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Impact of COVID-19 pandemic on stock market via sparse principal component analysis

  • Department of Statistics and Finance, School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUST-2021-0102
  • Received Date: 07 April 2021
  • Rev Recd Date: 13 April 2021
  • Publish Date: 31 May 2021
    Abstract

  • Abstract

    The COVID-19 pandemic has caused severe public health and economic consequences around the world. It is of great importance to evaluate the impact of the COVID-19 pandemic on the economy, especially the stock market. To this end, we proposed to use several state-of-art sparse principal component analysis (PCA) methods for the stock data of the CSI 300 index from February 1, 2019 to February 1, 2021. To show the influence of the outbreak of the COVID-19 pandemic, we divide this period into two periods, i.e., before and after January 1, 2020. Based on this division, we attempted to extract the principal components and construct portfolio accordingly. The results show that the proportion of principal components representing the market declined after the outbreak. For the constitution in the first two principal components, the important stock sets are substantially different after the outbreak. The stocks from the health care sector start to play an important role in the portfolio of the CSI 300 index after the outbreak. Compared with the CSI 300 index, the first two principal components from the sparse PCA methods can obtain higher returns with a much smaller set of stocks in the portfolio. In conclusion, the outbreak of the COVID-19 pandemic led to changes in both proportion and constitution of the principal component of the stocks in the CSI 300 index.

    Abstract

    The COVID-19 pandemic has caused severe public health and economic consequences around the world. It is of great importance to evaluate the impact of the COVID-19 pandemic on the economy, especially the stock market. To this end, we proposed to use several state-of-art sparse principal component analysis (PCA) methods for the stock data of the CSI 300 index from February 1, 2019 to February 1, 2021. To show the influence of the outbreak of the COVID-19 pandemic, we divide this period into two periods, i.e., before and after January 1, 2020. Based on this division, we attempted to extract the principal components and construct portfolio accordingly. The results show that the proportion of principal components representing the market declined after the outbreak. For the constitution in the first two principal components, the important stock sets are substantially different after the outbreak. The stocks from the health care sector start to play an important role in the portfolio of the CSI 300 index after the outbreak. Compared with the CSI 300 index, the first two principal components from the sparse PCA methods can obtain higher returns with a much smaller set of stocks in the portfolio. In conclusion, the outbreak of the COVID-19 pandemic led to changes in both proportion and constitution of the principal component of the stocks in the CSI 300 index.
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    • References(21)
  • [1]
    Yang L. An application of principal component analysis to stock portfolio management. Christchurch, New Zealand: University of Canterbury, 2015.
    [2]
    Cadima J, Jolliffe I T. Loading and correlations in the interpretation of principle components. Journal of Applied Statistics, 1995, 22(2): 203-214.
    [3]
    Vines S. Simple principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000, 49(4): 441-451.
    [4]
    Ma Z. Sparse principal component analysis and iterative thresholding. Annals of Statistics, 2013, 41(2): 772-801.
    [5]
    Jolliffe I T, Trendafilov N T, Uddin M. A modified principal component technique based on the LASSO. Journal of Computational and Graphical Statistics, 2003, 12(3): 531-547.
    [6]
    d’Aspremont A, El Ghaoui L, Jordan M I, et al. A direct formulation for sparse PCA using semidefinite programming. SIAM Review, 2007, 49(3): 434-448.
    [7]
    Journée M, Nesterov Y, Richtárik P, et al. Generalized power method for sparse principal component analysis. Journal of Machine Learning Research, 2010, 11(2): 517-553.
    [8]
    Moghaddam B, Weiss Y, Avidan S. Spectral bounds for sparse PCA: Exact and greedy algorithms. In: Proceedings of the 18th International Conference on Neural Information Processing Systems. Cambridge, MA: MIT Press, 2005: 915-922.
    [9]
    d’Aspremont A, Bach F, El Ghaoui L. Optimal solutions for sparse principal component analysis. Journal of Machine Learning Research, 2008, 9(7): 1269-1294.
    [10]
    Croux C, Filzmoser P, Fritz H. Robust sparse principal component analysis. Technometrics, 2013, 55(2): 202-214.
    [11]
    Shen H, Huang J Z. Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis, 2008, 99(6): 1015-1034.
    [12]
    Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. Journal of Computational and Graphical Statistics, 2006, 15(2): 265-286.
    [13]
    Tipping M E, Bishop C M. Probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1999, 61(3): 611-622.
    [14]
    Sigg C D, Buhmann J M. Expectation-maximization for sparse and non-negative PCA. In: Proceedings of the 25th International Conference on Machine Learning. New York: Association for Computing Machinery, 2008: 960-967.
    [15]
    Witten D M, Tibshirani R, Hastie T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics, 2009, 10(3): 515-534.
    [16]
    Friedman J, Hastie T, Tibshirani R, et al. The Elements of Statistical Learning. New York: Springer, 2001.
    [17]
    Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67(2): 301-320.
    [18]
    Avellaneda M. Hierarchical PCA and applications to portfolio management. https://ssrn.com/abstract=3467712.
    [19]
    Hsu Y L, Huang P Y, Chen D T. Sparse principal component analysis in cancer research. Translational Cancer Research, 2014, 3(3): 182-190.
    [20]
    Wen C, Zhang A, Quan S, et al. BeSS: An R package for best subset selection in linear, logistic and CoxPH models. Journal of Statistical Software, 2020, 94(1): 1-24.
    [21]
    Bertsimas D, Cory-Wright R, Pauphilet J. Solving large-scale sparse PCA to certifiable (near) optimality. https://arxiv.org/abs/2005.05195.
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    [1]
    Yang L. An application of principal component analysis to stock portfolio management. Christchurch, New Zealand: University of Canterbury, 2015.
    [2]
    Cadima J, Jolliffe I T. Loading and correlations in the interpretation of principle components. Journal of Applied Statistics, 1995, 22(2): 203-214.
    [3]
    Vines S. Simple principal components. Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000, 49(4): 441-451.
    [4]
    Ma Z. Sparse principal component analysis and iterative thresholding. Annals of Statistics, 2013, 41(2): 772-801.
    [5]
    Jolliffe I T, Trendafilov N T, Uddin M. A modified principal component technique based on the LASSO. Journal of Computational and Graphical Statistics, 2003, 12(3): 531-547.
    [6]
    d’Aspremont A, El Ghaoui L, Jordan M I, et al. A direct formulation for sparse PCA using semidefinite programming. SIAM Review, 2007, 49(3): 434-448.
    [7]
    Journée M, Nesterov Y, Richtárik P, et al. Generalized power method for sparse principal component analysis. Journal of Machine Learning Research, 2010, 11(2): 517-553.
    [8]
    Moghaddam B, Weiss Y, Avidan S. Spectral bounds for sparse PCA: Exact and greedy algorithms. In: Proceedings of the 18th International Conference on Neural Information Processing Systems. Cambridge, MA: MIT Press, 2005: 915-922.
    [9]
    d’Aspremont A, Bach F, El Ghaoui L. Optimal solutions for sparse principal component analysis. Journal of Machine Learning Research, 2008, 9(7): 1269-1294.
    [10]
    Croux C, Filzmoser P, Fritz H. Robust sparse principal component analysis. Technometrics, 2013, 55(2): 202-214.
    [11]
    Shen H, Huang J Z. Sparse principal component analysis via regularized low rank matrix approximation. Journal of Multivariate Analysis, 2008, 99(6): 1015-1034.
    [12]
    Zou H, Hastie T, Tibshirani R. Sparse principal component analysis. Journal of Computational and Graphical Statistics, 2006, 15(2): 265-286.
    [13]
    Tipping M E, Bishop C M. Probabilistic principal component analysis. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1999, 61(3): 611-622.
    [14]
    Sigg C D, Buhmann J M. Expectation-maximization for sparse and non-negative PCA. In: Proceedings of the 25th International Conference on Machine Learning. New York: Association for Computing Machinery, 2008: 960-967.
    [15]
    Witten D M, Tibshirani R, Hastie T. A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics, 2009, 10(3): 515-534.
    [16]
    Friedman J, Hastie T, Tibshirani R, et al. The Elements of Statistical Learning. New York: Springer, 2001.
    [17]
    Zou H, Hastie T. Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 2005, 67(2): 301-320.
    [18]
    Avellaneda M. Hierarchical PCA and applications to portfolio management. https://ssrn.com/abstract=3467712.
    [19]
    Hsu Y L, Huang P Y, Chen D T. Sparse principal component analysis in cancer research. Translational Cancer Research, 2014, 3(3): 182-190.
    [20]
    Wen C, Zhang A, Quan S, et al. BeSS: An R package for best subset selection in linear, logistic and CoxPH models. Journal of Statistical Software, 2020, 94(1): 1-24.
    [21]
    Bertsimas D, Cory-Wright R, Pauphilet J. Solving large-scale sparse PCA to certifiable (near) optimality. https://arxiv.org/abs/2005.05195.
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