Differentiability properties of the efficient (u,q2)-set in the Markowitz portfolio selection method

The set of efficient (Rho2)-combinations in the (Rho2)-plane of the Markowitz portfolio selection method consists of a series of strictly convex parabola. In the transition points from one parabola to the next one, the curve may be indifferentiable. The article gives necessary and sufficient conditions for differentiability and compares these conditions with statements on differentiability in the literature. A new proof of the differentiability property is presented using the portfolio selection model with one riskless asset.