Haircut Capital Allocation as the Solution of a Quadratic Optimisation Problem

Abstract

The capital allocation framework presents capital allocation principles as solutions to particular optimisation problems and provides a general solution of the quadratic allocation problem via a geometric proof. However, the widely used haircut allocation principle is not reconcilable with that optimisation setting. Our study complements and generalises the unified capital allocation framework. The goal of the study is to contribute in the following two ways. First, we provide an alternative proof of the quadratic allocation problem based on the Lagrange multipliers method to reach the general solution, which complements the geometric proof. This alternative approach to solve the quadratic optimisation problem is, in our opinion, easier to follow and understand by researchers and practitioners. Second, we show that the haircut allocation principle can be accommodated by the optimisation setting with the quadratic optimisation criterion if one of the original conditions is relaxed. Two examples are provided to illustrate the accommodation of this allocation principle.

Keywords

• capital allocation problem
• risk management
• optimisation
• haircut principle
• risk sharing