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:

• The 2002 paper "An Examination of Resampled Portfolio Efficiency." by professors Jonathan Fletcher and Joe Hillier, looked at back-tested data from 1983-2000. The authors found that resampled efficiency improved Sharpe ratios, but that the improvements aren't statistically significant.
• The 2002 paper "Portfolio Resampling: Review and Critique," by Bernd Scherer, professor at the EDHEC Business School, pointed out several problems with portfolio resampling. He pointed out that deteriorating Sharpe ratios (caused by higher volatility) led to increased allocation of those assets in the high-return portfolios. The reason is that the asset class will receive a high allocation in replications where the return is positive, but when the return is negative the allocation would receive an allocation of zero at most.
• The 2003 paper "Resampled Frontiers vs. Diffuse Bayes: An Experiment," by economist Harry Markowitz and finance professor Nilufer Usmen, compared resampled efficiency to Bayesian inference. The authors found that, on average, the resampled frontier won.
• Further confusing matters, in the 2008 paper "Bayes vs. Resampling: A Rematch," professors John Liechty, Campbell Harvey, and Merrill Liechty altered the assumptions in the 2003 study and found that the Bayes method almost always won.

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.

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