Research On The Application Of The Black-Litterman Model In Security Assest Allocation

Markowitz portfolio theory laid the theoretical foundation of modern finance, the mean-variance model as an asset allocation approach, plays an irreplaceable role in determining the optimal portfolio. Mean - variance model is essentially an optimization model, utilizing optimization algorithm to select the optimal portfolio, either at a given expected return or given risk level to minimize the portfolio variance or maximize expected return of portfolio respectively. Mean-variance model provides a basic analytic framework for determing optimal portfoliofor and is widely used in practice.Mean - variance model contains two important input variables:a vector of expected return of the assets contained in portfolio, the other input variable is the covariance matrix of the returns of assets included in the portfolio. Empirical studies show that the impact of the covariance matrix of the optimal portfolio is relatively stable, while mean-variance model is more sensitive to small changes in expected return of assets, even a little change may lead to significant changes of weight of the optimal portfolio. In addition, the mean-variance model implicitly assumes that all investors hold the same view in terms of expected return of assets. This assumption excludes investors individual subjective point of view.Black-Litterman model is another important asset allocation model since the invention of Markowitz mean-variance model.Based on Bayesian framework, Black-Litterman model set out from CAPM equilibrium returns as neutral starting point, make a resonalble combination of the market equilibrium and investors individual subjective point of view on assets expected return to synthetise the the posterior distribution of asset return, then resort to the mean - variance model to select the Black-Litterman optimal portfolio. Compared with Markowitz mean - variance model, Black-Litterman model established a complex mapping between the market equilibrium and the expected return of individual investors and the optimal portfolio.Empirical studies show, Black-Litterman model is of great flexibility to incorporate individual investors perspective into optimal portfolio,which breakthrough the limitations of the mean - variance model,while greatly reducing the sensitivity of the optimal portfolio to changes of expected return of assets. Using the Black-Litterman Model optimal portfolio to construct optimal portfolio, we need to determine the CAPM equilibrium income, market risk aversion, investors subjective views about return of assets as well as the uncertainty investor’s view. In practice, correctly address these issues and to promote the use of Black-Litterman model has important practical value.This paper explain the Black-Litterman mode from both theoretical and empirical aspects. The theory part focuses on the method of determining Black-Litterman model input variables of the model and make the necessary explanations. Specifically, this paper introduced the structur of the model and methods to set the parameters embeded in the model and introduce the proces in detail to import subjective point of view of investors, and process to build the optimal portfolio.Also the paper provides mathematical derivation of the model.In the empirical part, we use ten stocks selected by GARP stratrgy as the sample of empirical analysis, a sample of three years of closing price data. Then use GARCH model to fit the yields and volatility of ten stocks and make forecast, which was a good reference for investors to construct optimal portfolio.For different types of investors, due to their own experience to interpret information and understanding of the market is different, different investors in the face of the same assets, may hold different views. Thus, this article assumes that the two belong to aggressive and sound-based investors, and analyzes the impact of individual investors views on Black-Litterman model expected rate of return and the optimal portfolio.The empirical results show that when investors subjective viewpoint expected return of assets above the equilibrium excess return, as investor confidence in the subjective view of the rising, the expected return model B-L model also increased, at the same time, when investors’ assets expected rate of return below the equilibrium excess return, B-L model expected return will decrease while confidence level of subjective view rising. In addition, the article also analyzes Black-Litterman model optimal portfolio weights’ sensitivity to investors’ views. The empirical results show that when investors assets views yield is higher than equilibrium excess return, Black-Litterman model will corresponding increase the weights in optimal portfolio, while reducing the weight of assets which was not contained in investors" views. Also while investor confidence level rise,the portfolio weights of assets contained in portfolio show a increasing trend; on the contrary, when the rate of return investors’ point of view below the equilibrium excess return, the weights of assets in optimal portfolio while exhibit a decreasing trend while the level of confidence rising.