Term Premia and Interest Rate Forecasts in Affine Models

Term Premia and Interest Rate Forecasts in Affine Models

First version November 1998, This version November 2000 | Gregory R. Duffee
This paper examines the forecasting ability of affine models in predicting future changes in Treasury yields. The author finds that standard affine models, which assume that the compensation for risk is a multiple of the variance of the risk, produce poor forecasts. These models fail to capture the empirical behavior of Treasury yields, particularly the relationship between expected returns and the slope of the yield curve. The models' inability to vary risk compensation independently of interest rate volatility is a key reason for their failure. To address this issue, the author proposes a broader class of models called "essentially affine" models. These models retain the tractability of standard affine models but allow the compensation for interest rate risk to vary independently of interest rate volatility. This additional flexibility enables essentially affine models to produce more accurate forecasts of future yields. The paper is organized into several sections, including an introduction to affine models, an explanation of why completely affine models fail, an empirical estimation technique, and the results of the analysis. The author uses historical data on Treasury yields to estimate both completely affine and essentially affine models and compares their performance in terms of in-sample and out-of-sample forecasts. The results show that essentially affine models outperform completely affine models in forecasting future yields. However, there is a trade-off between the flexibility in forecasting future yields and the flexibility in fitting interest rate volatility.This paper examines the forecasting ability of affine models in predicting future changes in Treasury yields. The author finds that standard affine models, which assume that the compensation for risk is a multiple of the variance of the risk, produce poor forecasts. These models fail to capture the empirical behavior of Treasury yields, particularly the relationship between expected returns and the slope of the yield curve. The models' inability to vary risk compensation independently of interest rate volatility is a key reason for their failure. To address this issue, the author proposes a broader class of models called "essentially affine" models. These models retain the tractability of standard affine models but allow the compensation for interest rate risk to vary independently of interest rate volatility. This additional flexibility enables essentially affine models to produce more accurate forecasts of future yields. The paper is organized into several sections, including an introduction to affine models, an explanation of why completely affine models fail, an empirical estimation technique, and the results of the analysis. The author uses historical data on Treasury yields to estimate both completely affine and essentially affine models and compares their performance in terms of in-sample and out-of-sample forecasts. The results show that essentially affine models outperform completely affine models in forecasting future yields. However, there is a trade-off between the flexibility in forecasting future yields and the flexibility in fitting interest rate volatility.
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Understanding Term premia and interest rate forecasts in affine models