by Lisa R. Goldberg
In Risk–Return Analysis: The Theory and Practice of Rational Investing, Harry M. Markowitz worries about a “great confusion” that reigns in finance — namely, “the confusion between necessary and sufficient conditions for the use of mean–variance analysis.” This is a serious matter. Mean–variance analysis has been the cornerstone of portfolio construction since Markowitz’s seminal 1952 article.
Meanwhile, academics and practitioners have been in constant search of the next holy grail that will guide the allocation of capital. Consider the endless stream of articles proposing enhancements to mean–variance analysis or substitutes for it. Substantial bodies of literature discuss optimizers that incorporate higher moments or attempt to replace variance with alternative risk measures. Another takes account of investors’ so-called irrational tendencies. I recall a former colleague saying, “Let’s not re-implement Harry Markowitz’s PhD thesis for the millionth time. We can do better.” But we have not.
What are the objections to mean–variance analysis, and are they well grounded? Markowitz has devoted Risk–Return Analysis to these questions, concluding that mean–variance analysis is central to finance for good reason. This book proceeds in unhurried steps from a set of incontrovertible premises to the conclusion that mean–variance analysis is the best tool available for addressing a wide range of portfolio-construction problems.
None of the material in Risk–Return Analysis is brand new; much of it has been around for more than half a century. The packaging, however, is vintage 2014. Proceeding against an earlier inclination, Markowitz begins Risk–Return Analysis with an axiomatic treatment of expected utility theory that is similar to what he wrote in his 1959 book on portfolio selection. He explains that the material was “at the back rather than the front of Markowitz (1959) because [I] feared that no practitioner would read a book that began with an axiomatic treatment of the theory of rational decision making under uncertainty. But now, clearly, these matters have become urgent.”
Markowitz is betting that now, financial practitioners will pause to consider the theoretical foundation of the quantitative tools they use routinely. I hope he is right. Every financial practitioner, every scholar in a quantitative field, and everyone attempting to explain a scientific theory stands to benefit from Markowitz’s lucid exposition.
The hero of the book is a rational decision maker (RDM). A gender-neutral incarnation of the “rational man” introduced in Chapter 10 of his 1959 book, the RDM “makes no mistakes in arithmetic or logic in attempting to achieve his clearly defined objectives.” Markowitz argues in Chapter 1 of Risk–Return Analysis that an RDM will seek to maximize expected utility of return. Further, it is the tendencies of the RDM, and not the tendencies of the human decision maker, that are relevant to the formulation of investment goals. After establishing maximization of expected utility as the foundation of portfolio construction, Markowitz argues that mean–variance analysis is the key to maximizing expected utility.
The remainder of the book is an elegant interplay of theory, empiricism, and practicality. In Chapter 2, Markowitz draws on several sources, including a 1979 article he wrote with Haim Levy, to conclude that under broad conditions, a mean–variance optimal portfolio approximately maximizes expected utility. Moreover, mean–variance optimization is more practical than utility maximization. Taken from an article Markowitz authored in 2012, Chapter 3 considers a long-horizon investor who is naturally concerned with geometric return rather than arithmetic return. Using a century’s worth of data, Markowitz considers six mean–variance approximations to the geometric mean for a diverse collection of portfolios and macroeconomic indicators. Three of the six turn out to be useful.
In Chapter 4, Markowitz again uses a century’s worth of data to approximate log utility with functions of such alternative risk measures as value at risk, conditional value at risk, and semideviation. Markowitz finds that approximations based on variance alternatives do not improve on approximations based on variance. The chapter concludes with an acknowledgment that the study is not comprehensive and challenges proponents of alternative risk measures:
“Conceivably, other functions [of the alternatives] would perform better than those tried here. If such is to be shown, proponents of alternative risk measures need to get beyond their current line of argument, which goes roughly as follows: Distributions are not normal; therefore, mean–variance is inapplicable; therefore, my risk measure is best.”
The final chapter, which relies on prior research by Markowitz and several others, considers the question of how an investor should choose a portfolio from the mean–variance efficient frontier. The essential parameter is risk aversion, and Markowitz proposes to gauge an investor’s risk aversion by using estimates of return distributions for actual portfolios.
If mean–variance analysis is truly sound, what explains the effort dedicated to pre-empting it? Markowitz suggests that neglect may play a role: “Quiggin (1998, p. 8) says, ‘The Expected Utility approach initially faced strong competition from mean–variance analysis, exemplified by the work of Markowitz (1959) on portfolio analysis, but the logical foundations of this approach were far more dubious than those of expected utility theory.’ An examination of the Table of Contents of Markowitz (1959) would have shown that the premises of utility analysis and the premises that Markowitz (1959) proposed in support of mean–variance analysis are identical.”
But then, it is easy to identify with John Quiggin: In a 2003 article, M.V. Simkin and V.P. Roychowdhury estimated that only 20% of citers have read the article or book they cite. This finding highlights a dilemma: How can a researcher master an overwhelming body of literature when time is so limited?
In the preface to Risk–Return Analysis, Markowitz explains that the current volume is the first of a four-volume series, and he outlines the material for the subsequent volumes. Future topics include von Neumann and Morgenstern’s game theory; the Bellman equation and dynamic programing; decision making under uncertainty as developed by Descartes, Hume, and Savage; the role of Bayesian statistics in portfolio construction; data mining; and the question of whether portfolio analysis can take advantage of advancing technology.
The preface concludes with this:
“This is clearly an ambitious program, especially considering that the undersigned is in his mid-eighties. Following this preface and acknowledgments is an outline of plans for Parts II, III, and IV. The aim is to provide enough information so that a diligent scholar could more or less reproduce these parts as now planned in the event that the undersigned is unable to do so.”
So, the current volume is really just a beginning. Risk–Return Analysis is a wonderful work in progress by a remarkable scholar who always has time to read what matters, who has the deepest appreciation of scientific achievement, and who has the highest aspirations for the future.
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