SHRINKAGE ESTIMATION OF MEAN-VARIANCE PORTFOLIO

Yan Liu (), Ngai Hang Chan, Chi Tim Ng () and Samuel Po Shing Wong ()
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 01, 1-25

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.

Keywords: Investment analysis; matrix inequalities; mean-variance portfolio; shrinkage covariance matrix (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219024916500035

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