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