Measurement Of Variance Of Views In Black-Litterman Model

Black-Litterman model is the mainstream model in asset allocation research.The model allows investors to input "market view" as a parameter,and requires investors to input a variance matrix Ω for each "market view",which indicates investors’confidence in the "market view".However,it is very difficult to measure the varianceΩ,which makes the model difficult to apply to the real market.This paper proposes two methods to measure variance Ω based on the framework of the Black-Litterman model.The direct method estimates the variance Ω directly according to the variance of return rate of assets and the posterior probability of classifier,while the indirect method estimates the rate of change of the Black-Litterman portfolio to solve the optimal variance Ωin the sense of minimizing the square error.The empirical research shows that the Black-Litterman portfolios using both two measurement methods perform better than the mean-variance model in the market,have higher Sharpe ratio than the Standard&Poor’s 500 index,and can still obtain positive returns in the economic downturn.