无需跨资产收益协方差的投资组合风险界：来自语言模型表征的分布场

摘要

投资组合风险评估通常依赖于对跨资产收益协方差的可靠估计，而在短时期、高维度的面板数据中，这类估计难以获得。本文表明，企业层面的分布值特征反而能够提供投资组合风险的单边保证。在特征与系统性风险敞口之间以及敞口与收益之间的既有关联假设下，多企业Wasserstein-2离差可给出系统性投资组合方差的紧上界，并相应地给出标准化收益的界。加权成对松弛法产生一个在可检验条件下为凸的目标函数，且仅需边际波动率尺度，无需跨资产收益协方差。当企业特定松弛为零时，公共映射尺度会改变经认证的方差缩减幅度，但不会改变归一化配置，后者仅取决于观测到的信息几何。在2018—2022年的52家企业面板数据中，基于Qwen3-Embedding-8B新闻表示构建的配置在四种预先设定的封顶投资组合总体中位于样本内方差百分位数的0.69至1.33之间；等风险加权则位于21.1至28.6百分位数之间。相对于等风险加权的较低样本内方差排名，在所报告的冻结语言模型表示中同样成立。因此，该框架将分布值的企业信息转化为一致的风险界和一种可在无需跨资产收益协方差的情况下构建的可执行配置规则。

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.