The paper investigates the applicability of Schaefer's model for explaining changes in the yield to maturity (YTM) curve for the case of Poland and proposes some modification to the model. The YTM curve is a plot of yield to maturity against term to maturity for bonds with similar risk characteristics that changes over time. There exist many approaches for modeling changes of YTM curve, based on different assumptions. The correct use of Macaulay duration as a measure of the sensitivity of bond or portfolio price to small changes of interest rates is based on the assumption that the YTM curve is subject to proportional shifts. This assumption is not always satisfied in reality. One way of modelling deformation of the YTM curve is to use the two-factor Schaefer model. Schaefer (1984) expresses the change in each 'm'-year maturity rate by two explanatory variables - the change in the long rate (maturity 20 years) and the change in the spread - and then estimates structural parameters of these regressions. Empirical investigation of applicability of Schaefer's model for Poland needs construction of YTM curve. The data used in the present study of the Polish market is from the Reuter agency and covers the period 17.07.2002 - 7.01.2004. Estimation was carried out in E-views using the ordinary least squares method. The results of the empirical investigation show that Schaefer's model can be used to model the changes of the YTM curve in Poland, but his choice of explanatory variables is not optimal. Instead of using the change in the long-term rate as an explanatory variable it is better to use the change in the 4-year rate. With this modification, the model provides a much better representation of the changes of the curve. The stability of the structural parameters was investigated. Stability tests available in E-views showed that there is no structural change in the modeled relationships, except in the case of September - November 2003, where the hypothesis of parameter constancy was rejected at the 5 percent level for two of models. This temporary instability can be enplained by the faci that the YTM curve become more steep in this period. The results confirm the usefulness of applying two measures of risk instead of the traditional Macaulay duration. The models make it possble to obtain so called 'long' duration (or duration of other rate of reference) and 'spread' duration. If changes in the YTM curve can be described by Schaefer's model, these measures can be applied to interest risk management in the construction of bond portfolios.
R. Górska, u. Warszawska 9A m. 42, 05-400 Otwock, Poland
Publication order reference
CEJSH db identifier