Sparse and Robust Normal and t-Portfolios by Penalized Lq-Likelihood Minimization

31 Pages Posted: 22 May 2014 Last revised: 2 Jun 2017

See all articles by Davide Ferrari

Davide Ferrari

University of Melbourne

Margherita Giuzio

European Central Bank (ECB)

Sandra Paterlini

University of Trento - Department of Economics and Management

Date Written: May 22, 2014

Abstract

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 minimum description length 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 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 in comparison to state-of-art benchmarks.

Keywords: q-entropy, penalized least squares, sparsity, index tracking

JEL Classification: C15, C61, G11

Suggested Citation

Ferrari, Davide and Giuzio, Margherita and Paterlini, Sandra, Sparse and Robust Normal and t-Portfolios by Penalized Lq-Likelihood Minimization (May 22, 2014). Available at SSRN: https://ssrn.com/abstract=2440421 or http://dx.doi.org/10.2139/ssrn.2440421

Davide Ferrari

University of Melbourne ( email )

185 Pelham Street
Carlton, Victoria 3053
Australia

Margherita Giuzio

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314
Germany

Sandra Paterlini (Contact Author)

University of Trento - Department of Economics and Management ( email )

Via Inama 5
Trento, I-38100
Italy

Register to save articles to
your library

Register

Paper statistics

Downloads
17
Abstract Views
189
PlumX Metrics