Analytical overview and applications of modified black-litterman model for portfolio optimization

Abstract

The paper makes analytical overviews of the Markowitz portfolio and the Capital Asset Pricing models and motivates the advances of the Black-Litterman (BL) one. This overview implies that for a small set of assets the BL model needs the characteristics of a specific market point, which cannot be taken from a global market index. The paper derives analytic relations for the new specific market point with analytical approximation of the efficient frontier. The BL model insists also expert views, which influence the portfolio solution. The paper derives formalization of the expert views from the difference between the evaluated implied returns and historical mean assets returns. Such form of expert views makes modifications of the BL model. This allows comparisons between Markowitz (MV) and BL portfolio performance. Benefits of this research are demonstrated with market data and comparison of the MV and BL portfolio results.