Harry Markowitz passed on June 22, 2023; some four years short of reaching 100 years old. Dr. Markowitz was not a traditional economist. That fact was well-established and documented from his thesis defense at the University of Chicago. When Milton Friedman uttered lines to the effect that Harry’s thesis has nothing wrong with it, but is not an economics dissertation, Dr. Friedman applied a very narrow definition of economics. Harry was building the field of Financial Economics. Who was Harry Markowitz and how did his mind work? This author, having worked for, worked with, and co-authored papers for years with Harry Markowitz knows who he is. Harry is acknowledged as a (the) creator of Portfolio Theory. His dissertation was its Genesis (capitalized for a reason which will become obvious to the reader). Harry, as I will hereafter refer to him, was not a traditional person at all. Harry was included in a Springer monograph, Profiles in Operations Research (2010), as were several economists, several of whom won, or were finalists, for the Nobel Prize. Yes, for his work in portfolio theory, sparce matrices and simulation, Harry was awarded the 1989 John von Neumann Theory Prize from the Operations Research Society of America. Using ideas from sparce matrices, Harry developed an approach and a pivot selection rule, now called Markowitz rule, which applied to a large-scale problem, reduced the generation of the transformed matrix’s non-zero elements (Markowitz 1957). The sparsity of the transformed matrix is the key to solve large scale linear equations efficiently.
In 1990, Harry, William F. Sharpe, hereafter “Bill”, and Merton Miller shared the Nobel Prize in Economic Sciences. In two years, Harry had reached the pinnacle of two disciplines. During these two years, Harry was the chaired Professor of Finance at Baruch College, City University of New York, and a co-head of research at Daiwa Securities Trust Company, in Jersey City, New Jersey. This is who Harry was in 1990. This author cannot comprehend how Harry’s mind worked, given the very large breadth of subjects that he not only wrote on, but actively contributed to their development. Harry belonged to a very small subset of mankind, who were great thought-thinkers and even smaller subset who were great thought-thinkers and accomplished the objectives of their thoughts. Harry was so far above mere mortals in intellect that his mind was understood only by the likes of Paul Samuelson, James Tobin, Gerard Debreu, Kenneth Arrow, Bill Sharpe, Haim Levy, Martin Gruber, and Ed Elton, and several practitioners, including Richard Michaud, Ganlin Xu, John Blin, Bruce Jacobs, and Ken Levy.
Our intended audience is a set of MS and Ph.D. students in Financial Engineering, Computational Finance, Optimization, and Decision Sciences, particularly data mining. The majority of our readers are probably between 25 and 35 years old. That means that most of our readers were born about the time that Harry won the Nobel Prize.
Harry Markowitz was born in Chicago on August 24, 1927. It has been reported for years that Harry’s father was a grocer. Harry told many of his followers and audiences that he was not aware of The Depression growing up because his family always had food. Moreover, he told his audiences that he enjoyed comic books and reading, although he was not a great student, but passed an entrance exam to gain admission to The University of Chicago. There he read David Hume and studied liberal arts, graduating in 1947. Harry entered the graduate program in Economics where he studied under economists, including Milton Friedman, Tjalling Koopmans, Jacob Marschak, and Leonard Savage. Professor Tjalling Koopmans was the Director of the Cowles Foundation. Harry did well at Chicago, enough to be invited to become a Research Fellow at the Cowles Foundation in 1950-1951. Harry would earn an MA in Economics in 1952 and Ph.D. in 1954.
The Cowles Foundation: Behavioral Finance and Portfolio Selection
Why was the Cowles Foundation so important to Harry? The Cowles Foundation for Research in Economics at Yale University has as its purpose the conduct and encouragement of research in economics. The Cowles Foundation seeks to foster the development and application of rigorous logical, mathematical, and statistical methods of analysis.[1] The Cowles Foundation continues the work of the Cowles Commission for Research in Economics in publishing papers and monographs. The Cowles Foundation was founded in 1932 by Alfred Cowles at Colorado Springs. Mr. Cowles authored several papers on forecasting stock prices during The Depression. The Cowles Commission moved to Chicago in 1939 and was affiliated with the University of Chicago until 1955. Other Research Associates in 1950-1951 included Carl Christ, Gerard Debreu, Jacob Marschak, and Leonid Hurwicz.[2] The Cowles Foundation adopted its motto “Theory and Measurement,” in 1952. It was during the 1950 -1951 period that Harry researched three Cowles Foundation papers that would be published in 1952 while he was at the Rand Corporation. The first paper was Cowles Foundation Paper No. 57, “The Utility of Wealth”, better known to the world as “The Utility of Wealth”, Journal of Political Economy 60 (1952), pp. 151-158. The JPE, as the Journal of Political Economy is popularly known, has been a top-four economics journal since its founding under James Laurence Laughlin in the early 1890s. The Markowitz paper on utility theory was a contradiction to the Friedman and Savage classic paper, which sought to explain the existence of insurance and lotteries.[3] Instead of different social classes, as Friedman and Savage hypothesized, Harry based his utility discussion on income and economic observation. Harry stated that lower income persons would not accept a fair (lottery) bet below a certain level, nor would higher income persons accept a fair lottery bet above a certain level. People with wealth levels between the lower wealth and the higher wealth level would accept a fair bet. [4] As Harry stated on p. 152:
“We do not observe persons of middle income taking large symmetric bets. We expect people to be repelled by such bets. If such a bet were made, it would certainly be considered unusual and probably irrational.”
The bet which this person would like most, according to the Friedman and Savage (F&S) hypothesis, is one which if won would raise him to a rich level of income, if lost it would lower him to the lower level of income. The investor would be willing to take a small chance of a large loss for a large chance of a small gain. Contrarily, he would be anxious to underwrite insurance. He would even be willing to extend insurance at an expected loss to himself.
Harry, on p. 153 stated:
“Again such behavior is not observed. On the contrary we find that the insurance business is done by companies of such great wealth that they can diversify to the point of almost eliminating risk. In general, it seems to me that circumstances in which a moderately wealthy person is willing to risk a large fraction of his wealth at actuarially unfair odds will arise very rarely.”
Harry believed that the Friedman and Savage utility function was inconsistent with economic behavior. The Markowitz utility function was shaped like a snake, changing second derivatives as wealth increased. Harry noted on page 155:
“To summarize my hypothesis: the utility function has three inflection points. The middle inflection point is defined to be at the “customary” level of wealth. Except in cases of recent windfall gains and losses, customary wealth equals present wealth. The first inflection point is below, the third inflection point is above, customary wealth. The distance between the inflection points is a nondecreasing function of wealth. The curve is monotonically increasing but bounded; it is first concave, then convex, then concave, and finally convex. “
The Markowitz utility theory paper became one of the great foundations of behavioral economics and has had a profound impact on researchers in behavioral finance.
The second paper, “Portfolio Selection”, Cowles Foundation Paper No. 60, is better known to the world as “Portfolio Selection”, Journal of Finance 7 (1952), pp. 77-91. Harry developed the concept of the Efficient Frontier, where efficient portfolios offered the greatest returns for a given risk, or the minimum risk for a given level of return. Investment managers should not buy low price-to-earnings stocks, as advocated by Graham and Dodd (1934) and John Burr Williams (1938) without assessing their risk. It was risk and return that must be considered for an optimal portfolio. The Efficient Frontier required statistical inputs of stocks’ expected returns and the measurement of risk, the stocks’ variances and the covariances among the stocks. Furthermore, risk could be reduced by investing in assets with lower covariances. Harry emphasized the role of covariances. Investment managers should systematically create portfolios to maximize return for a given level of risk.
The concept of the efficient frontier can now be found in most textbooks on financial management or investment management and analysis. The efficient frontier is used to discuss why many investors prefer stock-intensive portfolios to cash or bond investments, why smaller-capitalized stocks may be preferred to larger-capitalized stocks, and why portfolios composed of global stocks are very often preferred to portfolios composed of domestic-only stocks. Before Harry’s work, investors described in words what was meant by the risk–return trade-off; after Harry, investors were able to precisely quantify, in mathematical terms, the risk–return trade-off (Rubinstein 1991). Investors tended to disregard the risk of assets. The risk–aversion of the investor identified the portfolios to choose from among the portfolios on the efficient frontier. If one seeks to maximize the long-run rate of return of the portfolio and maximize the expected utility of (final) terminal wealth, then one selects the portfolio that maximizes the excess return-to-risk measure, known as the Sharpe Ratio (Sharpe , 1966 and 1994). This portfolio maximizes the geometric mean of the strategy, as well (Bloch et al. 1993; Markowitz 1959).
The third paper of 1952 was Cowles Foundation Paper No. 67, co-authored with Leo Goodman, on individual social welfare functions published in the American Journal of Sociology (1952).
The Cowles Foundation Research Consultants in 1950 -1951 included Kenneth Arrow, Harold Davis, William Hood, Trygve Haavelmo, Lawrence Klein, Franco Modigliani, and Herbert Simon. Why do we stress the Numbers (capitalized for a reason) of the papers? Harry did, when he talked to friends and researchers. He referred to his 1952 papers by their Cowles Foundation numbers. Herbert Simon published Cowles papers 47 and 70; Kenneth Arrow published papers Numbers 54 and 62; Lawrence Klein authored papers 55 and 69; and Paul Samuelson authored Cowles Paper Number 61. All these Cowles papers were published in 1951-1952! Of this Cowles Foundation group, Harry, Debreu, Arrow, Klein, Modigliani, and Simon won Nobel Prizes in Economics. Harry received some of the greatest training available to American economists.
In 1955, the professional research staff of the Commission accepted appointments at Yale and, along with other members of the Yale Department of Economics, formed the research staff of the newly established Cowles Foundation. Harry took a leave from Rand and went to Yale, at the invitation of Professor and the new Cowles Foundation Director James Tobin. From August 1955 to May 1956, Harry was at the Cowles Foundation at Yale, supported by a grant from the Merrill Foundation for Advancement of Financial Knowledge. It was at Yale that Harry penned his Portfolio Selection: Efficient Diversification of Investments (New York: John Wiley & Sons 1959). [5] Harry expected educated people to be familiar with his book. He expected readers to remember Chapter 5 was on diversification and how risk could be altered by covariances and the number of stocks. Chapter 6 introduced the Geometric Mean to its readers, and its promise to produce the greatest return in the long run. Chapter 7 was the geometric analysis of the Efficient Frontier, one seen in his 1952 Journal of Finance (JF) paper. Chapter 8 crunched the numbers on the Efficient Frontier. Chapter 9 was on the semi-variance, or downside risk. Chapter 10 was the maximization of expected utility and Chapter 12 was applications to portfolio selection. In some 350 pages, Harry wrote the Cowles Foundation monograph 16, Portfolio Selection, that changed the world of investments. Harry always referred to his book to the author as Cowles Foundation 16. Of the first 21 Cowles Foundation monographs, 11 were authored or co-authored by Nobel Prize winners. Harry always enjoyed showing younger researchers the list of Cowles Foundation monographs and telling them of how he, Koopmans, Klein, Debreu, and Tobin and the Cowles Foundation researchers brought “Theory and Measurement” to Economics.
RAND, Simulation, and Arbitrage
Harry had not completed his dissertation despite these three major publications. Harry’s early career was both extremely productive and he was very ambitious. The author worked with Harry on the Markowitz chapter in Profiles of Operations Research (Guerard, 2011), to completely understand his employment between 1952 to 1971. This section draws heavily on that chapter. In 1952, he felt that it was time to find a job. While attending a meeting of the American Economic Association, he met members of the RAND Corporation’s economics department. At the time, RAND was a research organization in Santa Monica, California, supported by the U.S. Air Force. They expressed interest in Harry’s research and offered him a job at 50% more than an offer he already had from a university. Harry left the University of Chicago for RAND in early 1952 (Yost 2002, 7–8). Harry’s initial RAND research was applying linear programming (LP) to economic problems. Harry’s first exposure to LP occurred at RAND when he was asked to read George Dantzig’s paper on the simplex method (Dantzig 1951) and to supervise the computer programming and the running of RAND’s first simplex code on an IBM Card Programmed Calculator (CPC). George Dantzig, the developer of LP and the simplex method, joined the RAND staff in June 1952, and over time, with the programming talent of William Orchard-Hays, RAND’s ability to solve LP problems made great advances as computer speeds increased and computer-based LP algorithms improved (Markowitz 2002; Orchard-Hays 1984). Dantzig’s work contributed to the solution of the portfolio selection problem in the following ways: Markowitz (1956) defined the portfolio selection problem as that of finding mean-variance efficient portfolios subject to linear equality and inequality constraints. This is the same constraint set as that of linear programming, but with mean-variance efficiency rather than the optimization of a linear function as the objective. The portfolio with maximum expected return, when it exists, is the natural starting point in tracing out the set of efficient portfolios, allowing short positions Since expected return is a linear function of portfolio investments, finding the portfolio with maximum expected return is a linear-programming problem. Dantzig’s simplex algorithm not only provides the solution to this problem, but also provides the critical line algorithm [for generating the efficient frontier] with various other services. In particular, it determines whether or not the constraint set specified by the analyst is feasible, whether or not feasible portfolio expected return is bounded and, if the model is rank deficient, it provides an equivalent model which is not rank deficient (Markowitz 2002, p. 155).
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In the 1950s, RAND was using computer-based simulation procedures to evaluate military situations, with special emphasis on war games. To that end, RAND created a logistics laboratory within its Economics Department. Although Harry was familiar with simulation ideas and techniques as applied to industrial operations and warfare research, his first hands-on exposure to such simulations was when he was assigned to the laboratory to coordinate the development of its computer-based simulation models (Markowitz 2002; Yost 2002). The laboratory’s first simulation model, called LP1, “was a man-machine simulation in which actual air force logistics officers played the role of air force logistics officers. The computer flew simulated missions, generated part failures and other maintenance requirements, and kept track of parts supplies and aircraft status” (Markowitz 2002, 157). Some time after LP1 was finished, Harry received a job offer from the General Electric (GE) Company and accepted a position within the Manufacturing Services Department located in New York City. Alan Rowe was now with GE and was the supervisor of the programming of a large, detailed job-shop simulator. Harry, based on Rowe’s experiences and his own understanding of the problems in building a simulator, had developed ideas as to how to reduce programming time and increase a simulator’s flexibility. He applied his ideas to the building of the GE Transformer Department’s shop simulator, the General Electric Manufacturing Simulator (GEMS). Although GEMS was well received at GE, it was not as flexible as Harry hoped it would be. Harry gave much thought to what attributes a simulation should have and decided to write a nonproprietary simulation language. He did not want to develop it at GE because it would then be proprietary. He went to the job market and returned to RAND to put his ideas to work. At RAND, Harry teamed up with Bernard Hausner and, with the help of Herbert Karr, developed SIMSCRIPT, a very powerful, influential, and long-lived computer-based simulation system (Markowitz et al. 1963). Hausner was a RAND computer programmer and was responsible for the development of the computer-based simulation language using Harry’s novel simulation concepts of entities, sets, and events. The initial name for the language was Simulation Programming System One (SPS1). Herb Karr, a friend of Harry’s, was hired to write the SPS1 manual. Herb wrote the manuscript for the evolving language. SIMSCRIPT introduced some novel concepts. It was ‘‘designed to facilitate the programming of ‘discrete event’ simulation models, especially ‘asynchronous’ discrete event simulators, as compared to continuous time or difference equation models’’ (Markowitz 2002, p. 157).
Sparse matrix methods are now widely used to solve very large systems of simultaneous equations whose coefficients are mostly zero. SIMSCRIPT has been widely used to program computer simulations of manufacturing, transportation, and computer systems as well as war games. SIMSCRIPT (I) included the Buddy memory allocation method, which was also developed by Markowitz. The company that would become CACI International was founded by Herb Karr and Harry Markowitz on July 17, 1962 as California Analysis Center, Inc. They helped develop SIMSCRIPT, the first simulation programming language, at RAND and after it was released to the public domain, CACI was founded to provide support and training for SIMSCRIPT. Under contract to IBM, Harry, based on SIMSCRIPT II, helped to develop an experimental programming language integrated with a database management system, the EAS-E system (Markowitz 2002). EAS-E (pronounced EASY) was built around the entity, attribute, and set (EAS) view of application development. IBM used EAS-E for an internal application, but it was never released as a product. CACI developed and marketed a proprietary version of SIMSCRIPT II, SIMSCRIPT II.5. In 1968, Harry left CACI and, for the first time, joined academia as a professor at the business school of the University of California-Los Angeles (UCLA). For those who thought that Harry’s departure from CACI was his Exodus (capitalized for a reason) from CACI, his demise, oh were they wrong.
In 1968, Markowitz joined Arbitrage Management Company founded by Michael Goodkin. Working with Paul Samuelson and Robert Merton, he created a hedge fund that represents the first known attempt at computerized arbitrage trading. He took over as chief executive in 1970. After a successful run as a private hedge fund, AMC was sold to Stuart & Co. in 1971. A year later, Markowitz left the company.
About the Author
John Guerard
Scientific Advisory Board, McKinley Capital Management, LLC
Anchorage, AK
[1] https://cowles.yale.edu/about-cowles.
[2] Cowles Commission for Research in Economics. “Rational Decision-Making and Economic Behavior. 19th Report Annual Report, July 1, 1951 – June 30, 1952.
[3] M. Friedman and L. J. Savage, “The Utility Analysis of Choices Involving Risk,” Journal of Political Economy 56 (1948), pp. 279-304.
[4] H. Markowitz, “The Utility of Wealth”, Journal of Political Economy 60 (1952), pp. 151-152.
[5] Harry Markowitz, Portfolio Selection: Efficient Diversification of Investments (New Haven: Yale University Press, 1970). The author’s copy is the second printing, page xiii.
