Risk Premiums of Excess Bond Returns Have a Unit Root

Abstract

We develop a term structure model that can match two stylized facts of excess returns on long-term bonds. The first stylized fact is the predictability of excess returns, which requires sufficient volatility in the price of risk. The second stylized fact is that yields are dominated by a level factor, which requires persistence in the spot interest rate or in the price of risk, or both. We calibrate a stochastic discount factor that is consistent with both stylized facts. Doing so we need time series processes that are outside the essentially affine class of term structure models. For parsimony we choose a fractionally integrated process, which leads to tractable analytical solutions. As an important implication we find that risk premiums of excess bond returns are very persistent.