On Markowitz Geometry

Abstract

By Markowitz geometry we mean the intersection theory of ellipsoids and affine subspaces in a real finite-dimensional linear space. In the paper we give a meticulous and self-contained treatment of this arch-classical subject, which lays a solid mathematical groundwork of Markowitz mean-variance theory of efficient portfolios in economics.

Keywords

• Affine subspace
• Efficient financial portfolio
• Ellipsoid
• Markowitz mean-variance theory

References

1. [1] H. Markowitz, Portfolio Selection, J. Finance, 7 (1952), 77-91.
2. [2] H. Markowitz, (2nd ed.), Portfolio Selection, Blackwell, 1991.
3. [3] S. Stoyanov, S. Rachev, F. Fabozzi, Optimal financial portfolios, Appl. Math. Finance, 14 (2007), 401-436.