Are Fund Alphas Robust Proxies for Funds Managers' Managerial Skill?

Abstract

This study provides formal theoretical evidence that constructions of fund alpha that are implemented using robust specifications of asset pricing models generate alpha estimates that are well defined. Regardless, the formal theoretical model shows fund alphas that are constructed with the market portfolio as benchmark (`global alphas') cannot be construed to be robust metrics for either of stability of fund performance, or expected aggregate future fund performance. Suppose benchmarks for distinct realizations (echelons) of risk tolerance are substituted for the market portfolio. Formal predictions show alphas constructed in relation to such benchmarks (`echelon-specific alphas') have exactly the same functional form as global alphas, as such while they are well defined, they are not robust metrics for global forecasts of funds' expected future performance. This is evident in the formally derived theoretical prediction that long positions in all zero alpha funds have feasibility of superior performance in relation to long positions in all positive alpha funds. Suppose, however, that investors restrict their sample of funds to a specific echelon of risk tolerance. In presence of managerial capacity for taking advantage of stock market imperfections, echelon-specific fund alphas either vary stochastically and asymptotically around zero, or are positive. In presence stated restriction and caveat, echelon-specific alphas are robust metrics for expected future performance of managed funds.