Essays on the term structure of interest rates and long run variance of stock returns

My dissertation contains three chapters. It studies the bond market as well as the stock market. For the bond market I examine aspects of the term structure of interest rates using macro models with the goal of advancing our understanding of the pricing of bonds with different maturities from a macroeconomic perspective. For the stock market, I study the variance of stock returns over different investment horizons.;In Chapter 1, "Bond Pricing with Model Uncertainty", I propose and implement a term structure model based on risk-sensitive preferences. Following Hansen and Sargent (2008), I model a risk-sensitive consumer who shows aversion to uncertainties, and I evaluate his utility using the max-min utility function. He considers three types of uncertainties: (a) uncertainty of future states conditional on current states; (b) uncertainty about current states; and (c) uncertainty about the model generating the data. I use a parameter to represent his aversion to the each type of uncertainty. The max-min utility function implies multiplicative adjustments to the standard pricing kernel. A term premium results because these uncertainties figure more prominently in the pricing of long term bonds.;The pricing kernel is combined with the exogenous processes of consumption growth and inflation to price the bond yields. I specify two bivariate long run risk models to represent the model uncertainty. The two models share a common specification of consumption growth, but the inflation process differs across the models: in one model inflation is non-stationary, while in the other it is stationary. The risk-sensitive consumer behaves as if the probability estimates for the models are tilted in favor of the one implying lower lifetime utility. The model with non-stationary inflation turns out to have the lower lifetime utility. As the probability estimates are tilted to favor the model with non-stationary inflation, both the short rate and yield spread increase. I show that this phenomenon helps to explain the high short rate and yield spread in the 1980's. More generally, I show that the model fits the observed shape of the yield curve, volatility of long yields, predictability of excess bond returns and correlation between yields of different maturities.;In Chapter 2, "Forecasting Bond Returns in a Macro Model", I consider the predictability of excess bond returns. Recent research has shown that a forecasting factor based on the forward rates has significant predictive power for excess bond returns at all maturities. In this chapter, I investigate the macroeconomic factors underlying those forward rates. I specify a rich stochastic general equilibrium model and use the Bayesian method to extract key macro variables such as habit, the government spending shock, the technology shock, the inflation target and the monetary policy shock. I then relate them to the forecasting factor and show that the forecasting factor is mostly capturing the effect of technology shock. Following the literature, I construct a forecasting factor based on a linear combination of extracted macro variables. This new factor predicts both excess bond returns and equity returns better than the forecasting factor based on forward rates.;In Chapter 3, "Decomposing the Variance-covariance Matrix: A Reinvestigation of Long Run Stock Variance", I reinvestigate the long run variance of stock returns following Pastor and Stambaugh (2009), who find that stock returns are riskier in the long run. As in Pastor and Stambaugh (2009), I use a Bayesian approach to assess the risk. I find that their conclusion is likely to be sensitive to the prior of the correlation between innovation in expected returns and unexpected returns. The correlation plays a key role in determining the riskiness of stock returns in the long run through the mean reverting component. My analysis suggests that their result depends critically on a prior that is sufficiently uninformative. If the prior of a highly negative correlation is sufficiently informative, the result would be overturned. I also find that their conclusion is robust to the addition of dividend growth into the predictive system. By estimating rhouw with a sharp prior distribution, I show that the posterior draws of rhouw are sufficiently negative to generate a variance ratio smaller than 1 for 30 year stock returns.