Efficient Cardinality/Mean-Variance Portfolios

Abstract

Abstract. We propose a novel approach to handle cardinality in portfolio selection, by means of a biobjective cardinality/mean-variance problem, allowing the investor to analyze the efficient tradeoff between returnrisk and number of active positions. Recent progress in multiobjective optimization without derivatives allow us to robustly compute (in-sample) the whole cardinality/mean-variance efficient frontier, for a variety of data sets and mean-variance models. Our results show that a significant number of efficient cardinality/mean-variance portfolios can overcome (out-of-sample) the naive strategy, while keeping transaction costs relatively low.

Efficient skewness/semivariance portfolios

“…The 'Notation' Section, the 'Benchmark portfolios' Section and the 'The skewness/semivariance' biobjective model' Section partly overlap a previous paper by Brito and Vicente (2014) (a previous working paper can be found at www.mat.uc.pt/~lnv/papers/cardMV.pdf?). A previous version of this article was published as a working paper by the Group for Monetary and Financial Studies (GEMF).…”

“…We have thus decided to solve this problem through a derivative-free solver, based on direct multisearch (see Custódio et al, 2011, for a description of direct multisearch). This derivative-free solver was, previously and for the first time, used in the portfolio selection framework for solving a cardinality constrained problem (Brito and Vicente, 2014).…”

Portfolio management with higher moments: the cardinality impact

“…This model can be seen as a mixed‐integer quadratic problem that is no longer solved in polynomial time, therefore most studies have focused on providing efficient algorithms to solve this problem. These algorithms vary from exact algorithms (Bienstock, ; Vielma et al., ; Bertsimas and Shioda, ) to heuristics (Chang et al., ; Fieldsend et al., ; Cesarone et al., ; Anagnostopoulos and Mamanis, ; Woodside‐Oriakhi et al., ; Brito and Vicente, ). With the aim of promoting regularization of ill conditioning, DeMiguel et al.…”

“…For each framework, based on the investor's expected utility maximization criterion, we propose a biobjective model that allows the investor to directly analyze the efficient trade‐off between expected utility and cardinality. Given the lack of derivatives of the cardinality function, and inspired by Brito and Vicente (), we apply a directional derivative free algorithm (Custódio et al., ) to obtain the solution of the biobjective optimization problems.…”

“…For each framework, we propose a biobjective model that allows the investor to directly analyze the efficient trade‐off between expected utility and cardinality. Given the nonsmoothness of the cardinality function and inspired in Brito and Vicente (), we have decided to solve each biobjective model using a derivative‐free solver based on direct multisearch (Custódio et al., ).…”