Principal component and second generation wavelet analysis of Treasury yield curve evolution

Prices of U.S. Treasury securities vary over time and across maturities. When the market in Treasurys is sufficiently complete and frictionless, these prices may be modeled by a function time and maturity. A cross-section of this function for time held fixed is called the yield curve; the aggregate of these sections is the evolution of the yield curve. This dissertation studies aspects of this evolution. ^ There are two complementary approaches to the study of yield curve evolution here. The first is principal components analysis; the second is wavelet analysis. In both approaches both the time and maturity variables are discretized. In principal components analysis the vectors of yield curve shifts are viewed as observations of a multivariate normal distribution. The resulting covariance matrix is diagonalized; the resulting eigenvalues and eigenvectors (the principal components) are used to draw inferences about the yield curve evolution. ^ In wavelet analysis, the vectors of shifts are resolved into hierarchies of localized fundamental shifts (wavelets) that leave specified global properties invariant (average change and duration change). The hierarchies relate to the degree of localization with movements restricted to a single maturity at the base and general movements at the apex. Second generation wavelet techniques allow better adaptation of the model to economic observables. Statistically, the wavelet approach is inherently nonparametric while the wavelets themselves are better adapted to describing a complete market. ^ Principal components analysis provides information on the dimension of the yield curve process. While there is no clear demarkation between operative factors and noise, the top six principal components pick up 99% of total interest rate variation 95% of the time. An economically justified basis of this process is hard to find; for example a simple linear model will not suffice for the first principal component and the shape of this component is nonstationary. ^ Wavelet analysis works more directly with yield curve observations than principal components analysis. In fact the complete process from bond data to multiresolution is presented, including the dedicated Perl programs and the details of the portfolio metrics and specially adapted wavelet construction. The result is more robust statistics which provide balance to the more fragile principal components analysis. ^

Testing the random walk hypothesis with variance ratio statistics

Mestrado em Finanças

A two-factor model of the U.K. yield curve

I model the forward premium in the U.K. gilt-edged market over the period 1982–96 using a two-factor general equilibrium model of the term structure of interest rates. The model permits the decomposition of the forward premium into separate components representing interest rate expectations, the risk premia associated with each of the underlying factors, and terms capturing the direct impact of the variances of the factors on the shape of the forward curve.

Principal component analysis of the yield curve

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Profitable opportunities around macroeconomic announcements in the U.S. Treasury market

This thesis studies the impact of macroeconomic announcements on the U.S. Treasury market and investigates profitable opportunities around macroeconomic announcements using data from the eSpeed electronic trading platform. We investigate how macroeconomic announcements affect the return predictability of trade imbalance for the 2-year, 5-year, IO-year U.S. Treasury notes and 30-year U.S. Treasury bonds. The goal of this thesis is to develop a methodology to identify informed trades and estimate the trade imbalance based on informed trades. We use the daily order book slope as a proxy for dispersion of beliefs among investors. Regression results in this thesis indicate that, on announcement days with a high dispersion of beliefs, daily trade imbalance estimated by informed trades significantly predicts returns on the following day. In addition, we develop a trade-imbalance based trading strategy conditional on dispersion of beliefs, informed trades, and announcement days. The trading strategy yields significantly positive net returns for the 2-year T-notes.

Forecasting the Yield Curve of Government Bonds: A Comparative Study

For the past 20 years, researchers have applied the Kalman filter to the modeling and forecasting the term structure of interest rates. Despite its impressive performance in in-sample fitting yield curves, little research has focused on the out-of-sample forecast of yield curves using the Kalman filter. The goal of this thesis is to develop a unified dynamic model based on Diebold and Li (2006) and Nelson and Siegel’s (1987) three-factor model, and estimate this dynamic model using the Kalman filter. We compare both in-sample and out-of-sample performance of our dynamic methods with various other models in the literature. We find that our dynamic model dominates existing models in medium- and long-horizon yield curve predictions. However, the dynamic model should be used with caution when forecasting short maturity yields

Dependence of sea ice yield-curve shape on ice thickness

In this note, the authors discuss the contribution that frictional sliding of ice floes (or floe aggregates) past each other and pressure ridging make to the plastic yield curve of sea ice. Using results from a previous study that explicitly modeled the amount of sliding and ridging that occurs for a given global strain rate, it is noted that the relative contribution of sliding and ridging to ice stress depends upon ice thickness. The implication is that the shape and size of the plastic yield curve is dependent upon ice thickness. The yield-curve shape dependence is in addition to plastic hardening/weakening that relates the size of the yield curve to ice thickness. In most sea ice dynamics models the yield-curve shape is taken to be independent of ice thickness. The authors show that the change of the yield curve due to a change in the ice thickness can be taken into account by a weighted sum of two thickness-independent rheologies describing ridging and sliding effects separately. It would be straightforward to implement the thickness-dependent yield-curve shape described here into sea ice models used for global or regional ice prediction.

What will be the risk-free rate and benchmark yield curve following European monetary union?

Using a linear factor model, we study the behaviour of French, Germany, Italian and British sovereign yield curves in the run up to EMU. This allows us to determine which of these yield curves might best approximate a benchmark yield curve post EMU. We find that the best approximation for the risk free yield is the UK three month T-bill yield, followed by the German three month T-bill yield. As no one sovereign yield curve dominates all others, we find that a composite yield curve, consisting of French, Italian and UK bonds at different maturity points along the yield curve should be the benchmark post EMU.

Emerging markets yield curve dynamics

This work extendes Diebold, Li and Yueís (2006) about global yield curve and proposes to extend the study by including emerging countries. The perception of emerging market su§ers ináuence of external factors or global factors, is the main argument of this work. We expect to obtain stylized facts.that obey similar pattern found by those authors. The results indicate the existence of global level and global slope factors. These factors represent an important fraction in the bond yield determination and show a decreasing trend of the global level factor low ináuence of global slope factor in these countries when they are compared with developed countries. Keywords: Kalman Filter, Emerging Markets, Yield Curve, and Bond.

A Proper Yield Curve for Greece to Kick-Start Financial Intermediation. ECMI Policy Brief No. 21, 10 December 2013

At present, the market is severely mispricing Greece’s sovereign risk relative to the country’s fundamentals. As a result of the mispricing, financial intermediation in Greece has become dysfunctional and the privatisation of state-owned assets has stalled. This mispricing is partially due to an illiquid and fragmented government yield curve. A well-designed public liability management exercise can lead to a more efficient pricing of Greece’s government bonds and thereby help restore stable and affordable financing for the country’s private sector, which is imperative in order to overcome Greece’s deep recession. This paper proposes three measures to enhance the functioning of the Greek government debt market: i) Greece should issue a new five-year bond, ii) it should consolidate the 20 individual series of government bonds into four liquid securities and iii) it should offer investors a swap of these newly created bonds into dollar-denominated securities. Each of these measures would be beneficial to the Hellenic Republic, since the government would be able to reduce the face value and the net present value of its debt stock. Furthermore, this exercise would facilitate the resumption of market access, which is a necessary condition for continuous multilateral disbursements to Greece.

A shape-based decomposition of the yield adjustment term in the arbitrage-free Nelson and Siegel (AFNS) model of the yield curve

The appealing feature of the arbitrage-free Nelson-Siegel model of the yield curve is the ability to capture movements in the yield curve through readily interpretable shifts in its level, slope or curvature, all within a dynamic arbitrage-free framework. To ensure that the level, slope and curvature factors evolve so as not to admit arbitrage, the model introduces a yield-adjustment term. This paper shows how the yield-adjustment term can also be decomposed into the familiar level, slope and curvature elements plus some additional readily interpretable shape adjustments. This means that, even in an arbitrage-free setting, it continues to be possible to interpret movements in the yield curve in terms of level, slope and curvature influences. © 2014 © 2014 Taylor & Francis.

The role of no-arbitrage on forecasting: lessons from a parametric term structure model

Parametric term structure models have been successfully applied to innumerous problems in fixed income markets, including pricing, hedging, managing risk, as well as studying monetary policy implications. On their turn, dynamic term structure models, equipped with stronger economic structure, have been mainly adopted to price derivatives and explain empirical stylized facts. In this paper, we combine flavors of those two classes of models to test if no-arbitrage affects forecasting. We construct cross section (allowing arbitrages) and arbitrage-free versions of a parametric polynomial model to analyze how well they predict out-of-sample interest rates. Based on U.S. Treasury yield data, we find that no-arbitrage restrictions significantly improve forecasts. Arbitrage-free versions achieve overall smaller biases and Root Mean Square Errors for most maturities and forecasting horizons. Furthermore, a decomposition of forecasts into forward-rates and holding return premia indicates that the superior performance of no-arbitrage versions is due to a better identification of bond risk premium.