Before revision:  we show that the first-order benefit of  little bit of robustness  is a significant reduction in the variance of the out-of-sample reward while the corresponding impact on the mean is almost an order of magnitude smaller.
After revision:  we show that the first-order benefit of little bit of robustness " (i.e., \delta small, positive) is a significant reduction in the variance of the out-of-sample reward while the corresponding impact on the mean is almost an order of magnitude smaller.