Robust Portfolio Optimization Using Pseudodistances

Abstract

The presence of outliers in financial asset returns is a frequently occurring phenomenon which may lead to unreliable mean-variance optimized portfolios. This fact is due to the unbounded influence that outliers can have on the mean returns and covariance estimators that are inputs in the optimization procedure. In this paper we present robust estimators of mean and covariance matrix obtained by minimizing an empirical version of a pseudodistance between the assumed model and the true model underlying the data. We prove and discuss theoretical properties of these estimators, such as affine equivariance, B-robustness, asymptotic normality and asymptotic relative efficiency. These estimators can be easily used in place of the classical estimators, thereby providing robust optimized portfolios. A Monte Carlo simulation study and applications to real data show the advantages of the proposed approach. We study both in-sample and out-of-sample performance of the proposed robust portfolios comparing them with some other portfolios known in literature.

Robust approach for comparing two dependent normal populations through Wald-type tests based on Rényi’s pseudodistance estimators

“…The updating recursive elements comprise only of the weights, as the name Iteratively Reweighted Moments Algorithm suggests. The semi-explicit expressions given in the inner iterations of Algorithm 1 are particular cases of ( 6) and ( 7) of Toma and Leoni-Aubin (2015) with N equals 2. However, our proposed algorithm is different from the one proposed in the Monte-Carlo simulations of Toma and Leoni-Aubin (2015) in two features.…”

“…The semi-explicit expressions given in the inner iterations of Algorithm 1 are particular cases of ( 6) and ( 7) of Toma and Leoni-Aubin (2015) with N equals 2. However, our proposed algorithm is different from the one proposed in the Monte-Carlo simulations of Toma and Leoni-Aubin (2015) in two features. First, their algorithm does not consider outer iterations as the estimation is initialized always with the MLE and second, they do not consider the reparameterization of the variancecovariance matrix.…”

Robust Estimation for the Single Index Model Using Pseudodistances

“…For an overview on the robust methods for portfolio optimization, using robust estimators of the mean and covariance matrix in the Markowitz’s model, we refer to [ 14 ]. We also cite the methods proposed by Vaz-de Melo and Camara [ 15 ], Perret-Gentil and Victoria-Feser [ 16 ], Welsch and Zhou [ 17 ], DeMiguel and Nogales [ 18 ], and Toma and Leoni-Aubin [ 19 ].…”

Robust Model Selection Criteria Based on Pseudodistances

“…These estimators have the advantage of not requiring any prior smoothing and conciliate robustness with high efficiency, providing a high degree of stability under model misspecification, often with a minimal loss in model efficiency. Such estimators are also defined and studied in the case of the multivariate normal model, as well as for linear regression models in [17,18], where applications for portfolio optimization models are also presented.…”