We introduce a reduced form term structure model with closed form solutions for yields where the short rate and market prices of risk are nonlinear functions of Gaussian state variables. The nonlinear model with three Gaussian factors matches both the time-variation in expected excess returns and yield volatilities of U.S. Treasury bonds from 1961 to 2014. Yields depend on all three factors, yet the model exhibits features consistent with unspanned risk premia (URP) and unspanned stochastic volatility (USV). The probability of a high volatility scenario increases with the monetary experiment and remains high during the Greenspan area, even though volatilities came back down to normal levels.
We study how disagreement about inflation impact real and nominal Treasury bonds both theoretically and empirically. We show that inflation disagreement raises the level and volatility of real and nominal Treasury bond yields in a frictionless pure exchange economy with identical risk preferences. Using survey data, we document that an increase in disagreement about the one year inflation rate of consumers/professionals by one standard deviation (1.89%/0.37%) raises the level and volatility of real and nominal yields by at least 30% of its standard deviation. The results remain economically and statistically significant after a series of robustness checks involving changes in the sample period, regression controls, and proxies for the level and volatility of real and nominal yields. We also calibrate a simple learning model to real and nominal Treasury bond data and show that the economic impact of inflation disagreement is consistent with the data.
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.