P vs NP Problem in Portfolio Optimization: Integrating the Markowitz –CAPM Framework with Cardinality Constraints and Black –Scholes Derivative Pricing

Battle Count: 50

The paper is highly relevant to quantitative trading in terms of portfolio construction methodology, cardinality-constrained optimization (reflecting real-world position limits), and the integration of derivative overlays. However, it uses model-implied (CAPM) returns rather than realized returns, focuses on industry-level portfolios rather than individual securities, and does not address execution, market microstructure, or dynamic rebalancing. The computational complexity framing and heuristic evaluation protocols are directly applicable to practical portfolio management systems.

The core MIQP formulation is standard, but the full pipeline requires: (1) CAPM calibration from external data, (2) single-index covariance construction with PSD validation, (3) implementation of three distinct heuristic algorithms (greedy, Monte Carlo, GA with repair operators), (4) continuous re-optimization via QP, (5) Black-Scholes pricing and delta-based linearization, (6) comprehensive diagnostics (eigenvalue checks, correlation heatmaps, convergence curves), and (7) multi-seed reproducibility infrastructure. The paper provides detailed algorithmic specifications but no code repository.

The paper explicitly emphasizes reproducibility as a core design principle: random-seed logging (10 seeds), distributional reporting (median/IQR/quantiles), full Σ and ρ matrices provided as supplementary CSV/Excel, explicit units conventions, PSD validation gates, provenance labeling for every table/figure, and a complete input table with stable industry IDs. The methodology section includes a dedicated reproducibility checklist. All computations are labeled as 'Author's calculations' with exact inputs and algorithm parameters disclosed.