Expectation puzzles, time-varying risk premia, and affine models of the term structure

Linear projections of returns on the slope of the yield curve have contradicted the implications of the traditional “expectations theory”. This paper shows that these findings are not puzzling relative to a large class of richer dynamic term structure models. Specifically, we match all the key empirical findings reported by Fama and Bliss ((1987) American Economic Review 77 (4), 680–692) and Campbell and Shiller ((1991) Review of Economic Studies 58, 495–514), among others, within large subclasses of affine and quadratic-Gaussian term structure models. Additionally, we show that certain “risk-premium adjusted” projections of changes in yields on the slope of the yield curve recover the coefficients of unity predicted by the models. Key to this matching are parameterizations of the market prices of risk that let the risk factors affect the market prices of risk directly, and not only through factor volatilities. The risk premiums have a simple form consistent with Fama’s findings on the predictability of forward rates, and are also shown to be consistent with interest-rate feedback rules used by a monetary authority in setting monetary policy.