Treasury Yield Curve Research Articles

Restrictions on Risk Prices in Dynamic Term Structure Models

Restrictions on the risk-pricing in dynamic term structure models (DTSMs) can unleash the power of no-arbitrage by creating a tighter link between cross-sectional and time-series variation of interest rates. This paper presents a new econometric framework for estimation of affine Gaussian DTSMs under restrictions on risk prices, which addresses the issues of a large model space and of model uncertainty using a Bayesian approach. A simulation study demonstrates the good performance of the proposed method, both for model choice and for inference about the objects of interest. I obtain novel results for the U.S. Treasury yield curve. The data strongly favor tight restrictions on risk pricing: only level risk is priced, and only changes in the slope affect term premia. Incorporating the restrictions into an otherwise standard model substantially alters its conclusions. Interest rate persistence is significantly higher than in a maximally-flexible model, hence expectations of future short rates are more variable, and the role for term premia is somewhat diminished. Hence, restrictions on risk prices help resolve the puzzle of implausibly stable short-rate expectations which has plagued this literature. Restricted models attribute a larger share of the secular decline in long-term interest rates over the last twenty years to the expectations component, consistent with survey evidence on expectations of future interest rates and inflation.

Assessing the Effectiveness of Date-Based Forward Guidance at the Zero Lower Bound with a Non-Gaussian Affine Term-Structure Model

Using a non-Gaussian affine term-structure model, this paper evaluates the effectiveness of the date-based forward guidance at the zero lower bound. The model extracts the expected dynamics of two state variables (the short-term interest rate and its mean) embedded in the entire Treasury yield curve. Using simulations and an event study, we find that the model’s dynamics were significantly altered by the first announcement of date-based forward guidance in August 2011 and speculation about tapering in May 2013. The model offers a probabilistic approach in assessing the market’s perception towards the Federal Reserve’s projections of the federal funds rate.

Inflation Bets on the Long Bond

The liquidity premium theory of interest rates predicts that the Treasury yield curve steepens with inflation uncertainty as investors demand larger risk premia to hold long-term bonds. Using the dispersion of inflation forecasts to measure this uncertainty, we find the opposite. Since the prices of long-term bonds move more with inflation than short-term ones, investors also disagree and speculate more about long-maturity payoffs with greater uncertainty. Shorting frictions, measured using Treasury lending fees, then lead long maturities to become over-priced and the yield curve to flatten. We estimate this inflation-betting effect using time variation in inflation disagreement and Treasury supply.

International Yield Curves and Principal Components Selection Techniques: An Empirical Assessment

Using a common database, we provide a controlled empirical comparison of recently-proposed principal component (PC) methods for selecting a combination of common and local factors that characterize the joint dynamics of multi-country term structures. We build a database of daily Treasury yield curves for U.S., Germany, U.K. and Japan, using common criteria to filter coupon bond data, to ensure liquidity, and to interpolate the discount function. We then estimate each proposed PC method for all subgroups of these countries, using both yield levels and yield differences at weekly frequency. We find, in general, that the proposed methods do not agree with one another on the preferred combination of common and/or local factors. We identify the explained variability decision criterion as an important source of this lack of agreement and recommend consideration of alternative statistical model selection techniques for the purpose of identifying common and local yield curve factors in international data.

Does the Short Rate Revert to its Mean in the Risk-Neutral World?

We propose a methodology to calibrate the non-linear and non-affine short rate models under physical and risk-neutral probability measures, based on the U.S treasury yield curve data. For this purpose, we price the default-free bond using the Markov chain approximation method built on the well-established idea of local consistency. Integrating the standard recursive filtering algorithm and the Markov chain approximation bond price formula, we propose a Markov chain filter in which the transition equation is a general stochastic differential equation for the short rate dynamics, and the measurement equation can be based on observations of any interest rate derivatives. Our simulation experiments show that popular parameter estimators can generate spurious non-linear drift estimates. However, the proposed Markov chain filter does not. In contrast to the existing literature, through our empirical findings we argue that the short rate does not revert to its mean under the risk-neutral probability measure. Our findings corroborate the observations that yields on the short end term structure have remained near 0% for more than 30 months since the implementation of Quantitative Easing monetary policy.

Risk Premiums in Dynamic Term Structure Models with Unspanned Macro Risks

This paper quantifies how variation in real economic activity and inflation in the U.S. influenced the market prices of level, slope, and curvature risks in U.S. Treasury markets. We develop a novel arbitrage-free dynamic term structure model in which bond investment decisions are influenced by real output and inflation risks that are unspanned by (imperfectly correlated with) information about the shape of the Treasury yield curve. Our model reveals that, over the period 1985-2007, these unspanned macro risks accounted for a large portion of the variation in forward terms premiums, and there was pronounced cyclical variation in the market prices of level and slope risks. We compare fitted term premiums for the post-2007 crisis period to those from a model with spanned macro risks, and use our findings to reassess some of Chairman Bernanke's remarks on the interplay between term premiums, the shape of the yield curve, and the macroeconomy.

Unconventional monetary policies and the corporate bond market

The paper uses a reduced-form vector autoregressive framework to study the effects of quantitative easing and operation “twist”, as well as a conventional monetary expansion, on corporate bond yields and spreads. We construct rating- and maturity-based weekly bond portfolios using TRACE and simulate monetary policies as shocks to the Treasury yield curve. We find that none of the policies can persistently lower corporate spreads, and that operation twist is the only policy capable of lowering corporate yields. This latter finding can be accounted for by the operation twist’s ability to keep the monetary base constant and, therefore, to flatten the riskless yield curve without generating inflationary expectations.

Ex-Post Merger Review and Divestitures

This dissertation consists of four papers in structural empirics that can be broadly categorized into two areas. The first three papers revolve around the structural estimation of demand for differentiated products and several applications thereof (Berry (1994), Berry, Levinsohn and Pakes (1995), Nevo (2000)), while the fourth paper examines the U.S. Treasury yield curve by estimating yields as linear functions of observable state variables (Ang and Piazzesi (2003), Ang et al. (2006)).The central focus of each paper are the underlying economics. Nevertheless, all papers share a common empirical approach. Be it prices of beers in Sweden or yields of U.S. Treasury bonds, it is assumed throughout that the economic variables of interest can be modeled by imposing specific parametric functional forms. The underlying structural parameters are then consistently estimated based on the variation in available data.Consistent estimation naturally hinges on the assumption that the assumed functional forms are correct. Another way of viewing this is that the imposed functions are flexible enough not to impose restrictive patterns on the data that ultimately lead to biased estimates of the structural parameters and thereby produce misleading conclusions regarding the underlying economics.In principle, the danger of misspecification could therefore be avoided by adopting sufficiently flexible functional forms. This, however, typically requires the estimation of a growing number of structural parameters that determine the underlying economic relationships. As an example, we can think of the estimation of differentiated product demand. The key object of interest here is the substitution patterns between the products. That is, we are interested in what happens to the demand of good X and all its rival products, as the price of good X increases. With N products in total, we could collect the product-specific changes in demand in a vector with N entries. It is also possible, however, that the price of any other good Y changes and thereby alters the demands for the remaining varieties. Thus, in total, we are interested in N2 price effects on product-specific demand. With few products, these effects could be estimated directly and the risk of functional misspecification could be excluded (Goolsbee and Petrin (2004)). With 100 products, however, we are required to estimate 10,000 parameters, which rarely, if ever, is feasible. This is the curse of dimensionality.Each estimation method employed in the four papers breaks this curse by imposing functions that depend on relatively few parameters and thereby tries to strike a balance between the necessity to rely on parsimonious structural frameworks and the risk of misspecification. This is a fundamental feature of empirical research in economics that makes it both interesting and challenging.

Effects of Explicit FOMC Policy Rate Guidance on Market Interest Rates

We quantify the impact of explicit FOMC policy rate guidance used as an unconventional monetary policy tool at the zero lower bound of the policy rate on market interest rates. We study the impact on short- to medium-term interest rates implied by Eurodollar interest rate futures contracts, and on near- to long-term interest rates implied by US Treasury securities. We find that explicit policy rate guidance announcements significantly reduced interest rates implied by Eurodollar futures at horizons of 1 to 5 years ahead, with the largest effect at the intermediate horizon of 3 years. We also find that they significantly reduced forward interest rates implied by US Treasuries at horizons of 1 to 7 years ahead, with the largest effect at the intermediate horizons of 4 and 5 years. Moreover, we find that explicit FOMC policy rate guidance led to a significant reduction in the term spread, ie to a fiattening of the yield curve, both for the Eurodollar futures curve and the US Treasury yield curve.

Reactions of Real Yields and Inflation Expectations to Forward Guidance in the United States

We study the impact of forward guidance used as an unconventional monetary policy tool at the zero lower bound of the policy rate on real and breakeven US Treasury yield curves. We find that explicit FOMC policy rate guidance announcements led to a significant reduction in real yields. By contrast, breakeven inflation rates were barely affected, if at all, suggesting that inflation expectations have remained well-anchored, and that explicit FOMC policy rate guidance has not adversely affected central bank credibility.

Pricing TIPS and Treasuries with Linear Regressions

We present an affine term structure model for the joint pricing of TIPS and Treasury yield curves that adjusts for TIPS’ relative illiquidity. Our estimation via linear regressions is computationally efficient and can accommodate a large number of pricing factors. The baseline specification with seven principal components extracted from Treasury and TIPS yields as well as a liquidity factor generates negligibly small pricing errors for both real and nominal yields. Model-implied expected inflation adjusted for risk premia and liquidity provides a better prediction of actual inflation than unadjusted breakeven inflation. Analysis of model-implied Treasury and TIPS decompositions shows that the Federal Reserve’s large-scale asset purchases lowered nominal and real Treasury yields primarily via a reduction of real term premia, the compensation investors demand for bearing real short-rate risk. Real term premia also account for the large response of long-term real forward rates to monetary policy surprises. The deflation floor embedded in TIPS is generally small in magnitude, but spiked during the recent crisis. We also show that the nominal and real term structures from the United Kingdom have qualitatively similar features to the U.S. yields.

Understanding the Term Structure of Credit Default Swap Spreads

The shape of the term structure of credit default swap (CDS) spreads displays large variations over time and across firms. Consistent with the predictions of structural models of credit risk, we find that the slope of CDS spread term structure increases with firm leverage and volatility, but decreases with the level and the slope of the Treasury yield curve. However, these variables together have rather limited explanatory power for CDS slope and there is a significant common component in the regression residuals. In addition, we find that CDS slope predicts future changes in CDS spreads, even after controlling for the contemporaneous variables that determine changes in CDS spreads according to the structural models. Our results suggest that while structural models are qualitatively useful for understanding the shape of credit term structure, there are missing factors that importantly affect the term structure of CDS spreads.

Forecasting the Yield Curve with the "Stock Dog" Technique

We design an innovative technique coupled with Monte Carlo simulation that accurately forecasts the yield curve. This stock dog technique forces the simulated yield curve inside bands, using the information embedded in the shapes of the most recent yield curves captured by the level, the slope and the curvature provided by the Nelson and Siegel (1987) model. Based on the RMSE criteria, we show that, on a sample of 2,321 U.S. Treasury yield curves over the 2002-2012 period, the stock dog technique, coupled either with the Cox, Ingersoll and Ross (1985) or a Stochastic Fifth-Order Polynomial models, is superior to the Diebold and Li (2006) model when forecasting the yield curve over a 20-day horizon. The stock dog technique is a variation of the Diebold and Li (2006) model and improves significantly its forecasting power. It may help market participants in need of an accurate short term forecast of the yield curve.

The Impact of Chinese Purchases of U.S. Government Debt on the Treasury Yield Curve

Examining monthly data from May of 1985 to May of 2008, we find that increases in Chinese purchases of U.S government debt lead to decreases in Treasury yields. The effect is stronger as the maturity increases: a one percent increase in purchases of U.S. Treasuries by Chinese investors lowers the two-year (ten-year) Treasury yield by 10 to 38 basis points (39 to 55 basis points) on average, ceteris paribus . Overall, the demand-side variable capturing Chinese purchases of U.S. Treasuries improves the cointegrating properties of U.S. interest rates. In-sample and out-of-sample forecasts reinforce that the model with Chinese purchases greatly outperforms basic models of the yield curve. This study has implications for the business world since we document that Chinese investors contribute to lower U.S. Treasury yields and thus to lower U.S. interest rates in general.

The Pre-FOMC Announcement Drift

We document large average excess returns on U.S. equities in anticipation of monetary policy decisions made at scheduled meetings of the Federal Open Market Committee (FOMC) in the past few decades. These pre-FOMC returns have increased over time and account for sizable fractions of total annual realized stock returns. While other major international equity indices experienced similar pre-FOMC returns, we find no such eff ect in U.S. Treasury securities and money market futures. Other major U.S. macroeconomic news announcements also do not give rise to pre-announcement excess equity returns. Pre-FOMC returns are higher in periods when the slope of the Treasury yield curve is low, implied equity market volatility is high, and when past pre-FOMC returns have been high. We discuss challenges at explaining these returns with standard asset pricing theory.

Policy options for state pension systems and their impact on plan liabilities

AbstractWe calculate the present value of state pension liabilities under existing policies and separately under policy changes that would affect pension payouts. If promised payments are viewed as default free, then it is appropriate to use discount rates given by the Treasury yield curve. If plans are frozen at June 2009 levels, then the present value of liabilities would be $4.4 trillion. Under the typical actuarial method of recognizing future service and wage increases, this figure rises to $5.2 trillion. Compared to $1.8 trillion in pension fund assets, the baseline level of unfunded liabilities is therefore around $3 trillion. A 1 percentage point reduction in cost-of-living adjustments (COLAs) would lower total liabilities by 9–11%; implementing actuarially fair early retirement would reduce them by 2–5%; and increasing the retirement age by 1 year would reduce them by 2–4%. Dramatic policy changes, such as the elimination of COLAs or the implementation of Social Security retirement age parameters, would leave liabilities around $1.5 trillion more than plan assets. This suggests that taxpayers will bear the lion's share of the costs associated with the legacy liabilities of state DB pension plans.

Noise as Information for Illiquidity

We propose a broad measure of liquidity for the overall financial market by exploiting its connection with the amount of arbitrage capital in the market and the potential impact on price deviations in US Treasurys. When arbitrage capital is abundant, we expect the arbitrage forces to smooth out the Treasury yield curve and keep the dispersion low. During market crises, the shortage of arbitrage capital leaves the yields to move more freely relative to the curve, resulting in more “noise.” As such, noise in the Treasury market can be informative and we expect this information about liquidity to reflect the broad market conditions because of the central importance of the Treasury market and its low intrinsic noise – high liquidity and low credit risk. Indeed, we find that our “noise” measure captures episodes of liquidity crises of different origins and magnitudes and is also related to other known liquidity proxies. Moreover, using it as a priced risk factor helps explain cross-sectional returns on hedge funds and currency carry trades, both known to be sensitive to the general liquidity conditions of the market.

Simultaneous nonparametric inference of time series

We consider kernel estimation of marginal densities and regression functions of stationary processes. It is shown that for a wide class of time series, with proper centering and scaling, the maximum deviations of kernel density and regression estimates are asymptotically Gumbel. Our results substantially generalize earlier ones which were obtained under independence or beta mixing assumptions. The asymptotic results can be applied to assess patterns of marginal densities or regression functions via the construction of simultaneous confidence bands for which one can perform goodness-of-fit tests. As an application, we construct simultaneous confidence bands for drift and volatility functions in a dynamic short-term rate model for the U.S. Treasury yield curve rates data.

Canonical Least-Squares Monte Carlo: Empirical Evidences from S&P 100 Index and IBM Puts

This paper tests empirically the recently proposed canonical least-squares Monte-Carlo (CLM) method for pricing American options. Market data used are daily last prices for the American style S&P 100 Index puts (OEX puts) and IBM puts from 30 July 2008 to 30 January 2009, the period of which covers the US financial crisis of 2008. Unlike what have been done in many other similar empirical studies, rates interpolated from the US Treasury yield curve are used, and dividends, a continuous constant yield for the S&P 100 Index and a fixed cash amount for the IBM common stock, are taken into consideration. Compared with the benchmark prices from finite difference using historic volatilities, CLM outperforms in almost all twelve categories of moneyness and maturity for both OEX and IBM puts, and is shown to be a viable alternative for pricing American style options.

Embedded Options in Treasury Bond Futures Prices: New Evidence

The Treasury bond futures contract has known embedded options, namely the quality option that permits the short side to deliver the cheapest bond and the three timing options that permit the short side to deliver at the most favorable time. In this article, the authors use a two-factor Cox–Ingersoll–Ross term structure model calibrated to the Treasury yield curve to compute the futures price with the forward pricing methodology. Using weekly futures prices from January 1992 through December 2000, they discover a substantial difference between the risk-neutral expectation used in the literature and the forward expectation that requires a recursive algorithm. The authors find that the correctly estimated futures price with the quality option is 1% lower on average than the futures price estimated in the literature. They also estimate the end-of-month timing option to be 23 basis points on average. This indicates that the end-of-month timing option value has been overestimated in the literature because of a wrongly estimated quality option value.