Name, Sometimes Called:
Parabolic Stop and Reversal
Sometimes called Parabolic SAR, P-SAR, or PSAR.
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
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.
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
If Price(Close, Period 1) >= Price (Close, Period 2)
we have a declining price, trend down, hence a short position
If Price(Close, Period 2) > Price (Close, Period 1)
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,
the first EP is the lowest price
we’re going up pick the low)
If initial trend is down,
the first EP is the highest price
we’re going down pick the high)
Having established the first point we can compute the subsequent
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
A is the acceleration factor for today (see Acceleration
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:
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
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
occurs when PSAR crosses under the Price. (PSAR x- PRICE)
PSAR is no longer positive when it crosses over Price. ( PSAR x+
If PSAR was a new positive development yesterday (or previously)
, and is still positive today, then PSAR becomes a cumulative positive
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