Father of Modern Portfolio Theory

By Alan Lavine

Harry Markowitz’s Nobel Prize win- bonds and gold bullion. These investments liked reading comic books. But in high ning Modern Portfolio Theory was put to performed well while stocks worldwide school, he took to studying physics and the supreme test in The Great Recession and high-yield corporate bonds plunged, astronomy. He also read the philosophy of 2008. The stock market plunged nearly MarkowitzStill says. Diverof David Humes andifie Charles Darwin’sd The 40%, stock and corporate bond markets For over six decades, “MPT,” as Mod- Origin of Species. crashed, the money markets froze up. ern Portfolio Theory is nicknamed, has Markowitz said he had no plans to go Uncle Sam had to bail out major banks, provided money managers and sophisti- into economics when he graduated from while letting Bear Stearns and Lehman cated investors with a tried-and-true way the University of Chicago after completing Brothers fail. to select portfolios. a Bachelor’s degree in two years. He was It raised the big question: Does Modern Markowitz’s work is the key to squeez- fascinated with the economics of uncer- Portfolio Theory hold up during once-in- ing the best returns with the least amount tainty, and credits a course on “Observa- a-lifetime events? of risk out of portfolios of different asset tion, Interpretation and Integration” with “It is sometimes said that portfolio the- classes. It analyzes the effects of asset risk, having a strong impact on him. ory fails during a financial crisis because correlation and diversification on expected Modern Portfolio Theory did not all asset classes go down and all correla- portfolio returns. But much depends upon emerge from a vacuum. The use of sta- tions go up,” Markowitz said in a tele- how you split up your investment pie, tistical methods has its roots in the 17th phone interview from his office in San Markowitz stresses. and 18th centuries. Christian Huygens, in Diego, CA. Markowitz, at 84 years old, teaches his 1657, published a work on the calculus of But this, stressed the Ph.D. winner of the landmark Modern Portfolio Theory at the probabilities, based on communications Nobel Prize for economics, is already pre- Rady School of Management at the Uni- with French mathematicians Blaise Pascal dicted by his Modern Portfolio Theory. versity of California, San Diego. He is also and Pierre de Fermat. Swiss mathemati- “Generally, asset classes move roughly working on a book and consulting with cian Johann Bernoulli published studies in proportion to their historical betas,” he companies, such as Index Fund Advisors, on mathematical expectations. Work by said. The beta value is a measure of how an investment advisory firm, and Guided English mathematician Thomas Bayes in risky an asset is in relation to the overall Choice, advisor to 401(k) plan sponsors. 1763 determined probabilities based on stock market. The S&P 500, for example, Markowitz was born an only child in observed frequencies could be applied to has a beta value of one. So a stock or Chicago in 1927. His parents, Morris and social decision making. In 1812, a Pierre- mutual fund that has a beta value greater Mildred, owned a neighborhood gro- Simon Laplace book, The Analytic Theory than one will lose more money when the cery story. Because his family was in the of Probabilities, revealed probability esti- market declines than a stock that has a food and dry goods business, he was not mates could be used to solve many differ- beta value less than one. severely affected by the Great Depression. ent types of problems. Portfolio managers that limited risk Like other boys his age, he liked playing In the early 20th century, many of the during the 2008 recession kept a percent- basketball and football. He also played the faculty members in the economics depart- age of their portfolios in US Treasury fiddle in the high school orchestra and ment of University of Chicago emphasized

www.MoAF.org | Fall 2011 | Financial History 17 mathematics in economic decision-mak- on Wall Street in 1792. But the invest- dissertation. At the time, he was working ing. His mentors included renowned fac- ments were often more highly correlated for the Cowles Foundation. Economist ulty members Leonard Savage, Tjalling and riskier than anticipated. The reason Milton Friedman argued that portfolio Koopmans, Milton Friedman and Jacob was that they failed to use the tools to theory was not economics, so Markowitz Marschak. mathematically evaluate performance should not be awarded his Ph.D. But after One study, published by Milton Fried- relationships. a short debate by the dissertation commit- man and Leonard Savage in The Jour- Markowitz believed variance should be tee, the work was approved. nal of Political Economy in August 1948, used as a measure of risk in conjunction “At the time I defended my disserta- especially influenced him. The study, with expected rates of return on a portfo- tion, portfolio theory was not part of eco- “The Utility Analysis of Choices Involv- lio of stocks. The expected rate of return, nomics,” he said. “But now it is.” ing Risk,” revealed that when individuals simply put, is the average of the probabil- Markowitz looks at the world based on choose occupations, investments or busi- ity distributions of returns. The variance, utility and personal probability. When he ness ventures, they essentially make one or standard deviation, which is the square goes for daily lunchtime walks, he notices of two decisions. They either take risks or root of the variance, measures how far the license plate numbers and routinely cal- play it safe. Also influencing his thinking numbers spread out from each other. culates the probability of seeing the same was Tjalling Koopmans’ graduate course “Variance came to mind as a measure number reoccur. For example, the prob- on activity analysis. of risk,” Markowitz said. “The fact that ability of seeing a license plate with four While working on his Ph.D., Markowitz portfolio variance depended on security of a kind such as 6666 is one in one thou- was invited to become one of the student covariance added to the plausibility of sand, he said. But every year, if you walk members of the Cowles Commission for the approach. Since there were two crite- enough you will see another license plate Research in Economics, now the Cowles ria — risk and return — it was natural to with four of a kind. It’s the same, he said, Foundation at Yale University in New assume that investors selected from the set with the stock market. Haven, CT. The commission, affiliated of optimal risk-return combinations.” Markowitz advocated optimizing port- with the University of Chicago from 1939 In the 1959 edition of his book, Port- folios to get the best return per unit of risk to 1955, fosters the development and appli- folio Selection (Blackwell), Markowitz by using asset correlations dating back to cation of rigorous logical, mathematical explained that that variance does not go 1926, rather than short-term and current and statistical methods of analysis in eco- to zero when risks are correlated. Variance correlations. History tends to repeat itself, nomics. Economist Alfred Cowles III, its can be substantial even if correlations are he believes, but not in the same sequence. founder, was a fellow and treasurer of the just .1 to .3 among securities, on average. So there is always a chance the investor New York-based Econometric Society, an Markowitz said investors should esti- could experience losses similar to 1929, international society for the advancement mate the likely returns, risks and correla- 1982, 2002 and 2008. of economic theory in relation to statistics tions among various asset classes and use “Personally I think that nature draws and math. Cowles, whose grandfather was these inputs to conduct a Modern Portfo- from the basket known as the S&P 500 a founder of The Chicago Tribune, applied lio Theory analysis. This produces a curve randomly every year,” he said. “The stock statistical techniques to compare financial of “efficient” risk-return combinations. If market losses in 2008 have a probability performance. you want greater return on average, you of occurring about once out of every 40 Markowitz said his experience work- have to take on greater risk. If you want years. The 38.5% loss on the S&P 500 was ing on the Cowles Commission helped less month-to-month and year-to-year more than 2.5 standard deviations below him get an idea for his dissertation. While fluctuations, you have to accept less return the mean.” waiting to see his dissertation advisor, on the average in the long run. Yes, the 2008 market crash could hap- Jacob Marschak, he began chatting with In 1989, Markowitz won the John von pen again, he said, but you don’t know Marschak’s stockbroker, who also awaited Neumann Theory Prize by the Institute when. The losing cards are in the deck. Marschak. Markowitz already had learned for Operations Research and Manage- Markowitz’s famous portfolio theory from Marschak about using probability ment Sciences, a Hanover, MD organiza- for allocating assets was refined by later mathematics to study the elasticity of tion dedicated to applying scientific meth- research. The Capital Asset Pricing Model, demand for money and the relationship of ods to help improve decision-making, designed by William Sharpe in 1963, gave money to wealth. So he naturally expanded management and operations. The honor money managers an extra measure of that idea to financial market performance. was for his research on portfolio theory, risk to consider. Sharpe’s theory consid- Markowitz got some basic ideas of port- sparse matrix analysis to solve simultane- ers systematic risk, or how an asset moves folio theory while reading John Burr Wil- ous equations and SIMSCRIPT, which is in relation to the overall market. Under liam’s book, Theory of Investment Value used to program computer simulations in Sharpe’s theory, systematic risk is mea- (Fraser). Williams’ book stressed that the business and war games. sured by a portfolio’s “beta” value. value of a stock should equal the present His dissertation, “Portfolio Selection: Additional refinements were devised by value of future dividends that a company Efficient Diversification,” was published Eugene Fama and Kenneth French in 1995. is expected to pay shareholders. He began in the Journal of Finance in 1952 and in They fine-tuned the model to account for applying probabilities to determine the book form in 1959. That work won him the investment styles, such as large company, risk and return of portfolios. Nobel Prize in economics in 1990. medium-sized company and small com- Investors already had been spreading Though this sounds glorious, it wasn’t pany growth and value stocks. So to reduce their risks ever since the first bull market easy sailing in 1955 when he defended his volatility today, financial advisors often

18 Financial History | Fall 2011 | www.MoAF.org use Modern Portfolio Theory to construct classes as well as within asset classes, he trade-off curve. portfolios and incorporate a wide range of says. Diversifying between asset class port- “Depending on our risk capacity, per- United States and overseas asset classes. folios as well as within portfolios is more haps we will select a more cautious port- Markowitz says that investors con- “efficient” than doing only one of these, folio, loaded with lower beta securities or cerned about re-experiencing large mar- or neither. For example, riskier portfolios asset classes; or conversely, we will choose ket losses should optimize portfolios with may contain greater weightings in emerg- a point higher on the frontier, with higher the idea of trading off some return for less ing market and small company stocks, yield, but with higher beta securities or risk. Such portfolios would have lost less based on investment style. Less risky port- asset classes. in 2008, and they would have hit their folios might be weighted more toward “If the market goes up dramatically, break-even point in a shorter period. large capitalization US and foreign stocks, those with high beta portfolios will be For example, the S&P 500 lost 38% in based on investment style, as well as short- happy; if it goes down, they will be sad. 2008, and higher beta emerging mar- term and intermediate-term bonds. You pays your money and you takes your kets asset class indexes fell 54%, he said. He emphasizes that the shorter the choice!” Corporate bonds fell in value, but much investment horizon, the greater the risk less than stocks, and government bonds of losses because there is fatter tail risk. Alan Lavine is a columnist for Dow Jones rose in value. The five-year government But the longer you hold asset classes, the MarketWatch’s Retirement Weekly pub- bond index rose 8.4%. Small capitaliza- greater the probability the distribution is lication. He is also a contributing edi- tion stocks dropped in value, but not as normal. As a result, two-thirds of the time, tor with Financial Advisor magazine much as expected based on their standard returns typically fall between about -10% and Registered Rep magazine. He is the deviations. Meanwhile, large capitalization and +30%. author of 15 books including the bestseller, stocks performed worse than expected. A Markowitz is wary about adding alter- Rags to Riches: Motivating Stories of simple 50% S&P 500 and 50% Lehman native assets, such as private placements, How Ordinary People Achieve Extraor- Brothers Government Bond Index split commodities or exchange traded funds, to dinary Wealth (iUniverse and Dearborn), would have lost just 12.5%. portfolios. Those assets, he believes, must which was featured on Oprah. Diversify Over the long run, Modern Portfolio be properly valued and thus, are best left Your Way to Wealth (McGraw-Hill), Theory helps spread risk and build wealth. to people like Warren Buffett and David co-authored with Gerald Perritt, Ph.D., Nevertheless, the theory is not without Swenson of Yale University’s endowment was an alternate selection of the Fortune critics. A chief complaint is that Markow- fund. Book Club in 1990. itz’s model assumes that asset returns are He also won’t rely too much on Monte Sources normally distributed. Frequently, however, Carlo simulations that show the probabili- stock market returns are not normally ties of how long someone’s money will Alan Lavine interview with Harry Markowitz distributed. There can be large swings of last. Monte Carlo simulations can scare conducted on February 22, 2010. three to six standard deviations from the the general public because investors can American Finance Association’s “Masters in mean that occur more frequently than see that one out of 20 times, their money Finance” interview by Steve Buser with they would if the returns were normally might not last as long as they do. On the Harry Markowitz at the Rady School of distributed. Other research shows that plus side, however, the simulations often Management, University of California, San the Capital Asset Pricing Model cannot inspire 401(k) defined contribution plan Diego, October 8, 2004. always be explained by a portfolio’s beta participants to save more for retirement. Arrow, Kenneth J. Jacob Marschak, 1898–1977: value. Low beta stocks sometimes deliver Markowitz cautions against “model A biographical Memoir. National Academy higher returns than high beta stocks. risk.” If you are using a specific type of of Sciences, 1991. Markowitz disagrees. He says he does investment model that makes decisions not assume that the probability distribu- about how to invest, based on fundamental, Cowles, Alfred III. “Can Stock Market Fore- tion is normal. His research shows that economic and/or technical data, the model casters Forecast?” A paper presented at a mean variance portfolio relationships are may ignore or downplay the possibility of joint meeting of the Econometric Society a good approximation of the expected large losses that have a one out of 20 or one and the American Statistical Association, value of a portfolio. out of 40 chance of occurring, he said. Cincinnati, Ohio on December 31, 1932. “It is not true that I ever assumed prob- It’s also important, he said, to properly Friedman, Milton and L. J. Savage, “The Util- ability distributions are normally distrib- allocate assets. Investors must identify ity Analysis of Choices Involving Risk,” The uted,” he said. “It is another myth that their risk exposure, based on five dimen- Journal of Political Economy, Vol. 56, No. 4, you can’t invest in assets (using Modern sions that include the time horizon, liquid- August 1948, pp. 279–304. Portfolio Theory) that are not normally ity needs, net income, net worth, investing Harry M. Markowitz autobiography, www. distributed.” knowledge and attitude toward risk. NobelPrize.org. For example, he stressed that deriva- “At any point in time, we look back at Markowitz, Harry. “Foundations of Portfolio tives, such as stock options, might be the past, and make our estimates and deci- Theory,” Nobel Lecture, Baruch College, optimized in a portfolio to improve risk- sions for the future,” Markowitz said. “The New York. December 7, 1990. adjusted rates of return as long as there is future is always uncertain. We should good data on the covariance relationships make our best estimates for ‘the next spin Markowitz, Harry. Portfolio Selection. Black- to other portfolio assets. of the wheel,’ and then choose an appro- well Publishing, MA. 1991. It is better to diversify across asset priate point from the implied risk-return

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