Optimal method for investing on assets using black litterman model

Abstract

The main goal of investors is to minimize risk at any point of given returns or maximize returns at any given risk. The Markowitz mean-variance (MV) model is widely used for solving investment problem but is tedious and the results are often extreme. The investors who use it encountered difficulties when adding many constraints into the model. There have been many attempts to alleviate the problems of MV model. On this basis, the Black-Litterman (BL) model was developed to search for the best solution to the problem. In this paper, we use the method of BL to estimate the effects of tau (τ) on variance which is the measure of risk and expected returns. Tau is calibrated into ten values, 0.1 to 1.0 with increment of 0.1. The S&P 500 index data is used for the returns on US stocks, Treasury bonds and Cash (Money market) from 1960 to 2003. The results discovered, demonstrate that as tau increases, the values of risk decrease and the values of returns for stock increase simultaneously.