马科维茨的投资组合理论是现代金融学的基础之一，在投资组合理论之中对于期望收益及其方差-协方差矩阵的估计将直接影响资产组合选择的有效性。为了改善资产组合的表现，在历史数据的基础上，本文将采用贝叶斯方法将参数不确定性以及投资者的先验观点纳入参数估计之中。参考前人研究，本文给出了先验期望收益及其方差-协方差矩阵的估计方法。随后研究了无信息先验分布及有信息先验分布的一种特殊情况——共轭先验分布下，最小方差组合及最大夏普比率组合这两种有效边界上最具有代表性的资产组合的表现情况。

    本文以沪深300指数成分股为资产池计算了2008年至2019年中各资产组合的收益情况。有信息先验分布下两种贝叶斯资产组合年化收益分别提高了8.1%、6.6%，证明在中国A股市场上，贝叶斯方法能够有效的减小参数估计误差对资产组合的影响。

Markowitz's portfolio theory is one of the foundations of modern finance, in which the estimation of expected return and its variance-covariance matrix will directly affect the effectiveness of portfolio selection. In order to improve the performance of the portfolio, based on the historical data, this paper adopts Bayesian method to incorporate the parameter uncertainty and investors' prior views into the parameter estimation. Based on the previous research, this paper gives the general method of estimate the prior expected return and its variance-covariance matrix. Then under the condition of non-informative prior distribution and informative prior distribution, we study the performance of the two most representative asset portfolios on the effective boundary, the least variance portfolio and the maximum Sharpe ratio portfolio.

Using the CSI 300 index constituent stocks as asset pool, this paper calculates the returns of each portfolio from 2008 to 2019. Under the condition of conjugate prior distribution, the annualized returns of the two Bayesian portfolios increased by 8.1% and 6.6% respectively, proving that the Bayesian method can effectively reduce the impact of parameter estimation error on the portfolio in the Chinese A-share stock market.

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