Distributional Portfolio Optimization (DPO): A Unified Framework for Distributions over Weights, Returns, and Parameters

Battle Count: 67

Directly addresses portfolio optimization with practical calibration claims. The Bayesian credible-radius rule for Wasserstein DRO radius selection (calibration without validation) is operationally relevant for quantitative portfolio managers. The paper provides explicit conic programs (LP/SOCP) for Wasserstein-CVaR DRO, Dirichlet policy parameterizations for RL-based allocation, and distributional Bellman contraction for dynamic portfolio MDPs. However, the paper explicitly acknowledges that naive baselines (1/N, Black-Litterman, Ledoit-Wolf) outperform distributional methods on raw Sharpe at tested dimensions, limiting immediate practical dominance claims. The framework is more valuable as a unifying theoretical lens and calibration tool than as a direct alpha-generating strategy.

The theoretical framework requires measure-theoretic probability, optimal transport (Wasserstein geometry), convex duality, and distributional RL. Numerical implementations use standard conic solvers (SCS) for Wasserstein-CVaR programs (LP/SOCP), Monte Carlo for Bayesian predictive sampling, and standard RL parameterizations (C51, QR-DQN, IQN). The Gaussian-NIW conjugate model is tractable. However, the full DPO framework with general couplings, utility-tilted posteriors, and risk-shifted Bellman operators requires significant mathematical sophistication. The Dirichlet policy and hierarchical allocation components add further complexity. Computational scaling is manageable for K up to ~500 on commodity solvers.

Companion code files are referenced (pit_backtest.py, experiment1_w1mc.py, experiment2_drosensitivity.py, experiment5_calibration.py, bootstrap_netofcost.py, experiment_highdim.py) but no public GitHub repository URL is provided. DJIA data is publicly available. Synthetic DGPs are fully specified with parameters. Theoretical proofs are self-contained. However, the point-in-time CRSP/Compustat study is deferred to a companion paper, and some numerical details (solver tolerances, exact seeds) require the companion notebook.