Portfolio Bounds Line Chart
The Portfolio Bounds Line Chart appears on the Charts Worksheet. It shows the selected percentile bounds for each asset weight in the selected optimal portfolio to facilitate determining significant results. Check the box at the top left corner of the chart to force the axis to end at 100%.
Proper bounds should be constructed from Michaud Resampled Efficient Frontiers generated from statistically equivalent inputs. Calculation of a separate resampled frontier for each simulation requires meta-simulation, which is performed during the rebalance test. In order to streamline the workflow, this meta-resampling is removed from the first optimization pass when the Optimize Button is pressed. Thus, the intervals shown after an optimization are a fast approximation and not precise. These intervals will normally be substantially wider than the intervals produced after the second step and should not be taken literally as confidence ranges for the asset weight. These intervals should be taken to show the operating characteristics of the simulated optimizations in the resampling process. Also note that loading a relative variance table for the rebalance test will bypass the meta-resampling stage of the computation, so that the more accurate intervals will be unavailable. The fast-approximated intervals will be shown instead when relative variance tables are loaded instead of a full meta-resampling computation of the rebalance test.
After a rebalance step, the intervals will reflect the overlapping data or information between initial and optimal portfolios as entered in the Typical Rebalance Periods Field in the Rebalance section of the ribbon and can be interpreted as valid confidence intervals for the portfolio weights. However, each interval is a test on its own, so at the 50% confidence level, only half of the assets would be expected to be within the bounds under the null hypothesis of statistical equivalence of initial and optimal portfolios. A better and statistically valid indication of global portfolio significance is found from the result of the rebalance test.
One peculiarity of the Excel implementation of interval graphs is that the central value of each interval must lie within the outer two values. Because of the skewed distribution of portfolio weights, the mean of all the simulations can easily be outside of the quantiles, when the upper tail of portfolio weights is long. Excel displays this case by extending the interval limit to the value. Thus, for example, a quantile range of 10%-20% with a portfolio weight of 25% will be shown as an interval of 10%-25% with the central value of 25%. The distinct behavior of mean versus quantiles combined with Excel's extension of all intervals to contain the mean can occasionally explain some curious-looking intervals.