Positive Alphas, Abnormal Performance, and Illusory Arbitrage

Jensen's alpha is well-known to be a measure of abnormal performance in the evaluation of securities and portfolios where abnormal performance is defined to be an expected return that exceeds the equilibrium risk adjusted rate. It is also well known that in estimating Jensen's alpha, a non-zero value can be obtained by using incorrect factors or not employing time varying betas. This paper makes two additional contributions to the performance evaluation literature. First, we show that a stronger statement is true regarding the meaning of a non-zero Jensen's alpha. In fact, a non-zero Jensen's alpha represents an arbitrage opportunity. Second, we show that even if the correct factors and time varying betas are used, a non-zero Jensen's alpha can result if the estimate is conditioned on the wrong information set in the presence of an asset price bubble. We call this illusory arbitrage. Both facts are relevant to interpreting the existing empirical literature evaluating the performance of mutual and hedge funds