<abstract xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Cybernetics and Information Technologies

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

The paper makes analytical overviews of the Markowitz portfolio and the Capital Asset Pricing models and motivates the advances of the Black-Litterman (BL)...

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

Published Online: Jun 12, 2020

Page range: 30 - 49

Received: Apr 07, 2020

Accepted: May 21, 2020

DOI: https://doi.org/10.2478/cait-2020-0014

Keywords
Size Portfolio optimization, mean-variance portfolio model, Black-Litterman portfolio model, active portfolio management, decision making

© 2020 Todor Stoilov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jun 12, 2020

Page range: 30 - 49

Received: Apr 07, 2020

Accepted: May 21, 2020

DOI: https://doi.org/10.2478/cait-2020-0014

KeywordsSize Portfolio optimization, mean-variance portfolio model, Black-Litterman portfolio model, active portfolio management, decision making

© 2020 Todor Stoilov et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Size Portfolio optimization, mean-variance portfolio model, Black-Litterman portfolio model, active portfolio management, decision making