Ilias Lekkos

A Critique of Factor Analysis of Interest Rates

Term structure models typically attempt to explain the full range of observed fluctuation in the yield curve with a small number of independent factors. Factor analysis, a common tool in this effort, generally shows that three factors capture a large proportion of the variation in the curve. The first (most important) factor applies across all maturities and reflects the level of yields; the second affects the slope of the yield curve; and the third relates to its curvature. In this article, Lekkos argues that much of the apparent explanatory power of this factor structure may be an artifact induced by the arbitrage relationship that requires a given spot rate to equal the average of the forward rates over that maturity. Factor analysis on spot rates in four major countries shows that three factors explain about 97% of the variance in each case, but the fit with forward rates is distinctly less good. Lekkos then demonstrates that even in a simulated economy with completely independent forward rates, as long as spot rates are arbitrage-free and equal to averages of the relevant forward rates, standard factor analysis produces a factor structure that explains over 90% of overall yield variation, and loadings on the individual factors that closely resemble the patterns found for the actual markets.

Time-varying excess returns on UK government bonds: A non-linear approach

Abstract This paper provides an empirical examination of the behaviour of excess returns on UK government discount bonds in terms of risk factors such as the forward premium, the slope of the term structure, dividend yields and excess stock returns. We identify the existence of a time-varying term structure of expected excess returns. Further, the dynamics of the expected returns are characterised by regime-switching behaviour where the transition from one regime to the other is controlled by the slope of the term structure of interest rates. The first regime, which is characterised by flat or downward sloping term structures, occurs during periods of economic recession. The second regime, which is characterised by upward sloping term structures, occurs during periods of economic expansion. The main risk factors explaining expected returns are the slope of the term structure in the recessionary regime and the excess stock returns in the expansionary regime.

An Analysis of the Relationship between International Bond Markets

It is frequently suggested that the globalisation of financial markets has been responsible for reducing the scope for independent monetary policy action by strengthening the relationship between national fixed income markets. An associated concern is that the linkages between these markets become stronger in times of financial market stress. This paper reports a decomposition of the relationship between the government bond markets of Germany, the United Kingdom and the United States. It is found that the yield curves for each of these markets are influenced by international factors. Furthermore the impact of these increases significantly during times of financial stress. It is also found that while the total covariation between these markets is relatively stable, components of the covariance can vary substantially over time.

Distributional Properties of Spot and Forward Interest Rates: USD, DEM, GBP, and JPY

This article provides analysis of the distributional properties of spot and forward interest rates without imposing any ad hoc assumptions on the behavior of interest rates. Using the kernel density estimation method, we estimate the distributions of spot and forward interest rates in levels and first differences. By comparing the two distributions, we show that examination of interest rates in levels can provide incremental information about the data generation process. In addition, we examine whether commonly used distributions, like the normal and lognormal distribution, can provide an adequate description of interest rate distribution. Finally we examine a more flexible mixture of two distributions as an alternative characterization of the distribution of interest rate changes.

Factor models and the correlation structure of interest rates: Some evidence for USD, GBP, DEM and JPY

Abstract The aim of this paper is to develop models for producing accurate forecasts for the correlation of spot and forward interest rates. Correlation forecasts generated from factor models, where the correlations are expressed as a function of few underlying factors, are compared to forecasts produced by less sophisticated models like the full historical and constant correlation model. Contrary to previous studies, where the selection of factors is rather arbitrary, we test two factor identification methodologies. The first is based on factor analysis and the second is based on minimising the residual cross-correlations. We show that a three-factor model, with factors identified by minimising the residual cross-correlation criterion is sufficient to describe the correlation structure of interest rates. Furthermore, we show that it might be preferable to assume that all forward rate correlations are equal rather than using a misspecified factor model and that the spot factor model developed, consistently outperformed long established models like the “Barbell” model.

Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.