Term premia and interest rate forecasts in affine models

The standard class of affine models produces poor forecasts of future Treasury yields. Better forecasts are generated by assuming that yields follow random walks. The failure of these models is driven by one of their key features: Compensation for risk is a multiple of the variance of the risk. Thus risk compensation cannot vary independently of interest rate volatility. I also describe a broader class of models. These “essentially affine” models retain the tractability of standard models, but allow compensation for interest rate risk to vary independently of interest rate volatility. This additional f lexibility proves useful in forecasting future yields. CAN WE USE F INANCE THEORY to tell us something about the empirical behavior of Treasury yields that we do not already know? In particular, can we sharpen our ability to predict future yields? A long-established fact about Treasury yields is that the current term structure contains information about future term structures. For example, long-maturity bond yields tend to fall over time when the slope of the yield curve is steeper than usual. These predictive relations are based exclusively on the time-series behavior of yields. To rule out arbitrage, the cross-sectional and time-series characteristics of the term structure are linked in an internally consistent way. In principle, imposing these restrictions should allow us to exploit more of the information in the current term structure, and thus improve forecasts. But in practice, existing no-arbitrage models impose other restrictions for the sake of tractability; thus their value as forecasting tools is a priori unclear. I examine the forecasting ability of the affine class of term structure models. By “affine,” I refer to models where zero-coupon bond yields, their physical dynamics, and their equivalent martingale dynamics are all affine functions of an underlying state vector. A variety of nonaffine models have been developed, but the tractability and apparent richness of the affine class has led the finance profession to focus most of its attention on such models. Although forecasting future yields is important in its own right, a model that is consistent with finance theory and produces accurate forecasts can make a deeper contribution to finance. It should allow us to address a key