Extracting inflation expectations and inflation risk premia from the term structure: A joint model of the UK nominal and real yield curves

This paper analyses the UK interest rate term structure over the period since October 1992, when the United Kingdom adopted an explicit inflation target, using an affine term structure model estimated using both government bond yields and survey data. The model imposes no-arbitrage restrictions across nominal and real yields, which enables interest rates to be decomposed into expected real policy rates, expected inflation, real term premia and inflation risk premia. The model is used to shed light on major developments over the period, including the impact of Bank of England independence and the low real bond yield ‘conundrum’.     

The high-frequency impact of news on long-term yields and forward rates: Is it real?

Macroeconomic news announcements move yields and forward rates on nominal and index-linked bonds and inflation compensation. This paper estimates the reactions using high-frequency data on nominal and index-linked bond yields, allowing the effects of news announcements on real rates and inflation compensation to be parsed far more precisely than is possible using daily data. Long-term nominal yields and forward rates are very sensitive to macroeconomic news announcements. Inflation compensation is sensitive to announcements about price indices and monetary policy. However, for news announcements about real economic activity, such as nonfarm payrolls, the vast majority of the sensitivity is concentrated in real rates. Accordingly, most of the sizeable impact of news about real economic activity on the nominal term structure of interest rates represents changes in expected future real short-term interest rates and/or real risk premia rather than changes in expected future inflation and/or inflation risk premia. Such sensitivity of real rates to macroeconomics news is hard to rationalize within the framework of existing macroeconomic models.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

Pricing the term structure of inflation risk premia: Theory and evidence from TIPS

In this paper, we study inflation risk and the term structure of inflation risk premia in the United States' nominal interest rates through the Treasury Inflation Protection Securities (TIPS) with a multi-factor, modified quadratic term structure model with correlated real and inflation rates. We derive closed form solutions to the real and nominal term structures of interest rates that drastically facilitate the estimation of model parameters and improve the accuracy of the valuation of nominal rates and TIPS prices. In addition, we contribute to the literature by estimating the term structure of inflation risk premia implied from the TIPS market. The empirical evidence using data from the period of January 1998 through October 2007 indicates that the expected inflation rate, contrary to data derived from the consumer price indices, is very stable and the inflation risk premia exhibit a positive term structure.     

Uninsurable risk and financial market puzzles

We compare the empirical performances of three risk-sharing arrangements involving idiosyncratic skill shocks: (a) where individuals are unable to directly insure their consumption against individual-specific shocks, (b) where agents strike long-term insurance contract with financial intermediaries involving a truth revelation constraint as in Kocherlakota and Pistaferri (2009), (c) full risk sharing. Based on the widely accepted assumption of cross-sectional log-normality of individual consumption levels, we work out closed form expressions of the pricing kernels for (a) and (b). We put these three models to test four financial market anomalies, namely the equity premium, currency premium, risk-free rate, and consumption-real exchange rate puzzles simultaneously in an integrated framework. We find that the pricing kernel associated with (a) outperforms the other two models in terms of the produced estimates of the agent’s preference parameters and the model ability to predict the equity and currency premia, the risk-free rate, and the log growth in the exchange rate. However, the predictive ability is still far from satisfactory for all three models under scrutiny.     

Time‐Varying Asset Volatility and the Credit Spread Puzzle

Most extant structural credit risk models underestimate credit spreads—a shortcoming known as the credit spread puzzle. We consider a model with priced stochastic asset risk that is able to fit medium‐ to long‐term spreads. The model, augmented by jumps to help explain short‐term spreads, is estimated on firm‐level data and identifies significant asset variance risk premia. An important feature of the model is the significant time variation in risk premia induced by the uncertainty about asset risk. Various extensions are considered, among them optimal leverage and endogenous default.     

Long-term foreign exchange risk premia and inflation risk

As highlighted by recent literature, long-term foreign exchange risk premia (FRP) of a currency pair tend to covary negatively with short-term real interest rate differentials (RIRD) of the pair. We fit an affine term structure model for 9 major currencies against the US dollar and estimate two components of this covariance: the real risk premia (RRP) component and the inflation risk premia differential (IRPD) component. We find that the IRPD component is significantly negative for all currency pairs in our sample. We propose a macro-finance model to understand the types of shocks that generate such covariance.     

Time-varying risk premia in foreign exchange and equity markets: evidence from Asia–Pacific countries

This paper examines the validity of the risk premia hypothesis in explaining deviations from Uncovered Interest Parity (UIP) and the role of deviations from Purchasing Power Parity (PPP) in the pricing of foreign exchange rates and equity securities in five Asia–Pacific countries and the US. Using weekly data from 1 January, 1988 to 27 February, 1998, I find that conditional variances are not related to the deviations from UIP in any statistical sense based on an univariate GARCH(1,1)-M model. As I consider both foreign exchange and equity markets together and test a conditional international CAPM (ICAPM) in the absence of PPP, I cannot reject the model based on the J-test by Hansen (Econometrica 50 (1982), 1029–1054) and find significant time-varying foreign exchange risk premia present in the data. This empirical evidence supports the notion of time-varying risk premia in explaining the deviations from UIP. It also supports the idea that the foreign exchange risk is not diversifiable and hence should be priced in both markets.     

Real Rates, Expected Inflation, and Inflation Risk Premia

This paper studies the term structure of real rates, expected inflation, and inflation risk premia. The analysis is based on new estimates of the real term structure derived from the prices of index-linked and nominal debt in the U.K. I find strong evidence to reject both the Fisher Hypothesis and versions of the Expectations Hypothesis for real rates. The estimates also imply the presence of time-varying inflation risk premia throughout the term structure.     

Inflation risk premia and the expectations hypothesis

We study the properties of the nominal and real risk premia of the term structure of interest rates. We develop and solve the bond pricing implications of a structural monetary version of a real business cycle model, with taxes and endogenous monetary policy. We show the relation of this model with the class of essentially affine models that incorporate an endogenous state-dependent market price of risk. We characterize and estimate the inflation risk premium and find that over the last 40 years the ten-year inflation risk premium has been has averaged 70 basis points. It is time-varying, ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping. The inflation risk premium explains 23% (42%) of the time variation in the five (ten)-year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates.     

Mortgage timing

We study how the term structure of interest rates relates to mortgage choice at both household and aggregate levels. A simple utility framework of mortgage choice points to the long-term bond risk premium as distinct from the yield spread and the long yield as a theoretical determinant of mortgage choice: when the bond risk premium is high, fixed-rate mortgage payments are high, making adjustable-rate mortgages more attractive. We confirm empirically that the bulk of the time variation in both aggregate and loan-level mortgage choice can be explained by time variation in the bond risk premium, whether bond risk premia are measured using forecasters’ data, a vector autoregressive (VAR) term structure model, or a simple household decision rule based on adaptive expectations. The household decision rule moves in lock-step with mortgage choice, lending credibility to a theory of strategic mortgage timing by households.     

An Anatomy of Commodity Futures Risk Premia

We identify two types of risk premia in commodity futures returns: spot premia related to the risk in the underlying commodity, and term premia related to changes in the basis. Sorting on forecasting variables such as the futures basis, return momentum, volatility, inflation, hedging pressure, and liquidity results in sizable spot premia between 5% and 14% per annum and term premia between 1% and 3% per annum. We show that a single factor, the high‐minus‐low portfolio from basis sorts, explains the cross‐section of spot premia. Two additional basis factors are needed to explain the term premia.     

The term structure of euromarket interest rates: An empirical investigation

This paper is an empirical investigation of the predictability and co-movement of risk premia in the term structure of Euromarket interest rates. We present regression results which suggest that risk premia in three Euromarket term structures and on uncovered foreign asset positions move together. We test formally the hypothesis that these risk premia move in proportion to a single latent variable. We are unable to reject this hypothesis. The single latent variable model can be interpreted as in Hansen and Hodrick (1983) and Hodrick and Srivastava (1984) as a specialization of the ICAPM in which assets have constant betas on a single, unobservable benchmark portfolio.     

Canonical Term‐Structure Models with Observable Factors and the Dynamics of Bond Risk Premia

We derive a canonical representation for the no‐arbitrage discrete‐time term structure models with both observable and unobservable state variables, popularized by Ang and Piazzesi (2003) . We conduct a specification analysis based on this canonical representation and we analyze how alternative parameterizations affect estimated risk premia, impulse response functions, and variance decompositions. We find a trade‐off between the need to obtain parsimonious parameterizations and the ability of the models to match observed patterns of variation in risk premia. We also find that more richly parameterized models uncover a greater influence of macroeconomic fundamentals on the long‐end of the yield curve.     

The high-frequency response of exchange rates and interest rates to macroeconomic announcements

The joint movements of exchange rates and U.S. and foreign term structures over short-time windows around macro announcements are studied using a 14-year span of high-frequency data. In order to evaluate whether the joint effects can be reconciled with conventional theory, the implications of these joint movements for changes in expected future exchange rates and changes in foreign exchange risk premia are deduced. For several real macro announcements, a stronger than expected release appreciates the dollar today, and must either (i) lower the risk premium for holding foreign currency rather than dollars, or (ii) imply net expected dollar depreciation over the ensuing decade.     

Testing the expectations hypothesis of the term structure with permanent-transitory component models

This study proposes a new application of Permanent-Transitory Component Models (PTCMs) to test the Expectation Hypothesis of the Term Structure (EHTS). Unlike previous approaches, tests based on PTCMs can simultaneously detect departures from rational expectations and time varying term premia. We set out analytically and empirically the links across previous tests and PTCMs. We also show that PTCMs identify an additional restriction for rational expectations, on top of the one-to-one relationship between forward and spot rates, that must be imposed in estimations of term premia. Data for the short-end of the US term structure suggest that both factors contribute to the rejection of the EHTS. Moreover, the empirical estimates of term premia are persistent and exhibit sign fluctuations. Their stochastic properties depend crucially on whether the additional restriction for rational expectations is imposed in estimation.     

Term structure determinants of time-varying risk of 1-year bond returns

Term structure drivers of 1-year bond premia and conditional bond return risk are distinct. Consequently, the Cochrane–Piazzesi factor captures aggregate price of risk and not the amount of risk in 1-year bond returns. One linear combination of forward rates captures most of the variation in bond return risk across maturities. Interest rate level captures substantial amount of variation in the conditional return risk, a finding consistent with rising inflation uncertainty with level of inflation and interest rates. The 4-5 yield spread, an important positive predictor of bond return premia, has an opposing but limited impact on the conditional volatility.     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

Research and Development Activity and Expected Returns in the United Kingdom

Fama and French (1992) show that size and book-to-price dominate CAPM betaand other variables such as the price-earnings ratio and dividend yield in explainingthe cross-section of US stock returns. Comparable evidence for the UK points to abook-to-price effect, but not a size effect (Chan and Chui, 1996; Strong and Xu, 1997).In this paper, our first contribution is to show that a measure of research and development (RD) helps explain cross-sectional variation in UK stock returns. Our cross-sectional results on the association between stock returns and RD are consistent with recent US evidence reported by Lev and Sougiannis (1996, 1999) and Chan, Lakonishok and Sougiannis (2001). Fama and French (1993, 1995, 1996) also show that a three-factor model captures a high proportion of the time series variation in portfolio returns, again for the US. Our second contribution is to show, for the UK, that a modification to the three-factor model to take account of RD activity can significantly enhance the explanatory power of the three-factor model. We show that, as a practical matter, estimated risk premia based on the modified three-factor model can differ considerably from risk premia estimated using the CAPM or the three-factor model. In particular, risk premia for industries in whichfew firms undertake RD activities tend to be over-estimated.     

Time-varying state variable risk premia in the ICAPM

We find that the relation between state variables, such as the t-bill rate and term spread, and consumption growth is time-varying. In the cross-section of U.S. stocks, risk premia for exposure to state variables vary over time accordingly. When a state variable predicts consumption strongly relative to its own history, its annualized risk premium increases by 6% (0.4 in Sharpe ratio). This effect implies that risk premia can switch signs and are increasing in the conditional variance of the state variable. These common drivers of time-varying risk premia are consistent with the Intertemporal CAPM. Benchmark factors contain the same conditional expected return effects as state variable risk premia.