We propose an expansion of Gaussian term structure models where the short rate and market price of risk are non-linear in the state variables. We provide closed-form solutions for bond prices and since the latent factors are Gaussian our expanded model is as tractable as the Gaussian model. We estimate a three- factor expanded model and find that the model matches the time variation in both expected excess returns and yield volatilities of U.S. Treasury bonds. A significant part of expected excess returns in the model is not linearly spanned by the cross section of yields. This suggests that the hidden factor documented in Duffee (2011) might be spanned by the yield curve, but in a non-linear way.
We study how differences in beliefs about expected inflation affect the nominal term structure when investors have "catching up with the Joneses'' preferences. In the model, "catching up with the Joneses'' preferences help to match the level and slope of yields as well as the level of yield volatilities. Disagreement about expected inflation helps to match the dynamics of yields and yield volatilities. Expected inflation disagreement induces a spillover effect to the real side of the economy with a strong impact on the real yield curve. When investors share common preferences over consumption relative to the habit with a coefficient of relative risk aversion greater than one, real average yields across all maturities rise as disagreement increases. Real yield volatilities also rise with disagreement. To develop intuition concerning the role of different beliefs between investors, we consider a case where the real and nominal term structures can be computed as weighted-averages of quadratic Gaussian term structure models. We numerically find increased disagreement about expected inflation between the investors increases nominal yields and nominal yield volatilities at all maturities. We find empirical support for these predictions.
We study how information about an asset affects optimal portfolios and
equilibrium asset prices when investors are not sure about the model that predicts
future asset values and thus treat the information as ambiguous. We show
that this ambiguity may lead to asset demand that is insensitive to changes in
news and investors use only their prior information when making portfolio decisions.
This insensitivity to news is more severe when prices deviate a lot
from its unconditional mean and in contrast to other ambiguity models it also
occurs when demand is sensitive to changes in the price. In equilibrium, we
show that stock prices may not react to public information that is worse than
expected even though there are no information processing costs or other market
frictions. The severity of this mispricing depends on the risk of the stock and
the magnitude of the news surprise.
I decompose inflation risk into (i) a component that is correlated with real returns on positive-net-supply securities (stocks, real estate, etc.) and factors that determine investor’s preferences and investment opportunities and (ii) a residual component. In equilibrium, only the first component earns a risk premium. Therefore investors should avoid exposure to the residual component. All nominal bonds, including the nominal money-market account, are equally exposed to the residual component except inflationprotected bonds, which provide a means to hedge it. Every investor should put 100% of his wealth in positive-net-supply securities and inflation-protected bonds and should finance every long/short position in nominal bonds with an equal amount of other nominal bonds or by borrowing/lending in the nominal money market account; i.e. investors should hold a zero-investment portfolio of nominal bonds and the nominal money market account.