performance evaluation - Separating the wheat from the chaff: What quant methods separate skillful managers from lucky ones?

Fund managers are acting in a highly stochastic environment. What methods do you know to systematically separate skillful fund managers from those that were just lucky?

Every idea, reference, paper is welcome! Thank you!

Answer

Larry Harris has a chapter on performance evaluation in Trading and Exchanges. He states that over a long period of time, a skilled asset manager will consistently have excess returns whereas a lucky one will be expected to have random and unpredictable returns. Thus, we start with the portfolio's market-adjusted return standard deviation:

\begin{equation} \sigma_{adj} = \sqrt{\sigma^2_{port} + \sigma^2_{mk} - 2\rho\sigma_{port}\sigma_{mk}} \end{equation}

where $\rho$ is the correlation between the market and portfolio returns.

For a sample size $n$ (generally number of years), the average excess returns, and the adjusted standard deviation from above, we have a t-statistic:

\begin{equation} t = \frac{\overline{R_{port}} - \overline{R_{mk}}}{\frac{\sigma_{adj}}{\sqrt{n}}} \end{equation}

Now we can simply determine the probability that the manager's excess returns were luck by plugging this t-statistic into the t-distribution's PDF with degrees-of-freedom $n - 1$. The lower the probability, the more we can believe the manager's excess returns were from skill.