The optimal portfolio strategy is developed for an investor who has detected an asset pricing anomaly but is not certain that the anomaly is genuine rather than merely apparent. The analysis takes account of the fact that the parameters of both the underlying asset pricing model and the anomalous returns are estimated rather than known. The value that an investor would place on the ability to invest to exploit the apparent anomaly is also derived and illustrative calculations are presented for the Fama and French SMB and HML portfolios, whose returns are anomalous relative to the CAPM. We would like to thank two anonymous referees and seminar participants at the Western Finance Association.