Portfolio Risk Bounds without Cross-Asset Return Covariances: Distributional Fields from Language-Model Representations

Battle Count: 78

Highly relevant to quantitative portfolio construction. The paper provides a novel framework for portfolio risk assessment that bypasses the covariance estimation problem in short/high-dimensional panels. The news-only allocation achieves near-first-percentile variance ranking across multiple reference populations without using cross-asset return covariances. Directly applicable to minimum-variance portfolio construction, diversification assessment, and robust portfolio choice. However, the in-sample nature, representation sensitivity, and maintained transmission assumptions limit immediate practical deployment. The framework complements rather than replaces conventional covariance-based methods.

Moderate-to-high complexity. Requires: (1) article retrieval and preprocessing from news archives, (2) embedding model inference (Qwen3-Embedding-8B via API or local deployment), (3) balanced quadratic optimal transport computation for pairwise W2 distances, (4) construction of the W2 distance matrix, (5) solving a convex optimization problem for portfolio weights (under conditional negative definiteness check), (6) marginal volatility estimation for capital-weight implementation. The theoretical framework involves multi-marginal optimal transport, Wasserstein geometry, and coherent joint law constraints. The zero-slack standardized case simplifies to maximizing q^T W2^2 q over the simplex.

The paper provides detailed mathematical derivations, formal verification via Lean 4/mathlib v4.31.0, explicit data construction procedures (Nasdaq news archive, Yahoo Finance returns, Qwen3-Embedding-8B via OpenRouter API), and complete empirical design specifications. However, the article corpus construction, balanced-cloud rules, and specific API calls are not fully reproducible without access to the same data sources. The in-sample nature and specific 52-firm panel limit external reproducibility. No code repository is mentioned.