High-dimensional Markowitz portfolio optimization problem: empirical comparison of covariance matrix estimators. Issue 7 (3rd May 2019)

• Record Type: Journal Article
• Authors: Choi, Young-Geun; Lim, Johan; Choi, Sujung
• Is Part Of: Journal of statistical computation and simulation. Volume 89:Issue 7(2019)
• Page Start: 1278
• Page End: 1300
• Publication Date: 2019-05-03
• Subjects: Markowitz's portfolio optimization -- minimum variance portfolio -- high-dimensional covariance matrix -- S&P500 data; 62H99 -- 62P20; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2019.1577855
• Languages: English
• ISSNs: 0094-9655

Abstract

ABSTRACT: We compare the performance of recently developed regularized covariance matrix estimators for Markowitz's portfolio optimization and of the minimum variance portfolio (MVP) problem in particular. We focus on seven estimators that are applied to the MVP problem in the literature; three regularize the eigenvalues of the sample covariance matrix, and the other four assume the sparsity of the true covariance matrix or its inverse. Comparisons are made with two sets of long-term S&P 500 stock return data that represent two extreme scenarios of active and passive management. The results show that the MVPs with sparse covariance estimators have high Sharpe ratios but that the naive diversification (also known as the 'uniform (on market share) portfolio') still performs well in terms of wealth growth.