Quantum Portfolio Optimization Achieves Higher-Order Moment Modeling with Skewness and Kurtosis

Portfolio optimization, a cornerstone of modern finance, continually seeks methods to better assess and manage investment risk, and researchers are now exploring the potential of quantum computing to address its complexities. Valter Uotila from Aalto University and University of Helsinki, alongside Julia Ripatti from Aalto University and Bo Zhao, present a novel quantum approach to portfolio optimization that incorporates higher-order statistical moments, such as skewness and kurtosis, to provide a more detailed understanding of potential investment returns. This work represents a significant step forward, as previous quantum formulations have largely focused on simpler models, and the inclusion of these higher-order moments traditionally poses a substantial computational challenge for classical algorithms. The team’s results demonstrate that their quantum method often identifies superior portfolio allocations compared to established classical techniques, suggesting a promising pathway for tackling computationally demanding financial problems on future quantum hardware.

Portfolio optimization incorporating these higher-order moments has received attention within classical approaches, but remains relatively unexplored in quantum formulations. Within quantum optimization, the inclusion of higher-order moments generates corresponding higher-order terms in the cost Hamiltonian, naturally leading to a higher-order unconstrained binary optimization (HUBO) problem suitable for a parametrized quantum circuit. The research employs realistic integer variable encoding to address this complex optimization challenge.

Quantum Finance and Portfolio Optimisation

This extensive list of references details research related to quantum computing, optimization, finance, and portfolio management, highlighting key themes and potential areas of research at the intersection of these fields. The collection centers around quantum computing and optimization, financial portfolio optimization, and higher-order optimization techniques, with a significant portion focusing on using quantum algorithms to solve optimization problems, particularly those involving higher-order terms. A large section deals with applying optimization techniques to build and manage investment portfolios, extending traditional methods to include skewness and kurtosis for better risk and return modelling. The repeated mention of higher-order problems suggests a focus on tackling complex optimization landscapes that are difficult for traditional methods.

The bibliography also demonstrates an interest in benchmarking quantum algorithms against classical algorithms, and in practical implementation using Python libraries. Potential research directions include developing quantum algorithms for higher-order optimization, benchmarking quantum versus classical algorithms on real-world financial problems, and portfolio optimization with higher moments. Further research could also focus on risk management with quantum computing, developing hybrid quantum-classical algorithms, and exploring new quantum algorithms for optimization tasks.

Higher-Order Portfolio Optimization with Quantum Computing

Scientists have achieved a significant breakthrough in portfolio optimization by developing the first quantum formulation capable of handling higher-order moments, specifically skewness and kurtosis. This advancement addresses a limitation in existing quantum formulations and expands the potential for more accurate risk assessment and improved investment strategies. The team’s approach formulates a higher-order unconstrained binary optimization (HUBO) problem naturally suited to a parametrized quantum circuit, incorporating realistic integer variable encoding and a capital-based budget constraint to mirror real-world financial markets. By employing an integer programming-based discretization method, the team effectively bridges the gap between continuous optimization models and the discrete nature of asset quantities and prices.

Extensive experimental evaluation, encompassing 100 portfolio optimization problems, demonstrates that solutions derived from the HUBO formulation consistently yield better portfolio allocations compared to classical baseline approaches. This result is particularly promising given the inherent computational complexity of portfolio optimization with higher-order moments, which poses a significant challenge for classical computers. Furthermore, the experiments confirm the effectiveness of incorporating higher-order terms into this practically relevant problem, showcasing the potential of quantum computing to tackle complex financial modeling tasks. The team’s method addresses limitations of continuous variable models by directly incorporating discrete variables, leading to more practical and accurate solutions that account for minimum purchase sizes and indivisible assets. This breakthrough delivers a powerful new tool for financial professionals seeking to optimize portfolios, manage risk, and achieve superior investment outcomes.

Higher-Order Moments Improve Quantum Portfolio Optimisation

This research presents a novel quantum approach to portfolio optimization, extending existing methods to incorporate higher-order statistical moments, specifically, skewness and kurtosis. By including these moments, the problem transforms into a higher-order unconstrained binary optimization (HUBO) problem, naturally suited to quantum circuit implementation. The team successfully implemented realistic constraints, such as integer variable encoding and a capital-based budget, enhancing the practical relevance of the model. Extensive testing across 100 portfolio optimization problems demonstrates that solutions derived from the HUBO formulation frequently yield better portfolio allocations compared to a classical baseline using integer programming.

This result is particularly significant given the computational complexity of portfolio optimization with higher-order moments, suggesting a potential advantage for quantum computing in this domain. The authors acknowledge that further research is needed to explore the robustness and scalability of the approach. Future work will focus on investigating the performance of the model with larger and more complex portfolios, and exploring the potential for hybrid quantum-classical algorithms to further enhance its capabilities.