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, Wing Keung WONG*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    41 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)85-95
    Number of pages11
    JournalEuropean Journal of Operational Research
    Volume222
    Issue number1
    DOIs
    Publication statusPublished - 1 Oct 2012

    Scopus Subject Areas

    • Computer Science(all)
    • Modelling and Simulation
    • Management Science and Operations Research
    • Information Systems and Management

    User-Defined Keywords

    • Consistency
    • Estimation of optimal portfolio weights
    • Inverted wishart distribution
    • Markowitz mean-variance optimization

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