In this paper, we study the reward-to-risk ratio, using monthly euro-dollar, euro-mark and euro-franc term structures between 1975 and 1997. We test the relationship between excess holding return and volatility in an ARCH-in-Mean framework. We first obtain that the conditional volatility displays a non-stationary pattern, that there is no asymmetric effects from shocks to volatility, and that the conditional density is well represented by a student's t distribution for the euro-dollar and by a GED for the euro-mark and the euro-franc. We then find that the best relation between excess return and risk is obtained when the risk is represented by the logarithm of the conditional volatility. Last the estimates of the reward-to-risk ratio are lower than to those obtained in previous empirical studies on stock returns but similar to those obtained on monetary and bond returns.