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Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization

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  • Li, Hua
  • Bai, Zhidong
  • Wong, Wing-Keung
  • McAleer, Michael
Abstract
The portfolio problem for high dimensional data when the dimension and size are both large is considered. The traditional Markowitz mean-variance (MV) portfolio by large dimension matrix theory is analyzed, and it is found that the spectral distribution of the sample covariance is the main factor to make the expected return of the traditional MV portfolio overestimate the theoretical MV portfolio. Therefore, a new spectrally corrected method is introduced to correct the spectral elements of the sample covariance to a sample spectrally-corrected covariance, by which the spectrally-corrected portfolio and the corresponding return and risk are provided naturally. Moreover, the limiting behavior of the expected return and risk on the spectrally-corrected MV portfolio is deduced and the superior properties of the spectrally-corrected MV portfolio are illustrated. In simulations, the spectrally-corrected estimates get the best performance in both portfolio return and portfolio risk. The comparisons of their performance by using the S&P 500 data show the superiority of the proposed spectrally-corrected estimates get over the traditional and bootstrap-corrected estimates. Then, the empirical analysis shows that consistent with the theory developed, the proposed spectrally-corrected estimates outperform both the traditional and bootstrap-corrected estimates. Further, the findings show that all risk-averters will get improvement in portfolio returns or risk-adjusted portfolio returns, by adopting our proposed methods.

Suggested Citation

  • Li, Hua & Bai, Zhidong & Wong, Wing-Keung & McAleer, Michael, 2022. "Spectrally-Corrected Estimation for High-Dimensional Markowitz Mean-Variance Optimization," Econometrics and Statistics, Elsevier, vol. 24(C), pages 133-150.
    • Handle: RePEc:eee:ecosta:v:24:y:2022:i:c:p:133-150
    DOI: 10.1016/j.ecosta.2021.10.005
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    Citations

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    Cited by:

    1. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Management Information, Decision Sciences, and Financial Economics: A Connection," Tinbergen Institute Discussion Papers 18-004/III, Tinbergen Institute.
    2. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Econometric Institute Research Papers 18-024/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    3. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    4. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2016. "Management Science, Economics and Finance: A Connection," Tinbergen Institute Discussion Papers 16-040/III, Tinbergen Institute.
    5. Bai, Zhidong & Liu, Huixia & Wong, Wing-Keung, 2016. "Making Markowitz's Portfolio Optimization Theory Practically Useful," MPRA Paper 74360, University Library of Munich, Germany.
    6. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.
    7. Kai-Yin Woo & Chulin Mai & Michael McAleer & Wing-Keung Wong, 2020. "Review on Efficiency and Anomalies in Stock Markets," Economies, MDPI, vol. 8(1), pages 1-51, March.

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    More about this item

    Keywords

    Markowitz Mean-Variance Optimization; high-dimensional data; spectrally-corrected estimation;
    All these keywords.

    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
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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