How Well Does a Rolling-Volatility Band Calibrate?

Volatility bands are among the most widely used objects on a price chart, yet the simplest question about any band — how often does the next close actually land inside it? — is rarely measured. We measure it for a simple, causal construction: a band built from the rolling mean and standard deviation of recent returns, projected from the prior close.

On the S&P 500 (1927–2024) the one-standard-deviation band contains the next close 71.20% of the time and stays between 68.7% and 73.7% in every calendar decade. Across forty instruments (indices, stocks, currencies, commodities, bonds, crypto) the mean is 71.65% (cross-asset SD 2.06pp), and the result survives out-of-sample tests, weekly and monthly bars, and a 2025–2026 holdout.

The small excess over the correct finite-sample benchmark (67.46%, not the textbook 68.27%) is consistent with heavy-tailed returns: a heavy-tailed GARCH model reproduces it and a Gaussian one does not. Scored by the same causal question, a standard price-space Bollinger band covers 82.64% against 94.00% here; the gap is the return-space construction, not the choice of variance estimator.

The band describes the size of typical next-bar moves, not their direction, and coverage falls at crisis onset (65.29% when the VIX exceeds 30).

Working paper. Not peer-reviewed. Comments welcome at hello@oisigma.com.