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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