Extension And Application Of BL Model

Since Markowitz's pioneering work in 1952, asset manager began to introduce the quantitative models to the asset portfolio management. However, the traditional mean-variance model is very sensitive to the changes of input parameters, so the allocation results are less diversification, and the model is hardly put into practice. For this reason, Black and Litterman put forward the BL model which combining the views of investors and the market equilibrium expected return through a Bayesian approach, and get a new mixed-expected return (implied expected return).BL model has two advantages for the asset management. First, incorporating the market equilibrium views into the model by inverse optimization method makes the asset weights of BL model more decentralized. Second, BL model provides a clear way to specify the investor's views and to blend the views into the model, which sets up a good framework for the strategic investment. However, when the original model is applied to the common stocks, two problems arise. First, numerous stocks led to excessive calculation, and second, the parameters of the model are also very difficult to set. Therefore, we propose a new BL model with benchmark portfolios optimized. This new model extends benchmark portfolio beyond the market portfolio, and under the assumption that the tracking error caused by investor views is comparable to that caused by the historical return optimization, we determines the value of the parameterτ.Regarding to the portfolio selection problem, we use the optimal tracking error model instead of the traditional mean-variance model. And the inverse optimization method must be substituted with tracking error model. In this case, the implied equilibrium expected return vector equals to 0, which makes the model more intuitive.Finally, we also focus on weights constraints on model. We analyze the effects of different constraints on the BL model. At last, we find that proper weight constraints can improve the characteristics of the return.