Implementing Portfolio Risk Management and Hedging in Practice

Abstract

In academic literature portfolio risk management and hedging are often versed in the language of stochastic control and Hamilton-Jacobi-Bellman (HJB) equations in continuous time. In practice the continuous-time framework of stochastic control may be undesirable for various business reasons. In this work we present a straightforward approach for thinking of cross-asset portfolio risk management and hedging, providing some implementation details, while rarely venturing outside the convex optimisation setting of (approximate) quadratic programming (QP). We pay particular attention to the correspondence between the economic concepts and their mathematical representations; the abstractions enabling us to handle multiple asset classes and risk models at once; the dimensional analysis of the resulting equations; and the assumptions inherent in our derivations. We demonstrate how to solve the resulting QPs with CVXOPT.

Keywords: risk, hedging, portfolio management, risk management, optimisation, quadratic programming, convex optimisation