# Wilder’s Parabolic SAR

Developed by Welles Wilder, creator of the RSI and DMI, the Parabolic SAR sets trailing price stops for long and short positions. Also referred to as the stop-and-reversal indicator (SAR stands for ‘stop and reversal’), Parabolic SAR is more popular for setting stops than for establishing direction or trend.

Wilder recommended establishing the trend first, and then trading with the Parabolic SAR in the direction of the trend. If the trend is up, buy when the indicator moves below the price. If the trend is down, sell when the indicator moves above the price.

## Calculation

To understand the mechanics of the system we must assume and accept that a previous trend has reversed by the triggering of an appropriate SAR point. Once this has occurred we are now in a trade.

The first SAR is the extreme point reached in the previous trend, for instance, if we’ve just gone long, the initial stop is the extreme low of the previous down trend shortly before we were signalled to go long; if we’ve just gone short then the initial stop is the extreme high of the previous up trend shortly before we were signalled to go short.

Once the trade has been opened and the initial SAR value established the SAR for each time period (week, day, hour or whatever time frame you’re working in) is calculated as follows:

For the new trend, the first SAR value is the extreme point (EP) reached in the previous trend. (i.e. the lowest low in a previous downtrend or the highest high in a previous uptrend).

To calculate the current SAW value:

SARt = SARt-1 + a(EP – SARt-1)

Where:

• SARt = the current SAR value
• SARt-1 = the previous events SAW value
• EP = the extreme point (the highets point reached during a developing uptrend, or the lowest price reached during a developing down trend)
• a = the acceleration factor, which usually starts at 0.02 for a new trend and rises by 0.02 only when each new EP is achieved (to a maximum of 0.2)

The SAR is never advanced into the previous periods range or the current periods range.

• If long, using daily data: Never move tomorrows applicable SAR above yesterdays or today’s low. If the calculated SAR is higher than either of these lows then use the lower low of these two days as the SAR and use this value for SAR calculation for the next day.
• If short, using daily data: Never move the SAR below the high of yesterday or today. If the calculated SAR is lower than either of these values then use the higher high of these as the SAR for the day and for the calculation for the following days SAR.

## Interpretation

The dotted lines below the price establish the trailing stop for a long position and the lines above establish the trailing stop for a short position. At the beginning of the move, the Parabolic SAR will provide a greater cushion between the price and the trailing stop. As the move gets underway, the distance between the price and the indicator will shrink, thus making for a tighter stop-low as the price moves in a favorable direction.

### Variables

There are two variables: the step and the maximum step.

Step

The higher the step is set, the more sensitive the indicator will be to price changes. If the step is set too high, the indicator will fluctuate above and below the price too often, making interpretation difficult.

Maximum Step

The maximum step controls the adjustment of the SAR as the price moves. The lower the maximum step is set, the further the trailing stop will be from the price. Wilder recommends setting the step at 0.02 and the maximum step at 0.2.

The chart below shows how the Parabolic SAR works well in directional trends, but loses money by being whipsawed in non-directional markets. The default settings that Wilder recommends diminishes distracting fluctuations, but does not make the indicator immune to these whipsaws. A proper interpretation of this indicator would suggest that a trader should close long positions when the price falls below the SAR and close short positions when the prices rises above the SAR.

The Parabolic SAR works best during strong trending periods, which Wilder himself estimates occur roughly 30% of the time. Therefore, the user may first want to determine if the market is trending by using other indicators such as Wilder’s ADX line.

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