Performance of active portfolio managers when the benchmark is not observable

We present a specialized methodology designed for evaluating the performance of active portfolio managers in situations where the common benchmark portfolio cannot be directly observed or determined by the analyzing agent. This method assesses performance by examining the excess alpha of an optimal active fund with respect to a combination of such funds that efficiently minimizes residual risk. After establishing the theoretical underpinnings of this approach and deriving the necessary statistical tests, we then showcase its practical application in assessing the historical performance of pension fund administrators operating within the Peruvian Private Pension System.