Rejection Sampling

Rejection sampling is designed to measure certain characteristics of each simulation in the resampling procedure, and replace them with new simulations if they fail a test. This test measures the filter score of the maximum return portfolio. Normally the filter is set up so that the higher risk assets, perhaps the stocks, obtain higher scores when the total portfolio weight of these assets is greater. If a particular simulation assigns a greater expected return to an asset which does not add to the filter score, this simulation may not attain a high filter score at the top of its frontier, since the optimal assets to load on for that frontier do not add to the filter score. This could be construed to mean that the simulation in question is “upside down”, i. e. assigns more attractive inputs to assets which are less attractive in the main inputs.

The rejection sampling feature will replace simulations whose maximum filter scores (at the top of the frontier) are less than a specified threshold with new simulations that attain a filter score greater than or equal to the threshold. This means that all of the simulations will be “pointing in the same direction,” at least with respect to the filter score metric. Under many circumstances this can increase the out-of-sample performance of the Michaud optimal portfolio.

• To use the feature, enable Rejection Sampling in the Advanced Options menu. This will open a dialog box in which the threshold for rejecting can be entered.

• To turn the feature off, disable it in the Advanced Options menu.

• To change the threshold, you must turn the feature off and on again, which will allow entry of a new threshold parameter.