The Long Neglected Critically Leveraged Portfolio

TL;DR

This paper reveals a unique efficient frontier for portfolios with offsetting long and short positions, highlighting overlooked cases due to the use of portfolio weights instead of actual asset amounts.

Contribution

It introduces a new perspective on the efficient frontier for offsetting long and short positions, which has been neglected in traditional mean-variance analysis.

Findings

Efficient frontier for offsetting portfolios is a pair of straight lines through the origin.

Traditional models implicitly exclude this case by using portfolio weights.

Properties of portfolios dominated by short positions are elucidated.

Abstract

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.