Portfolio Optimization of 60 Stocks Using Classical and Quantum Algorithms (2008.08669v1)

Abstract: We continue to investigate the use of quantum computers for building an optimal portfolio out of a universe of 60 U.S. listed, liquid equities. Starting from historical market data, we apply our unique problem formulation on the D-Wave Systems Inc. D-Wave 2000Q (TM) quantum annealing system (hereafter called D-Wave) to find the optimal risk vs return portfolio. We approach this first classically, then using the D-Wave, to select efficient buy and hold portfolios. Our results show that practitioners can use either classical or quantum annealing methods to select attractive portfolios. This builds upon our prior work on optimization of 40 stocks.

• The paper demonstrates that quantum annealing and classical algorithms can both achieve efficient risk-return portfolios.
• The methodology leverages D-Wave’s 2,048-qubit system alongside genetic, simulated annealing, and Monte Carlo methods.
• Key findings reveal rapid quantum sampling and highlight scalability challenges due to hardware constraints.

Portfolio Optimization of 60 Stocks Using Classical and Quantum Algorithms: An Analytical Overview

The paper under review presents an investigation into leveraging quantum computational methods, particularly quantum annealing, alongside classical methodologies for optimizing a portfolio from a set of 60 U.S. listed equities. This analysis employs the D-Wave quantum annealer and compares its performance with several classical and hybrid approaches. The authors' objective is to determine the efficacy of quantum algorithms in finance, specifically in creating an optimal risk-return profile for portfolios using quantum resources.

The problem formulation not only retains elements from previous research focused on a subset of 40 stocks but also introduces new classical techniques, further calibrating and scaling up the quantum approach. Central to their methodology is the Chicago Quantum Net Score (CQNS) and the Chicago Quantum Ratio (CQR), which guide the portfolio selection by analyzing variance and covariance with market indices like the S&P 500.

Methodological Approach

The research employs various optimization methods:

1. Quantum Annealing via D-Wave: The quantum annealer's performance is benchmarked on a 2,048 qubit system implementing the Chimera topology. The paper highlights the complexities involved, such as managing coupling strengths, chain traversals, and affine transformations to maintain portfolio integrity across quantum reads.
2. Classical Algorithms: Five advanced classical techniques, including Genetic Algorithms, Simulated Annealing, and Monte Carlo sampling, are explored. These are run on conventional computational resources and serve to provide a comparative baseline for quantum methods.
3. Hybrid and Tabu Methods: Experimental use of the D-Wave’s Tabu sampler and hybrid algorithm solutions showcase attempts at integrating quantum and classical techniques, although these showed limitations compared to pure quantum or classical approaches.

Results and Analysis

Strong numerical results reported indicate that both quantum and classical strategies can identify efficient portfolios that are near or on the efficient frontier. Notably, the quantum annealer displayed rapid sampling times, averaging portfolio generation in milliseconds, which significantly outpaced many classical methods.

Key findings discuss the relative advantages of quantum algorithms in rapidly exploring vast combinatorial spaces for potential investment portfolios. However, they also underscore a challenge: the quantum annealer struggles with adequately large portfolios due to the quadratic function’s diminishing influence as the dimension of the problem increases (particularly with covariance shrinkage issues at higher asset counts).

Discussion on Scalability and Future Prospects

The scalability to portfolios beyond 60 assets is cautiously optimistic, acknowledging computational bottlenecks within quantum hardware, particularly qubit interconnectivity and stability. To surmount these, the authors suggest potential improvements in embedding strategies and QUBO (Quadratic Unconstrained Binary Optimization) formulations.

The theoretical implications suggest that quantum computing holds promising potential, especially as quantum hardware evolves to handle deeper and broader QUBO formulations. This anticipates more robust exploratory ventures into a greater number of assets, potentially aligning closer to real-world trading datasets.

Conclusion

The research successfully demonstrates the applicability of quantum methods in financial optimizations, matching them against classical strategies. While current hardware constraints limit their present utility to niche explorations or small asset universes, ongoing advancements in quantum technology could significantly alter the landscape of computational finance. As the next generation of quantum processors becomes more practical, deeper integration in portfolio management workflows may realize superior asset allocation strategies.

This paper is a substantive addition to the growing field exploring quantum finance, offering a thorough comparative analysis of current computational capabilities in optimizing stock portfolios. Future research directives could expand upon this foundation to explore additional financial models and quantum algorithms, fostering enhanced synergy between quantum computing and financial analytics.