The two-block covariance matrix and the CAPM. (1st January 2012)

• Record Type: Journal Article
• Authors: Disatnik, David; Benninga, Simon
• Is Part Of: International journal of portfolio analysis & management. Volume 1:Number 1(2012)
• Page Start: 32
• Page End: 42
• Publication Date: 2012-01-01
• Subjects: portfolio optimisation -- block covariance matrix -- tangency portfolio -- market portfolio -- capital asset pricing model -- CAPM; Investment analysis -- Periodicals; 332.605
• Languages: English
• ISSNs: 2048-2361

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).