We investigate delegated investment management in private pension accounts using data from Australian accumulation (superannuation) funds. In Australian non-profit pension funds, trustees choose investment managers on behalf of members. We find that funds with many delegated managers have higher risk-adjusted returns than those with few. However funds with 13 or less specialized managers show no improvement over funds with a single diversified manager. All do worse than a benchmark portfolio of asset-class indices. Further, by using random selection to mimic the choices of an uninformed individual choosing from the same menu of delegate managers as used by trustees, we show that returns from pension funds with large numbers of trustee-selected managers compare favorably with returns from randomly selected, equally weighted portfolios. However this improvement falls off quickly for funds with fewer trustee-selected managers, or when randomly selected portfolios are also diversified across asset classes. Results indicate that an uninformed individual following a naive diversification strategy would have done as well as most trustee boards in this sample.