Morningstar Advisor - June/July 2010 - 44

Morningstar Conversation

Harry Markowitz

I never ever assumed that probability distributions were normal. I never justified mean-variance analysis in terms of probability distributions being normal.

value—the discounted value of future dividends. Because future dividends are not certain, he said you should use the expected value of future dividends. Now, I knew that if you were maximizing an expected value, the way you would do that was to put all your money into just one stock. That didn’t make sense. People do diversify. You could see it in Wiesenberger’s Investment Companies and Their Portfolios. They diversified because they were worried about risk as well as seeking return. So, I postulated that investors were interested in expected return and standard deviation. I drew a trade-off curve, like economists always do, and so that afternoon in the business school library at the University of Chicago, I came up with the first efficient frontier. Williams asserted that with sufficient diversification, risk would disappear; you would receive the expected value. But risk only disappears with diversification if you have uncorrelated risk and, of course, markets are not uncorrelated. So, that was when and how the moment of epiphany happened.

published an introduction to the de Finetti paper, which you graciously titled, “De Finetti Scoops Markowitz.” In your view, what was the historical significance of de Finetti’s work?
Markowitz: The historical significance was nil

because the importance of de Finetti’s work was not understood. If it had any impact at all, it was among Italian actuaries. It was a response to the problem of optimum reinsurance, so it was an actuary thing. I do not believe that it ever got into the American actuary literature, and it certainly didn’t get into our financial literature. So, it was a dead end, not because it deserved to be a dead end, but that was, in fact, its historical destiny. In terms of the merits of de Finetti’s contributions, it turns out that he correctly posed the problem of mean variance. He understood that you had to take into account the correlations. Williams didn’t understand that something happened differently when you diversify among correlated risk. De Finetti did. He was able to solve the problem of tracing out mean-variance efficient frontiers assuming uncorrelated risk. He would’ve liked to have solved it using correlated risk, but he couldn’t solve that one. As I explain in my paper, de Finetti had some conjectures about what the solution must be, and at least one of the conjectures was wrong. So he gets a gold star for posing the problem, and I get a gold star for solving it.
Kaplan: Sam, I believe you have some personal

Sam Savage: I do. In the 1950–51 academic year, when I was six, my dad (Leonard J. Savage) was on sabbatical in Paris working on his book, The Foundations of Statistics. It was at that time that he discovered the random walk thesis of Bachelier and passed this information on to Paul Samuelson, which started the whole “Random Walk Down Wall Street” craze.

I don’t know why he knew of de Finetti, but he sure did. And at one point, we visited Italy. I’ll never forget Venice in 1951. We met de Finetti. I remember him well from then. I have to say, Paris and Venice are very exciting places for a 6-year-old. Later, in 1958, we spent a year in Rome, and my dad visited the Università di Roma and worked even more closely with de Finetti. So I knew him personally. I knew his daughter, Fulvia. I was not following the probabilistic arguments at all in those days.
Kaplan: Harry, much of the criticism leveled at the mean-variance approach is the allegation that it assumes that returns follow a normal distribution. In the late 1970s, you did some work with professor Haim Levy at the Hebrew University of Jerusalem that shows that the mean-variance optimization does not rely on this assumption. Please explain your work with Levy and how it answers this criticism. Markowitz: The work that I did with Levy that was published in 1979 in The American Economic Review, called “Approximating Expected Utility by a Function of Mean and Variance,” is an amplification of ideas I already

De Finetti’s Scoop
Kaplan: In 2006, the Journal of Investment

Management published the first English translation of a paper by the Italian mathematician Bruno de Finetti on mean-variance optimization. The Italian version of the paper was published in 1940, 12 years before your famous paper. In the same issue of the Journal of Investment Management, you

recollection of de Finetti.

44 Morningstar Advisor June/July 2010

Morningstar Advisor - June/July 2010

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