Maximum likelihood estimation of covariance matrices with constraints on the efficient frontier

Hilal Yilmaz and Neil D. Pearson

International Journal of Computational Economics and Econometrics, 2016, vol. 6, issue 1, 71-92

Abstract: This paper develops an improved covariance matrix estimator in the mean-variance optimisation setting. Well-known problems with the sample covariance matrix are that it is singular when the number of observations is less than the number of assets, and can be nearly singular when the number of observations exceeds the number of assets. Therefore, using the sample covariance matrix as an input in mean-variance optimisation can result in unreasonable optimal portfolios and badly biased estimates of Sharpe ratios. We address this problem by imposing structure on the estimated covariance matrix by putting constraints on the Sharpe ratio, asset return variances, and the variance of the global minimum variance portfolio. We show that the constrained maximum likelihood estimator (CMLE) performs better than the sample covariance matrix. Moreover, when the shrinkage approach is applied to the CMLE and single index covariance matrix, it performs better than the shrinkage estimator of Ledoit and Wolf (2004).

Keywords: covariance matrix; mean-variance optimisation; constrained MLE; maximum likelihood estimation; Sharpe ratio; shrinkage estimator; global minimum variance portfolio; Monte Carlo simulation; singular; quadratic matrix equation; sample covariance matrix; efficient frontier. (search for similar items in EconPapers)
Date: 2016
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