Risk Budgeting Portfolios from Simulations

Paper: arXiv 2302.01196

Authors: Bernardo Freitas Paulo da Costa, Silvana M. Pesenti, Rodrigo S. Targino

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.

Complexity vs Empirical Score

• Math Complexity: 7.0/10
• Empirical Rigor: 6.0/10 (capped from 6.5: transaction costs not modelled; see penalty flags)
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical and mathematical foundation for risk budgeting portfolios under non-Gaussian distortion risk measures like Expected Shortfall. It translates complex convex optimization and SGD techniques into practical application supported by an open-source Julia package and real market data backtests.

Research Flowchart

  flowchart TD
    A[Goal: Estimate Risk Budgeting Portfolios using Simulations] --> B[Data Inputs: Historical Financial Data & Asset Return Simulations]
    B --> C[Methodology: Coherent Distortion Risk Measures & Expected Shortfall]
    C --> D[Algorithms: Cutting Planes Method & Tailored SGD]
    D --> E[Implementation: Custom Julia Package vs. Standard Convex Solvers]
    E --> F[Outcomes: Efficient Simulation-Based Portfolio Allocation & Comparison to Classical Strategies]