Morningstar Advisor - June/July 2010 - 46

Morningstar Conversation

I’m a Bayesian, and I am not worried about Mandelbrot’s stable Paretian distributions.
Harry Markowitz

fat-tail distributions myself for the past two years. What is your view of this research?
Markowitz: When I was at Baruch College,

they gave me a research assistant, Nilufer Usmen. Because I’m a theoretician, I wondered, what am I going to do with a research assistant? What I decided to do was experiment with Bayesian inference. programming. I remember I was introduced to Harry and said, “Oh my God, it’s Harry Markowitz!” As I recall, Harry said something like, “Oh my God, it’s Jimmie Savage’s son!” He told me he had been indoctrinated at point-blank range in expected utility theory by my dad.
Markowitz: I have in my cabinet several copies of the Foundations of Statistics, which I give out like Gideon Bibles to people that I’m trying to convert to Bayesianism. Kaplan: And just to complete the circle,

start at the top and go down the list until they run out of money for investing. This guy said, “Why aren’t they using Markowitz portfolio theory to do this?” This was my introduction to a fellow named Ben Ball, who was an adjunct professor at MIT at the time, and a former VP of planning at Gulf Oil. My response to Ben was that this was indeed a good question. But I wondered how the heck you would actually calculate the covariance matrix for a bunch of oil prospects. I knew enough about the Markowitz model to know that it took covariances. It was several years before the answer appeared for how you would, in fact, do portfolio analysis with these things. Ultimately, I applied this approach with some success at Royal Dutch/Shell. The approach is known, I believe in the profession, as scenario optimization. Certainly, I was not the person who discovered scenario optimization, but it shaped my career. The notion is, you don’t describe a probability distribution parametrically, like with a mean and standard deviation. You describe it as a bunch of realizations, perhaps generated by Monte Carlo.
Kaplan: How did you meet Harry? Savage: I met him at George Dantzig’s 80th

What we did was to look at how much Bayesians should shift their belief among various hypotheses concerning the probability distribution of the log of the S&P 500 today divided by the S&P 500 yesterday. What we used was a very broad class of probability distributions called the Pearson family. We found that Bayesians should shift their beliefs massively against normal or Gaussian distributions in favor of a Student’s t-distribution with between four and five degrees of freedom.1 A Student’s t-distribution has fat tails, but as long as it has more than two degrees of freedom, variances exist. Therefore, the central limit theorem works. If you average together 250 trading days’ worth of daily returns, the distribution will get a lot closer to normal. However, the Pearson family does not include stable Paretian distributions. The interesting thing about stable Paretian distributions is that they are either normal, Gaussian, distributions or distributions with infinite variance. So if you assume stable, then you either have to accept normality, which is no way true, or you have to assume infinite variance, in which case you cannot do mean-variance analysis. Subsequent to doing this research with me, Nilufer Usmen married Tony Tessitore, who was my Ph.D. student. Tony is now a client of mine. Tony took it about himself to

Sam, when you were teaching at the University of Chicago, one of your students was Joe Mansueto, the founder of Morningstar. Harry, in the early 1960s, the French mathematician Benoît B. Mandelbrot and one his doctoral students at the University of Chicago, Eugene Fama, were publishing papers that claimed that changes in security prices were so erratic that they were best modeled using a fat-tail distribution, known technically as stable Paretian distributions. Under this model, variance is not a meaningful concept. So, even your work with Levy cannot justify a meanvariance approach. Largely ignored for decades, there has been renewed interest in Mandelbrot’s line of research, especially after the global market meltdown of 2008. As readers of this magazine know, I have been working with these

birthday party. Dantzig was a famous mathematician at Stanford who invented linear

1 Harry M. Markowitz and Nilufer Usmen, “The Liklihood of Various Stock Market Return Distributions, Part 2: Empirical Results,” Journal of Risk and Uncertainty, November 1996.

46 Morningstar Advisor June/July 2010

Morningstar Advisor - June/July 2010

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