Portfolio Risk Bounds without Cross-Asset Return Covariances: Distributional Fields from Language-Model Representations
Marcus Gawronsky, Chun-Sung Huang
q-fin.ST
2026-08-30
Qwen3 news embeddings yield a Wasserstein-2 bound on portfolio variance. On 52 firms in 2018-2022, the news rule ranks at the 0.69th-1.33rd percentiles vs 21.1-28.6 for equal risk.
Mean-variance allocation wants a covariance matrix. For n names that object has n(n+1)/2 entries, and a short return history cannot identify it. Shrinkage and factor models stabilize the estimate, yet they still start from joint returns.
Gawronsky and Huang ask a prior question: how much portfolio risk can observable firm information rule out before any cross-asset covariance is estimated. Each firm is a cloud of news embeddings. Quadratic optimal transport compares those clouds. Under a maintained map from information to latent factor exposures, separation in text space certifies that latent risks cannot be perfectly aligned.
Firm i has an observed news law Ci (the distribution of article embeddings) and a latent systematic-exposure law Pi. The two objects live in different units; text is not exposure. Three maintained links carry the argument:
The observable pairwise floor is ℓij = [L⁻¹ W2(Ci,Cj) − τi − τj]₊. For normalized long-only weights q, the certificate is C(q) = (1/2) Σ qi qj ℓij². Theorem 1 then bounds systematic variance by the weighted marginal second moments minus C(q). A return bridge (standardized return = systematic piece plus residual, orthogonal across the two) yields Var(Rq) ≤ 1 − C(q). The 1 is the perfect-positive-dependence benchmark; C(q) is what the observed geometry certifies away.
With zero slack, L scales how much variance is deducted but does not change the normalized allocation: maximizing C(q) is the same as maximizing qᵀ W2² q. The empirical rule, called the news-only allocation, is that zero-slack program. It uses marginal scales at most, never cross-asset return covariances.
The panel is Nasdaq ticker-indexed news plus Yahoo adjusted-close returns, 1,207 aligned days from 2018-03-19 through 2022-12-30, 52 firms after a coverage screen. The primary encoder is frozen Qwen3-Embedding-8B at 4,096 dimensions with row-normalized vectors. Each firm is truncated to a balanced article cloud; pairwise W2 is balanced quadratic transport. Evaluation is in-sample standardized covariance. Four Dirichlet laws with single-name caps, 20,000 draws each, locate the allocation in the conventional-variance distribution.
Under the primary encoder, the news-only allocation sits between the 0.69th and 1.33rd variance percentiles across the four reference populations. Equal-risk weights sit between the 21.1st and 28.6th. The percentile is the share of reference portfolios whose variance is no higher; lower is better.
| Reference law | News-only | Equal risk |
| Uniform, 12.5% cap | 0.72% | 28.6% |
| Uniform, 15% cap | 0.69% | 28.4% |
| Effective-N matched, 15% cap | 0.89% | 25.4% |
| Concentrated, 15% cap | 1.33% | 21.1% |
Standardized variance is 0.357 for news-only, 0.390 for equal risk (8.3% lower), and 0.264 for the in-sample long-only GMV. Relative to GMV at 100, the two rules score 135.6 and 147.8. The largest weight is 12.1% (AZN), effective N is 23.65, and 38 of 52 names get positive weight. Of certificate credit, 87.1% is cross-sector. Expanding the article window year by year keeps effective N between 22.95 and 24.56; one-way turnover runs 13.2% to 26.8%.
Encoder swaps on the same returns: Qwen3-8B@1024 lands at the 0.82nd percentile, BGE-large-v1.5 at 0.80, both close to the primary 0.89. Truncating to 64 dimensions reaches 0.02. That cell is a stress test, not a preferred spec. Three matched EttaX Wikipedia vintages span 2.48 to 7.27 and fail the paper's own equivalence check.
When the covariance matrix is the fragile input, a frozen text geometry can produce a long-only rule that never touches cross-asset covariances, then be scored with ordinary variance. It does not recover covariance-free GMV: 8.3% below equal risk still leaves it 35.6% above the in-sample GMV.
At zero slack the normalized weights depend only on observed W2 geometry, so the carrier scale need not be calibrated to get a portfolio. Turning those weights into capital still needs marginal volatilities, the same first-order input as inverse-volatility, without the off-diagonal block.
The certificate is conditional on the antilipschitz carrier, slack, a coherent joint exposure law, and the return bridge. Text does not identify that transmission. The 52 names are a coverage-screened survivor panel, not a historical index universe. Geometry and returns share 2018–2022, so the percentile is in-sample; the expanding-cutoff diagnostic changes the corpus, not the return window, and is not an out-of-sample test. The empirical exercise uses unit-scale assets; the raw-capital objective still contains A(x)², and that gap is unquantified. The four Dirichlet-capped laws are design choices. Cap-weighted or factor-tilted draws could rank the same allocation differently.