Abstract: The estimation errors in the mean vector as well as the covariance matrix make it still challenging to calculate accurately efficient portfolios in real stock markets. To address such issue, this paper introduces new shrinkage estimators for the mean vector and covariance matrix based on mixed normal distribution, which better fits the actual distribution of stock returns. The new estimators effectively correct estimation errors and are utilized by this paper to construct efficient portfolios in the Chinese A-share market. The main conclusions are as follows: 1) The new shrinkage estimators reduce estimation errors for the mean vector and covariance matrix by 65% and 6%, respectively, compared to existing shrinkage estimators; 2) The reliability and robustness of efficient portfolios based on the new shrinkage estimators are improved by 24% and 60%, respectively; 3) In the Chinese A-share market, efficient portfolios based on the new shrinkage estimator maintain a monthly net Sharpe ratio above 0.1, representing a 40% improvement over portfolios based on existing estimators. Therefore, it is recommended that investors use shrinkage estimators under mixed normal to construct efficient portfolios, especially when dealing with a high number of assets and limited sample sizes.

Key words: Stock Market, Efficient Portfolios, Shrinkage Estimation, Mixture of Normal