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Shrinkage Estimation Of Mean-Variance Portfolio

Author

Listed:
  • YAN LIU

    (Department of Finance, Ocean University of China, No. 238 Song Ling Road, Qing Dao, Shan Dong 266100, P. R. China)

  • NGAI HANG CHAN

    (Department of Statistics, The Chinese University of Hong Kong, N.T. Shatin, Hong Kong, P. R. China)

  • CHI TIM NG

    (Department of Statistics, Chonnam National University, 77 Yongbong-ro, Buk-gu, Gwangju 500-757, Republic of Korea)

  • SAMUEL PO SHING WONG

    (Department of Statistics, The Chinese University of Hong Kong, N.T. Shatin, Hong Kong, P. R. China)

Abstract

This paper studies the optimal expected gain/loss of a portfolio at a given risk level when the initial investment is zero and the number of stocks p grows with the sample size n. A new estimator of the optimal expected gain/loss of such a portfolio is proposed after examining the behavior of the sample mean vector and the sample covariance matrix based on conditional expectations. It is found that the effect of the sample mean vector is additive and the effect of the sample covariance matrix is multiplicative, both of which over-predict the optimal expected gain/loss. By virtue of a shrinkage method, a new estimate is proposed when the sample covariance matrix is not invertible. The superiority of the proposed estimator is demonstrated by matrix inequalities and simulation studies.

Suggested Citation

  • Yan Liu & Ngai Hang Chan & Chi Tim Ng & Samuel Po Shing Wong, 2016. "Shrinkage Estimation Of Mean-Variance Portfolio," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(01), pages 1-25, February.
    • Handle: RePEc:wsi:ijtafx:v:19:y:2016:i:01:n:s0219024916500035
    DOI: 10.1142/S0219024916500035
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    References listed on IDEAS

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    1. Frankfurter, George M. & Phillips, Herbert E. & Seagle, John P., 1971. "Portfolio Selection: The Effects of Uncertain Means, Variances, and Covariances," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 6(5), pages 1251-1262, December.
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    4. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
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