Jean-Sebastien Fontaine

What Fed Funds Futures Tell Us About Monetary Policy Uncertainty

The uncertainty around future changes to the Federal Reserve target rate varies over time. In our results, the main driver of uncertainty is a “path” factor signaling information about future policy actions, which is filtered from federal funds futures data. The uncertainty is highest when it signals a loosening cycle. The uncertainty raises the risk premium in a loosening cycle, reducing the transmission of target changes to longer maturities. Our results trace the information content of federal funds futures to hedging demand.This paper introduces a novel affine dynamic term structure model estimated using daily futures, LIBOR and target rates. The results uncover substantial cyclical changes in the uncertainty surrounding target changes that are induced by the Fed’s response to economic conditions. The uncertainty is lowest (highest) in tightening (loosening) cycles, especially when the economy emerges from (enters) a recession. This adds to risk premium variations over the impact of changes in the price of macro risk. The model correctly characterizes risk premium since (i) it fits interest rates more accurately and (ii) it delivers unbiased target rate forecasts that match or improve upon standard benchmarks, including predictive regressions based on federal funds futures. The information content of Fed funds futures have been neglected in the term structure literature, perhaps due to technical challenges. The paper traces this predictive content to the ability hedging demands in the futures market.

Non-Markov Gaussian Term Structure Models: The Case of Inflation

We provide a decomposition of nominal yields into real yields, expectations of future inflation and inflation risk premiums when real bonds or inflation swaps are unavailable or unreliable due to their relative illiquidity. We combine nominal yields with surveys of inflation forecasts within a no-arbitrage model where conditional expectations are latent but spanned by the history of the observed data, analog to a GARCH model for the conditional variance. The filtering problem is numerically trivial and we conduct a battery of out-of-sample comparisons. Our favored model matches the quarterly inflation forecasts from surveys and uses the information in yields to produce the best monthly forecasts. Moreover, we restrict the distribution of the inflation Sharpe ratios to achieve economically reasonable estimates of the inflation risk premium and of the real rates. We find that the inflation risk premium (i) is positive on average, (ii) rises when the unemployment rate increases and (iii) when the level of interest rates decreases. Hence, real yields are more pro-cyclical than nominal yields due to variations of the inflation risk premiums.Standard Gaussian term structure models impose the Markov property: the conditional mean is a function of the risk factors. We relax this assumption and consider models where yields are linear in the conditional mean (but not in the risk factors). To illustrate, yields should span expected inflation but not inflation. Second, expected and surprise yield changes can have opposite contemporaneous effects on expected inflation. Third, the survey forecasts and inflation rate can both be in the state. These three features are inconsistent with the Markov assumption. These effects matter empirically in the USA and in Canada.

Estimating the Policy Rule from Money Market Rates when Target Rate Changes Are Lumpy

Most central banks effect changes to their target or policy rate in discrete increments (e.g., multiples of 0.25%) following public announcements on scheduled dates. Still, for most applications, researchers rely on the assumption that the policy rate changes linearly with economic conditions and they do not distinguish between dates with and without scheduled announcements. This assumption is not innocuous when estimating the policy rule based on daily frequency. For the 1994-2011 period, and using an otherwise standard term structure model, I find that accounting for discrete changes leads to economically different estimates. Only the model based on discrete changes depicts a picture that is consistent with existing evidence on the monetary policy rule and risk premium. I study the information content of key policy announcements in the period from the end of 2008, where the policy rate reached a lower bound in the US, until the end of 2011.

Discrete Choice Term Structure Models: Theory and Applications

The relationship between inflation, unemployment and the Federal Reserve Target rate is not linear. This is clear when the Target rate reaches its lower bound but it is also the case more generally. We introduce the class of Discrete Choice Dynamic Term Structure [DCDTS] models where the latent policy indicator and the latent threshold points are stochastic. The resulting Target rate is discrete, non-linear and can be restricted to non-negative values. Empirically, we focus on the response of the Central Bank, the responses of bond yields and that of interest rate derivatives to inflation and employment growth news. We find significant non-linearities where, in contrast with latent factors or regime-switching models, sensitivity coefficients can be interpreted directly as functions of inflation and employment. The evidence is consistent with the Fed varying the weights given to each component of its dual mandate with varying economic conditions.

Bond Risk Premia and Gaussian Term Structure Models

Cochrane and Piazzesi (2005) show that (i) lagged forward rates improve the predictability of annual bond returns, adding to current forward rates, and that (ii) a Markovian model for monthly forward rates cannot generate the pattern of predictability in annual returns. These results stand as a challenge to modern Markovian dynamic term structure models (DTSMs). We develop the family of conditional mean DTSMs where the yield dynamics depend on current yields and their history. Empirically, we find that (i) current and past yields generate cyclical risk-premium variations, (ii) the model risk premia offer better returns forecasts, and (iii) the model coefficients are close to Cochrane-Piazzesi regressions of long-horizon returns. Yield decompositions differ significantly from what a standard model suggests - the expectation component decreases less in a recession and increases less in the recovery. A small Markovian factor “hidden” in measurement error (Duffee, 2011) explains some of the differences but is not sufficient to match the evidence.Cochrane and Piazzesi (2005) show that lagged forward rates add to current forward rates, improving the predictability of annual bond returns, and that a Markovian model applied to forward rates at the monthly frequency cannot generate the pattern of predictability in annual returns. These results stand as a challenge to dynamic modern term structure models (DTSM). We develop the family of Conditional Mean DTSM where the time-series dynamics of yield factors depend on current yields and on their history. Empirically, we find that both current and past yields generate substantial bond risk premium variations: the model-implied premiums are close to the return-forecasting factors obtained from direct predictability regressions. In addition, the population coefficients from our monthly model are close to the tent-shaped coefficient from CP regressions across different returns horizons. Finally, we find that since 2007 the risk premium on the 10-year yield is lower, and the expectation component is higher, by 0.5% than what a standard Markovian model would suggest.

Tractable term-structure models and the zero lower bound

We greatly expand the space of tractable term-structure models. We consider one example that combines positive yields with rich volatility and correlation dynamics. Bond prices are expressed in closed form and estimation is straightforward. We find that the early stages of a recession have distinct effects on yield volatility. Upon entering a recession when yields are far from the lower bound, (i) the volatility term structure becomes flatter, (ii) the level and slope of yields are nearly uncorrelated, and (iii) the second principal component of yields plays a larger role. However, these facts are significantly different when yields are close to the lower bound. Entering a recession in such a setting, (i) the volatility term structure instead steepens, (ii) the level and slope factors are strongly correlated, and (iii) the second principal component of yields plays a smaller role. Existing dynamic term-structure models do not capture the changes in the cyclical responses of the volatility term structure near the lower bound.