Wednesday, October 2, 2013

Markowitz, Risk-Return Analysis, vol. 1

Harry M. Markowitz, now in his mid-80s, has embarked on a four-volume series entitled Risk-Return Analysis, of which this volume, The Theory and Practice of Rational Investing (McGraw-Hill, 2013), is the first.

Most of us grew up with modern portfolio theory, first enunciated in a 1952 journal article and later proclaimed to be the beginning of modern finance. Brokerage firms provided clients with graphs showing optimal portfolios that offered the highest expected return for a given level of risk, achieved largely through diversification, and investors who wanted to sound knowledgeable threw around the phrase “the efficient frontier”. Modern portfolio theory seemed to work pretty well for decades. But then came the financial crisis, and critic after critic began sounding the death knell for MPT.

Markowitz’s response is masterful. He doesn’t launch a frontal attack on his critics. (Well, here and there he does let loose. For instance, on p. 72 he writes that “the persistence of the Great Confusion—that MV [mean-variance] analysis is applicable in practice only when return distributions are Gaussian or utility functions quadratic—is as if geography textbooks of 1550 still described the Earth as flat.”) Instead, for the most part he invites them to understand just what it is he is saying (which is different from what they are criticizing). This exercise involves a lot more than catch phrases and graphs. Moreover, he explains where and how his own thinking has evolved over the decades.

The result is a book that every finance professional should own. Serious retail investors who are not afraid of a little statistically related math will also be rewarded intellectually, perhaps financially as well. But, casual reader beware, this book is not one that I would describe as a good read.

The book is divided into five chapters: the expected utility maxim, mean-variance approximations to expected utility, mean-variance approximations to the geometric mean, alternative measures of risk, and the likelihood of various return distributions.

Perhaps the most fundamental mistaken notion about MPT that Markowitz has sought to dispel over the years, the one that he addressed in the passage I quoted above, is that mean-variance analysis should not be used if distributions are not normal. Markowitz explains that this criticism is misguided because he bases his “support for mean-variance analysis on mean-variance approximations to expected utility.” (p. 34)

Why, some might ask, “if one believes that action should be in accordance with the maximize EU rule, … seek to approximately maximize it via a mean-variance analysis? Why not just maximize expected utility?” (p. 41) One very important reason is that “the only inputs required for a mean-variance analysis are the means, variances, and covariances of the securities or asset classes of the analysis.” The formula for the expected return of a portfolio, according to this analysis, “is true whether or not returns are normally distributed, or even symmetrical, and whether or not the return distributions have ‘fat tails’….” (pp. 42-43)

In this book Markowitz also assesses competing risk measures (variance, mean absolute deviation, semivariance, value at risk, and conditional value at risk). His findings are provocative and, I’m sure, will elicit fervent rebuttals from proponents of these risk measures.

The Theory and Practice of Rational Investing is an important work, inviting academics and finance professionals to take a second look (or perhaps a first genuine look) at modern portfolio theory and thereby more fully understand its foundations, tenets, and consequences.

1 comment:

  1. It may be true that the formula for the expected return is true regardless of the distribution. That's the mean in the mean-variance analysis, but it's only half the picture. For the risk half, the distribution of returns matters a great deal. MPT and the efficient frontier concept is based on the idea of risk-adjusted returns and the correlation of asset returns. The mean-variance analysis fails miserably on this measure, and did so long before the financial collapse of 2008. So experience does tend to undermine MPT and the efficient frontier model. That doesn't mean it should be abandoned, but it should be used with a great deal of caution and a recognition of its shortcomings.