  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.
