Using Historical Return Data in the Black-Litterman Model for Optimal Portfolio Decision
In this paper, the Black-Litterman model which is the improved mean-variance optimization model, is discussed. Basically, the views given by the investors were incorporated into this model so that their views on risk and return, and risk tolerance could be quantified. For doing so, the market rates of return for the assets were calculated from the geometric mean. Moreover, the views of the investors were expressed in the matrix form. Then, the covariance matrix and the diagonal covariance matrix of the assets return were calculated. Accordingly, the mean rate of the asset return was computed. On this basis, the Black-Litterman optimization model was constructed. This model formulation was done by taking a set of possible rates of return for the assets. Particularly, the corresponding optimal portfolios of the assets with lower risk and higher expected return were further determined. For illustration, the historical return data for S&P 500, 3-month Treasury bill, and 10-year Treasury bond from 1928 to 2016 were employed to demonstrate the formulation of the ideal investment portfolio model. As a result, the efficient frontier of the portfolio is shown and the discussion is made. In conclusion, the Black-Litterman model could provide the optimal investment decision practically.
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