history of capm.pdf

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APUBEF Proceedings - Fall 2006 207

A BRIEF HISTORY OF THE CAPITAL ASSET PRICING MODEL

Edward J. Sullivan, Lebanon Valley College

ABSTRACT

This paper explores the near-simultaneous development of the capital asset pricing model by four men:Jack Treynor, William Sharpe, John Lintner, and Jan Mossin. Further, it identifies the key ideas that inspired theresearch of these men. Lastly, it considers why the work of only one of them resulted in a Noble Prize in economicscience.

INTRODUCTION

The history of scientific thought is repletewith examples of individuals who independently andsimultaneously discover the same concept.Undoubtedly, the most famous example of such acoincidence is the development of calculus by bothIsaac Newton and Gottfried Leibniz in theseventeenth century. Such examples are considerablyless common in the history of economic thought.However, during the early 1960s, four economists --John Lintner (1965a, b), Jan Mossin (1966), WilliamSharpe (1964), and Jack Treynor (1962) -- developedessentially the same model for describing securityreturns. The capital asset pricing model (CAPM), asit later became known, revolutionized the theory andpractice of investments by simplifying the portfolioselection problem. Interestingly, only one of thesemen, William Sharpe, received the 1990 Nobel Prizein economic science for this work. Further, Jack

Treynor, who arguably wrote the earliest draft of thismodel, never had his work published until recently.This paper defines the intellectual milieu that inspiredthese men to develop this remarkable model at thesame time and explains why only Sharpes work wasrecognized by the Nobel Committee.

THE BEGINNINGS OF A MODEL

In tracing the origins of the CAPM, twopapers appear to have been the primary inspirations.In 1952, Harry Markowitz provided the first trulyrigorous justification for selecting and diversifying a

portfolio with the publication of his paper PortfolioSelection. Later, he would expand his mean-variance analysis to a book-length study (1959)which firmly established portfolio theory as one of the pillars of financial economics. Markowitzs workpresents a direct and obvious root to the CAPM.After publishing his initial paper, Markowitz becameinterested in simplifying the portfolio selectionproblem. His original mean-variance analysispresented difficulties in implementation: to find a

mean-variance efficient portfolio, one needs tocalculate the variance-covariance matrix with N(N-1)/2 elements. Thus, a reasonably sized portfolio of 100 securities requires the daunting task calculating4,950 variances or covariances. Markowitzsuggested a possible solution to this problem byproposing a single index model (now referred to inthe literature as a one-factor model). Indeed, it wasthis idea that involved William Sharpe withMarkowitz and put Sharpe on a line of research thatculminated in his version of CAPM.

The other paper which motivatedresearchers is Franco Modigliani and Merton Millersclassic 1958 analysis, The Cost of Capital,Corporation Finance, and the Theory of Investment.In their original analysis, they explore theconnections between a firms capital structure and itscost of capital or discount rate. The absence of atheory for determining the correct discount rate

provided the impetus for Jack Treynor to develop thefirst truly theoretical analysis for determining thediscount rate.

FOUR ECONOMISTS IN SEARCH OF A

MODEL

In reviewing the literature, it appears thatJack Treynor developed the earliest version of theCAPM. Jack Treynor attended Haverford College inthe early 1950s. He notes that his real love wasphysics. lvi Unfortunately, the physics departmentconsisted of only two professors, one of whom was

blind and the other one about to retire. Rethinkinghis choice of majors, he chose mathematics. Aftercompleting his undergraduate studies, Treynorattended Harvard Business School where he wasawarded an MBA in 1955. At Harvard BusinessSchool I hadnt begun to think about the CAPMproblem except that I was dissatisfied with theanswers of finance guys, especially the corporatefinance guys, were giving me for the choice of discount rate for evaluating long-term corporate


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projects. In 1958, during a summer vacation,Treynor read Modigliani and Millers paper. Hereturned from the vacation with 44 pages of mathematical notes notes which eventually evolvedinto a paper entitled Market Value, Time, and Risk,which he never published. Treynor believes he firstshowed his paper to John Lintner at Harvard. Hewas the only economist I knew, which is why I gavehim the paper. He didnt give much encouragement.I suppose my paper seemed like a bunch of gobbledygook to John. Interestingly, Lintner thenpublished his version of the CAPM several yearslater.

In time, Treynors paper found its way toMerton Miller who then sent it along to FrancoModigliani at the Massachusetts Institute of Technology (MIT). Eventually, Modigliani calledTreynor and invited him to lunch. Treynor recallsthat Modigliani said, Merton gave me your paper,Ive read it and frankly you need to studyeconomics. Treynor then took a sabbatical fromArthur D. Little, where he was working at the time,and studied economics at MIT. While at MIT,Modigliani suggested that Treynor split his paper intotwo parts. The first paper, written in 1962 andpublished in 1999, became Toward a Theory of Market Value of Risky Assets. The second paper,written in 1963 and never published, was calledImplications for the Theory of Finance. Treynorobserves, The second paper was a failure. It wasntright. But the first paper was the CAPM. So basicallyFranco rescued the part of paper that was valid from

the rest. Interestingly, the second paper was laterreworked with Fischer Black and published in 1976as Corporate Investment Decisions.

After leaving MIT and returning to ArthurD. Little, Treynor received a call from Modiglianitelling him that William Sharpe was working on acapital asset pricing model. Modigliani suggestedthat Treynor and Sharpe exchange papers, which theydid. At this point, Treynor made a fateful decisionthat cost him the Noble Prize. He recalls, I thoughtthat if Sharpe was going to publish, whats the pointof my publishing my paper?

William Sharpe was born June 16, 1934 inBoston. He attended the University of California atLos Angeles where he earned three degrees ineconomics: Bachelor of Arts in 1955,a Masters of Arts in 1956 and a doctorate in 1961. Aftercompleting his masters degree and a tour in thearmy, Sharpe took a job as an economist at theRAND Corporation and began his Ph.D. studies.Sharpe took finance as one of his fields of

specialization. Here, he first studied the work of Harry Markowitz. Fortuitously, Markowitz wasworking at RAND when Sharpe joined the think tank.At the suggestion of one of his professors, Sharpeasked Markowitz if he had any ideas for adissertation topic. In his Noble Prize autobiography,Sharpe recalls, He had, and I proceeded to workclosely with him on the topic Portfolio Analysis

Based on a Simplified Model of the Rela tionships Among Securities . Although Harry was not on mycommittee, he filled a role similar to that of dissertation advisor. My debt to him is trulyenormous. The dissertation was approved in 1961, atwhich time I received the PhD degree. lvii In the finalchapter of his dissertation, Sharpe developed the firstdraft of his capital asset pricing model which featuresthe now famous security market line a positivelysloped straight line depicting the relationshipbetween expected return and beta. In 1961, Sharpebegan teaching finance at the University of Washington. While there, he began reworking thefinal chapter of his dissertation. He attempted topublish his analysis in the Journal of Finance .Initially, the paper was rejected. A referee deemedthe assumptions of his analysis too restrictive and theresults uninteresting (French, 2003, p.68).Eventually, the Jou rna l changed editors andpublished his paper in 1964.

The third individual credited withdeveloping CAPM was John Lintner. Born in 1916,Lintner received his undergraduate degree from theUniversity of Kansas. He started his graduate work

at Harvard in 1940 at the age of 24 after spendingtwo years in a sanitorium recuperating fromtuberculosis. In 1945, he completed a dissertationentitled Tax Restrictions on Financing BusinessExpansion. In his book, Fischer Black and the

Revolutionary Idea of Finance (2005), PerryMehrling agrues that Lintners analysis was inspiredby the Modigliani and Miller paper, just like Treynorhad been. Clearly, an examination of Lintnersearlier research reveals an interest in corporatefinance. For example, after CAPM research,Lintners most famous paper is arguably his 1956empirical study of corporate dividend policies.

Indeed, Mehrling argues that Lintner believed thatModigliani and Millers analysis was wrong.Specifically, Lintner hoped to refute their theory of an optimal capital structure by developing a theoryfor valuing risky assets a capital asset pricingmodel (Mehrling, 2005, ch.3). While Mehrlingmakes a plausible case for Lintners independentdevelopment of CAPM, it is important to rememberthat Lintner saw Treynors earliest draft of CAPM in1960 or 1961at least four years before Lintners


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own version of the model was published. (In theMehta interview, Treynor says he believes this paperwas typed in 1960, but he is not certain.) Did Treynorfeel that Lintner stole his work? If so, he has neverstated so publicly. How closely do the two papersresemble each other? In fairness to Lintner, his 1965papers are the most mathematically impressive of allthe models published. In them, he providesnumerous proofs and analyzes a variety of specialcases where his model still applies.

While Treynor never felt compelled tocompare his model with Lintner, Lintner did nothesitate to compare his own work with the then onlypublished competitor William Sharpe. Lintner feltthat his model was different and more general thanSharpes model. For a short time, at least, heconvinced Sharpe also. In his Journal of FinanceReply, Sharpe agrees that conflicts exist betweentheir models and that Lintners analysis supercedeshis model (Fama, 1968, p. 29). A closer examinationof the two models by Eugene Fama (1968), however,reveals that their general models representequivalent approaches to the problem of capital assetpricing under uncertainty (Fama, 1968, p.40). Famanotes, Unfortunately, Sharpe puts the major resultsof his paper in his footnote 22 (Fama (1968), p.37).Like Treynor, it seems, Sharpe failed to fullyappreciate the significance of his anlaysis. In theMehta interview, Treynor notes, We can look backnow and talk about the significance of the CAPM,but if it has any real significance, it wasnt evident atthe time to anybody

The last to publish the CAPM was JanMossin in 1966. Born in Oslo, Norway in 1936,Mossin graduated from the Norweigan School of Economics and Business in 1959. He did hisgraduate studies in economics at the CarnegieInstitute of Technology (now Carnegie MellonUniversity) in Pittsburgh. In his studies, hegravitated toward the study of risk in financialmarkets. In the last chapter of his dissertation,Studies in the Theory of Risk Bearing, contains achapter that is the basis of his CAPM analysis.Mossin was quick to realize the importance of his

work because he published his paper two yearsbefore completing his thesis in 1968. Once again, itis difficult to pin down exactly when he began workon CAPM and what he knew about the other threemens work. As noted on the first page of his paper,the revised manuscript was received by

Ec on om et ri ca in December, 1965. Assuming, atminimum, a one years lag between originallysubmitting the paper to the journal and writing hisfirst draft of the model, we can safely conclude that

Mossin began work on CAPM no later than 1964 --the year Sharpe published his first paper. In fact,Mossin cites Sharpes 1964 paper and critiques hislack of precision in the specification of equilibriumconditions (Mossin, 1966, p. 769.) lviii

In comparing the Treynor, Lintner, Sharpeand Mossin models, it takes some time before it isapparent that they are all talking about the sameissue. Indeed, the equivalence of Mossins model tothe three others work was not demonstrated until1970 (Stone, 1970). One simple reason for thisdifficulty is that the mathematical notation in thepapers are inconsistent; only a very close reading of the texts reveals that the key equations are essentiallythe same. At a more profound level, each paperreveals a different point of view. For example,Treynor was originally interested in capitalbudgeting/ cost-of-capital issues. Hence, hisemphasis on Modigliani and Millers famousProposition I that the capital structure of a firm isirrelevant to its value. Lintners approach appears tobe motivated by the concern of a firm issuingequities. Unlike Modigliani and Miller, Lintnerremained convinced that a firms financial policymattered a great deal. Sharpe approached theproblem via optimum portfolio selection, inspired, nodoubt, by the work of his mentor Harry Markowitz.Similarly, Mossins work was grounded in portfoliotheory but with a greater interest and emphasis onspecifying equilibrium conditions in the asset market.

CONCLUSIONS

The 1990 Noble Prize in economic sciencewas awarded to Harry Markowitz, Merton Miller, andWilliam Sharpe for their contributions in financialtheory. Until that moment, finance received littlerespect as a valid area of economic research. Sadly,the Noble Prize is not awarded posthumously. If itwere, John Lintner, who died in 1983, and JanMossin, who died in 1987, would have beenconsidered, most certainly, for the Noble Prize.Sadly, the first man to truly write down the capitalasset pricing model failed to appreciate thesignificance of his model. By not publishing his

work, Treynor effectively took himself out of contention for the award. Recently, his work wasfinally published (Korajczyk, 1999) and is now beingacknowledged by scholars in the field. It remains tobe seen if his momentous contribution will beacknowledged by a wider audience.


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REFERENCES

Fama, E. (1968). Risk, Return, and Equilibrium:Some Clarifying Comments. Journal of Finance, 23 ,29-40.

French, C.W. (2003). The Treynor Capital AssetPricing Model. Journal of Investment Management ,1(2), 60-72.

Lintner, J. (1956). Distribution of Incomes of Corporations among Dividends, Retained Earnings,and Taxes. American Economic Review , 46 (2), 97-113.

Lintner, J. (1965a). The Valuation of Risk Assets andthe Selection of Risky Investments in StockPortfolios and Capital Budgets. Review of Economicsand Statistics, 73 , 13-37.

Lintner, J. (1965b). Security Prices, Risk andMaximal Gains from Diversification. Journal of Finance, 20 , 587-615.

Markowitz, H. (1952). Portfolio Selection. Journal of Finance, 12, 71-91.

Markowitz, H. (1959). Portfolio Selection: Efficient Divers ifi cat ion of Inves tments . New York: JohnWiley & Sons.

Mehrling, P. (2005) . Fischer Black and the Revolutionary Idea of Finance. Hoboken: John Wiley

& Sons.

Mehta, N. (2005). Jack Treynor: The FEN Interview.Retrieved November 26, 2006, from http://www.fenews.com/fen49/one_on_one.html.

Modigliani, F. & Miller, M. (1958). The Cost of Capital, Corporation Finance, and the Theory of Investment. American Economic Review, 48 (3), 261-297 .

Mossin, J. (1966). Equilibrium in a Capital AssetMarket. Econometrica, 34 (4), 768-83.

Sharpe, W.F. (1964). Capital Asset Prices: A Theoryof Market Equilibrium under Conditions of Risk.

Journal of Finance, 19 (3), 425-42.

Sharpe, W.F. (1966). Reply. Journal of Finance,20 (4), 743-744.

Stone, B. K. (1970). Risk, Return, and Equil ibrium: AGeneral Single-Period Theory of Asset Selection and Capital Market Equilibrium . Cambridge: MIT Press.

Tobin, J. (1958). Liquidity Preference as Behaviortoward Risk. Review of Economic Studies, 67, 65-86.

Treynor, J. L. (1999). Toward a Theory of MarketValue of Risky Assets. Robert Korajczyk (Ed.),

Asset Pricing and Portfolio Performance . London:Risk Books.

Treynor, J. L. & Black, F. (1976). CorporateInvestment Decisions. Modern Developments inFinancial Management. Stewart C. Myers (Ed.),New York, Praeger.

lvi All quotes by Treynor are from the Mehta (2005)interview.lvii Sharpes dissertation advisor was Armen Alchian.His autobiography is available online at:http://nobelprize.org/nobel_prizes/economics/laureates/1990/sharpe-autobio.html.lviii It is interesting to note that the title of Mossinsdissertation chapter is exactly the same as his

Econometrica paper. Further, there are only eightreferences in that chapter including Markowitzs

book, Sharpes 1964 paper, and Tobins LiquidityPreference paper.

Edward J. Sullivan is an associate professor of business and economics at Lebanon Valley College. He earnedhis Ph.D. in Economics at The Pennsylvania State University. His research interests include monetary andfinancial economics.

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