Under conventional notions about rational expectations and market efficiency, expected returns differ from the actual expost returns by a forecast error that is uncorrelated with current information. In this paper, we describe how small departures from conventional notions of rational expectations and market efficiency can produce trends in excess returns. These trends are in addition to the trends typically found in the level of asset prices themselves. We report strong evidence for the presence of additional trends in excess foreign exchange and bond returns. We also estimate the additional trend component in excess returns on foreign exchange and find that it varied between -.8% and 1% for one month returns and between -6% and 8% for three month returns.