Parameter Optimization Of Black-litterman Model And Its Application In Industry Asset Allocation

The mean-variance model proposed by Markowitz,the Nobel Prize Laureate in 1952,pioneered the modern portfolio theory,the Markowitz model provides an analytical framework for investors to get maximum returns,however,the model has defects such as magnification error,sensitive to input parameters and so on.Black and Litterman integrate investor views into the Markowitz model and improve the model.The original Black-Litterman model sets investor views according to the analyst's opinion,a large number of studies in behavioral finance show that individuals and institutional investors often have psychological biases,this leads to limited application of the model.Therefore,the method of seeking a more effective investor views has become a problem for people to study.For the problem of the quantification of investor views in the Black-Litterman model,based on the analysis of several basic models in portfolio theory,this paper uses the data of Shanghai 380 industry index to carry out the following two aspects of research:(1)The excess returns predicted by the Gradient Boosting Regression Tree(GBRT)algorithm is used as the view returns,when the algorithm converges,the mean square error is used as the view error,optimized parameter setting method in Black-Litterman model.Analysis shows that,without constraint,the Black-Litterman model has the highest annual returns and Sharpe ratio,and the investment performance is the best;under the same constraint conditions,in the Markowitz model,the Black-Litterman model and the market strategy,the annual returns and the Sharpe ratio of the Black-Litterman model are the highest;in addition,the coverage of asset allocation of Black-Litterman model is higher than that of Markowitz model,which can achieve the purpose of decentralized investmentt.Therefore,it is valuable to use this method to set view returns and view error.(2)Considering that investor's psychological factors have an impact on investment decisions,this paper analyses the problem of asset allocation under different confidence levels.The industry price index predicted by the Kalman filtering algorithm is converted into view returns,under the investor confidence levels of 20%?35%?50%?65% and 80% where the asset allocation results are compared.The results show that,under the condition of the short selling limit and the upper limit of asset allocation weight of 30%,the confidence level has an impact on the asset allocation results.There are differences in asset allocation coverage under different confidence levels,the posterior excess return increases with the increase of investor's confidence level;however,at any confidence level,the Black-Litterman model has higher annual returns than the market strategy,and the Sharpe ratio is higher than the Markowitz model.It shows that it is reasonable to use the Kalman filtering algorithm to predict the view returns in the Black-Litterman model.In summary,the parameter optimized Black-Litterman model has advantages in investment practice,therefore,it is feasible and effective to apply the GBRT algorithm and the Kalman filtering algorithm to the Black-Litterman model,and it provides a new way for the wider application of the Black-Litterman model.