Sampling distribution of the relative risk aversion estimator: Theory and applications

Brown and Gibbons (1985) developed a theory of relative risk aversion estimation in terms of average market rates of return and the variance of market rates of return. However, the exact sampling distributions of the relative risk aversion estimators have not been derived. The main purpose of this paper is to derive the exact sampling distribution of an appropriate relative risk aversion estimator. First, we have derived theoretically the density of Brown and Gibbons' maximum likelihood estimator. It is shown that the centralt is not appropriate for testing the significance of estimated relative risk aversion distribution. Then we derived the minimum variance unbiased estimator by a linear transformation of the Brown and Gibbons' maximum likelihood estimator. The density function is neither a central nor a noncentralt distribution. The density function of this new distribution has been tabulated. There is an empirical example to illustrate the application of this new sampling distribution.