Estimation of the global minimum variance portfolio in high dimensions

Taras Bodnar, Nestor Parolya and Wolfgang Schmid

European Journal of Operational Research, 2018, vol. 266, issue 1, 371-390

Abstract: We estimate the global minimum variance (GMV) portfolio in the high-dimensional case using results from random matrix theory. This approach leads to a shrinkage-type estimator which is distribution-free and optimal in the sense of minimizing the out-of-sample variance. Its asymptotic properties are investigated assuming that the number of assets p depends on the sample size n such that pn→c∈(0,+∞) as n tends to infinity. The results are obtained under weak assumptions imposed on the distribution of the asset returns: only the existence of the fourth moments is required. Furthermore, we make no assumption on the upper bound of the spectrum of the covariance matrix. As a result, the theoretical findings are also valid if the dependencies between the asset returns are described by a factor model which appears to be very popular in the financial literature nowadays. This is also documented in a numerical study where the small- and large-sample behavior of the derived estimator is compared with existing estimators of the GMV portfolio. The resulting estimator shows significant improvements and it turns out to be robust if the assumption of normality is violated.

Keywords: Finance; Global minimum variance portfolio; Large-dimensional asymptotics; Covariance matrix estimation; Random matrix theory (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (35)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221717308494
Full text for ScienceDirect subscribers only

Related works:
Working Paper: Estimation of the Global Minimum Variance Portfolio in High Dimensions (2015)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:266:y:2018:i:1:p:371-390

DOI: 10.1016/j.ejor.2017.09.028

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().