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

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

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.

Suggested Citation

  • Leung, Pui-Lam & Ng, Hon-Yip & Wong, Wing-Keung, 2012. "An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment," European Journal of Operational Research, Elsevier, vol. 222(1), pages 85-95.
  • Handle: RePEc:eee:ejores:v:222:y:2012:i:1:p:85-95
    DOI: 10.1016/j.ejor.2012.04.003
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    3. Bernard, C. & Vanduffel, S., 2014. "Mean–variance optimal portfolios in the presence of a benchmark with applications to fraud detection," European Journal of Operational Research, Elsevier, vol. 234(2), pages 469-480.
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    7. Ahmar, Ansari Saleh & Arifin, Andi Nurani Mangkawani, 2017. "Optimalisasi Risiko Saham Menggunakan Optimalisasi Portofolio Markowitz (Studi Kasus Saham Di Indonesia)," INA-Rxiv 5v27k, Center for Open Science.
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    More about this item

    Keywords

    G11; C13; Markowitz mean–variance optimization; Estimation of optimal portfolio weights; Inverted wishart distribution; Consistency;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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