Empirical tests of some equilibrium stochastic processes of the term structure of interest rates.

Abstract

In duration-based immunization models, the measure of duration is dependent on the assumed stochastic process of the term structure of interest rates. Most tests of immunization have been based on single factor duration models. However, specifications of term structure motions in earlier models permit the possibility of riskless arbitrage profits, as demonstrated by Ingersoll, Skelton and Weil (1978). This paper draws upon the work of Bierwag (1987b) and presents some discrete equilibrium two-state one-factor model of the return generating process. These models are based on processes that give rise to some familiar measures of duration, namely the Fisher-Weil(FW) duration from the Fisher-Weil Equilibrium Process(FWEP), the special additive duration from the Special Additive Process(SAP), and the additive duration measure from the Additive Discrete Equilibrium Stochastic Process(ADEP). All of durations were initially based on disequilibrium processes. Therefore, measures of duration associated with disequilibrium processes can also be associated with discrete equilibrium stochastic processes and hence the criticism of these duration measures as being inconsistent with equilibrium is without merit in this discrete time framework. The focus in this work is to test empirically discrete equilibrium stochastic processes which give rise to the FW, SAP, and ADEP durations. The empirical approach consists of directly testing the implications of the models using Treasury Bill data and not the immunization efficacy approach utilized in most studies of term structure modelling. Initial tests indicate no support for the SAP and the ADEP and partial support for the FWEP. Tests also indicate that the tax treatment of Treasury Bills has some effect on the sensitivity measures and may partly explain from initial regression tests the weak support for the FWEP model. The support for the FWEP varies with the choice of independent variables and errors in variables as a possible explanation is explored. Various techniques, including two non-parametric techniques, which attempt to overcome the bias induced by errors in variables are explored. Overall, additional tests using these techniques strongly support the FWEP.