SHRINKAGE ESTIMATION OF MEAN-VARIANCE PORTFOLIO

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.