioners as a whole. This model wouldread as follows:

Amended Market Model

Expected Return = Different Kind of + Adjustment for + Random Ifrom a Stock Specific Return Market Risk Noise

Rjt +

Consider how an analyst typically predicts returns for commonstocks. He calculates the likely return as (approximately) the sum ofthe growth rate,the yield, and the rate of change in the multiple. Thistotal rate of return is calculated over some useful time horizon on every

CAPITAL MARKET THEORY AND IMPLlCAJ10NS 51

stock being considered for use by his insti tu tion. This return is alreadyin his files, but would provide a much larger "alpha" component (or,specific return) than the one used in the academic market modeL Ineffect, it would be the total return expected from the stock.

How much would this new alpha exceed the old one? To answerthe question, a number we need is the expected normal longer termreturn from the market itself. One would be inclined to select a numberthat considered historial market returns and any reasonable argumentsfor expecting the future to be different from the past. For purposes ofdiscussion let us assume that, say, nine percent is the expected future rateof return for the stock market generally. With this as a bench mark, thenew alpha, or specific return, would exceed the old one by an amountequal to the beta for the particular stock multiplied by nine percent.

Having added beta times nine percent to the first element on theright-hand side of the equation, it must be substracted somewhere else.It makes no sense to subtract it from the random noise, which we don'treally need much anyway. Therefore let us subtract it from the secondcomponent on the right-hand side of the equation. Thus, the secondcomponent would now read {3 (R mt - Rn ), or {3 (Rmt - nine percent),where R mt is the expected rate of return from the market over thesame period for which the (new) alpha was projected, and R il , the ninepercent of course, is the long-term expected return from the market.

What does the second component of the equation, as amended,now provide?-simply that portion of the return that can be attributedto expected departures from the normal level of market return. Thus,the second component is no longer a mixture of return and risk, butrather a simple risk or variability measure. The analyst mayor may notchoose to estimate this element. Over very long time horizons, it will bezero. If an opinion is held on the market return for the appropriatetime horizon, the Amended Market Model provides an absolute returnforecast for that time period. If the market return is arbitrarily assumedto be normal, the second element becomes zero and the equationbecomes an estimate of return relative to the marhet. Over the shortertime periods, if no strong opinion is held about market returns, theanalyst could simply substitute, say, plus or minus one standarddeviation. The opportunities to manipulate the Amended Market Modelare expanded by its similarity to the sort of relative and absoluteforecasts which analysts are already making. The conventional model isclumsy in this respect.

52 FRANK E. BLOCK

Lest we upset some of our friends in academia, it should bepointed out that all we have really done to the graph of thecharacteristic line is to move the vertical axis (zero) to the righ t by ninepercentage points, or so. (At that point, the vertical axis should fallapproximately on the center of moment, thereby removing some of thestatistical problems concerning the reliability of estimated alphas.) Allof the points representing observations would be plotted in their samerelative position to the line, and the slope of the line (f3) would remainunchanged.

We would submit that the amended market model is more usefulin terms of the sort of return and risk estimates currently made bypractitioners than is the academic market model, and that it thereforedeserves some study for possible use in developing theoreticalconstructs, as well as possible practical applications in such areas asperformance measurement.

LONG TERM INVESTING

Jack L. Treynor

The investor who would attempt to improve his portfolioperformance through unconventional, innovative research is currentlybeing challenged on three fronts: (1) The efficient marketers say he willbe unable to find any ideas that haven't been properly discounted bythe market; (2) Lord Keynes says that even if he finds these ideas hisportfolio will be viewed as "eccentric" and "rash" by conven tionallyminded clients (and by his professional peers); and (3) finally, theinvestmen t Philistine says that even if he stands by his ideas he won't berewarded because actual price movements are governed by conventionalthinking, which is immune to these ideas.

1. Successful response to the first challenge lies in dis tinguishingbetween two kinds of investment ideas: (a) those whose implicationsare straightforward and obvious, take relatively little education orspecial expertise to evaluate, and consequently travel quickly (e.g., "hotstocks"); and (b) those that require reflection, judgment, specialexpertise, etc., for their evaluation, and consequently travel slowly. (Inpractice, of course, actual investment ideas lie along a continuousspectrum between these two polar extremes, but we can avoid somecircumlocution by focusing on the extremes.) Pursuit of the secondkind of idea-rather than the obvious, hence quickly discounted, insightrelating to "long-term" developments-is, of course, the onlymeaningful definition for "long-term investing."

According to Professor Eugene Fama, "disagreement amonginvestors about the implications of given information does not m itselfimply market inefficiency unless there are investors who canconsistently make better evaluations of available information than areimplicit in market prices." Thus when one talks about marketefficiency it is important to distinguish between ideas that requirethoughtful analysis and ideas that don't: if the market is inefficient, itis not going to be inefficient with respect to ideas understood with a

54 JACK L. TREYNOR

mmlmum of education or special trammg, since, by definition, theseideas are unlikely to be misevaluated by the great mass of investors.

Under what circumstances will investors' errors in appraisinginformation available to all lead to investment opportunities for some?If investors disagree on the value of a security even when they have thesame information, their differences in opinion must be due to errors inanalysis. If investors err independen tly, then a kind of law of averagesoperates on the resulting error in the market consensus. If enoughindependent opinions bear on the determination of the consensus price,the law of "large numbers" effect will be very powerful, and the errorimplicit in the consensus will be small compared to errors made on theaverage by the individual investors contributing to the consensus.

The key, however, to the averaging process underlying an accurateconsensus is the assumption of independence. If all-or even asubstantial fraction-of these investors make the same error, then theindependence assumption is violated and the consensus can divergesignificantly from true value, and the market ceases to be efficient inthe sense of pricing available information correctly. I see nothing in thearguments of Fama or the other efficient markets advocations tosuggest that large groups of investors may not make the same error,particularly in appraising the kind of abstract ideas that take specialexpertise to understand and evaluate, and that consequently travelrelatively slowly.

Thus Fama's statement can best be revised to read: "Disagreementamong investors due to independent errors in analysis does notnecessarily lead to market inefficiency." If the independenceassumption is violated in practice, every violation represents a potentialopportunity for fundamental analysis.

2. The assertion that the great bulk of practicing investors findlong-term investing impractical was set forth almost forty years ago byLord Keynes:

Most of these persons are in fact largely concerned not withmost superior long-term forecasts of the probable yield of aninvestment over its whole life, but with foreseeing changes inthe Conven tional basis of evaluation a short time ahead of thegeneral public. They are concerned not with what aninvestment is really worth to a man who buys it for keeps,but with what the market will evaluate it at under theinfluence of mass psychology three months or a year hence.

LONG TERM INVESTING 55

Obviously, if an investor is concerned with how the "mass psychology"appraisal of an investment will change over the next three months, he isconcerned with the propagation of ideas that can be apprehended withvery little analysis and that consequently travel fast.

On the other hand, the investment opportunity offered by marketinefficiency is most likely to arise with investment ideas that pn:mag,lte

or hardly at all. went on to explain practicalinvestors are not interested in such ideas:

It is the long-term investor, he who rnost promotes the publicinterest, who will in come in for the most criticism,wherever investment funds arc committees orboards or banks. For it is in the essence of his behavior thathe should be unconventional and rash in theeyes of average opinion. If he is that willcon firm the general belief in his rashness; and if in the shortrun he is unsuccessful, which is very likely, he will not receivemuch mercy. Worldly widom teaches that it is better forreputation to fail conventionally than to succeedunconven tionally.

Thus Keynes not only described accurately the way most professionalinvestors still behave; he also supplied their reasons for so behaving. It isnoteworthy, however, that he was careful never to say that thelong-term investor who sticks by his guns will not be rewarded.

Eu t is the price of unconventional holdings as high as Keynesalleges? Modern portfolio theory says that the holding of an individualsecurity can be assessed only in the context of the overall portfolio: Solong as the overall portfolio has a reasonable level of market sensitivityand is reasonably well diversified, the beneficiary has nothing to fearfrom "unconventional" holdings-and still less to fear fromconventional holdings bought for unconventional reasons. There is, ofcourse, marketing advantage in holding securities enjoying wide popularesteem but, as investors as a class become more sophisticated,professional investors are less likely to be challenged on specificholdings.

3. There is finally a widely held school of thought that assertsthat research directed toward improving our analytical tools isautomatically impractical because it does not describe the behavior of arnarket consensus based on opinions of investors unfamiliar with these

56 JACK L. TREYNOR

tools. This line of argument puts a premium on investmen t ideas thathave broad appeal or are readily persuasive, while rejecting the ideasthat capture abstract economic truths in terms too recondite to appealto the mass of investors.

The investment Philistine who asserts that it is impossible tobenefit from superior approaches to investment analysis if the marketconsensus is not based on these approaches misunderstands whatappraisal of a security means: An analyst's opinion of the value of asecurity is an estimate of the price at which, risk-adjusted, the return onthe security is competitve with the returns on other securities availablein the market. A superior method for identifying undervalued securitiesis therefore tantamount to a method of identifying securities which attheir present prices offer superior long-term returns. The mere inclusionof such securities in a portfolio will guarantee a superior investmentperformance.

Suppose, for example, that the investor identifies a stock forwhich the market persistently underestimates actual earnings. We canformalize this idea by appealing to a standard stock valuation modelsuch as the Gordon-Shapiro model. For simplicity, the Gordon-Shapiromodel assumes that: (1) the future dividend payout ratio will beconstant over time; and (2) the percentage rate g at which earnings(hence, given (1), dividends) grow will be constant over time. The valueof the stock equals the present worth of the growing stream ofdividends, discounted at rate p (i.e., the "cost of capital").

Let the ratio A of the consensus forecast of earnings at any pointin time to true earnings (which, assuming the consensus correctlyanticipates the constant payout rate, will also be the ratio of theconsensus forecast of dividends to true dividends) also be constant overtime. Then true earnings, true dividends, the consensus forecast ofearnings, and the consensus forecast of dividends will all grow at thesame rate g. If A equals one (i.e., if the consensus correctly anticipatesfuture earnings), return (dividends and appreciation combined) to theshareholder pi will equal p, the cost of capital. If A is less than one (i.e.,if the consensus consistently underestimates future earings), the returnto the shareholder pi will exceed the cost of capital. The difference, pi -p, is the shareholder's reward for being right when the consensus iswrong. If the consensus continues to be wrong indefinitely his rewardwill continue indefinitely.

The table below provides a rough basis for estimating how big thereturn differential pi - P from holding undervalued stocks will be under

LONG JERM INVESTING 57

the assumption that the general mass of investors never come around toforecasting earnings correctly (see Appendix A). It should be noted thatthese are returns per annum. The trading rate required to realize thesereturns is obviously very low.

TABLEassume p = 10%

AI

g P - p

0 0.5 ] 0%

5% 0.5 5%

0 0.67 5%

5% 0.67 2.5%

g

pi _P

rate of growth in earnings anddividends

ratio of market-consensusestimate of magnitude of futureearnings to true mar-magnitude

abnormal rate of return that willbe realized by holding stock indef-initely, even if market continues tounderestimate true earnings.

Summary

To the threefold challenge, we have offered a threefold reply: (1)the efficient marketer's assertion that no improperly or adequatelydiscounted ideas exist is both unproved and unlikely; (2) Keynes'suggestion that unconventional investing is impractical ignores thewisdom of modern portfolio theory (quite understandably, since MPTis a post-war development); and (3) the investment Philistine who saysgood ideas that can't persuade the great mass of investors have noinvestment value is simply wrong.

We can sum up our case by asking the following question: If aportfolio manager consistently exhibited the kind of abnormal returnssuggested in the Table, while maintaining reasonable levels of marketsensitivity and diversification, how long would it be before hisinvestment record began to outweigh, in the eyes of his clients, theunconventionality of his portfolio holdings?

58

APPENDIX A

JACK L. TREYNOR

Let E(t) be earnings of the firm at time t, be the dividend payoutratio, p the market discount rate (the cost of capital) and g theprojected growth rate. If, for the sake of argument, we define "correct"pricing of the company in terms of the well known Gordon-Shapiroform ula, we have for the in trinsic value v.

bE(t)v = P_g

If the internal return on reinvested funds is T, we have

E( t) = T (1 - b)

If priced correctly, we have for price as a function of time,

v(t) = bEo egt

p - g

If underpriced by factor A, we have

AbE oegt

v( t) = --=---p - g

Differentiating, we obtain the rate of price appreciation

~ = AbE -R- egtdt 0 p - g

From previous considerations we know that the dividend is given by

For the price change and dividend together we have

bEgt Ag + P - g

'0 e p _ g

price + dividendrate of return = price

Ag + P - gA

=~ + g.A

The return differential realized by holding a stock underpriced by a

factor A is thereforef2J .!..p 1 _ P = A - (p - g) = (p - g) (A - 1)

But since 1 is always posItIve, we have p' - p > o.A

LONG TERM INVESTING

APPENDIX B

59

How would the price of a mispriced security have to behave in thefuture to prevent its holder from realizing an extraordinary return?

Ordinary return is p. If we replace A in the previous model by A(t), wecan state the condition as:

d bEoegt

+bE egt =PA(t) bEoegt

?(ftA(t) P_g 0 P-g

The left-hand side is the return from a mispriced security in the moregeneral case in which the value of A is changing over time. Theright-hand side is the normal return on the actual (mispriced) marketprice. We ask: How must A change over time if the investor is to realizeonly a normal return on the mispriced security (i.e., A =f i)?Differentiating, we have:

A(t) bE 0 --.lL egt + dA bE 0 egtp-g cit P-g

This can be simplified as follows:

+ bEo egt = PA (t}bEoegt

P - g

A(t)g + ~~ + (p - g) = pA(t),

(g-p)A(t) + dA =g-Pdt

The solution is:A(t)

When t 0, we have:

A(O) = AO + 1.

Hence, in(O) < 1, we have AO = A(O) - 1 < 0.

Since the exponent p - g > 0, market price must fall faster and faster toprevent investors from realizing an extraordinary return on anunderpriced stock (see table following).

60

TABLE

A(0) 0.5 => Ao -0.5

JACK L. TREYNOR

P-g = 5% P-g = 10%

(p : g)t A(t) (p -g)t A(t)

t = 0 0 0.5 0 0.51 0.05 0.474 0.10 0.4482 0.10 0.448 0.20 0.3904 0.20 0.390 0.40 0.2548 0.40 0.254 0.80 negative

16 0.80 negative

THE CAPITAL ASSET PRICING MODEL FROMA PROFESSIONAL'S POINT OF VIEW

Jerome L. Valentine, C.F.A.

The papers presented earlier were more than sufficient to explainthe assertions of the Capital Asset Pricing Model. This paper attemptsto discuss only two points from the standpoint of the practicinganalyst. First, what findings in the model are useful to current practice,and to what extent arc the findings unrealistic. Second, what practicalcomplexities in the market might limit the application of the model inrealis tic applications.

The model implies that the best portfolio will be somecombination of the "market portfolio" and the risk-free asset (whichcould be approximated by T-bills). Even if there were not a perfectagreement among investors, each investor would have his own "bestportfolio" of risky assets and then either increase or decrease his risk byborrowing or by buying T-bills. This argument is useful to thepractitioner because it does not presuppose the belief that investorsagree. It implies that we should re-think the idea that risk-adverseaccounts should be in a different set of securities from accounts willingto accept a high level of risk. It may very well be the case that bothtypes of accounts should have the same stock portfolio, but the formershould have a high percentage of assets in cash equivalents in order toreduce risk. This concept has some intuitve appeal, for it places allaccounts in the "best" set of stocks, and separates the risk adjustmentpart of the problem from the problem of equity selection, placing it inthe realm of the cash-bond-equity mix decision.

Another possible benefit of the model stems from the numeroustests of the theories implying short-term randomness in security pricemovement. Since there is now little doubt that hourly or dailymovements in prices are not predictable, the trading desk activity atinstitutions may need to be restructured to some extent. It is fairlycommon practice for traders to attempt to anticipate market behavior

62 jERONIE L VALENI1NE

On occaSlOn this may cause the orders from portfolio managers to bedelayed on the trading desk for quite some time. If fundamental

was valuable and short-term price prediction fruitless, thissituation obviously should be altered.

The problem is that capital asset pricing theory, if taken literally,implies that fundamental analysis is not useful. The impact of thetheory on the value of is obvious. Some conceptual problemsthat I have in relating the to the actual practice of investmentprofessionals have been presen ted in a Financial AnalystsResearch Foundation working paper. At this time, I would like torestrict consideration to only one problem in the theory-the problemof market structure. have held that the market'sbehavior is highly complex, whereas the capital market theory assertsthat it is describable by a fairly simple equation relating the "market"change and the change in the price of individual securities. The balanceof this paper presents some preliminary findings on a set of companiesconstituting over 50 percent of the market value of the S & P 425.Historical (or "ex post") returns were used, and the capital markettheory is theory of "ex ante") theory. Nevertheless,Jensen (in a paper published in the Bell Journal) has shown that the exante theory implies ex post returns which follow the "beta" equationand hence that the theory can be subjected to empirical testing. Thefollowing empirical evidence relates to the "market" concept treated asa single variable in the most fundamental portions of the thory.

The Capital Asset Pricing Model and beta theory frequently discuss

the "market" as if it were a single entity easily recognized andmeasured by investment professionals. Actually, of course, "marketbehavior" is some logical construct which is known only its

impact on individual stocks. It is possible, of course, toevaluate a number of the in order to gain some insight intoits and this is what the standard market indices attempt to do.These indices aggregate the behavior of a number of stocks in order toportray with some of accuracy the behavior of the "market"that lies behind each of the companies as a "common factor"influencing all companies.

A problem occurs immediately, however, since each index is anapproximation of the common factor, and it is not clear which"market" index to lise. Since the popular indices show quite differentperformances over time, it is not clear whether the beta based on oneindex should be preferred to the beta based on another.

THE CAPITAL ASSET PRICING MODEL 63

A more fundamental problem is whether the variations In thiscommon factor that we call the "market" can be described oneindex. It is at least logically possible that two independent indices (twocommon factors) would be needed to describe the behaviorpattern of stocks. A statistical technique known as factor canbe used to determine the number of common factors in stock

behavior. If this type of is to market swings asvariables, it produces the number of "common factors" toexpl

64

TABLE IData Cases

Identification of Firms

JEROME L. VALENTINE

1. American Home Products2. Atlantic-Richfield (ARCO)l3. American Tel & Tel4. Avon Products5. Burroughs6. Caterpillar Tractor7. Coca-Cola8. Continental Oil9. Dow Chemical

10. Du Pont11. Eastman Kodak12. Eli-Lilly13. Exxon (Standard Oil of

New Jersey)14. Ford15. General Electric16. General Motors17. Getty Oil18. Gulf Oil19. Hallib urton20. IBM21. In ternational Nickel22. International Tel & Tel23. International Paper24. J. C. Penney

25. Johnson &Johnson26. Kresge27. Merck28. Minnesota Mining & Manufac-

turing29. Mobil Oil (Socony)230. Pfizer31. Philip Morris32. Phillips Petroleum33. Polaroid34. Procter & Gamble35. Royal Dutch36. Schering-Plough (Schering)337. Schlumberger4

38. Sears-Roebuck39. Shell Oil40. Standard Oil of California41. Standard Oil of Indiana42. Sun Oil43. Texaco5

44. Texas Instruments45. Union Carbide46. Warner-Lambert47. Westinghouse48. Xerox6

NOTES

1. Taken as Atlantic Refining until merger with Richfield Oil. First jointobservation: 10/7/66.

2. Taken as Socony Oil until Mobil Oil formed. First observation as Mobil:10/7 /66.

3. Taken as Schering until merger with Plough. First join t observation: 4/28/71.4. Taken as Daystrom until Schlumberger formed. First observation as

Schlumberger: 6/26/62.'). Taken as Texas Company until Texaco formed. First observation as Texaco:

8/3/59.6. Taken as Haloid until Haloid Xerox formed; taken as Haloid Xerox until

Xerox formed. First observation of Haloid Xerox: 8/3/59; first observation ofXerox: 12/12/61.

THE CAPITAL ASSETPRICING MODEL

TABLE II

Time Periods

65

Fifteen market swings over the period from July 15, 1957 toNovember 30,1973 were studied. Each date delimiting a rise or fall wasselected as the highest or lowest point in the respective swing. Data onstock prices as of a given day 'were acquired from microfilm records ofthe Wall Street Journal. When only bid-ask spreads were quoted, the bidprices were recorded and used in subsequent calculations. Several of thestocks in the studies, in the earlier part of the period, were tradedover-the-counter and only bid-ask spreads were available. Informationregarding stock splits and payment of dividends was obtained from the1973 edition of Moody's Industrial lVlanual. Rates of return for eachstock were calculated for each market swing taking account of pricechange, stock splits, stock dividends, and cash dividends. The exactdates delimiting the chosen swing periods are as follows:

1. July 15, 1957

2. October 22,1957

3. August 3, 1959

4. October 25, 1960

5. December 12, 1961

6. June 26,1962

7. February 9, 1966

8. October 7, 1966

9. October 9, 1967

10. March 5, 1968

11. November 29, 1968

12. May 26, 1970

13. Apri128,1971

14. November 23,1971

15 . Jan uary 8, 1973

16. November 30,1973

The analytic procedure followed was a Factor Analysis of 48 cases (48

firms) by 15 variables (rates of return for 15 market swings).

66 JEROME L. VALENTINE

TABLE III

BETA STANDARDCOMPANY COEFFICIENT ERROR

American Home Products 0.78 5.6

Atlantic Richfield 1.11 12.4

American Tel & Tel 0.67 6.2

Avon Products 1.03 8.7

Burroughs 1.01 9.3

Caterpillar Tractor 1.35 8.3

Coca-Cola 0.86 6.0

Continental Oil 1.09 14.5

Dow Chemical 0.91 5.9

Du Pont 0.80 7.9

Eastman-Kodak 0.97 7.1

Eli-Lilly 0.88 8.4

Exxon (Standard Oil of N.J.) 0.64 7.1

Ford 1.13 8.7

General Electric 1.06 6.4

General Motors 0.99 5.8

Getty Oil 1.11 1l.5

Gulf Oil 0.90 7.8

Halliburton 1.23 10.0

IBM 1.09 7.4

International Nickel 0.82 9.8

International Tel & Tel 1.77 8.7

International Paper 0.92 8.3

J. C. Penney 1.28 5.2

Johnson & Johnson 1.01 8.9

Kresge 1.51 8.8

Merck 0.88 6.8

Minnesota Mining & Man. 1.12 5.3

Mobil Oil (Socony) 0.90 10.0

Pfizer 0.70 8.1

Philip Morris 0.98 11.1

Phillips Petroleum 0.88 11.8

THE CAPITAL ASSET PRICING MODEL

TABLE III (Continued)

67

COMPANY

Polaroid

Procter & Gamble

Royal Dutch

Schering-Plough (Schering)

Schlumberger

Sears-Roeb uck

Shell Oil

Standard Oil of Calif.

Standard Oil of Indiana

Sun Oil

Texaco

Texas Instruments

Union Carbide

Warner-Lambert

Westinghouse

Xerox

BETACOEFFICIENT

1. 78

0.83

0.78

0.761.27

1.03

0.99

1.04

0.83

0.65

0.871.43

1.03

0.93

0.86

1.05

STANDARDERROR

16.2

6.79.1

6.710.9

5.3

9.2

7.3

9.2

9.1

8.4

11.6

7.57.69.7

6.6

68 jERO/vlE L. VALENl1NE

to n companies' returns using the behavior of the"market" factors to characterize each company's behavior, chose onlytwo, he would lose half of his already limited explanatory power. If heused only one, he would lose three-fourths of his power. Beta theoryuses a one variable equation to move from a market return to acompany return, with the company characterized by only one numberand the "market" approximated only one index of doubtfulreliability. It is not hard to understand why beta-based predictions ofthe return of individual companies are not highly reliable.

The results were so sharply at odds with the theory that a numberof cross-checks were made to attempt to locate some logical flow in thestudy> Table IV shows alpha factor aneJysis results (a type of factoranalysis that assumes that the market swings were randomly sampledfrom the set of all possible swings) on the actual company pricerelatives (1), the logs of the price relatives (II), and the price relativesannualized (III). This might help to show whether the results stemmedfrom some inadequate way of presenting the company returns. As canbe seen from the table, the importance of the many factors was notreduced. The middle portion of the table shows the "communalities" ofthe market swings-the proportion of each swing's variation that couldbe explained by the factors. These communalities were about the sameusing each of the variable types.

Table V presents the results of studies using three types of factoranalysis. "PAl" refers to the principle components analysis, "PA2" tocommon factor analysis, and "Alpha" to alpha factor analysis. It is notnecessary to discuss the features of the techniques here. The importantpoint is that the bottom of the table shows that multiple factors appearregardless of technique. The factor loadings in the upper portion of thetable are the correlation coefficients of each of the market swings toeach of the first three factors.

Table VI shows the results of the actual alpha factor analysis inSection 1. Section II shows what the results would have been if thecompanies had behaved in accordance with their beta coefficient and anominal standard error. Section III shows the results (by a monte carlosimulation) if they had behaved in accordance with both their beta andtheir standard error. Notice that Section II has only one factorexplaining 100 percent of the behavior. Section III has the companies'actual standard error and shows 65 percent of the behavior explainedby the data. These values compare to 27.6 percent for the first factor

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