The Volatility of Long-term Bond Returns: Persistent Interest Shocks and Time-varying Risk Premiums

We develop a model that can match two stylized facts of the term-structure. The first stylized fact is the predictability of excess returns on long-term bonds. Modeling this requires sufficient volatility and persistence in the price of risk. The second stylized fact is that long-term yields are dominated by a level factor, which requires persistence in the spot interest rate. We find that a fractionally integrated process for the short rate plus a fractionally integrated specification for the price of risk leads to an analytically tractable almost affine term structure model that can explain the stylized facts. In a decomposition of long-term bond returns we find that the expectations component from the level factor is more volatile than the returns themselves. It therefore takes a volatile risk premium that is negatively correlated with innovations in the level factor to explain the volatility of long-term bond returns. The model also implies that excess bond returns do not exhibit mean reversion, consistent with the empirical evidence.