POSITIVE ALPHAS, ABNORMAL PERFORMANCE, AND ILLUSORY ARBITRAGE
论证了Jensen阿尔法非零不仅意味着异常表现，更代表套利机会；即使使用正确因子和时变贝塔，若基于错误信息集估计，仍可能得到非零阿尔法，即虚幻套利。这对解读共同基金和对冲基金的实证文献有重要意义。
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 nonzero 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 nonzero Jensen’s alpha. In fact, a nonzero Jensen’s alpha represents an arbitrage opportunity. Second, we show that even if the correct factors and time varying betas are used, a nonzero 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.