Bond Risk Premia: The Information in Really Long-Maturity Forward Rates
67 Pages Posted: 22 Feb 2021
Date Written: February 2, 2021
Long term forward rates contain information that greatly improves the precision with which expectations of future short rates can be distinguished from risk premia in the term structure. Indeed, in affine models, the slope of the term structure of risk premia for long maturities is very closely approximated by the sum of (i) the slope of the forward rate curve and (ii) a term that depends only of yield volatility and maturity ("convexity"), two quantities that can easily be estimated independently of the details of model specification. Key to extracting the risk premium information in long-term forward rates is capturing the dynamics of convexity, which requires a model with time-varying volatility. Using a four-factor ATSM, we find that risk premia on long term bonds are almost entirely driven by volatility. Short rate expectations in our model account for a much larger fraction of the volatility of yields than is typically reported, a result that we show is mainly the result of econometric bias in some estimates of Gaussian models. We also show - using Monte Carlo simulation - that including data on long-term yields in the estimation of term structure models greatly improves the precision of estimated values of short rate expectations, term premia and risk premia. Compared with benchmark estimates that use yield data up to 25 years, excluding data on yields longer than 10 years results in the standard errors of both estimated means and volatilities roughly tripling in size.
Keywords: Risk Premia, Forward Rates, Yield Volatility, Convexity, Term Structure
JEL Classification: E43, G12
Suggested Citation: Suggested Citation