We measure the total-risk-adjusted (as opposed to factor-risk-adjusted) performance of hedge fund indices in well-diversified portfolios. Alpha is defined as the difference between, on the one hand, the average return on a mean-variance efficient portfolio containing exclusively traditional market assets (such as stocks and bonds) and, on the other hand, the average return on a mean-variance efficient portfolio containing traditional market assets and the new asset (such as a hedge fund index), where both portfolios carry the same risk. Alpha is conditioned on this risk level. Outlier-robust mean-variance efficient portfolios are constructed by using Minimum Volume Ellipsoid (MVE) estimates of location and scatter. We find that, between July 1995 and December 2005, the broad Credit Suisse/Tremont hedge index did not deliver statistically significant alpha.