Volatility scaling cut Brier loss by 3.9% for Nasdaq Composite daily log returns at or below -2% in a 2018–2025 vintage test

We tested whether a fixed volatility scale improved daily loss probabilities for the Nasdaq Composite. Each forecast used ALFRED records available two calendar days before the target date. The final 2018–2025 test had 1,934 sessions and 153 log returns at or below -2%. Filtered historical simulation reduced mean Brier loss from 0.073592 to 0.070711 against a rolling 1,260-return empirical distribution. The relative reduction was 3.91%, with a paired stationary-bootstrap 95% interval of 1.18% to 6.39%. The gain remained positive in fixed checks with different decay factors, windows, block lengths, and without 2020. A direct comparison with a normal volatility model remained uncertain. The volatility scale left all zero-threshold probabilities unchanged. Positive scaling with no location change proves this identity for the same return window. A fixed freshness rule excluded 78 sessions during a source outage in 2023–2024. This is a historical forecast test for one index and horizon. It does not establish future calibration, return-direction skill, or a net trading gain. The package preserves code, source requests and hashes, the local plan, all forecasts, exclusions, scores, uncertainty draws, figures, and independent checks. Raw provider prices are excluded and remain under their original terms.

Nasdaq Composite · point-in-time data · filtered historical simulation · probability forecasts · Brier score · volatility · negative findings