Diversifying Investments and Maximizing Sharpe Ratio: A Novel Quadratic Unconstrained Binary Optimization Formulation

The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic program...

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Veröffentlicht in:Quantum reports Jg. 6; H. 2; S. 244 - 262
Hauptverfasser: Mattesi, Mirko, Asproni, Luca, Mattia, Christian, Tufano, Simone, Ranieri, Giacomo, Caputo, Davide, Corbelletto, Davide
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Basel MDPI AG 01.06.2024
Schlagworte:
Boolean
Diversification
Linear programming
Maximization
Multiple objective analysis
Optimization
Optimization models
portfolio optimization
Quadratic programming
quantum annealing
Quantum computing
QUBO
Sharpe Ratio
Variables
ISSN:2624-960X, 2624-960X
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Zusammenfassung:The optimization of investment portfolios represents a pivotal task within the field of financial economics. Its objective is to identify asset combinations that meet specified criteria for return and risk. Traditionally, the maximization of the Sharpe Ratio, often achieved through quadratic programming, has constituted a popular approach for this purpose. However, real-world scenarios frequently necessitate more complex considerations, particularly in relation to portfolio diversification with a view to mitigating sector-specific risks and enhancing stability. The incorporation of diversification alongside the Sharpe Ratio into the optimization model creates a joint optimization task, which can be formulated as Quadratic Unconstrained Binary Optimization (QUBO) and addressed using quantum annealing or hybrid computing techniques. These techniques offer promising solutions. We present a novel QUBO formulation for this optimization, detailing its mathematical formulation and demonstrating its advantages over classical methods, particularly in handling diversification objectives. By leveraging available QUBO solvers and hybrid approaches, we explore the feasibility of handling large-scale problems while highlighting the importance of diversification in achieving robust portfolio performance. We finally elaborate on the results showing the trade-off between the observed values of the portfolio’s Sharpe Ratio and diversification, as a natural consequence of solving a multi-objective optimization problem.
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ISSN:2624-960X
2624-960X
DOI:10.3390/quantum6020018