Using Rolling Log-Return Z-Scores to Flag Unusual Market Moves

Summary

This article explains a Sigma Score indicator that standardizes a bar’s log return against the mean and standard deviation of a recent rolling window. The resulting z-score expresses how unusual the current return is relative to recent behavior. The indicator plots the score with a zero line and configurable upper and lower reference levels; the suggested default thresholds are plus and minus two.

The implementation notes explain lookback requirements, series indexing, recalculation of newly formed bars, and safeguards for invalid prices or near-zero volatility. Log returns are used because they add across time, while their standard deviation serves as a historical volatility measure. The article frames threshold crossings as anomaly or stress signals, not guaranteed trading entries or probability estimates. Its normal-distribution rule of thumb is limited because financial returns can have fat tails, and the indicator is presented without a trading-system backtest or evidence of predictive profitability.

Key ideas

• The indicator compares the latest log return with the rolling mean and standard deviation of prior returns.
• A z-score reports the move in standard-deviation units relative to its recent window.
• Thresholds around plus and minus two can highlight unusually large moves, subject to fat-tail risk.
• The calculation needs sufficient price history and guards against invalid prices and near-zero volatility.
• Anomaly readings alone do not demonstrate a profitable trading signal.

Tags

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