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

Portfolio Risk Bounds without Cross-Asset Return Covariances. Distributional Fields from Language-Model Representations. By Marcus Gawronsky and one other, from the University of Cape Town. Published on the thirtieth of August. No code repository is linked to it.

Assessing the risk of a portfolio ordinarily depends on good estimates of how the returns of different assets move together: the cross-asset return covariances. Those are hard to estimate when the history is short and the number of assets is large. This work asks whether something else can stand in. Its candidate is a characteristic of each firm that is not a single number but a whole distribution, and its aim is narrower than a full risk estimate. It wants a one-sided certificate: a guaranteed ceiling on risk.

The main result is a bound. Under maintained links, from characteristics to systematic exposures and from exposures to returns, the dispersion of the firms' distributions measured across many firms in Wasserstein-2 distance yields a sharp upper bound on systematic portfolio variance. A corresponding bound holds for standardized returns.

To make the bound usable, the authors apply a weighted pairwise relaxation. That produces an objective that is convex under a condition which can be checked, and it needs only the volatility scale of each asset on its own. No cross-asset return covariances enter. One more property follows when firm-specific slack is zero. The scale of the common map then changes how much variance reduction is certified, but not the normalized allocation. The allocation depends only on the observed information geometry, which is to say on what the data shows, and not on the scale assumed for that map.

The empirical illustration uses a panel of fifty-two firms from two thousand eighteen to two thousand twenty-two. The firm distributions come from news representations produced by Qwen3-Embedding-8B. Compared against four prespecified populations of capped portfolios, the resulting allocation sits between the zero point six nine and the one point three three percentile of in-sample variance. Equal risk weighting, by contrast, sits between the twenty-one point one and the twenty-eight point six percentile. That lower in-sample variance ranking against equal risk also shows up across the other frozen language-model representations reported.

Everything rests on the maintained links. The bound holds if characteristics map to systematic exposures and exposures map to returns as assumed. It bounds systematic variance, not total risk, and it is one-sided. Convexity needs the checkable condition to hold. The empirical rankings are in-sample, on one panel of fifty-two firms.

The result reframes what a risk model needs as input. Instead of a matrix of return comovements that is hard to estimate, distribution-valued information about firms is turned into a coherent risk bound and an allocation rule that can actually be implemented, built without cross-asset return covariances at all.