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Efficient Frontier Chart

Optimizer Help Documentation

The Efficient Frontier Chart, which appears on both the Results and Charts Worksheets, displays the Michaud Resampled Efficient Frontier™ and additional data according to your preferences. The Display Box to the right of the chart provides numerous options that can be added to the chart. Checking a display option on either the Results or Charts Worksheet causes that option to activate or inactivate on both worksheets.

If a segment of the frontier appears in red, this means that the maximum return portfolio is not at the end of the frontier, and the red segment is actually lower in expected return than the maximum return portfolio, which is at the point where the transition from blue to red occurs.

By default, the chart plots the Michaud Resampled Efficient Frontier in blue on the axes measuring standard deviation (horizontal) and expected return (vertical). A legend with checkboxes that can be checked or cleared to enable or disable additional elements on the chart appears to the right. The table below details those checkboxes.

Selected Portfolio	the optimal portfolio currently selected in the Selected Column of the Results Table (Results Worksheet) or in the portfolio selection section of the Charts Worksheet. If Show Standard Deviation Confidence Intervals is selected in the Charts Menu in the Display section of the Optimizer Ribbon, a horizontal bar showing the confidence region for the risk of the selected portfolio will appear on the graph, with confidence limits set according to the selected percentile bounds in the Options menu in the Case Settings section of the Optimizer Ribbon.
RE Simulations	A scatter plot of the individual resampled portfolios appears in light blue. After a rebalance procedure is run, the meta-resampled portfolios appear in purple. This option helps to display the degree of variation among the alternative simulations. After rebalancing, the points are typically in a tighter arrangement around the parent frontier points. You can adjust the number of points displayed in the Preferences Menu. You can switch between the simulations corresponding to the entire frontier and those only corresponding to the selected portfolio in the Display--Charts Menu. The one-portfolio display is more informative in showing where the simulated equivalent portfolios are landing on the mean-variance chart, since they are no longer mixed in with simulations from other points on the frontier. After a rebalance procedure is run, the meta-resampled points are typically in a tighter arrangement around their parent frontier points, especially when typical rebalance periods are set to a small number. The cloud display on the efficient frontier chart shows simulations coming from a meta-resampled rebalance procedure in purple, instead of the light blue color used for optimization simulations.
Assets	the risk and return position of each individual asset If basic tax optimization is enabled, the assets' positions on the chart are tax-adjusted.
Initial Portfolio	the initial portfolio's risk and return position
Reference Portfolios	the risk and return position of each reference portfolio
Result Portfolios	the six representative optimal portfolios displayed on the Results Worksheet, if you change the selections in the table below, the result portfolios change
Rebalance Test	the rebalance probability graph overlay Note that the rebalance probability is graphed with respect to the vertical axis on the right (0-100%), not the left vertical axis (return).
Classical Frontier	the classical mean variance efficient frontier
Multiperiod Frontier	the efficient frontier over the multi-period horizon selected on the Inputs Worksheet
Stored RE Frontier	the efficient frontier stored during a previous optimization (Store Results option in the Edit Menu)
Max SR Portfolio	the maximum Sharpe ratio portfolio
Filtered Portfolios	the position of each of the portfolios that result from filtering
Yield	the yield of each optimal portfolio from the optimal frontier, if yield has been activated

If you have checked the Show Standard Deviation Confidence Intervals Option in the Charts Menu in the Display Section of the ribbon, confidence intervals appear around the standard deviation of the selected portfolio on the Efficient Frontier Chart. (To adjust the confidence interval limits, change the percentile bounds in the Options Menu. Also, you may need to re-run the optimization to calculate these intervals in order to enable them after an optimization is run without them.) This feature facilitates analysis of the standard deviation of the optimal portfolios, but disabling this option speeds up the optimization.

If you are using Quadratic Risk Penalties, the standard deviation calculations for this chart are affected by whether or not the Add Quadratic Risk Penalty to Risk option in the Charts sub-menu within the Display Menu on the ribbon is enabled.