278 Optimizing Optimization
where U 0 is the value of expected utility under the true density, Uˆ is our esti-
mate of expected utility, and U is the familiar power utility function. We see
that for large numbers of observations, the bias in our estimates of expected
utility translates into a certainty equivalent return differential of around six
basis points for the Pearson and Skew-T distributions and around two basis
points for the NIG and S U distributions (see Table 11.5 ). Thus, within a port-
folio optimization framework where the primary goal is to estimate expected
utility, the quantile estimator appears robust to potential misspecification.
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Table 11.5 Certainty equivalent return differential, CEDNo. Obs NIG Pearson Skew-T S (^) U
100 0.2175 0.0554 0.2577 0.0198
250 0.0436 0.0746 0.1411 0.0103
500 0.0220 0.0649 0.0613 0.0196
This table describes the percentage certainty equivalent return differential for our
expected utility calculations using Equation (11.21).