無需跨資產報酬共變異數的投資組合風險界限：來自語言模型表徵的分布場

摘要

投資組合風險評估通常依賴於對跨資產報酬共變異數的可靠估計，而在短期的、高維度的面板資料中，這類估計難以取得。我們證明，公司層級的分配值特徵（distribution-valued characteristics）反而能提供投資組合風險的單側認證（one-sided certificates）。在維持從特徵到系統性曝險、以及從曝險到報酬的關聯性假設下，多家公司的瓦瑟斯坦-2 離散度（Wasserstein-2 dispersion）可產生系統性投資組合變異數的銳利上界，以及對應的標準化報酬界。加權成對鬆弛（weighted pairwise relaxation）方法可產生一個目標函數，其在可檢驗的條件下具凸性，且僅需邊際波動規模，而無需跨資產報酬共變異數。在公司特定寬鬆度（firm-specific slack）為零的情況下，共同映射尺度（common-map scale）會改變被認證的變異數縮減幅度，但不會改變正規化配置——後者僅取決於觀測到的資訊幾何。在 2018 至 2022 年間一個包含 52 家公司的面板中，基於 Qwen3-Embedding-8B 新聞表徵所建構的配置，在四個預先指定的設限投資組合群體中，其樣本內變異數百分位數介於第 0.69 與第 1.33 百分位之間；而等風險權重配置則介於第 21.1 與第 28.6 百分位之間。相對於等風險配置的較低樣本內變異數排名，在所報告的凍結語言模型表徵中亦同樣出現。因此，此一架構將分配值的公司資訊轉化為連貫的風險界，以及一套在無需跨資產報酬共變異數的情況下所建構的可執行配置規則。

English

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-level distribution-valued characteristics can 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 from Qwen3-Embedding-8B news 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 reported frozen 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.