Good portfolios from bad forecasts: The anatomy of LLM volatility estimates

Portfolios built from large-language-model (LLM) volatility forecasts have been reported to beat portfolios built from historical volatility, a puzzling result if the forecasts themselves are poor. We evaluate the forecasts and explain the puzzle. Across more than thirty LLMs, from 3-billion-parameter open models to frontier systems, none significantly beats a log-HAR benchmark at forecasting next-day realized variance for 30 assets, and the verdict survives every sub-period, prompt design, history length, and query protocol we try. Dissecting five models mechanically, we find that capability buys calibration and responsiveness but not superiority: small open models are miscalibrated in model-specific directions and blind to volatility dynamics, while frontier models remove both problems yet only match the benchmark. The reported portfolio gains are instead covariance geometry. The returns-sampling estimator inflates cross-sectional dispersion, concentrating the covariance into a standing equity tilt that pays in a rising market. The tilt is statistically insignificant, concentrated in one half-year, and gone by fifteen basis points of trading costs.