Estimation of a utility-based asset pricing model using normal mixture GARCH(1,1)

Brown and Gibbons [Brown, D.P., Gibbons, M.R., 1985. A simple econometric approach for utilitybased asset pricing model. Journal of Finance 40, 359–381], Karson et al. [Karson, M., Cheng, D., Lee, C. F., 1995. Sampling distribution of the relative risk aversion estimator: theory and applications. Review of Quantitative Finance and Accounting 5, 43–54], and Lee et al. [Lee, C.F., Lee, J.C., Ni, H.F., Wu, C.C., 2004. On a simple econometric approach for utility-based asset pricing model. Review of Quantitative Finance and Accounting 22, 331–344] developed the theory and the distribution of unconditional relative risk aversion (RRA) estimates in utility-based asset pricing model by assuming normality for the log excess returns. While the normality assumption is not always appropriate for some security returns, Brown and Gibbons [Brown, D.P., Gibbons, M.R., 1985. A simple econometric approach for utility-based asset pricing model. Journal of Finance 40, 359–381] proposed generalized method of moments (GMM) to estimate unconditional RRA. However, RRA estimated by GMM is not statistically efficient with finite samples. The main purpose of this paper is to derive the process of estimating dynamic RRA with the maximum likelihood and a Bayesian method having a weakly informative prior density while assuming that the log excess returns on the market are distributed as normal mixture GARCH(1,1). This methodology will capture the variations of RRA across different periods. Empirical results are presented using market rates of returns and risk-free rates over the period 1941 to 2001. © 2006 Elsevier B.V. All rights reserved. JEL classification: C11; C15; D31