Parabolic SAR: the stop-and-reverse formula, step by step

1. 01

   Know the three numbers it carries.

   The SAR itself; the extreme point (EP), the highest high of a rising run or the lowest low of a falling one; and the acceleration factor (AF), which starts at the step, usually 0.02.

2. 02

   Move the SAR towards the extreme point.

   SAR = previous SAR + AF × (EP − previous SAR).

3. 03

   Keep it out of recent bars.

   In a rising run the SAR may not be above the lows of the two bars before; if it would be, it is held at the lower of them. In a falling run it may not be below the highs of the two bars before.

4. 04

   See whether the bar crossed it.

   In a rising run, a bar whose low is below the SAR reverses it. In a falling run, a bar whose high is above the SAR does.

5. 05

   If it did not, update.

   If the bar made a new extreme, EP becomes that price and AF grows by one step, up to the maximum, usually 0.2. Otherwise both stay as they are.

6. 06

   If it did, reverse.

   The SAR jumps to the extreme point of the run that has just ended. The new EP is the reversing bar’s low (or high), and AF goes back to the step.

Programs differ in how they start: there is no SAR for the first bar and no agreed rule for the first direction. This page begins at the second bar, rising if it closed at or above the first, with the SAR at the lower of the first two lows (or the higher of the two highs). On a reversal it uses the extreme of the ended run with the reversing bar included. The differences fade after the first reversal.

Six bars, written high / low: 10 / 9, then 11 / 10, then 12 / 11, then 13 / 11.5, then 13.5 / 12, then 12.5 / 11. The second bar closed above the first. Larger settings so it fits on a page: step 0.1, maximum 0.3.

1. Bar 2: rising. SAR = the lowest low so far = 9; EP = the highest high so far = 11; AF = 0.1
2. Bar 3: SAR = 9 + 0.1 × (11 − 9) = 9.2, but it may not be above the low of bar 1, so it is held at 9. The low, 11, is above it. New high 12: EP = 12, AF = 0.2
3. Bar 4: SAR = 9 + 0.2 × (12 − 9) = 9.6. The low, 11.5, is above it. New high 13: EP = 13, AF = 0.3
4. Bar 5: SAR = 9.6 + 0.3 × (13 − 9.6) = 10.62. The low, 12, is above it. New high 13.5: EP = 13.5; AF is already at its maximum, 0.3
5. Bar 6: SAR = 10.62 + 0.3 × (13.5 − 10.62) = 11.484. The low, 11, is below it: a reversal
6. The SAR jumps to the old extreme point, 13.5, and is now over the bars. EP = 11, the bar’s low; AF = 0.1 again

The dot gained 0.6, then 1.02, then 0.86 while the price climbed, and a single bar that dipped to 11 was enough to cross it. The reversal says the dot was touched. It does not say the rise is over.

The numbers in this example were chosen to be easy to add up. They are not prices of anything.

• The side the dots are on. Under the bars, the recent run has been upward; over them, downward. This is a description of the run so far.
• As a trailing level. The dot is used as a place for a stop that follows the price and never moves back. A stop is an instruction, not a promised price, and a gap can pass through it.
• The gap between dot and price. A wide gap early in a run narrows as the factor grows; a dot close to the price is crossed by an ordinary bar.
• The number of reversals. Many reversals in a short stretch show a market going sideways, where the method was not designed to work.

• It cannot stand aside. It is always under or over the price, so in a sideways market it reverses again and again, and every reversal looks like the others.
• It cannot say how far a run will go or when it will end. The dot follows; it does not anticipate.
• It cannot adapt to how lively a market is. The step and the maximum are fixed numbers, whatever the size of the bars.
• It cannot make a reversal mean a new trend. A reversal records one bar reaching one level.

• Treating each change of side as a signal to trade. Wilder’s own rule did, and he noted that it suits markets that trend. In a range it trades at every turn and pays the spread each time.
• Raising the step to make the dots hug the price. A tighter dot is crossed by smaller bars, so there are more reversals, not better ones.
• Reading a dot far from the price as safety. Its distance is a product of the formula, not of anything about the market.
• Forgetting that the dot for a bar is fixed before the bar begins. It is known in advance, which is useful, and it knows nothing of the bar, which is the limit.

What do 0.02 and 0.2 mean in parabolic SAR?

They are the step and the maximum of the acceleration factor. The factor starts at 0.02, so the dot first moves 2% of the way towards the extreme point each bar. Each new extreme adds another 0.02, up to 0.2, when the dot moves a fifth of the remaining distance each bar. They are the published defaults, kept by convention.

Does a parabolic SAR reversal mean the trend has changed?

It means one bar reached the dot. Sometimes a new run in the other direction follows; often the price carries on as before and the dots reverse again a few bars later. In a sideways market reversals are frequent and say little.

Why does the parabolic SAR speed up?

Because the acceleration factor grows by one step every time the run makes a new extreme. The idea in the design is that a level which trails a move should tighten as the move matures. The effect is that the longer and further a run goes, the closer the dot comes to the price.

• Trend
• Trailing Stop
• Stop Loss
• Whipsaw
• Range
• Indicator