A Consumption Based Arbitrage Model of the Term Structure of Interest Rates.

Abstract

The main objective of this dissertation was to study a consumption based arbitrage model for the term structure of interest rates which would provide a framework for developing successively more general term structure models by adding additional state variables. As a first step, based on economic intuition and the theoretical models of Breeden 1986 and Rubinstein 1976 , we chose aggregate consumption as the sole state variable. We then derived the term structure in an arbitrage free economy where all the real risks are captured by consumption. The final formulation of the model is consistent with the models developed by Breeden 1986 ; Cox, Ingersoll, and Ross 1985 ; and Garman 1977 . Therefore, the empirical analyses of this study apply to these models as well. An empirical formulation was obtained by assuming rational expectations. Specifically, all ex-ante variables were replaced by their rational expectations. The resulting empirical model was estimated using generalized least squares with the usual assumptions of constant parameters over time and across maturities. Estimation results were obtained for two data sets, one used by Fama 1976 and the other derived from the government bond types of the Center for Research in Security Prices (CRSP). Empirical estimates of the relative risk aversion and the patience factor were obtained and they were of the correct sign, economically plausible in magnitude, and statistically significant. The author believes these estimates to be the first empirical results demonstrating the consistency of consumption and interest rate data with theory. In addition the consumption-arbitrage model was compared with the arbitrage pricing theory (APT) model. The coefficient-of-determination of the consumption-arbitrage model was considerably larger than that of the APT model for the Fama data set as well as the CRSP data set. The APT methodology was also applied to the residuals from the consumption-arbitrage model, and at least one significantly priced common factor (different from consumption and inflation) was found for both data sets.