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50
The Structure of Risks in Equilibrium Affine Models of Bond Yields ∗
, 2013
"... Many equilibrium term structure models (ETSMs) in which the state of the economy follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the conditional variances of the state variables. We show that these two assumptions alone – ..."
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Cited by 6 (4 self)
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Many equilibrium term structure models (ETSMs) in which the state of the economy follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the conditional variances of the state variables. We show that these two assumptions alone – an affine state process with conditional variances that span expected excess returns – are sufficient to econometrically identify the factors determining risk premiums in these ETSMs from data on the term structure of bond yields. Using this result we derive maximum likelihood estimates of the conditional variances of the state – the “quantities of risk” – and evaluate the goodnessoffit of a large family of affine ETSMs. These assessments of fit are fully robust to the values of the parameters governing preferences and the evolution of the state, and to whether or not the economy is arbitrage free. Our findings suggest that, to be consistent with U.S. macroeconomic and Treasury yield data, affine ETSMs should have the features that: (i) inflation risk, and not longrun risks or variation in risk premiums arising from habitbased preferences, is a significant (and perhaps the dominant) risk underlying risk premiums in U.S. Treasury markets; and (ii) risks that are unspanned by bond yields have substantial explanatory power for risk premiums consistent with timevarying market prices of risks.
Core and “crust”: Consumer prices and the term structure of interest rates. Working Paper, Federal Reserve Bank of Chicago
, 2012
"... We estimate a model for nominal and real term structures of interest rates that includes dynamics for the three main components of total inflation: core, food, and energy. These dynamics combine together to produce a measure of expected total inflation that investors use to price nominal Treasuries. ..."
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Cited by 3 (0 self)
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We estimate a model for nominal and real term structures of interest rates that includes dynamics for the three main components of total inflation: core, food, and energy. These dynamics combine together to produce a measure of expected total inflation that investors use to price nominal Treasuries. This framework captures different frequencies in inflation fluctuations: shocks to core are more persistent and less volatile than shocks to food and, especially, energy (the ‘crust’). The model fits yields and inflation data well in sample, and produces inflation forecasts that outperform several benchmarks out of sample. A common structure of latent factors explains most of the variance of the forecasting error for core inflation and bond yields. This evidence suggests that interest rates contain useful predictive content for inflation. Moreover, we estimate real interest rates, as well as inflation and real rate risk premia, that are consistent with related marketbased measures. We are grateful to Larry Christiano, Charlie Evans, Spence Krane, Alejandro Justiniano, Michael McCracken,
Bias in Estimating Multivariate and Univariate Diffusions
, 2010
"... Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time sys ..."
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Cited by 3 (3 self)
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Multivariate continuous time models are now widely used in economics and finance. Empirical applications typically rely on some process of discretization so that the system may be estimated with discrete data. This paper introduces a framework for discretizing linear multivariate continuous time systems that includes the commonly used Euler and trapezoidal approximations as special cases and leads to a general class of estimators for the mean reversion matrix. Asymptotic distributions and bias formulae are obtained for estimates of the mean reversion parameter. Explicit expressions are given for the discretization bias and its relationship to estimation bias in both multivariate and in univariate settings. In the univariate context, we compare the performance of the two approximation methods relative to exact maximum likelihood (ML) in terms of bias and variance for the Vasicek process. The bias and the variance of the Euler method are found to be smaller than the trapezoidal method, which are in turn smaller than those of exact ML. Simulations suggest that when the mean reversion is slow the approximation methods work better than ML, the bias formulae are accurate, and for scalar models the estimates obtained from the two approximate methods have smaller bias and variance than exact ML. For the square root process, the Euler method outperforms the Nowman method in terms of both bias and variance. Simulation evidence indicates that the Euler method has smaller bias and variance than exact ML, Nowman’s method and the Milstein method.
Nominal bonds, real bonds, and equity
, 2011
"... We decompose the term structure of expected equity returns into (1) the real short rate, (2) a premium for holding real longterm bonds, or the real duration premium, the excess returns of nominal longterm bonds over real bonds which reflects (3) expected inflation and (4) inflation risk, and (5) a ..."
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Cited by 2 (0 self)
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We decompose the term structure of expected equity returns into (1) the real short rate, (2) a premium for holding real longterm bonds, or the real duration premium, the excess returns of nominal longterm bonds over real bonds which reflects (3) expected inflation and (4) inflation risk, and (5) a real cashflow risk premium, which is the excess return of equity over nominal bonds. All of these risk premiums vary over time. The shape of the unconditional nominal and real bond yield curves are upward sloping due to increasing duration and inflation risk premiums. The average term structures of expected equity returns and equity risk premiums, in contrast, are downward sloping due to the decreasing effect of shortterm expected inflation, or trend inflation, across horizons. Around 70 % of the variation of expected equity returns at the 10year horizon is due to variation in the output gap and trend inflation. 1
Bayesian Inference in a Stochastic Volatility NelsonSiegel Model
, 2010
"... In this paper, we develop and apply Bayesian inference for an extended NelsonSiegel (1987) term structure model capturing interest rate risk. The socalled Stochastic Volatility NelsonSiegel (SVNS) model allows for stochastic volatility in the underlying yield factors. We propose a Markov chain Mo ..."
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Cited by 1 (0 self)
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In this paper, we develop and apply Bayesian inference for an extended NelsonSiegel (1987) term structure model capturing interest rate risk. The socalled Stochastic Volatility NelsonSiegel (SVNS) model allows for stochastic volatility in the underlying yield factors. We propose a Markov chain Monte Carlo (MCMC) algorithm to efficiently estimate the SVNS model using simulationbased inference. Applying the SVNS model to monthly U.S. zerocoupon yields, we find significant evidence for timevarying volatility in the yield factors. This is mostly true for the level and slope volatility revealing also the highest persistence. It turns out that the inclusion of stochastic volatility improves the model’s goodnessoffit and clearly reduces the forecasting uncertainty particularly in lowvolatility periods. The proposed approach is shown to work efficiently and is easily adapted to alternative specifications of dynamic factor models revealing (multivariate) stochastic
An International Dynamic Term Structure Model with Economic Restrictions and Unspanned Risks
, 2012
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ii Acknowledgements
, 2012
"... Bank of Canada discussion papers are completed research studies on a wide variety of technical subjects relevant to central bank policy. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada. ..."
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Bank of Canada discussion papers are completed research studies on a wide variety of technical subjects relevant to central bank policy. The views expressed in this paper are those of the author. No responsibility for them should be attributed to the Bank of Canada.