基于Black-Litterman模型与Meucci理论确定投资组合权重

The Optimal Weight of Portfolio Based on Black-Litterman Model and Meucci Theory

为考虑投资者线性选择观点和非线性偏好,在确定投资组合中各资产的投资权重时,本文提出了以下的方法：首先利用Black-Litterman模型,结合投资者的线性选择观点,得到权重w的估计值w0-＊。其次以w0-＊为标准,用蒙特卡罗方法模拟出w1,w2,…,wM等M个权重,根据每个权重,基于历史数据确定整个投资组合的先验分布。再利用Meucci思想,从先验分布中得到情景点（zj,pj）,结合投资者非线性偏好,得到后验分布情景点（zj,pj）,继而得到整个投资组合的后验分布。最后以风险补偿率为标准,来得出最优的组合权重。该组合权重综合考虑了历史数据、投资者线性选择观点和非线性偏好多个方面的信息。

In order to identify the optimal weight of portfolio with the linear and non-linear views of a certain investors,we treat the problem as follows.At first,based on Black-Litterman model,by combing the linear views of the investor,we get the estimated w which we use to simulate weights w_1,w_2,…,w_m.Then we use each w and historical data.By implementing Meucci theory,we combine the investor＇s nonlinear views,then get prior scenario points（z_j,p_j）,and later posterior points（z_j,p_j）,thus we get the posterior distribution of the portfolio.We get a bunch of posterior distributions,so we can choose the best weight according to yield-risk ratio.