Significant Results

The ability to distinguish significant assets in an optimization result is another benefit of resampled optimization.  New Frontier provides percentile bounds to illuminate how much variability exists in the optimization results and therefore the significance of a particular recommended weight. You can change the percentile bounds through the Options Menu.  The default of 25%/75% indicates the 25th and 75th largest asset weights if 100 simulations are performed.  In other words, the default displays lower bounds for which 25% of the simulations are below and the upper bound for which 25% of the simulations are above in both the Asset Range Table and the Portfolio Bounds Line Graph, both of which appear on the Charts Worksheet.

Individual asset significance is most properly assessed using meta-resampled portfolios which are simulated to be equivalent to the main result optimal portfolios. Therefore, to obtain valid confidence ranges for asset weights, a rebalance test must be run first. Meta-resampled simulations should be set to standard or refined to obtain the most reliable and accurate confidence ranges. The confidence limits shown after an optimization only are a quick approximation and are not very accurate. They are an illustration of the operating characteristics of the Michaud resampling algorithm. Note also that if a relative variance table is loaded to bypass calculation of the rebalance test, the confidence limits shown will remain the quick approximation; to show accurate confidence intervals a full rebalance test must be run.

An asset's significance is also influenced by the assumptions used in the rebalance test - notably the forecast confidence, the resampled returns distribution, the and the typical rebalance periods. Generally, reducing the dispersion of the sampling distribution will tighten the intervals.

An individual asset is significant at the level of coverage of the percentile bounds if the interval shown for the asset and the selected optimal portfolio rank does not touch zero. Otherwise, a substantial number of simulations had zero portfolio weight for that asset and that target optimal portfolio, and the evidence that that asset matters to the portfolio is weaker. Of course the numerical values of the simulated portfolio weights also enter the decision process - an asset whose confidence limits are greater than zero, but all of the simulated weights are small, is less important than an asset whose confidence limits may touch zero, but the range extends to rather large portfolio weights.

Note also that assets often have significance in one part of the frontier versus another; the asset bounds chart applies to only one efficient frontier portfolio at a time. Low-risk assets may tend to be more significant in the lower parts of the frontier, whereas high return assets are more likely to be significant in the upper range of a Michaud Efficient frontier. Mid-range assets may be significant in the middle of the frontier but not at either end.

Overall significance of an arbitrary (reference or initial) portfolio is best assessed using the rebalance test.

If you have checked the Show Standard Deviation Confidence Intervals Option in the Charts Menu in the Display Section of the ribbon, confidence interval bars appear around the standard deviation of the selected portfolio on the Efficient Frontier Chart and in two rows of the Results Table. This feature facilitates analysis of the standard deviation of the optimal portfolios, but disabling this option speeds up the optimization.

For more information about the Michaud Resampled Efficient Frontier™, review New Frontier's website.