Risk Budgeting

Deep Declarative Risk Budgeting Portfolios ArXiv ID: 2504.19980 “View on arXiv” Authors: Manuel Parra-Diaz, Carlos Castro-Iragorri Abstract Recent advances in deep learning have spurred the development of end-to-end frameworks for portfolio optimization that utilize implicit layers. However, many such implementations are highly sensitive to neural network initialization, undermining performance consistency. This research introduces a robust end-to-end framework tailored for risk budgeting portfolios that effectively reduces sensitivity to initialization. Importantly, this enhanced stability does not compromise portfolio performance, as our framework consistently outperforms the risk parity benchmark. ...

Mirror Descent Algorithms for Risk Budgeting Portfolios ArXiv ID: 2411.12323 “View on arXiv” Authors: Unknown Abstract This paper introduces and examines numerical approximation schemes for computing risk budgeting portfolios associated to positive homogeneous and sub-additive risk measures. We employ Mirror Descent algorithms to determine the optimal risk budgeting weights in both deterministic and stochastic settings, establishing convergence along with an explicit non-asymptotic quantitative rate for the averaged algorithm. A comprehensive numerical analysis follows, illustrating our theoretical findings across various risk measures – including standard deviation, Expected Shortfall, deviation measures, and Variantiles – and comparing the performance with that of the standard stochastic gradient descent method recently proposed in the literature. ...

Asset and Factor Risk Budgeting: A Balanced Approach ArXiv ID: 2312.11132 “View on arXiv” Authors: Unknown Abstract Portfolio optimization methods have evolved significantly since Markowitz introduced the mean-variance framework in 1952. While the theoretical appeal of this approach is undeniable, its practical implementation poses important challenges, primarily revolving around the intricate task of estimating expected returns. As a result, practitioners and scholars have explored alternative methods that prioritize risk management and diversification. One such approach is Risk Budgeting, where portfolio risk is allocated among assets according to predefined risk budgets. The effectiveness of Risk Budgeting in achieving true diversification can, however, be questioned, given that asset returns are often influenced by a small number of risk factors. From this perspective, one question arises: is it possible to allocate risk at the factor level using the Risk Budgeting approach? First, we introduce a comprehensive framework to address this question by introducing risk measures directly associated with risk factor exposures and demonstrating the desirable mathematical properties of these risk measures, making them suitable for optimization. Then, we propose a novel framework to find portfolios that effectively balance the risk contributions from both assets and factors. Leveraging standard stochastic algorithms, our framework enables the use of a wide range of risk measures to construct diversified portfolios. ...

Risk Budgeting Allocation for Dynamic Risk Measures ArXiv ID: 2305.11319 “View on arXiv” Authors: Unknown Abstract We define and develop an approach for risk budgeting allocation - a risk diversification portfolio strategy - where risk is measured using a dynamic time-consistent risk measure. For this, we introduce a notion of dynamic risk contributions that generalise the classical Euler contributions and which allow us to obtain dynamic risk contributions in a recursive manner. We prove that, for the class of coherent dynamic distortion risk measures, the risk allocation problem may be recast as a sequence of strictly convex optimisation problems. Moreover, we show that self-financing dynamic risk budgeting strategies with initial wealth of 1 are scaled versions of the solution of the sequence of convex optimisation problems. Furthermore, we develop an actor-critic approach, leveraging the elicitability of dynamic risk measures, to solve for risk budgeting strategies using deep learning. ...