The Long Neglected Critically Leveraged Portfolio

We show that the efficient frontier for a portfolio in which short positions precisely offset the long ones is composed of a pair of straight lines through the origin of the risk-return plane. This unique but important case has been overlooked because the original formulation of the mean-variance model by Markowitz as well as all its subsequent elaborations have implicitly excluded it by using portfolio weights rather than actual amounts allocated to individual assets. We also elucidate the properties of portfolios where short positions dominate the long ones, a case which has similarly been obscured by the adoption of portfolio weights.