Measuring volatility with LLMs: Implications for covariance structure and portfolio construction

This study investigates whether volatility estimates generated by large language models (LLMs) improve portfolio construction. Using the LLMTime framework, we produce zero-shot volatility forecasts from return time series and incorporate them into mean-variance optimization. We find that LLM-based volatility estimates contain economically meaningful signals and lead to superior out-of-sample portfolio performance compared to portfolios constructed solely from historical volatility estimates. To understand the source of this improvement, we examine the spectral properties of the resulting covariance matrices. Covariances constructed from LLM estimates exhibit a higher largest-eigenvalue share and lower effective rank than historical covariance estimates, indicating a more concentrated and lower-dimensional risk structure.