Which assumption states that a manager's value-added returns are independent and normally distributed?

The assumption that a manager's value-added returns are independent and normally distributed indicates that the distribution of those returns follows a normal distribution pattern centered around an expected value of zero. This means that the average performance of the manager should not deviate significantly from zero, suggesting that, on average, the manager is neither adding nor subtracting value from the investment returns.

In this context, the notion of independence implies that past performance does not influence future returns. Therefore, each return can be evaluated on its own merit without being impacted by previous results. The normal distribution aspect suggests that extreme performance (both very high and very low) is unlikely, reinforcing the idea of randomness and average performance occurring around the mean.

Understanding this assumption is critical for evaluating a manager's performance accurately, as it helps investors to identify whether any apparent excess returns are due to skill or simply random fluctuations in performance.