Non-Convex Portfolio Optimization via Energy-Based Models: A Comparative Analysis Using the Thermodynamic HypergRaphical Model Library (THRML) for Index Tracking

Battle Count: 57

Directly addresses cardinality-constrained portfolio optimization and index tracking, core problems in quantitative finance. Demonstrates statistically significant outperformance (p<0.0001) over five established baselines. Achieves 4.31% tracking error with 128.63% total return vs 79.61% index. The probabilistic inference paradigm offers natural regularization against overfitting, a critical concern in quantitative portfolio management. Regime-adaptive coupling based on VIX provides practical market-awareness. However, the approach is primarily for index tracking/enhanced index rather than active trading strategies, and the 3-year backtest period limits confidence in robustness.

Requires proficiency in JAX, GPU programming, statistical mechanics (Ising models, Boltzmann distributions), and probabilistic graphical models. The THRML library abstracts much of the sampling infrastructure, but understanding block Gibbs sampling, simulated annealing schedules, and energy-based model formulation is essential. The bias/coupling computation pipeline is well-defined but requires careful parameter tuning. Sector-aware post-processing adds implementation complexity. GPU hardware (NVIDIA RTX series) needed for practical runtimes. The mathematical formulation (mapping portfolio selection to Ising Hamiltonian) requires interdisciplinary knowledge spanning physics and finance.

Detailed algorithm pseudocode (Algorithm 1), comprehensive parameter tables (Tables I, II, III), and explicit mathematical formulations are provided. However, code is only 'available upon request' rather than publicly hosted. THRML library is open-source (docs.thrml.ai). Data sourced from Yahoo Finance (publicly available). Walk-forward methodology clearly described. Reproducibility limited by lack of direct code access and specific universe selection criteria beyond 'top 100 by market cap from S&P 500'.