Markowitz vs Black--Litterman: A Comparison of Two Portfolio Optimisation Models

Abstract: Modern portfolio theory first gained its ground among researchers and academics, but has become increasingly popular among practitioners. This paper examines the two popular portfolio optimization models, Markowitz mean-variance model and Black-Litterman formula and compares their results on real data. In second chapter mean-variance model is derived step-by-step using Lagrange multipliers and matrices, whereas in third chapter Black-Litterman formula is proved by two different methods - by Maximum Likelihood method and Theil's model. Two portfolio optimization models are used on real data, monthly data from November 2007 to November 2017. In order to build the two models, Microsoft Excel is used. Swedish 30-day Treasury Bill is taken as risk-free asset and SIXPRX as a benchmark. Detailed results are presented in Chapter 4. In Black-Litterman model two different views are implemented to see if the model outperforms Markowitz mean-variance model. All in all there is a significant difference in the outcomes, Black-Litterman portfolio performs better than mean-variance portfolio.