1. Why does the Michaud Resampled Efficient Frontier (REF) plot below the classical Markowitz mean-variance (MV) frontier?

Unlike MV optimization, the REF includes statistical uncertainty of risk-return estimates in the optimization process. If you are 100% certain of your risk-return estimates (to 16 decimal places or more accuracy), then the Markowitz efficient frontier is the one you should use. In practice, investors are never 100% certain of their estimates. A realistic view of uncertainty leads to expectations of less return and less willingness to put money at risk. When uncertainty is included in the optimization process the efficient frontier portfolios plot below the classical MV frontier and generally do not recommend taking as much risk. Resampled Efficiency (RE) optimization is the natural framework for rational decision making under conditions of information uncertainty.

2. The Michaud Resampled Efficient and mean variance frontiers appear to plot close together; is there any real difference between them?

Efficient frontier portfolios are graphed in terms of their mean and variance. If you compare RE and MV portfolios at the same risk level, the allocations typically vary even though the risks and returns are similar. The portfolio composition exhibits on the Charts Worksheet display the MV and RE optimal asset allocations from low risk on the left-hand side of the charts to high risk on the right-hand side. Each color represents the weight of a particular asset in the optimization for a given level of portfolio risk risk. The left panel provides the MV efficient frontier, the right panel the REF.

The exhibits show that the two frontiers have different asset allocations for the same risk-return inputs. The MV composition map displays sharp changes in allocations while the RE allocations reflect smooth transitions as risk is increased. The RE exhibit includes allocations for all the assets in the optimization universe while MV excludes some assets. The maximum return RE optimized portfolio (far right) is well diversified, while the MV maximum return portfolio is a single asset. REF portfolios reflect better diversification and more investment intuitiveness whether or not the frontiers are close in mean-variance space.

3. If the same risk and return estimates are used, why are the MV and RE portfolios different?

RE optimization includes investment information uncertainty in the optimization process. As a consequence, the optimized portfolios will generally be different from the classical portfolios.

4. Do RE optimal portfolios outperform MV portfolios?

RE optimized portfolios can be shown on average to enhance return or reduce risk relative to associated MV portfolios. The method used for proving the superiority of RE optimized portfolios is not based on a backtest. Backtests are always unreliable because they depend on the special character of a particular time period. A different time period may show very different results. The proofs use Monte Carlo simulation methods or simulation tests. These mathematically and statistically rigorous reflect what happens on average when RE or MV optimization is used relative to some given "truth" about the past or future. While in-sample MV portfolios show more return for a given level of risk, they overuse the information in a set of risk-return estimates and on average provide less return when implemented.

5. How important is a better optimizer?

A remarkable study by Markowitz and Usmen (2003) addressed the question of whether better inputs are more important than using the RE optimizer. They invented a sophisticated procedure for improving investment information in a given set of data then compared their performance with a MV optimizer relative to unimproved risk-return estimates with RE optimization. The RE optimized portfolios outperformed the traditional optimization with better inputs.

When announced, these results surprised many. However, the results are easy to explain. MV optimization always overuses the information in any set of realistic risk-return estimates resulting in portfolios that are unlikely to have much investment value whatever the quality of the inputs. While such tests are important, they are largely of academic interest. Investing should consist of useful risk-return estimates and an investment effective RE optimizer.