Estimating the Chance of an ATR-Sized Price Move Over a Fixed Horizon

Summary

The Probability of ATR Index estimates the chance that price will move a chosen distance, expressed in ATR units, within a chosen number of bars. It combines ATR with a measure of recent price dispersion calculated from highs and lows, then maps the scaled distance through an approximation to the normal cumulative distribution. The chart plots the current estimate and a long-term average, with color changes indicating different probability ranges.

The author describes an earlier Taylor-series approximation to the error function and says a later revision replaced it with a simpler, more accurate formula. The document gives no out-of-sample tests, calibration study, or evidence that the displayed probabilities match realized frequencies. Its normal-distribution framing and use of recent volatility statistics may fail when returns are skewed, fat-tailed, or changing regimes. Suggested uses include judging stop-distance risk and assessing whether an options position may remain within a desired price range; these are applications to investigate, not validated trading rules.

Key ideas

• The indicator estimates the probability of an ATR-scaled move over a selected bar horizon.
• Its inputs combine ATR, recent high-low price dispersion, target distance, and time horizon.
• A normal-distribution approximation converts the scaled distance into a probability estimate.
• The chart compares the current estimate with a long-term average and uses colors to show levels.
• The document offers no empirical calibration evidence, so the estimates should not be treated as proven frequencies.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.