Aspects of time-varying risk and return in bond markets

This dissertation consists of two parts, both of which are based on quadratic-Gaussian (QG) models in which interest rates are quadratic functions of state variables that follow a multivariate Gaussian process. The first part focuses on the nominal term structure of interest rates and examines whether there is a trade-off between capturing the time-varying volatility of interest rates and fitting the time-varying risk premia implicit in the predictability of nominal bond returns. This trade-off had been documented for affine models, but QG models are found not to entail an analogous trade-off: QG models outperform pure-Gaussian models in forecasting yields and capture the time-variation of the volatilities of short-term and long-term yields reasonably well. The first part also develops useful techniques that facilitate the empirical analysis QG models.; The second part develops a more extensive framework in which real interest rates, nominal interest rates, and inflation expectations are all quadratic functions of Gaussian state variables. Specification restrictions are developed to obtain a model that can be identified from data on inflation and the nominal term structure. The model is found to capture the variation of TIPS (Treasury Inflation Protected Securities) yields well. Furthermore, the model's implications for the term structure of inflation expectations and inflation uncertainty (the conditional variance of future inflation) agree in many respects with survey data on long-term and short-term inflation forecasts.