Practical Quantum Portfolio Optimization Under Discrete Lot Constraints with CVaR-Based Evaluation for the Taiwan Stock Market

Abstract

This paper proposes a CVaR-based quantum portfolio optimization framework designed to address discrete market constraints. Unlike traditional models that often assume continuous asset allocation or normal return distributions, the proposed approach utilizes Conditional Value-at-Risk (CVaR) as the objective function within the hybrid optimization loop of a gate-based Quantum Approximate Optimization Algorithm (QAOA) to better manage extreme tail risk in realistic financial portfolios. We formulate the portfolio selection and discrete constraints as a Knapsack-style Quadratic Unconstrained Binary Optimization (QUBO) model, explicitly incorporating the “one-lot” (1,000 shares) trading convention common in the Taiwan Stock Exchange (TWSE). Experimental results on small-scale TWSE instances indicate that the proposed framework achieves lower CVaR values than standard expectation-based QAOA, albeit with a moderate reduction in expected return. These findings provide preliminary evidence that quantum optimization can support risk-aware portfolio selection under discrete trading constraints.