Testing for Preference Orderings Efficiency

In the literature several parametric methods have been proposed to test the mean variance efficiency of a given portfolio. These tests serve to value the efficiency only in the case the underlying portfolios are uniquely determined by the mean and the variance. However, the return distributions could depend on many parameters. In addition, investors are not always risk averse and they do not necessarily follow the classical stochastic dominance rules. In this paper we propose a class of parametric, semi-parametric and non parametric methods to value the efficiency of a given portfolio with respect to a given ordering of preferences. Parametric and semi-parametric tests suggest to value the distributional distance of some parameters between the given portfolio and few other optimal portfolios. Non-parametric tests value the efficiency preference of the given portfolio with respect to all optimal portfolios. The empirical application reveals that the Fama and French market portfolio is efficient with respect to all preference orderings while the S&P500 stock index is inefficient.