Implementing portfolio risk management and hedging in practice

TL;DR

This paper presents a practical approach to portfolio risk management and hedging that simplifies the complex continuous-time stochastic control framework into a convex quadratic programming method, facilitating implementation.

Contribution

It introduces a straightforward, implementable quadratic programming approach for cross-asset portfolio risk management and hedging, bridging theory and practice.

Findings

Effective quadratic programming formulation for risk management

Implementation details using CVXOPT provided

Handles multiple asset classes and risk models

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.