Term Premia and Interest Rate Forecasts in Affine Models

Term Premia and Interest Rate Forecasts in Affine Models

November 2000 | Gregory R. Duffee
Duffee examines the forecasting ability of affine term structure models and finds that they produce poor forecasts of future changes in Treasury yields. He argues that this failure is due to a key feature of these models: risk compensation is a fixed multiple of the variance of the risk, limiting the ability to vary independently of interest rate volatility. He introduces a broader class of models, "essentially affine," which retain the tractability of affine models but allow risk compensation to vary independently of volatility, improving forecast accuracy. Duffee estimates three-factor essentially affine models and finds they produce more accurate yield forecasts than completely affine models, both in-sample and out-of-sample. However, there is a trade-off between flexibility in forecasting future yields and flexibility in fitting interest rate volatility. The paper shows that completely affine models fail to replicate the key empirical relation between expected returns and the slope of the yield curve, as they cannot simultaneously reproduce two features of term structure behavior: wide variation in yields and small unconditional mean excess returns relative to conditional mean excess returns. The paper concludes that while completely affine models are popular in finance, they are not suitable for forecasting future yields. The "essentially affine" models, which allow for more flexibility in risk compensation, provide a better fit to the empirical behavior of Treasury yields and can produce more accurate forecasts. The paper also highlights the importance of understanding the relationship between the slope of the yield curve and expected excess returns, which is crucial for explaining the failure of the expectations hypothesis of interest rates.Duffee examines the forecasting ability of affine term structure models and finds that they produce poor forecasts of future changes in Treasury yields. He argues that this failure is due to a key feature of these models: risk compensation is a fixed multiple of the variance of the risk, limiting the ability to vary independently of interest rate volatility. He introduces a broader class of models, "essentially affine," which retain the tractability of affine models but allow risk compensation to vary independently of volatility, improving forecast accuracy. Duffee estimates three-factor essentially affine models and finds they produce more accurate yield forecasts than completely affine models, both in-sample and out-of-sample. However, there is a trade-off between flexibility in forecasting future yields and flexibility in fitting interest rate volatility. The paper shows that completely affine models fail to replicate the key empirical relation between expected returns and the slope of the yield curve, as they cannot simultaneously reproduce two features of term structure behavior: wide variation in yields and small unconditional mean excess returns relative to conditional mean excess returns. The paper concludes that while completely affine models are popular in finance, they are not suitable for forecasting future yields. The "essentially affine" models, which allow for more flexibility in risk compensation, provide a better fit to the empirical behavior of Treasury yields and can produce more accurate forecasts. The paper also highlights the importance of understanding the relationship between the slope of the yield curve and expected excess returns, which is crucial for explaining the failure of the expectations hypothesis of interest rates.
Reach us at info@study.space
[slides and audio] Term premia and interest rate forecasts in affine models