Supported in part by NSF grant DMS-0604020.
POSITIVE ALPHAS, ABNORMAL PERFORMANCE, AND ILLUSORY ARBITRAGE
Article first published online: 15 JUN 2011
© 2011 Wiley Periodicals, Inc.
Volume 23, Issue 1, pages 39–56, January 2013
How to Cite
Jarrow, R. and Protter, P. (2013), POSITIVE ALPHAS, ABNORMAL PERFORMANCE, AND ILLUSORY ARBITRAGE. Mathematical Finance, 23: 39–56. doi: 10.1111/j.1467-9965.2011.00489.x
- Issue published online: 8 JAN 2013
- Article first published online: 15 JUN 2011
- Manuscript received September 2009; final revision received December 2010.
- Jensen’s alpha;
- excess expected return;
- state price density;
- arbitrage opportunities;
- martingale measures;
- local martingale measures;
- systematic risk;
- performance evaluation;
- asset pricing model;
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.