Risk Budgeting Portfolios from Simulations

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