Relations between foreign exchange risk premia, exchange rate volatility, and the volatilities of the pricing kernels for the underlying currencies, are derived under the assumption of integrated capital markets. As predicted, the volatility of exchange rates is significantly associated with the estimated volatility of the relevant pricing kernels, and foreign exchange risk premia are significantly related to both the estimated volatility of the pricing kernels and the volatility of exchange rates. The estimated foreign exchange risk premia mostly satisfy Fama's (1984) necessary conditions for explaining the forward premium puzzle, but the puzzle remains in several cases even after taking account of the pricing kernel volatilities.

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.