Covariance matrix estimation methods for constrained portfolio optimization in a South African setting

Madume, Jaison Pezisai

Covariance matrix estimation methods for constrained portfolio optimization in a South African setting

Master Thesis

2010

Publisher

University of Cape Town

Department

School of Economics

Faculty

Faculty of Commerce

Abstract

One of the major topics of concern in Modern Portfolio Theory is portfolio optimization which is centred on the mean-variance framework. In order for this framework to be implemented, esti- mated parameters (covariance matrix for the constrained portfo- lio) are required. The problem with these estimated parameters is that they have to be extracted from historical data based on certain assumptions. Because of the di erent estimation methods that can be used the parameters thus obtained will su er either from estimation error or speci cation error. In order to obtain results that are realistic in the optimization, one needs then to establish covariance matrix estimators that are as good as possi- ble. This paper explores the various covariance matrix estimation methods in a South African setting focusing on the constrained portfolio. The empirical results show that the Ledoit shrinkage to a constant correlation method, the Principal Component Analy- sis method and the Portfolio of estimators method all perform as good as the Sample covariance matrix in the Ex-ante period but improve on it slightly in the Ex-post period. However, the im- provement is of a small magnitude, as a result the sample covari- ance matrix can be used in the constrained portfolio optimization in a South African setting.

Keywords

Mathematical Finance

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