Portfolio performance ambiguity and benchmark inefficiency revisited

We prove that an active manager can almost always obtain a positive alpha without having any market-timing or stock-picking ability by exploiting benchmark inefficiency. This suggests that rank ordering portfolio performance against a peer group following the same benchmark is preferable. We show that the benchmark beta and inefficiency value pairs that minimise the optimal portfolio beta follow an approximate, positively sloped straight line. We demonstrate that, consistent with observed portfolio betas, the minimum optimal portfolio beta is less than one for reasonable values of the benchmark beta (less than 1.5) and benchmark inefficiencies (less than 25 per cent). Furthermore, we show that the optimal portfolio beta after reaching its minimum and the information ratio increase at increasing and decreasing rates, respectively, with increases in benchmark inefficiency.