Better efficient frontier models still slack

(MoneyWatch) As I've previously discussed, efficient frontier models -- which are programs designed to spit out an asset allocation giving a maximum achievable return for a given set of risks and parameters -- give very different results when the input assumptions are changed even slightly. In 1989, investment advisers Richard Michaud and Robert Michaud, authors of "Efficient Asset Management," improved on traditional efficient frontier models with an idea called "resampled efficiency."

Resampled efficiency is based on resampling the optimization inputs. In technical terms, resampling is a Monte Carlo simulation procedure to create alternative optimization inputs that are consistent with the uncertainty in all forecasts. Risk, return, and the relationships between assets are all treated as uncertain forecasts. This is a significant improvement over traditional efficient frontier models. It allows for uncertainty in the inputs, provides more stable outputs, and generally recommends more diversified portfolios than traditional efficient frontier models.

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There have been several academic papers that have examined the resampled efficiency approach. Below is a summary of some of their conclusions:

My own view is that the main shortcoming of efficient frontier models, including resampled ones, is that they assume we live in a one-factor world. We know from economist Eugene Fama and finance professor Ken French that we live in a three-factor world. Volatility isn't the only source of risk in a portfolio, yet these models assume that it is.

Image courtesy of taxbrackets.org

[perlich]

In their practice at New Frontier Advisors, LLC, Michaud and Michaud employ both (a) sophisticated Bayesian techniques to create better forecasts of risk and return distributions that take uncertainty as well as financial insights into account, and more importantly, (b) Michaud rather than Markowitz optimization to turn those forecasts into portfolios. Thus they simultaneously avail themselves of both of the kinds of improvements Markowitz and Usmen compared separately.

Other tests of Michaud optimization in the literature Swedroe cites fail to implement the idea correctly and hence obtain flawed results. More details can be found on the New Frontier Advisors, LLC website at www.newfrontieradvisors.com.

Finally, we note that Swedroe's terminology "efficient frontier models" may encapsulate his confusion - and propagate it to his readers - as succinctly as possible. "Models" are normally descriptive or predictive in nature, while "strategies" and "procedures" are words that imply normative frameworks instead. Most financial analysts would understand "efficient frontier models" to refer to CAPM or other descriptive frameworks. Again, neither Markowitz nor Michaud optimization rely on or assume any such frameworks or their associated baggage; they simply assume that an investor wants the highest-returning portfolio for its level of risk. Therefore, referring to them as "efficient frontier strategies" rather than "efficient frontier models" could lessen the probability that they will be erroneously understood as assuming a one-factor model (or the efficiency of the market portfolio) in any way.

New Frontier Advisors, LLC
Boston, MA

[perlich]

This article makes several erroneous claims concerning the Markowitz and Michaud optimization paradigms which we would like to correct. We think it likely that Swedroe is confusing several concepts in descriptive finance (mathematical or qualitative models of how markets work, forecasting of returns and risks, etc.) with similar-sounding concepts in normative finance (prescriptions for how one should invest given some such set of descriptive beliefs)

Firstly, Swedroe claims that Markowitz's and Michaud's notions of portfolio efficiency assume a one-factor model, in contrast to, say, French's three-factor model. This is simply not the case and may be a result of confusing "market efficiency" with "portfolio efficiency".

Swedroe may be thinking of the Sharpe-Lintner CAPM model from the 1960s. CAPM's conclusions, which include a single-factor model of expected returns and the mean-variance (MV) efficiency of the entire market taken as a whole (i.e., of the "market portfolio"), are derived from certain strong assumptions about how investors can borrow, lend, and invest. This is a descriptive, not normative, framework. Many of Markowitz's own articles, such as "Market Efficiency: A Theoretical Distinction and So What?" (FAJ 2005), attack the highly unrealistic assumptions of the CAPM model and show that replacing those with more plausible assumptions yields the conclusions that there is no single-factor model of expected returns and that the market portfolio is not MV efficient. However, the MV efficiency of the portfolio held by each individual investor is still consistent with Markowitz's more plausible set of assumptions. (These include the realistic assumption that at least some investors face some finite constraints on borrowing and/or shorting, which replaces the unrealistic CAPM assumption of universally unlimited shorting/borrowing at the risk-free rate).

Portfolio efficiency in normative finance - how one should invest -- can be defined with respect to any set of forecasts of return, forecasts of risk, and portfolio constraints. The forecasts can come from a single- or multi-factor model or from any procedure whatsoever, though single-factor models of risk or return - or assumptions of market efficiency -- are in fact seldom used in this context (except in the Black-Litterman framework, critiqued by Michaud, Esch, and Michaud in their forthcoming JOIM paper; see http://www.newfrontieradvisors.com/Announcements/documents/BLESAug2012.pdf). MV efficiency in normative finance simply means that one should invest in a portfolio with maximum expected return for its level of risk - there are no descriptive assumptions here. Markowitz originally (1952) suggested solving the problem through a straightforward mathematical (quadratic) optimization procedure that takes historical sample returns, correlations, and risks as the forecasts of those quantities (again, with no assumptions about whether or how they can be modeled with one or more factors).

Secondly, Swedroe correctly points out that small changes in the input data can lead to drastically different "mathematically optimal" portfolios under the Markowitz optimization procedure. However, the idea Swedroe cites of "a procedure to create alternative optimization inputs that are consistent with the uncertainty in all forecasts" -- followed by feeding those inputs into a Markowitz optimization -- actually better describes the "diffuse Bayes" approach that Markowitz and Usmen pit against a Michaud approach in their 2003 paper (JOIM). In those tests, it is the Michaud approach that uses the naive, purely historical inputs that Markowitz had suggested using in 1952, but these inputs are fed into the patented Michaud optimization procedure (which is designed to account for the inevitable uncertainty of input forecasts). Markowitz and Usmen perform 30 tests and find that, despite the naive, purely historical inputs used in their tests of the Michaud procedure, the Michaud optimizer performed better (lower risk and higher return out-of-sample) than the diffuse Bayes/Markowitz procedure in all 30 tests. Hence it appears that the drastic sensitivity of Markowitz optimization to the precise inputs hurts out-of-sample performance severely enough to trump the advantages obtained by any single method of altering those inputs to reflect forecasting uncertainty. In other words, the best known method of accounting for forecasting uncertainty in the descriptive part of the problem, when combined with Markowitz optimization, does not produce better portfolios than the "Michaud" method of accounting for forecasting uncertainty only in the normative part of the problem instead. Hence, Michaud provides a better answer than Markowitz or diffuse Bayes/Markowitz to the question: Given a description of the historical data, how should one invest?

(to be continued)

[LarryswedroeCBS]

maynardkeynes
Suggest you should take a deep breath, and stop being so "literal"

Of course the FF is a model of how the markets work. And it is not backward looking or forward looking. It is an explanatory model: Explaining the vast majority of the differences in returns between diversified portfolios. It was never meant to have predictive value. What it does show is that it's asset allocation that determines the vast majority of the differences in returns, not stock selection or market timing.

It also is helpful in designing portfolios, providing insights in terms of diversification across risk factors.

Best wishes
Larry

[maynardGkeynes]

Larry, do you seriously believe we live in even a 3 factor world? What Fama and French present is a 3 factor model, not a world. Moreover, their additional factors, small cap, and value vs growth stocks, are basically tweaks to the standard model. In addition, they are totally backward looking, which is precisely what makes the the standard model so uselessly lacking in predictive value. We live in a world, not a model, and a world has unknowable numbers of factors. This is why all such "efficient frontier" advice is useless. Not just the standard model you critique.