Dynamic Term Structure Models Research Articles

Inflation Expectations and Risk Premia in Emerging Bond Markets: Evidence from Mexico

To study inflation expectations and associated risk premia in emerging bond markets, this paper provides estimates for Mexico based on an arbitrage-free dynamic term structure model of nominal and real bond prices that accounts for their liquidity risk. In addition to documenting the existence of large and time-varying liquidity premia in nominal and real bond prices that are only weakly correlated, the results indicate that long-term inflation expectations in Mexico are well anchored close to the inflation target of the Bank of Mexico. Furthermore, Mexican inflation risk premia are larger and more volatile than those in Canada and the United States.

Interest Rate Volatility and No-Arbitrage Affine Term Structure Models

Within the affine framework, many have observed a tension between matching conditional first and second moments in dynamic term structure models (DTSMs). Although the existence of this tension is generally accepted, less understood is the mechanism that underlies it. We show that no arbitrage along with the rich information in the cross section of yields has strong implications for both the dynamics of volatility and the forecasts of yields. We show that this link implied by the absence of arbitrage—and not the factor structure per se—underlies the tension between first and second moments found in the literature. Adding to recent research that has suggested that no-arbitrage restrictions are nearly irrelevant in Gaussian DTSMs, our results show that no-arbitrage restrictions are potentially relevant when there is stochastic volatility. This paper was accepted by Gustavo Manso, finance.

Zero-Coupon Yields and the Cross-Section of Bond Prices

Abstract I estimate a dynamic term structure model on an unbalanced panel of Treasury coupon bonds, without relying on an interpolated zero-coupon yield curve. A linearity-generating model, which separates the parameters that govern the cross-sectional and time-series moments of the model, takes about 8 min to estimate on a sample of over 1 million bond prices. The traditional exponential affine model takes about 2 hr, because of a convexity term in coupon-bond prices that cannot be concentrated out of the cross-sectional likelihood. I quantify the on-the-run premium and a “notes versus bonds” premium from 1990 to 2017 in a single, easy-to-estimate no-arbitrage model. (JEL G12, G14, C33) Received: April 30, 2018; editorial decision November 3, 2020 by Editor Nikolai Roussanov

Can Interest Rate Factors Explain Exchange Rate Fluctuations?

This paper explores whether interest rate factors, derived from the yield curve, can explain exchange rate fluctuations at different horizons. Using a dynamic term structure model under no-arbitrage, exchange rates are modeled as the ratio of two countries’ stochastic discount factors. Key to this framework is that factors are observable, which allows the model to be estimated by Maximum Likelihood. Results show that interest rate factors can explain half of the variation in one-year exchange rates and up to ninety percent of five-year movements, for free-floating currencies from 1999 to 2014. These findings suggest that yield curves contain important information for modeling exchange rate dynamics, particularly at longer horizons. JEL codes: G15, F31, E43 * Julieta Yung, Federal Reserve Bank of Dallas, Research Department, 2200 N. Pearl Street, Dallas, TX 75201. 214 922-5443. julieta.yung@dal.frb.org. I am grateful to Tom Cosimano, Jun Ma, Mark Wohar, and many others for helpful comments and suggestions. This paper also benefited from comments made by the participants at the Macroeconomics Seminar and the Mathematical Finance Research Group at the University of Notre Dame. The views in this paper are those of the author and do not necessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System.

Global Evidence on Unspanned Macro Risks in Dynamic Term Structure Models

There are mixed results on whether macro risks are spanned by the yield curve. This paper reviews the major arguments and takes a global perspective to obtain comprehensive evidence. We study a large cross-section of 22 countries, including both developed and emerging markets. Our regression evidence confirms that macro information provides explanatory power for bond excess returns on top of yield factors. This finding is particularly strong in emerging markets. However, from a mechanical perspective, discriminating between spanned and unspanned models when considering in-sample fit and term premium predictions makes no difference.

Inflation Expectations and Risk Premia in Emerging Bond Markets: Evidence from Mexico

To study inflation expectations and associated risk premia in emerging bond markets, this paper provides estimates for Mexico based on an arbitrage-free dynamic term structure model of nominal and real bond prices that accounts for their liquidity risk. In addition to documenting the existence of large and time-varying liquidity premia in nominal and real bond prices that are only weakly correlated, the results indicate that long-term inflation expectations in Mexico are well anchored close to the inflation target of the Bank of Mexico. Furthermore, Mexican inflation risk premia are larger and more volatile than those in Canada and the United States.

Accounting for Low Long-Term Interest Rates: Evidence from Canada

In recent decades, long-term interest rates around the world have fallen to historic lows. We examine this decline using a dynamic term structure model of Canadian nominal and real yields with adjustments for term, liquidity, and inflation risk premiums. Canada provides a useful case study that has been little examined despite its established indexed debt market, negligible distortions from monetary quantitative easing or the zero lower bound, and no sovereign credit risk. We find that since 2000, the steady-state real interest rate has fallen by more than 2 percentage points, long-term inflation expectations have edged down, and real bond and inflation risk premiums have fluctuated but shown little longer-run trend. Therefore, the drop in the equilibrium real rate appears largely to account for the lower new normal in interest rates.

The role of time‐varying risk premia in international interbank markets

AbstractWe study international interbank spreads within a no‐arbitrage dynamic term structure model and attempt to disentangle time‐varying risk premia in the interbank market for major currencies. Our results suggest that, at the peak of financial crisis, the interbank spread was clearly driven by liquidity risk. In the aftermath of the crisis, credit risk has become the dominant driver of the spread. This effect is stronger in the Euro and UK markets, due to the escalation of the European sovereign debt crisis, and weaker in the Japanese market which experienced remarkably low credit pressures. Furthermore, we assess the effectiveness of monetary policy actions and demonstrate that the establishment of the unconventional policy programmes led to the deterioration of liquidity risk in the interbank market, and the policy of major Central banks to substantially cut interest rates kept credit pressures at low levels. We also partition the spread into expectation hypothesis and time‐varying risk premium components and reject the hypothesis of constant risk premium. We find strong evidence of predictability inferred from the interbank spread model with time‐varying risk premia.

Recovering Yield Curves from Dynamic Term Structure Models with Time-Varying Factors

A dynamic version of the Nelson-Siegel-Svensson term structure model with time-varying factors is considered for predicting out-of-sample maturity yields. Simple linear interpolation cannot be applied to recover yields at the very short- and long- end of the term structure where data are often missing. This motivates the use of dynamic parametric term structure models that exploit both time series and cross-sectional variation in yield data to predict missing data at the extreme ends of the term structure. Although the dynamic Nelson–Siegel–Svensson model is weakly identified when the two decay factors become close to each other, their predictions may be more accurate than those from more restricted models depending on data and maturity.

Estimating nominal interest rate expectations: Overnight indexed swaps and the term structure

Abstract No-arbitrage dynamic term structure models (DTSMs) have regularly been used to estimate interest rate expectations and term premia, but are beset by empirical challenges. I propose augmenting DTSMs with overnight indexed swap (OIS) rates to better estimate the decomposition along the term structure at daily frequencies. A Gaussian affine DTSM, augmented with 3 to 24-month OIS rates, generates estimates of US expectations that closely correspond to survey-implied measures out to a 10-year horizon and are more stable across sub-samples, compared to existing models. In addition, I provide narrative evidence, in the form of an event study around US unconventional monetary policy announcements, to further exemplify the benefits from OIS augmentation.

Unifying Gaussian dynamic term structure models from a Heath–Jarrow–Morton perspective

In this paper, we show that most existing Gaussian dynamic term structure models (GDTSMs) can be nested as special cases under a unified Heath–Jarrow–Morton (HJM)-based framework of GDTSM construction. Our study provides not only a systematic way to examine the commonality of many seemingly distinct GDTSMs, but also a novel and convenient approach to constructing GDTSMs that are otherwise unavailable or intractable under the traditional approach. In our empirical study using the Euro area forward rates, we conduct a specification analysis based on this novel approach. The analysis reveals that the traditional models impose restrictive constraints limiting their flexibility in capturing key features of the correlations and volatilities of the forward rates.

The Secular Decline in Long-Term Yields around FOMC Meetings

In this paper I document a striking fact: a narrow window around Fed meetings fully captures the secular decline in U.S. Treasury yields since 1980. By contrast, yield movements outside this window are transitory and wash out over time. This is surprising because the forces behind the secular decline are thought to be independent of monetary policy. However, it is possible that the bond market learns about these forces from the Fed. Two additional facts support this interpretation: (i) long-term yields drop immediately following Fed announcements, and (ii) the Fed’s expectation about the long-run level of the federal funds rate – revealed through the dot plot – has a strong impact on long-term yields. To explain these facts, I present a dynamic term structure model in which the Fed learns from the yield curve and the market learns from Fed meetings. The model rules out alternative explanations such as business cycle information and risk premia. It further implies that the Fed possesses important information about the long-run neutral interest rate. This can explain why Fed announcements have a powerful impact on the valuations of long-lived assets like the stock market.

PRINCIPAL-COMPONENT-BASED GAUSSIAN AFFINE TERM STRUCTURE MODELS: CONSTRAINTS AND THEIR FINANCIAL IMPLICATIONS

This work builds on the work by Joslin et al. [(2011) A new perspective on Gaussian dynamic term structure Models, The Review of Financial Studies 24, 926–970] on the affine dynamics of portfolios of yields and addresses the unresolved issues of ‘internal consistency’ mentioned in the same paper. It shows the unexpected constraints that have to be satisfied by the [Formula: see text]-measure evolution of the yield curve if the portfolio of yields has to be interpreted as their principal components. This choice of state variables is common in the recent literature and so our findings are intrinsically interesting. However, we show that our results also extend to a wide class of choices for state variables, when these are chosen as linear combinations of yields. We show that these constraints have important financial consequences, which, to our knowledge, have not been appreciated. In particular, this paper highlights some puzzling issues of compatibility between the [Formula: see text]- and [Formula: see text]-measure dynamics of Gaussian dynamic term structure models when principal components are chosen as state variables, once the constraints we derive are taken into account.

Modeling Volatility in Dynamic Term Structure Models

We propose no-arbitrage term structure models in which the volatility factors follow GARCH processes. The models’ tractability is similar to that of canonical affine term structure models, but they capture the conditional variances of yields much more accurately. We estimate a model with one volatility factor using Treasury yield data for 1971-2019. Relative to standard affine term structure models with stochastic volatility, the model improves the fit of yield volatility substantially, especially for long-maturity yields. This improvement does not come at the expense of a deterioration in yield fit. We conclude that the ability of no-arbitrage term structure models to extract and model conditional volatility critically depends on the specification of the volatility factors. Modeling volatility as a function of (lagged) squared innovations to factors improves on models where volatility is a linear function of the factors.

A New Normal for Interest Rates? Evidence from Inflation-Indexed Debt

Abstract The downtrend in U.S. interest rates over the past two decades may partly reflect a decline in the longer-run equilibrium real rate of interest. We examine this issue using dynamic term structure models that account for time-varying term and liquidity risk premiums and are estimated directly from prices of individual inflation-indexed bonds. Our finance-based approach avoids two potential pitfalls of previous macroeconomic analyses: structural breaks at the zero lower bound and misspecification of output and inflation dynamics. We estimate that the longer-run equilibrium real rate has fallen about 2 percentage points and appears unlikely to rise quickly.

Defining and Exploiting Value in US Treasury Bonds

In this article, the authors propose a definition of value in Treasury bonds that, the authors believe, is more satisfactory than definitions found in the recent literature, and that allows for statistically significant and economically relevant predictions of cross-sectional excess returns. The authors’ value pricing factor exploits the differences between the market and the theoretical values of Treasury bonds, where the theoretical value is assessed using an economically-justifiable Gaussian dynamic term structure model. The authors show that the profitability of the strategy they build using their value signal is statistically and economically significant and is closely linked to the Treasury market volatility. The authors provide an explanation for this strong link using arguments similar to what can be found in the recent literature on liquidity in Treasuries; and the authors show that their value signal is not subsumed by the best-known return-predicting factors. With an eye to practical applications, the authors also present a long-only version of their strategy. TOPICS:Analysis of individual factors/risk premia, factor-based models, style investing

Term Structure Analysis with Big Data: One-Step Estimation Using Bond Prices

Nearly all studies that analyze the term structure of interest rates take a two-step approach. First, actual bond prices are summarized by interpolated synthetic zero-coupon yields, and second, some of these yields are used as the source data for further empirical examination. In contrast, we consider the advantages of a one-step approach that directly analyzes the universe of bond prices. To illustrate the feasibility and desirability of the one-step approach, we compare arbitrage-free dynamic term structure models estimated using both approaches. We also provide a simulation study showing that a one-step approach can extract the information in large panels of bond prices and avoid any arbitrary noise introduced from a first-stage interpolation of yields.

" A New Normal for Interest Rates? Evidence from Inflation-Indexed Debt"

The downtrend in U.S. interest rates over the past two decades may partly reflect a decline in the longer-run equilibrium real rate of interest. We examine this issue using dynamic term structure models that account for time-varying term and liquidity risk premiums and are estimated directly from prices of individual inflation-indexed bonds. Our finance-based approach avoids two potential pitfalls of previous macroeconomic analyses: structural breaks at the zero lower bound and misspecification of output and inflation dynamics. We estimate that the longer-run equilibrium real rate has fallen about 2 percentage points and appears unlikely to rise quickly.

The influence of real interest rates and risk premium effects on the ability of the nominal term structure to forecast inflation

Based on an empirically attractive Gaussian dynamic term structure model and data on the short-term real interest rate and per capita real consumption, this paper examines the information content of the nominal term structure of interest rates with respect to inflation, real interest rates and risk premium effects. The paper finds a number of interesting results, which have monetary policy implications. First, it shows that the suggested model fits well the data and provides estimates of real interest rates and expected inflation rates which are very close to those given by survey data. Second, it provides clear cut evidence that the nominal term structure is mainly determined by movements in real interest rates and, to a lesser extent, by inflation and risk premium effects. These results mean that term spreads between long and short-term nominal rates fail to forecast future changes in inflation rates because are dominated by real term structure effects, which are not orthogonal to inflation rate shocks (changes). Third, to retrieve information from the term spread models of nominal interest rates about future inflation rate changes, the paper suggests a regression model which adjusts the nominal interest rates term spreads for the real term structure effects.

Expectations and Risk Premia at 8:30 a.m.: Deciphering the Responses of Bond Yields to Macroeconomic Announcements

What explains the sharp movements of the yield curve upon the release of major U.S. macroeconomic announcements? To answer this question, we estimate an arbitrage-free dynamic term structure model with macroeconomic fundamentals as risk factors. We assume that the yield curve reacts to announcements primarily because of the information they contain about the fundamentals of output, inflation, and the Fed’s inflation target. We model the updating process by linking the factor shocks to announcement surprises. Fitting this process to data on yield curve movements in 20-min event windows, we find that most major announcements, especially those about the labor market, are informative largely about the output gap rather than about inflation. The resulting changes in short-rate expectations account for the bulk of observed yield movements. But adjustments in risk premia are also sizable. In partly offsetting the effects of short-rate expectations, these adjustments help to account for the well-known hump-shaped pattern of yield reactions across maturities.