With the publication of his simply titled dissertation,
"Portfolio Selection," 55 years ago, Harry Markowitz, a
doctoral candidate in economics at the University of Chicago,
presented the investment world with a new paradigm for
allocating capital among risky assets. He also laid the
foundation for work by William Sharpe, then a Ph.D. candidate
at the University of California at Los Angeles, that led to
their development of modern portfolio theory -- and earned both
men, along with economist Merton Miller, the 1990 Nobel Prize
In "Portfolio Selection," which appeared in the March 1952
Journal of Finance, Markowitz introduced the concept of the
efficient frontier: the curve representing all portfolios that
maximize the expected return for a given level of risk, or,
alternatively, minimize the risk for a given level of expected
return. Markowitz presented an algorithm for constructing
optimal portfolios based on estimated returns and risks and the
correlations between securities. His mean-variance optimization
model, or MVO, has been an indispensable tool for allocating
capital among risky assets for more than half a century.
Nonetheless, academics and investors have been debating the
practical merits of the MVO methodology for decades. Now a
father and son team -- Richard Michaud, president and chief
investment officer of New Frontier Advisors, and Robert
Michaud, managing director of research and development at the
Boston firm -- have developed what some major money managers
see as a significant enhancement of Markowitz's algorithm.
About 20 firms, including Atlantic Trust Private Wealth
Management and Wachovia Securities, have licensed the Michaud
model. "Our solution is very simple but very powerful,"
contends Richard, the father, winner of a Graham and Dodd
Scroll award for financial writing for his work on optimization
and an editorial board member of the Financial Analysts
Journal. The Michauds have patented their so-called resampled
efficiency optimizer and portfolio rebalancing technology.
To be sure, not all academics and practitioners are
convinced that the Michauds have come up with a better
mousetrap. Yet Markowitz himself has acknowledged the
significance of the Michauds' work. "The Michauds have made an
important suggestion about how to [incorporate the fact that]
estimates are uncertain, and they have stimulated a good
discussion," Markowitz tells Institutional Investor.
In a study, "Resampled Frontiers Versus Diffuse Bayes: An
Experiment" (Journal of Investment Management, Fourth Quarter
2003), Markowitz and Nilufer Usmen, a finance professor at New
Jersey's Montclair State University School of Business, compare
Michaud resampling with the traditional Markowitz
mean-variance-optimizer model, using improved inputs. Markowitz
and Usmen use a statistical technique known as "Bayes with a
diffuse prior" to adjust the estimates of risk and return for
uncertainty. "We wanted a formal procedure that takes into
account the sampling error in historical averages," Markowitz
The Markowitz and Usmen experiment revealed that the
Michauds' resampled efficient frontier produces portfolios with
more diversified collections of stocks and better returns for a
given level of risk, or the converse. "Much to our surprise,
the Michaud methodology did better than ours," says
Of course, the Markowitz-Usmen study is but one experiment.
Some academics and practitioners contend that a different
Bayesian approach to generating the inputs would produce a
A recent working paper by Campbell Harvey, a finance
professor at Duke University, and co-authors John Liechty, an
assistant professor of marketing and statistics at Pennsylvania
State University, and Merrill Liechty, an assistant professor
in the department of decision sciences at Drexel University,
shows that a minor change in the estimation procedure used in
the Markowitz-Usmen experiment can produce the opposite result.
"Our study shows that the Bayes technique beats resampling at
lower levels of risk," Harvey says.
The Michauds' system is meant to address a weakness of the
Markowitz optimization algorithm: its insensitivity to
estimation errors. The problem with the Markowitz algorithm,
Richard Michaud explains, has to do with how the computer uses
the information plugged into it.
"As humans, we see the data as an estimate," Michaud says,
"but the computer-driven optimizer assumes an unrealistic
accuracy in the estimation of inputs." Inputs in this case
consist of estimated returns, risk and asset correlations.
Because the classic Markowitz optimizer operates on these
inputs as if they were known with certainty, the MVO algorithm
is highly sensitive to estimation error. Its recommended
portfolios tend to have heavy concentrations in one or two
"The classic Markowitz optimizer generates an asset mix
that's unsuitable for our clients," says Michael Jones, a
managing director in advisory services at Wachovia Securities
in Richmond, Virginia.
Pioneering studies of the practical limits of the Markowitz
framework date to the early 1980s, when J.D. Jobson, curently
associate dean of the MBA program at the University of Alberta,
and Bob Korkie, professor emeritus of finance at the
university, concluded that the certainty that the Markowitz
optimizer attaches to input estimates tends to make the
solutions highly sensitive to small changes in those
Investors who use mean-variance optimization attempt to
counter its tendency to generate concentrated portfolios by
adding constraints and improving the inputs, often using
sophisticated statistical techniques. "We've had to add so many
constraints that the process is no longer rigorous," Wachovia's
Jones says. Adds Jeffrey Thomas, CIO of Atlantic Trust in
Boston, "The fix negates the model's value."
Imposing too many constraints is "torturing the optimizer,"
says Richard Michaud. "If you torture it enough, it will tell
you exactly what you want."
Investors have also sought to address the estimation problem
by using statistical methods to generate better inputs. One of
the most widely used methods was developed in the early 1990s
by thenGoldman, Sachs & Co. vice chairman Fischer
Black (of the Black-Scholes option pricing model) and Robert
Litterman, a Goldman Sachs managing director. Their
Black-Litterman model plugs assumed-to-be-efficient market
portfolio weights into the Sharpe-Lintner capital asset pricing
model (a formula that equates the expected return on a security
to the risk-free rate of return plus a risk premium) and solves
for the starting inputs.
"The results are intuitive because Black-Litterman is
grounded in modern portfolio theory," says Thomas Idzorek,
director of research at Ibbotson Associates in Chicago, which
uses a proprietary resampling algorithm. "The inputs can then
be fed into a traditional Markowitz optimizer or a resampled
optimizer, such as the Michaud framework."
The Michauds' solution to the shortcomings of the Markowitz
algorithm was to add the element of uncertainty. The
father-and-son team pursued a Monte Carlo simulation to
forecast multiple sets of inputs (i.e., return, risk and asset
correlations), as proposed by Jobson and Korkie in 1981 and by
Philippe Jorion in 1992.
The Michauds feed the Monte-Carlo-generated inputs into a
Markowitz mean-variance optimizer and generate multiple
efficient frontiers -- one for each set of inputs. They then
collapse these into a single efficient frontier, or optimal
"We generate the optimal portfolio under multiple scenarios,
and we take the average," explains the younger Michaud. "The
average is very robust; it's almost always close to the right
Many practitioners and academics praise the Michaud model as
an advance over Markowitz's methodology. "It tends to produce
portfolios that are more intuitive," says Atlantic Trust's
Thomas. Users are less tempted to preconstrain, he adds, and
the Michaud model is less sensitive than the Markowitz
optimizer to changes in input estimates. Ibbotson incorporates
its own version of the Michaud resampling algorithm into its
flagship portfolio analysis software product, Encorr.
"Resampling overcomes the weakness of traditional mean-variance
optimization and leads to better-diversified portfolios," says
research director Idzorek. Bernd Scherer, head of advanced
applications at Deutsche Asset Management in Frankfurt, says
that "Michaud resampling appears to produce better portfolios
than traditional Markowitz optimization." But he is troubled
that no one seems to fully understand why.
Another weakness of the Michaud resampling model, according
to Deutsche's Scherer, is that it outperforms the Markowitz
optimizer only when a long-only constraint is applied. When the
model is allowed to recommend both long and short allocations,
he says, the Michaud frontier coincides perfectly with the
Markowitz efficient frontier.
"A methodology that claims to effectively deal with
estimation error should work in all circumstances," Scherer
argues. He says that Michaud resampling defaults to the
Markowitz optimization in the one circumstance where investors
need the improved methodology the most: when they can go long
and short without limits. "Michaud has made a significant
contribution, but it's [only] the first step," says Duke's
Harvey. "More work needs to be done to explicitly address
uncertainty in asset allocation decisions."
The perfect optimizer, like the perfect portfolio, doesn't