Risk Budgeting Portfolios from Simulations

TL;DR

This paper introduces a simulation-based numerical framework for constructing risk budgeting portfolios, featuring algorithms tailored for Expected Shortfall and demonstrating practical applications with real financial data.

Contribution

It develops a novel simulation-driven approach with specialized algorithms for risk budgeting, including for Expected Shortfall, and provides a Julia package for practical implementation.

Findings

Algorithms outperform standard convex solvers

Effective risk budgeting portfolios on real data

Comparison with classical strategies shows advantages

Abstract

Risk budgeting is a portfolio strategy where each asset contributes a prespecified amount to the aggregate risk of the portfolio. In this work, we propose an efficient numerical framework that uses only simulations of returns for estimating risk budgeting portfolios. Besides a general cutting planes algorithm for determining the weights of risk budgeting portfolios for arbitrary coherent distortion risk measures, we provide a specialised version for the Expected Shortfall, and a tailored Stochastic Gradient Descent (SGD) algorithm, also for the Expected Shortfall. We compare our algorithm to standard convex optimisation solvers and illustrate different risk budgeting portfolios, constructed using an especially designed Julia package, on real financial data and compare it to classical portfolio strategies.