Smooth Monotone Covariance for Elliptical Distributions and Applications in Finance

38 Pages Posted: 11 May 2014

See all articles by Xiaoping Zhou

Xiaoping Zhou

Citizens Financial Group; State University of New York (SUNY) - Department of Applied Mathematics and Statistics

Dmitry Malioutov

IBM Research

Frank J. Fabozzi

EDHEC Business School

Svetlozar Rachev

Texas Tech University

Date Written: February 13, 2014

Abstract

Sample covariance is known to be a poor estimate when the data are scarce compared with the dimension. To reduce the estimation error, various structures are usually imposed on the covariance such as low-rank plus diagonal (factor models), banded models and sparse inverse covariances. We investigate a different non-parametric regularization method which assumes that the covariance is monotone and smooth. We study the smooth monotone covariance by analysing its performance in reducing various statistical distances and improving optimal portfolio selection. We also extend its use in non-Gaussian cases by incorporating various robust covariance estimates for elliptical distributions. Finally, we provide two empirical examples using Eurodollar futures and corporate bonds where the smooth monotone covariance improves the out-of-sample covariance prediction and portfolio optimization.

Keywords: Smooth monotone covariance, Regularization, Elliptical distributions

JEL Classification: C10, C16, C19

Suggested Citation

Zhou, Xiaoping and Malioutov, Dmitry and Fabozzi, Frank J. and Rachev, Svetlozar, Smooth Monotone Covariance for Elliptical Distributions and Applications in Finance (February 13, 2014). Available at SSRN: https://ssrn.com/abstract=2435435 or http://dx.doi.org/10.2139/ssrn.2435435

Xiaoping Zhou (Contact Author)

Citizens Financial Group ( email )

28 State St
Boston, MA 02109
United States

State University of New York (SUNY) - Department of Applied Mathematics and Statistics ( email )

Stony Brook University
Stony Brook, NY 11794
United States

Dmitry Malioutov

IBM Research ( email )

T. J. Watson Research Center
1 New Orchard Road
Armonk, NY 10504-1722
United States

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

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