PROFILES OF WORLD ECONOMISTS

WILLIAM F. SHARPE

doc. Ing. Veronika Piovarčiová, CSc. Faculty of National Economy, University of Economics in Bratislava

Financial markets form an indispensable portant indicator and accelerator of econo- part of well-functioning modern market eco- mic development. nomies. Their impact upon the development The theory of financial markets is relative- of the main macro-economic parameters ly new. In commemoration of Alfred Nobel, such as economic growth, employment and the Swedish Royal Academy of Sciences ga- balance of payments has been growing in ve the prize for economics for the year 1990 importance. These markets are a vehicle for to the pioneers in this area, Harry M. Mar- transferring savings from different sectors of kowitz, William F. Sharpe and Merton Mil- the economy to firms, which in turn transform them in ler, whose research laid the foundations of the econo- investments into buildings, equipment, and modern mic theory of finance. technologies. Financial markets are therefore an im-

William F. Sharpe was born in Boston, Massachussets on Ju- sertation. In terms of its title as well as contents, this paper con- ne 16, 1934. He received his secondary-level schooling from stituted a basis for what was later termed the Capital Asset Pri- eminent public schools in Riverside, California. In 1951 he en- cing Model (CAPM). rolled for the study of medicine and natural sciences at the Uni- In 1968 W. Sharpe moved to the University of California at Ir- versity of California at Berkeley. After one year, however, he vin, where he was supposed to take part in an attempt to create found that his interests lay somewhere else, and so he went to a school of social sciences with quantitative and interdisciplina- the University of California at Los Angeles, where he chose as ry orientation, which was not particularly successful. That is his major subjects corporate management, accounting and eco- why he left for the Stanford University Graduate School of Bu- nomics. In 1955 he received the degree of Bachelor of Econo- siness in 1970. At that time he finished the book called Portfolio mics and in 1956 he obtained the academic masters degree. Theory and Capital Markets, which summarized his research up Sharpe’s future career was notably influenced by two UCLA to that date, with a focus on the issues associated with the equi- professors. First and foremost it was Professor of Economics librium of capital markets and impacts on investors’ portfolio Armen Alchian, under whose influence he came to be enchanted choice. by the theory of microeconomics. He taught his students to chal- In 1973, W. F. Sharpe was appointed the Professor of Finan- lenge everything, to concentrate on the main issues and disre- ce at Stanford University. He extended his research into the ro- gard inessential ones, but most importantly, he was able to per- le of the investment policy of funds, focusing on the discharge of fectly defend his own thoughts. obligations with regard to the payment of pension benefits. At Fred Weston, Professor of Finance, under whose leadership that time he wrote his first textbook, Investments, which was Sharpe worked as a research assistant, not only introduced him published in 1978. It provided a summary of institutional, theo- to the work of Harry Markowitz, which at that time initiated the retical and empirical issues in the area of financial market in- revolution in the field of finance, but also recommended him to vestments and its publication met with great success. Its fourth consult with Markowitz on the topic of his dissertation entitled edition, co-authored by Gordon Alexander, has already been “Analysis of Portfolio Based on Simplified Model of Relations- published. The work on this textbook led Sharpe to extend his hips Between Securities”. Sharpe defended this dissertation in original theories and conduct new empirical analysis. This re- 1961, winning the PhD. degree. At the same time, he moved to sulted in the formation of a binomal process of option pricing, Seattle and started to teach finance, microeconomics, statistics, which provides a practical method for valuing instruments in- operational research and computer science at the Business volving multiple put options and is widely used today. He also School at the University of Washington, where he stayed until developed a simple, but efficient method – namely a portfolio 1968. analysis algorithm. In his dissertation work, Sharpe dealt in particular with the Apart from theoretical research, W. F. Sharpe also pursued positive theory of securities market behavior. The closing cha- the issue of practical utilization of findings made as part of the pter of this paper contained results similar to those nowadays economic theory of finance. During the course of his entire re- referred to as the securities market line relationship, but under search, he cooperated with a number of organizations in the the restricted conditions of a one-factor model. area of investment. He sat on the Board of Directors of nume- In 1963, he published a paper summarizing the normative rous investment firms and trusts. He worked as a consultant for conclusions from his dissertation work in Management Science, Merril Lynch, Pierce, Fenner and Smith and Wells Fargo In- and later on he expanded it for the generalization of the theory vestment Advisors. In 1980 he was elected the President of an of equilibrium contained in the concluding chapter of his dis- American financial corporation. His main focus was on decent-

BIATEC, Volume X, 9/2002 21 PROFILES OF WORLD ECONOMISTS ralized investment management, but he also continued his work help pension funds and foundations in making decisions about on issues relating to the investment policy of pension funds, stu- the allocation of assets, as well as the provision of consulting died the process of generation of earnings in the American mar- services. ket for shares, as well as the allocation of investors’ funds to the In 1989 he became Emeritus Professor of Finance at Stanford main classes of assets. In order to make his findings available to University, and mainly focused on research and consulting for the public at large, he developed a program to optimize softwa- his company William F. Sharpe Associates. re and databases under the title of Asset Allocation Tools. W. F. Sharpe holds a number of acknowledgments for out- In 1983 W. Sharpe was involved in the international invest- standing contributions he made while lecturing on and resear- ment management program offered by the Geneva International ching into the science of finance. In 1990 he was awarded The Management Institute, and later by the London Graduate Scho- Nobel Prize for Economics for the formation of the Capital As- ol of Business as well as the Nomura School of Advanced Ma- set Pricing Model. nagement. He aimed to acquaint domestic and foreign invest- In 1986 he got married. His wife, Kathryn, is a painter and ment specialists practicing in the field of investment with the trustee of William F. Sharpe Associates. Sharpe has two child- latest findings of the economic theory of finance. ren – daughter Deborah and son Jonathan. His hobbies include In 1986 he founded the Sharpe-Russel Research, a firm targe- yachting, opera, as well as American football and basketball ted at the research and development of procedures intended to matches.

The Contribution of W. Sharpe to the Science • taxes and transaction costs are negligible; of Economics • information is freely and immediately available to all inves- tors; The contribution W. Sharpe made towards the economic • investors have homogenous expectations, which means, science is very weighty and can be classified as falling under they have the same attitudes with respect to the expected re- the micro-economic theory of the capital market. According turns, standard deviation and covariance of securities. to his own words, he has always stayed within the confines of It is evident from the said assumptions that securities are as- positive economics, which enabled him to develop a descrip- sumed to be perfectly competitive under this model. These as- tive model of capital asset pricing. sumptions made it possible for Sharpe to examine what hap- Markowitz’s theory of portfolio choice presupposes that the pens to the prices of securities if everybody invests in a similar prices of securities are given and, assuming this, it defines manner, and thus to derive the essence of the resulting equilib- a procedure followed by a optimizing investor in his behavior. rium relationship between the risk and return of any security. Therefore the next necessary analytical step was to explain A very important feature of the CAPM is the so-called se- how prices of various assets are determined. The answer – alt- paration theorem, which reads as follows: an optimum com- hough very simple at first glance, that is by means of demand bination of risky securities can be determined without any for and supply of securities – however requires the definition knowledge about the investor’s attitude towards risk and re- of factors determining this demand and supply. That is why turn. The separation theorem relies on the attribute of a line- Sharpe concentrated on the determination of economic equi- ar efficient set, due to which all the portfolios located within librium through the price mechanism operating in the capital the linear effective set consist of a combination of one port- market. Drawing upon elementary microeconomic theory it folio solely formed of risky assets, involving either a risk-free holds true that current market prices for any security must al- investment or risk-free lending. From this it follows that the ways stand at such a level, where the number of each particu- risky portion of any investor’s portfolio is independent of the lar security demanded equals the number of this security offe- investor’s attitude towards return and risk. red. For this reason, a decisive role in his model is played by Another important attribute of the CAPM relying on the se- the examination of the market portfolio. In Sharpe’s view, paration theorem is that at the equilibrium point, any securi- from among a vast number of factors determining the capital ty must have a non-zero share in the portfolio mix. That is to market demand and supply, it is especially an equilibrium re- say, if no investments were made into securities with a share lationship between the risk and return that is decisive. He ar- in the portfolio of zero, the prices of securities with a zero rived at this conclusion based on a model known as: share would have to drop, thus leading to an increase in the expected return – up to the point at which they acquire a non- The Capital Asset Pricing Model – CAPM zero proportion. When the leveling of prices is stopped, the market reaches an equilibrium state, where it holds true that: Like any other model, the CAPM relies on certain simpli- • every investor will want to hold a certain amount of each fying assumptions: risky security; • investors appraise their portfolios according to expected re- • the current market prices of any security will stand at the le- turn and standard deviation over a certain period of time; vel, where the number of shares of each demanded security • they have an aversion to risk; equals the number of shares offered; • there is a risk-free rate, at which an investor may lend or • a risk-free rate is at the level where the total amount of mo- borrow money, which is identical for all investors; ney borrowed equals the amount lent.

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This will result in a portfolio mix known as a market port- ted below this line, since an individual security held separa- folio. The market portfolio (M) plays a key role in the CAPM tely does not constitute an efficient portfolio. and is defined by Sharpe as follows: it is a portfolio formed When using the CAPM, every investor would want to know of investments in all securities in such proportions that a por- the standard deviation of his market portfolio, since it is going tion invested in an individual security corresponds to its rela- to influence the amount of his investments. The contribution of tive market value. The relative market value of a security any security towards the market portfolio standard deviation equals aggregate market value of the security divided by the depends on the magnitude of its covariance with the market sum of aggregate market values of all securities. portfolio. The covariance between a security and the market δ An efficient set is formed of an investment in the market portfolio – im is therefore an essential rate of risk for the se- δ curity, which means that securities having higher values of im return will be considered, from the point of view of investors, to be rp securities contributing towards the market portfolio overall risk CML to a greater extent, but should not be considered as more risky r M than securities with lower standard deviations. This is due to m δ the fact that securities with greater values of im will have to yi- eld proportionally greater return in order for investors to beco- rf me interested in their purchase. In the opposite case these se- curities would be eliminated from the portfolio, which would δ M δ however lead to an increase in the market portfolio expected re- p risk turn relative to the standard deviation. The prices of securities portfolio associated with a required number of risk-free loans would then not be at equilibrium. That is why the equilibrium or borrowings. With the use of the CAPM it is possible to de- relationship between the risk and return had the precisely the δ2 δ termine a relationship between the risk and return of efficient following shape: ri = rf + [(rm – rf)/ m] im portfolios. This relationship between the covariance and expected re- The efficient portfolios diagram is defined by a line com- turn is known as a securities market line (SML), which can β β prising different combinations of risk and return obtained also be expressed as: ri = rf + (rm – rf) i, where the i coeffi- β δ δ 2 through the combination of market portfolio with risk-free lo- cient is defined as i = im/ m . β ans or borrowings. This CAPM linear efficient set is known The Beta factor – i of a security is an alternative way of as a capital market line (CML): expressing the security’s covariance risk. One of the proper- The M point represents a market portfolio, rf represents ties of Beta is that the Beta portfolio is a weighted average of δ a risk-free interest rate and rp and p stand for expected value Betas of individual securities forming this portfolio, where and standard deviation of an efficient portfolio. Efficient port- the respective weights are represented by proportions at folios chart is a line which starts at rf and passes through M. which investments are made in individual securities. This is Any portfolios employing a portfolio other than the market why the Beta factor constitutes the essential rate of risk for portfolio, and risk-free loans and borrowings would lie below a security. This means that the Beta portfolio is calculated β Σ N β the CML. The CML angular coefficient equals the difference according to the relationship: p = i =1Xi i. between an expected return of the market portfolio and the ex- The equilibrium relationship expressed by SML is based on pected return of a risk-free security rm – rf divided by the dif- the impact of investors’ adjustments to securities holdings on ference between their risks. That is why a line characterizing prices. If a set of securities prices is given, investors will cal- δ δ the CML has the following shape: rp= rf + p [(rm – rf)/ m]. culate expected returns and covariances, and then determine The capital market equilibrium can be characterized by two their optimum portfolios. If the number of securities deman- key values. The first one equals a section on the vertical axis ded in the aggregate differs from the number of securities of- of the CML (i.e. the risk-free rate) and is frequently referred fered, a pressure to increase or decrease their prices arises. In- to as the compensation for waiting. The second value is defi- vestors will reevaluate their securities holdings until ned by the CML angular coefficient and is frequently referred consistency between the number demanded and offered is re- to as the compensation for a unit of risk. That is why the ca- ached. Individual securities are valued according to their con- pital market is basically a place where trading is done at pri- tribution towards the market portfolio standard deviation, ces determined by supply and demand relative to time and where this contribution can be measured with the use of the risk. Since the CML represents an equilibrium relationship Beta factor. This is how the securities are priced under the between the expected return and standard deviation of effici- CAPM. ent portfolios, individual securities will always be represen-

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The best known works of W. F. Sharpe What makes the contribution of W. F. Sharpe’s work even • Introduction to Managerial Economics (1973) more valuable is the fact that he always reflected upon the • The capital asset pricing model: A multi-beta interpretation practical utilization of the theory of finance. That is why he (1977) published a great number of articles in different periodicals. • Investments (1978) It would take several pages to list them all. Thence we shall • Asset Allocation Tools (1985) only refer to his most important summary works: • An algorithm for portfolio improvement (1987) • The Economics of Computers (1969) • Fundamentals of Investments (1989) • Portfolio Theory and Capital Markets (1970)

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