1. samizdat in defense of the capm

7/29/2019 1. Samizdat in Defense of the CAPM

1/4

CFA Institute

Samizdat: In Defense of the CAPMAuthor(s): Jack L. TreynorReviewed work(s):Source: Financial Analysts Journal, Vol. 49, No. 3 (May - Jun., 1993), pp. 11-13Published by: CFA InstituteStable URL: http://www.jstor.org/stable/4479643 .

Accessed: 08/02/2013 07:22

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of

content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms

of scholarship. For more information about JSTOR, please contact [email protected].

.

CFA Institute is collaborating with JSTOR to digitize, preserve and extend access to Financial Analysts

Journal.

http://www.jstor.org
http://www.jstor.org/action/showPublisher?publisherCode=cfahttp://www.jstor.org/stable/4479643?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/stable/4479643?origin=JSTOR-pdfhttp://www.jstor.org/action/showPublisher?publisherCode=cfa


2/4

SamizdatIn Defense of the CAPM

Jack L. Treynor, TreynorCapitalManagementManytextbooks repeat two com-mon complaints about the CapitalAsset Pricing Model (CAPM):

1. Evidence that it takes morethan one factor to explainthe shared, or systematic,risk in securities refutes theCAPM.2. In demonstrating that therisk premium on an assetdepends only on its system-atic factor loadings, Arbi-trage Pricing Theory (APT)provides investors with a re-sult of great practical valuethat the CAPM oes not pro-vide.

It may not be coincidental thatsome of the same books thatmake the first complaint don'tactually discuss the CAPM.Somediscuss the market model, andsome discuss (usually without at-tribution) the Vasicek-McQuownpricing model. Both build on Wil-liam Sharpe'sDiagonal Model pa-per, which suggested (followingup on a footnote in HarryMarkowitz'sbook) thatsystematicrisk could usefully be accountedfor by a single factor.*Vasicek and McQuown's argu-ment proceeds as follows. As-sume a single systematic risk fac-tor exists, such that residual riskscan be uncorrelated both withthis factorand with each other. Bytaking appropriately long posi-tions in some securities and ap-propriately short positions in oth-ers, the individual investor canhedge away all systematic risk.

Thus he won't bear systematicrisk unless it competes success-fully with residual risk for inclu-sion in his portfolio. But if heincludes enough positions (longor short) in his portfolio, he candrive the portfolio's residual riskto zero. Now, if residual risk ispriced, this offers him an infinitereward-to-riskratio. In order formarket risk to compete success-fully, it must offer an infinite ex-pected return. Otherwise the in-vestor will choose not to holdany systematicrisk, and the mar-ket won't clear.The market model takes the as-sumptions of the Diagonal Modeland the result of the Vasicek andMcQuown model and concludesthat the actual,expost systematicreturn-surprise plus risk premi-um-of every asset will be pro-portional to the asset's marketsensitivity. Both Vasicek and Mc-Quown and the market modelthus assume a single systematicfactor;but the CAPMn its variousforms (Sharpe, Treynor, Lintner,Mossin,Black) makes no assump-tion about factor structure. Inparticular, it does not make theone-factor, Diagonal Model as-sumption that Vasicek and Mc-Quown and the market modelmake.Actually, a CAPM hat abandonsthe assumptionsof homogeneousexpectations (as Lintnerdid) andriskless borrowing and lending(as Blackdid) doesn't make manyother assumptions. All it does as-sume is that asset risk can beadequately expressed in terms ofvariances and covariances (withother assets); thatthese measuresexist; that investors agree onthese risk measures; and that in-vestors can trade costlessly to in-crease expected portfolio returnor reduce portfolio variance, to

which they are all averse. Short-selling is permitted.There is thus nothing about factorstructure in the CAPM's ssump-tions. But there is also nothingabout factor structure in theCAPM'sonclusions. Factorstruc-ture is about surprise-in partic-ular, the nature of correlationsbetween surprises in differentas-sets. In the Diagonal Model, asingle factoraccounts for all cor-relation. In richer,more complexfactor structures, correlations inasset surprises can be due to avariety of pervasive, market-wideinfluences. The conclusion of theCAPM-that an asset's expectedreturn is proportional to its cova-riance with the market portfo-lio-makes no assertions aboutthe surprise in that asset's return.Because expected returnand sur-prise are mutually exclusive ele-ments in ex post, actual return,there can be no conflict betweenthe CAPM nd factorstructure.Thispoint is the key to the secondcomplaint. In order to demon-stratethatAPT'sprincipal conclu-sion-that an asset's risk pre-mium depends only on itssystematic factor loadings-alsoholds for the CAPM,we can as-sume a perfectly general factorstructurewithout fear of trippingon either the assumptions of theCAPM r its conclusions.Consider a market in which abso-lute surprise for the ith asset, xi,obeys:Eq. 1Xi= 2,8ijuj + ei,where u1 are the systematic fac-tors in the market and ei is aresidual unique to the ith asset.

* This material will appear as an appendix tothe second edition of the Guide to PortfolioManagement by James L. Farrell Jr., to bepublished by McGraw-HillBook Company.

zD

-J

z-J

zzL11

This content downloaded on Fri, 8 Feb 2013 07:22:28 AMAll use subject to JSTOR Terms and Conditions
http://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp


3/4

The absolute surprise for themarket sawhole, x, is simply hesumof absolutesurprises or theindividual ssets:x = Exi = 28ijuj + Eei.The CAPM sserts that any riskpremiumof the ith assetdependsonly on its covariancewith themarket-i.e., on the expectationof the following product:Eq. 2

( f ijuj + ei)(E,BhkUk + Ieh).Bearing n mind that the u's ande's are surprise,and assumingthat all covariancesbetween e'sandbetweenu's ande's arezero,we have for thisexpectation:Eq. 3E[EZpijphkUjUk ei2],orEq. 4

2 3ij[2!3hkI'jk 2] + Si2,whereEq. 5O(jk = E[UjUk]andEq. 6Si2= E[ei2].We see that an asset's covariancewith the marketportfolio (abso-lute surprisewith absolute sur-prise) has two terms-one forsystematicfactors and one for theasset's unique surprise. A key is-sue is the relative size of thesetwo terms.We can, of course, make all thecovariance terms in the system-

Figure A Systematic vs. Unique RiskSame Order of Magnituder1;

WHOM)(13jlfl) + ... + (si)(si)t ~~~~~~tOrders of MagnitudeBigger

aticpartzero by choosing a set offactors hat are orthogonal.Thenthe covariance expression be-comes:Eq. 7

Pill&10hcr11 + A223n20f2222+ ...+ Si.

Among he manypossiblechoicesof orthogonal factors, we canchoose one in which only onefactorcorrelateswith the marketportfolio.Assign he factor ndexto thefactors o that hefirst ermin the bracketed xpression s thevarianceerm orthat actor.Thenwe can ignore for the momentthe other systematicterms andfocus on the firstand astterms nthe covariance xpression,Equa-tion (7). Factoringhe respectiveterms into standard deviationsgives us:Eq. 8

(8i11)(2I3h1lr1) + + (si)(s)Consider he first term. One fac-tor reflects the absolute factorweightof the asset,the othertheabsolute actorweightof the mar-ketportfolio.The former s of thesame order of magnitudeas thestandarddeviation of the asset'sunique risk; he latter s ordersofmagnitude arger (see FigureA).This is becauseall the systematicriskin the marketportfolio'sab-solutegain or loss is reflected nthe market's factor weight,whereas the unique risk in thesecond term is that for a singleasset. But this means thatthe sys-tematicproduct s orders of mag-nitude larger than the uniqueproduct.

To keep our exposition simple,we chose a special set of system-atic factors. Had we chosen differ-ent systematic factors,the marketportfolio could have been corre-lated with most or all of them,rather than merely one. Then thesystematic portion of an asset'scovariancewith the marketwouldhave non-zero terms for morethan one factor. Spreading itacross several factors, however,won't diminish the magnitude ofthe aggregate systematic portion.Whether one systematicfactor orseveral are correlated with themarket portfolio, then, the sys-tematicportion of an asset's cova-riance with the market will beorders of magnitude bigger thanthe unique portion.If we drop the unique term andrelax the assumption that onlyone systematic factor correlateswith the market, then the expres-sion within brackets in Equation(4) will in general have a differentvalue for each of the systematicfactors. But the value doesn't de-pend on i-the index that distin-guishes between individual as-sets. What is outside the bracketsis the factor loadings 3ij or the ithindividual asset on the factors ujin the factor structure.But this isthe principalconclusion of APT-that an asset's risk premiumshould depend only on its factorloadings. Any corollaries that flowfrom this APT result also flowfrom the CAPM.One of the differences betweenAPTand the CAPMs the specifi-cationby CAPM f how systematicfactors should be priced in rela-tion to each other. The expres-sion in brackets in the first termof Equation (4) is, to some con-stant of proportionality,the priceof risk. The value of the expres-sion, hence thatprice, is generallygoing to be different for differentfactors.APTcan'tspecify the valueof this expression; therefore itcan't specify how factors will bepriced in relation to each other.What the APTdoes do is weakenthe assumptions necessary to

z

zD

0

z- J

12



4/4

reach this conclusion. APT ap-peals to the older, better estab-lished traditionof arbitrageargu-ments exemplified by Modiglianiand Miller's1958 paper.APT oinsthe idea of specifying securityriskin terms of a factorstructure(Far-rar's 1960 doctoral thesis at Har-vard; Hester and Feeney's con-

temporaneous work atYale) withModigliani and Miller's arbitrageargument. Some may argue that,in effect, APTsubstitutes system-atic risk factors for Modiglianiand Miller's risk classes. Othersmay argue that the real prove-nance of APT is not Modiglianiand Miller, but ratherVasicek and

McQuown,with multiple risk fac-tors substituted for their singlerisk factor.This writer has no desire to take aposition in such controversies.His only purpose is to clear upcertain misunderstandings re-garding the CAPM.

Post-Modern Portfolio Theoy Comes Of AgeAn Infomercial from Sponsor-Software Systems, Inc.* Number Three in a Series e

In previous infomercialswe described how Post-ModernPortfolio ProtectivePutTheory PMPT)has eliminatedheproblems ssociatedwith tandarddeviation nd henormal istribution hendoingportfolio ptimization.Oneimmediatebenefitof these advances appliesto portfolios avingsignificant ption, utures,or otherderivative omponents.Since derivativeportfolios re highly kewed (see chart), thas been PMPTimpossible, until the advent of PMPT, to accurately model these 2 \strategies n ormal ptimizationtudies. Now, or he first ime,PMPT -allows the real risksand rewardsof derivatives o be measured.To help you evaluate derivatives, as well as improvethe overall Meffectivenessofallyou asset allocation ecisions,we havedeveloped MPT /TheAsset AllocationExpert, full-featured, C-based, post-modernportfolioptimizationystem. So, ifyou're eriousaboutyour nvestmentdecisions, retireyour old-fashionedoptimizerand get The AssetAllocationExpert, oday's most sophisticated, most accurate assetallocation oftware. Retum

For a demonstration program and additional information contact:SPONSOR-SOFTWARE SYSTEMS, INC.

Software for the Serious Investorm 860 Fifth Avenue * New York, NY 10021 * 212/724-7535 * 212/580-9703 (Fax)


1. samizdat in defense of the capm

Documents