The two-block covariance matrix and the CAPM

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).