Sparse and robust normal and t- portfolios by penalized Lq-likelihood minimization

Two important problems arising in traditional asset allocation methods are the sensitivity to estimation error of portfolio weights and the high dimensionality of the set of candidate assets. In this paper, we address both issues by proposing a new criterion for portfolio selection. The new criterion is a two-stage description of the available information, where the q-entropy, a generalized measure of information, is used to code the uncertainty of the data given the parametric model and the uncertainty related to the model choice. The information about the model is coded in terms of a prior distribution that promotes asset weights sparsity. Our approach carries out model selection and estimation in a single step, by selecting a few assets and estimating their portfolio weights simultaneously. The resulting portfolios are doubly robust, in the sense that they can tolerate deviations from both assumed data model and prior distribution for model parameters. Empirical results on simulated and real-world data support the validity of our approach.