Direct answer: Parabolic SAR in one worked example
Parabolic SAR (often written “Parabolic SAR”) is a technical indicator that creates a sequence of SAR values that are plotted as dots above or below price. Those dots move toward the price as the trend continues, and a flip happens when price crosses the SAR level.
A worked numerical example below shows one specific set of assumptions and calculations. Because indicator outputs depend on the chosen parameters and on the assumed starting trend, you can reproduce the math exactly and also see how sensitive results are to those assumptions.
Mechanism or definition: what Parabolic SAR computes
Parabolic SAR is based on these core ideas:
- SAR level: the next SAR value that will be plotted for the next period.
- Extreme Point (EP): the most extreme price reached so far in the current trend direction (highest high in an uptrend, lowest low in a downtrend).
- Acceleration Factor (AF): a multiplier that increases when a new EP is reached. It controls how quickly the SAR “catches up” to price.
Common parameter names (the indicator can be implemented with variations, but the underlying concept is similar) are:
- AF start (AF₀): the initial acceleration factor.
- AF step: the amount AF increases when EP updates.
- AF max (AFmax): an upper bound so AF does not grow without limit.
Sign convention (above/below price): In a typical implementation, when the current trend is an uptrend, dots are plotted below price; when it is a downtrend, dots are plotted above price. The direction flips when price crosses the SAR.
Evidence or example: step-by-step numerical scenario
Assumptions (state once, then use consistently)
This worked example assumes the following for the indicator logic:
- We start in an uptrend at period 1.
- The SAR value at the end of period 1 is SAR₁ = 9.00.
- The initial Extreme Point is the highest high seen so far, EP₁ = 11.00.
- AF start AF₀ = 0.02.
- AF step = 0.02.
- AF max = 0.20.
- We compute SAR for subsequent periods using the standard trend-continuation form:
- For an uptrend: SARₙ₊₁ = SARₙ + AFₙ × (EPₙ − SARₙ)
- We update EP to the highest high when a new high occurs, and we update AF to min(AFmax, AF + AF step) when EP updates.
- We flip the trend only if the new SAR would be above the next period’s low (a typical crossing condition used in many descriptions). If a flip occurs, the SAR formula is recalculated for the new trend with new starting values. (This example will show at least one non-flip continuation step and then a flip event.)
Price data (no live data): consider five consecutive periods with highs and lows:
- Period 1: high = 10.80, low = 9.50
- Period 2: high = 11.20, low = 10.20
- Period 3: high = 11.30, low = 10.70
- Period 4: high = 11.10, low = 10.40
- Period 5: high = 10.90, low = 9.60
Calculations
From Period 1 to Period 2 (uptrend continuation)
- Given: SAR₁ = 9.00, EP₁ = 11.00, AF₁ = 0.02
- Compute SAR₂:
- SAR₂ = 9.00 + 0.02 × (11.00 − 9.00)
- SAR₂ = 9.00 + 0.02 × 2.00 = 9.04
- Check EP update using Period 2 high:
- Period 2 high = 11.20, which is greater than EP₁ = 11.00, so EP updates to EP₂ = 11.20
- AF updates because EP updated: AF₂ = 0.02 + 0.02 = 0.04
No flip check is triggered by this step in this example description; SAR₂ (9.04) remains below price lows around this region.
From Period 2 to Period 3 (uptrend continuation)
- Given: SAR₂ = 9.04, EP₂ = 11.20, AF₂ = 0.04
- Compute SAR₃:
- SAR₃ = 9.04 + 0.04 × (11.20 − 9.04)
- SAR₃ = 9.04 + 0.04 × 2.16 = 9.04 + 0.0864 = 9.1264
- EP update using Period 3 high:
- Period 3 high = 11.30 > 11.20, so EP₃ = 11.30
- AF increases: AF₃ = 0.04 + 0.02 = 0.06
From Period 3 to Period 4 (possible reduced EP growth)
- Given: SAR₃ ≈ 9. 1264, EP₃ = 11. 30, AF₃ = 0. 06
- Compute SAR₄:
- SAR₄ = 9. 1264 + 0. 06 × (11. 30 − 9. 1264)
- Difference = 2. 1736
- SAR₄ = 9. 1264 + 0. 06 × 2.