Discrete Markowitz Portfolio Optimization with Open-Source Classical and Quantum-Inspired Solvers: A Cross-Market Walk-Forward Study

Discrete Markowitz Portfolio Optimization with Open-Source Classical and Quantum-Inspired Solvers: A Cross-Market Walk-Forward Study

Avdoshin S.M. (NRU HSE, Moscow, Russia)
Patrushev K.A. (NRU HSE, Moscow, Russia)

Abstract

The cardinality-constrained Markowitz problem is NP-hard and traditionally solved with commercial MIQP solvers. Following the 2022 export restrictions that rendered both commercial MIQP software and cloud quantum platforms (IBM Quantum, D-Wave Leap) inaccessible from the Russian Federation, practitioners require open-source alternatives. This paper systematically compares three solver families for the discrete mean-variance problem: two open-source classical MIQP solvers (SCIP and ECOS_BB via CVXPY), and a quantum-inspired simulated annealing solver (D-Wave neal) operating on a binary-inclusion QUBO with a two-stage hybrid pipeline. All solvers share a unified problem instance. In Experiment A (synthetic scalability), the quantum-inspired SA becomes the fastest solver at N≥150 (7× faster than SCIP at N=200) but incurs an 11–13% optimality gap. In Experiment D (walk-forward backtest on S&P 500 and MOEX with realistic transaction costs), discrete optimization delivers +39–42 bps/year over the 1/N benchmark on S&P 500, but neal SA underperforms SCIP by 159 bps/year due to residual optimality gap and elevated turnover. On the non-stationary Russian market, all MVO strategies underperform 1/N by 100–229 bps/year, reproducing the DeMiguel-Garlappi-Uppal paradox. The study quantitatively characterizes the scalability–quality trade-off, decomposes the optimality gap into formulation, sampler, and penalty-calibration components, and identifies conditions under which the current neal-based binary-inclusion pipeline is insufficient for practical deployment.

Keywords

portfolio optimization; Markowitz; QUBO; simulated annealing; quantum-inspired algorithms; mixed-integer quadratic programming; walk-forward backtest; cardinality constraint; QAOA.

Edition

Proceedings of the Institute for System Programming, vol. 38, issue 4, part 2, 2026, pp. 245-256

ISSN 2220-6426 (Online), ISSN 2079-8156 (Print).

DOI: 10.15514/ISPRAS-2026-38(4)-29

For citation

Avdoshin S.M., Patrushev K.A. Discrete Markowitz Portfolio Optimization with Open-Source Classical and Quantum-Inspired Solvers: A Cross-Market Walk-Forward Study. Proceedings of the Institute for System Programming, vol. 38, issue 4, part 2, 2026, pp. 245-256 DOI: 10.15514/ISPRAS-2026-38(4)-29.

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