The optimal portfolio strategy is developed for an investor who has detecte
d an asset pricing anomaly but is not certain that the anomaly is genuine r
ather than merely apparent. The analysis takes account of the fact that the
parameters of both the underlying asset pricing model and the anomalous re
turns are estimated rather than known. The value that an investor would pla
ce on the ability to invest to exploit the apparent anomaly is also derived
and illustrative calculations are presented for the Fama and French SMB an
d HML portfolios, whose returns are anomalous relative to the CAPM.