Black-Litterman Model : Practical Asset Allocation Model Beyond Traditional Mean-Variance

Abstract: Today the Black-Litterman model is used as an asset allocation tool by many of the largest investment banks around the globe. The Black-Litterman model was derived based on the Mean- Variance framework to maximize return for a given level of portfolio risk. It allows investors to incorporate their own unique views with the implied equilibrium return vector to construct a new combined return vector which as the result this vector leads to a well-diversified portfolio. This paper consolidates and compares the applicability and practicality of Black-Litterman versus traditional Mean-Variance model. Although well known model such as Mean-Variance is academically sound and popular, it is rarely used among asset managers due to it’s deficiencies. To put the discussion into context we shed light on the improvement made by Black-Litterman by putting the performance and practicality of both models into test. We first begin by illustrating detailed mathematical derivations of how the models are constructed by bringing clarity and profound understanding of the intuition behind the model. Consecutively, we generate portfolios in Excel, composing data from 10-Swedish equities over the course of 10-year period and respectively select 30-days Swedish Treasury Bill as a risk-free rate. The resulting portfolios orientates our discussion towards the better comparison of the performance and applicability of these two models, where we theoretically and geometrically illustrate the differences. Finally, based on extracted result of the performance of both models we demonstrate the superiority and practicality of Black-Litterman model which in our particular case outperform traditional Mean-Variance model when the views are close to reality which leads to more stable well-diversified portfolio.