Maximum likelihood estimation of covariance matrices with constraints on the efficient frontier Online publication date: Mon, 30-Nov-2015
by Hilal Yilmaz; Neil D. Pearson
International Journal of Computational Economics and Econometrics (IJCEE), Vol. 6, No. 1, 2016
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).
Existing subscribers:
Go to Inderscience Online Journals to access the Full Text of this article.
If you are not a subscriber and you just want to read the full contents of this article, buy online access here.Complimentary Subscribers, Editors or Members of the Editorial Board of the International Journal of Computational Economics and Econometrics (IJCEE):
Login with your Inderscience username and password:
Want to subscribe?
A subscription gives you complete access to all articles in the current issue, as well as to all articles in the previous three years (where applicable). See our Orders page to subscribe.
If you still need assistance, please email subs@inderscience.com
Our Blog 
Follow us on Twitter 
Visit us on Facebook