Portfolio Risk Bounds without Cross-Asset Return Covariances: Distributional Fields from Language-Model Representations
Summary
A framework using distribution-valued firm characteristics and language-model embeddings provides portfolio risk bounds without cross-asset covariance estimates, demonstrating low-variance allocations with Qwen3-Embedding-8B representations.
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Paper page - Portfolio Risk Bounds without Cross-Asset Return Covariances: Distributional Fields from Language-Model Representations
Source: https://huggingface.co/papers/2608.29692
Abstract
A framework using distribution-valued firm characteristics and embedding-based representations provides computable upper bounds on portfolio variance and yields low-variance allocations without cross-asset covariance estimates.
Portfolio risk assessment ordinarily relies on reliable estimates of cross-asset return covariances, which are difficult to obtain in short, high-dimensional panels. We show that firm-leveldistribution-valued characteristicscan instead provide one-sided certificates of portfolio risk. Under maintained links from characteristics to systematic exposures and from exposures to returns, multi-firm Wasserstein-2 dispersion yields a sharp upper bound on systematic portfolio variance and a corresponding bound for standardized returns. A weighted pairwise relaxation produces an objective that is convex under a checkable condition and requires marginal volatility scales but no cross-asset return covariances. With zero firm-specific slack, the common-map scale changes the certified variance reduction but not the normalized allocation, which depends only on observed information geometry. In a 52-firm panel from 2018-2022, an allocation constructed fromQwen3-Embedding-8Bnews representations lies between the 0.69th and 1.33rd in-sample variance percentiles across four prespecified capped portfolio populations; equal risk weighting lies between the 21.1st and 28.6th percentiles. The lower in-sample variance ranking relative to equal risk also appears across the reportedfrozen language-model representations. The framework therefore distribution-valued firm information into a coherent risk bound and an implementable allocation rule constructed without cross-asset return covariances.
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