Title: The two-block covariance matrix and the CAPM

Authors: David Disatnik; Simon Benninga

Addresses: Faculty of Management, Tel Aviv University, Tel Aviv, 69978, Israel. ' Faculty of Management, Tel Aviv University, Tel Aviv, 69978, Israel

Abstract: The classical assumptions of the capital asset pricing model do not ensure obtaining a tangency (market) portfolio in which all the risky assets appear with positive proportions. This paper gives an additional set of assumptions that ensure obtaining such a portfolio. Our new set of assumptions mainly deals with the structure of the covariance matrix of the risky assets returns. The structure we suggest for the covariance matrix is of a two-block type. We derive analytically sufficient conditions for a matrix of this type to produce a long-only tangency portfolio (as well as a long-only global minimum variance portfolio).

Keywords: portfolio optimisation; block covariance matrix; tangency portfolio; market portfolio; capital asset pricing model; CAPM; risky assets returns; global minimum variance portfolio; risk.

DOI: 10.1504/IJPAM.2012.046907

International Journal of Portfolio Analysis and Management, 2012 Vol.1 No.1, pp.32 - 42

Published online: 23 Aug 2014 *