In this paper we develop a new way of modelling time variation in term premia. This is based on the stochastic discount factor model of asset pricing with observable macroeconomic factors. The joint distribution of excess holding period US bond returns of different maturity and the fundamental macroeconomic factors is modelled using multivariate GARCH with conditional covariances in the mean to capture the term premia. We show how by testing the assumption of no arbitrage we can derive a specification test of our model. We estimate the contribution made to the term premia at different maturities by real and nominal macroeconomic sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the large number of reported failures of the rational expectations hypothesis of the term structure can be attributed to an omitted time-varying term premium.