A Conditional Single Index model with Local Covariates for detecting and evaluating active portfolio management

The intercept of standard Single Index and Conditional Single Index models, the so-called alpha, is often used to evaluate the long-run performance of managed portfolios. However, this measure is not always appropriate for detecting the presence and impact of active management strategies. Based on the conditional factor models literature, we introduce a Conditional Single Index model where the time-varying alpha and beta parameters depend only on the past history of the underlying portfolio returns and of the benchmark returns. The dynamics of the parameters have two components: the first describes the long-term behaviour of the alpha and beta, whereas the second is associated with the short-term performance of the underlying portfolio. The interpretation of parameters allows the identification of portfolio managers who implement active management strategies. An application on a set of 1300 U.S. mutual funds shows how widespread active management is on the U.S. market.