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POSITIVE ALPHAS, ABNORMAL PERFORMANCE, AND ILLUSORY ARBITRAGE
Author(s) -
Jarrow Robert,
Protter Philip
Publication year - 2013
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2011.00489.x
Subject(s) - arbitrage , economics , econometrics , hedge fund , alpha (finance) , asset (computer security) , statement (logic) , actuarial science , mathematical economics , financial economics , computer science , finance , health care , computer security , cronbach's alpha , political science , law , economic growth
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.