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TAI - Parabolic Stop and Reversal (PSAR)


Name, Sometimes Called:

Parabolic Stop and Reversal
Sometimes called Parabolic SAR, P-SAR, or PSAR.

Brief Description:

The Parabolic Stop and Reversal is a price and time trending indicator that is more often used to set exit points, but can also be used to detect new entry points for both long and short positions.

Definitions, Formulas:

Unlike most indicators PSAR is not a continuous line. It is composed of line segments (or a series of dots) alternating above the price line (shown in red in the graph below) and below the price line (shown in green in the graph below). The dotted lines above the price line indicate the trailing stop for a short position. The dotted lines below the price establish the trailing stop for a long position.

Getting Started
To compute the PSAR we need to know the initial trend direction before we can determine the appropriate stop and (maybe) reverse points. Examine the first two trading periods and note the closing prices.

If Price(Close, Period 1) >= Price (Close, Period 2)
          Then we have a declining price, trend down, hence a short position

If Price(Close, Period 2) > Price (Close, Period 1)
          Then we have a rising price, trend up, hence a long position

This is a bit different that what Wilder proposed for trend determination, but works well in automated computation. Once we have a trend, we need the first stop and reverse price. For the first SAR price we use the extreme price (see below) for the two trading periods above.

If initial trend is up,
          then the first EP is the lowest price
          (if we’re going up pick the low)

If initial trend is down,
          then the first EP is the highest price
          (if we’re going down pick the high)

Having established the first point we can compute the subsequent points.

PSAR(Today) =
      PSAR(Yesterday) + A(Today) * ( EP(Today) - PSAR(Yesterday) )


PSAR(Today) is the stop and reverse point for today.
PSAR(Yesterday) was yesterday’s stop and reverse point.
EP is the extreme price for today (see Extreme Price below)
A is the acceleration factor for today (see Acceleration Factor below)

Trading Period
A trading period (sometimes referred to as position duration) is the whole time you are long or short. So if you are long (looking for a price rise) from the 2nd to the 20th then the EP is the highest (extreme) intraday price for the 2nd to the 20th.

If you are short (looking for a price decline) from the 2nd to the 20th then the EP is the lowest (extreme) intraday price for the 2nd to the 20th.

The Acceleration Factors
Three parameters for acceleration affect the shape, slope and speed of the SAR. These parameters are the starting acceleration factor, the acceleration factor increment that can change when a new price high or low is made, and the maximum acceleration factor. Whenever we begin a new trading period the acceleration factor is set to the initial value. We use the following:

Acceleration factors

Initial .02
Increment .04
Maximum .22

The larger increment is more responsive than Wilder’s original value of .02 and the larger maximum (Wilder had .20) allows for a slightly expanded range.

The Extreme Price
The EP concept allows for expected market corrections without triggering a stop-and-reverse. Even though the market is correcting and the PSAR price comes closer and closer to the price during a correction, it takes more than a trivial price move to trigger the stop-and-reverse.

So when we are in an up trend (green, PSAR below price) the EP rises, but never declines. When we are in a down trend (red, PSAR above price) the EP declines, but never rises. PSAR shows arcs, never a peak or a dip. The angle changes (steeper or less steep), but never a change in direction (always headed higher or always headed lower).

When a new extreme price is set during a trading period the acceleration factor is increased. If the trend is up (PSAR green, the position long) the acceleration factor is increased with every new intraday high. If the trend is down (PSAR red, the position short) the acceleration factor increases for every new intraday low. If there are no new highs or new lows (ie the extreme price does not change) then the acceleration factor does not change. The acceleration factor is never increased past the maximum under any circumstances.

A Stop-And-Reverse Triggered
Whenever the stop-and-reverse occurs (ie PSAR x- PRICE or PSAR x+ PRICE) the new PSAR point becomes the extreme price from the immediately previous trading period. So when going from long (green) to short (red) the first red point above the price graph would be the highest (extreme) point during the immediately previous long (green) trading period. When there is a crossover (ie green PSAR below to red PSAR above or reverse) then acceleration factor is reset to the initial value. As shown above, once the first PSAR point in a trading period is known, subsequent points can be computed.

Positive Development Calculation:

If PSAR were a continuous line, when PSAR crosses UNDER the price line THAT is the positive development ie PSAR crosses under the PRICE. So, when PSAR starts a new line segment under the price line, that is the positive development we want to report.

For the Parabolic Stop And Reverse (PSAR) a new positive development (NPD) occurs when PSAR crosses under the Price. (PSAR x- PRICE)

PSAR is no longer positive when it crosses over Price. ( PSAR x+ PRICE)

If PSAR was a new positive development yesterday (or previously) , and is still positive today, then PSAR becomes a cumulative positive development (CPD).


In his book, New Concepts in Technical Trading Systems, J. Welles Wilder introduced the Parabolic SAR which is used to set trailing price stops for long or short positions. He also created the Relative Strength Index (RSI) and Directional Movement Index (DMI) which lead to the Average Directional Movement Index (ADX). Although Parabolic SAR is most often used setting stops it can also reports the reverse from short stop to long stop, or long stops to short stops. This can be used to indicate new entry points.

Wilder recommended first establishing the trend, then using PSAR to trade in the trend direction. Remember, dotted lines above the price line indicate the trailing stop for a short position. Dotted lines below the price establish the trailing stop for a long position

Below is PSAR in action. Remember, we wouldn’t know about the PSAR until after the close. So the earliest purchase date would be 11/12/2005. There was a drop on 11/16, but PSAR stayed green until 12/6/2005.

Chart Graphic showing PSAR


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