An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment

Pui-Lam Leung, Hon-Yip Ng and Wing-Keung Wong

European Journal of Operational Research, 2012, vol. 222, issue 1, 85-95

Abstract: Using the Markowitz mean–variance portfolio optimization theory, researchers have shown that the traditional estimated return greatly overestimates the theoretical optimal return, especially when the dimension to sample size ratio p/n is large. Bai et al. (2009) propose a bootstrap-corrected estimator to correct the overestimation, but there is no closed form for their estimator. To circumvent this limitation, this paper derives explicit formulas for the estimator of the optimal portfolio return. We also prove that our proposed closed-form return estimator is consistent when n→∞ and p/n→y∈(0,1). Our simulation results show that our proposed estimators dramatically outperform traditional estimators for both the optimal return and its corresponding allocation under different values of p/n ratios and different inter-asset correlations ρ, especially when p/n is close to 1. We also find that our proposed estimators perform better than the bootstrap-corrected estimators for both the optimal return and its corresponding allocation. Another advantage of our improved estimation of returns is that we can also obtain an explicit formula for the standard deviation of the improved return estimate and it is smaller than that of the traditional estimate, especially when p/n is large. In addition, we illustrate the applicability of our proposed estimate on the US stock market investment.

Keywords: G11; C13; Markowitz mean–variance optimization; Estimation of optimal portfolio weights; Inverted wishart distribution; Consistency (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (45)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221712002792
Full text for ScienceDirect subscribers only

Related works:
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:222:y:2012:i:1:p:85-95

DOI: 10.1016/j.ejor.2012.04.003

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 ().