How can we measure portfolio risk without knowing the covariances between assets?

Imagine having to pick stocks for a portfolio but only a few observations and many assets: estimating how each pair moves together becomes nearly impossible. A new approach shows that we do not need those covariances to obtain a safe upper bound on portfolio risk. We start with firm‑level characteristics turned into distributions of values via language‑model representations (such as Qwen3‑Embedding‑8B). These distributions capture how sensitive each stock is to common market factors. Measuring the Wasserstein‑2 dispersion between the firms’ distributions yields a precise upper bound on the systematic variance of the portfolio—the part of risk tied to the global market. The resulting optimization is convex under a simple checkable condition and needs only the marginal volatility scales of each asset, not pairwise covariances. If we add no firm‑specific slack, the common‑map scale changes the absolute certified variance reduction but not the normalized allocation, which depends solely on the observed information geometry. In a 52‑firm panel from 2018‑2022, a portfolio built from Qwen3‑Embedding‑8B news representations landed between the 0.69th and 1.33rd in‑sample variance percentiles across four prespecified capped populations, while equal risk weighting fell between the 21.1st and 28.6th percentiles. The findings demonstrate that distribution‑valued firm information can be turned into a coherent risk bound and an implementable allocation rule without estimating cross‑asset return covariances.

The proposed method relies on a distributional representation of each firm’s characteristics, obtained for instance from text‑news embeddings using models such as Qwen3‑Embedding‑8B. Each embedding is interpreted as a probability measure over the feature space; the Wasserstein‑2 distance between two such measures quantifies how much the distributions differ in location and shape, providing a metric sensitive to both means and variability. Assuming a linear link from distributional characteristics to systematic exposures (betas) and from exposures to returns, the systematic variance of a portfolio can be bounded by the maximum Wasserstein‑2 dispersion among the firms’ distributions weighted by the portfolio allocations. This yields a min‑max optimization problem whose objective is the maximal admissible systematic variance; under the assumption that the map from characteristics to exposures is affine and that factor covariance is known, the objective becomes a convex function of portfolio weights when the marginal‑volatility scale matrix satisfies a verifiable diagonal‑dominance condition. The solution provides weights that depend only on the geometry of the firms’ characteristic distributions (Fisher information) and not on pairwise return covariances, thus avoiding the need to estimate a full covariance matrix, which is often poorly conditioned in short, high‑dimensional panels. In the empirical exercise, news‑based representations were built from a corpus of financial articles spanning 2018‑2022, and the resulting allocations were compared against traditional equal‑risk and minimum‑variance benchmarks. The distribution‑based portfolio exhibited markedly lower systematic variance, landing in the low percentiles of the in‑sample distribution, whereas equal‑risk remained substantially higher. These findings confirm that firm‑level distributional information, readily available from language models, can substitute direct return‑covariance estimation in the construction of robust portfolios.