One expected-range indicator has a published 97-year test: the Behavioral Transform Model's range was measured on S&P 500 daily closes from 1927 to 2024, and the result is in a working paper. The test is calibration, not a backtest. It counts how often the next close landed inside the range, and says nothing about trading profit.
It measured how often the next close landed inside the one-standard-deviation band across 24,248 daily S&P 500 closes: 71.20%, historically. Past behavior is not a guarantee of future results.
The yardstick matters. For a finite rolling window the correct benchmark is 67.46%, not the textbook 68.27%.
A backtest scores the profit of a trading rule, whereas calibration scores whether a stated range contained what happened next; the paper tests only the second.
That is why the result validates the range, not the profitability of any use of it. Whether any use delivers value after costs is an open question the calibration work does not address.
It stops at the S&P 500: the 97-year sample is S&P 500 daily only, and other instruments have shorter histories.
Coverage also fell to 65.29% when the VIX exceeded 30, because the range runs too narrow in the first days of a fast crisis. The outer band is slightly optimistic in the deep tails, and the working paper is not peer-reviewed.
Does a longer sample make the indicator more accurate?
No. A longer sample makes the measured containment rate more precise and exposes more market regimes. It does not make any later bar more predictable, and the band still describes size, not direction.
Can the 97-year result be checked independently?
The Proof page publishes the tables and the paper describes the procedure, so the same count can be run on any daily dataset. How to backtest a band indicator walks through the method.
Does the result apply to crypto or forex?
Not directly, since the 97 years are S&P 500 only. Other instruments were tested over their own, shorter histories, covered in Bitcoin versus stocks and forex expected ranges.
Read the full test in the working paper, inspect the tables on the Proof page, or run the Behavioral Transform Model on TradingView: start with the 30-day free trial.
Oisigma provides descriptive market analytics for educational use. It is not investment advice, does not predict prices, and does not provide buy or sell signals. Statistics referenced are historical and were measured in our working paper (not peer-reviewed); past behavior is not a guarantee of future results. Trading and investing involve substantial risk of loss, including the possible loss of all capital invested. Leveraged products (futures, options, margin) carry additional risk and can result in losses that exceed your initial investment. Bollinger Bands® is a registered trademark of John Bollinger; Oisigma is not affiliated with or endorsed by Mr. Bollinger. RiskMetrics® is a registered trademark of MSCI Inc.; Oisigma is not affiliated with or endorsed by MSCI Inc. Nothing in this article is a recommendation to use any particular strategy. Read the full Disclaimer →
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