What is the Parabolic SAR? Definition, Formula, and Example
The Parabolic SAR (Stop and Reverse) is a trend-following indicator developed by J. Welles Wilder that plots dots above or below price to mark trailing stop levels and trend reversal points.
Plain-English Definition
The Parabolic SAR — short for "Stop and Reverse" — is a price-derived trend indicator that plots a single dot below price during uptrends and above price during downtrends. When price crosses the dot, the indicator "flips," reverses sides, and signals a new trend direction. J. Welles Wilder Jr. introduced the indicator in his 1978 book *New Concepts in Technical Trading Systems*, alongside RSI and Average True Range.
How the Parabolic SAR Is Calculated
Parabolic SAR uses a recursive formula updated each period:
SAR(t+1) = SAR(t) + AF × (EP − SAR(t))
Where:
- SAR(t) is the current period's SAR value.
- EP (Extreme Point) is the highest high reached during the current uptrend (or lowest low during a downtrend).
- AF (Acceleration Factor) starts at 0.02 and increments by 0.02 each time a new EP is registered, capped at 0.20. Wilder's defaults are universal.
Two constraints:
1. SAR cannot move into the prior two periods' price range (prevents premature flips on inside bars).
2. When price crosses SAR, the indicator flips: SAR for the new trend = the previous EP, AF resets to 0.02, and a new EP is established.
The "parabolic" name comes from the curve traced as AF accelerates — SAR converges on price along a parabolic arc, tightening the trailing stop as a trend matures.
Worked Example
Consider TSLA from January through March 2024. After the Jan 24, 2024 earnings gap-down, SAR flipped above price at $208. As TSLA declined to a Feb 22 low of $191.59, SAR ratcheted lower each session, with AF stepping from 0.02 to 0.16 over the 21-trading-day downtrend. On Feb 23, TSLA closed at $191.97 and SAR sat at $215.02. The Feb 26 rally to $200.50 still did not breach SAR. On Feb 28, TSLA traded $202.04, finally crossing SAR at $200.20 — the indicator flipped to $191.59 (the prior EP), AF reset to 0.02, and the new uptrend signal triggered. Traders who used SAR as a trailing stop closed shorts at $200.20, locking in $7.80 per share from the original $208 entry.
When Traders Use It
Parabolic SAR has two practical uses: (1) trailing stop placement — many trend-following systems use SAR mechanically as the stop level, since the acceleration factor naturally tightens the stop as trends extend, locking in more profit on mature moves; (2) entry/exit signals on flip — the dot-side change is a discrete buy-or-sell trigger requiring no interpretation. Wilder originally combined SAR with his Directional Movement Index (DMI/ADX) — SAR provides the entry, ADX confirms there is a trend strong enough to follow.
Limitations and Common Misconceptions
Parabolic SAR is built for trending markets; it whipsaws relentlessly in sideways action, generating dozens of false flips during chop. Wilder himself warned that SAR alone produces poor results unless paired with a trend-strength filter such as ADX > 25. The indicator is also lagging by construction — it cannot signal a reversal until price has already moved through the trailing level, meaning entries are always after the high or low. A common misconception is that the dots represent support or resistance; they are purely trailing stops derived from prior price extremes and have no bid/offer significance. Finally, the standard 0.02/0.20 settings were calibrated to 1970s commodity futures and are often suboptimal for modern equities, where higher acceleration factors (0.03–0.04 step) reduce false flips on intraday charts.