Copyright © 2012 Hiroyuki Taniai and Takayuki Shiohama. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We propose a semiparametrically efficient estimator for α-risk-minimizing portfolio weights. Based on the work of Bassett et al. (2004), an α-risk-minimizing portfolio optimization is formulated as a linear quantile regression problem. The quantile regression method uses a pseudolikelihood based on an asymmetric Laplace reference density, and asymptotic properties such as consistency and asymptotic normality are obtained. We apply the results of Hallin et al. (2008) to the problem of constructing α-risk-minimizing portfolios using residual signs and ranks and a general reference density. Monte Carlo simulations assess the performance of the proposed method. Empirical applications are also investigated.