Analytical Overview and Applications of Modified Black-Litterman Model for Portfolio Optimization

摘要

The paper makes analytical overviews of the Markowitz portfolio and theCapital 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 thecharacteristics of a specific market point, which cannot be taken from a global marketindex. The paper derives analytic relations for the new specific market point withanalytical approximation of the efficient frontier. The BL model insists also expertviews, which influence the portfolio solution. The paper derives formalization of theexpert views from the difference between the evaluated implied returns and historicalmean 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 theMV and BL portfolio results.