# Parabolic Stop & Reverse System (Parabolic SAR)

##### Overview

Parabolic SAR is a trend following system constantly tailing the price action. It is a time series of stop-level points, portrayed on the chart in the form of dots, plotted below or above each price mark. A dot placed below the price is deemed to be a bullish signal while a dot placed above the prices is considered to be a bearish indicator. As prices trend higher, the system follows just below and as prices trend lower it follows from above. The aim, as with all trend following approaches, is to pinpoint when there is a higher-than-normal probability of a trend reversal.

Parabolic SAR, as the name suggests, is built to provide stop and reverse signals and it is often used by traders as a trailing price stops setter. Due to a built-in acceleration factor, the system starts out slower initially, allowing a trend to develop, and as the trend extends over time it accelerates based on the trends strength. The Parabolic SAR system is designed to be always in the market since whenever a position is closed out it is also reversed. Although the Parabolic SAR is used for both entering and managing positions, it is mainly used to set stops once in a position.

The SAR appears to be similar to a trendline following the underlying instrument price, but it has a decreasing lag since the distance between the SAR point and the current instrument price decreases with time due to the Acceleration Factor. As the Parabolic SAR begins to move faster (pursuing prices closely), if the price trend reverses and crosses the indicator, a stop & reverse signal is generated.

Parabolic SAR works superbly during trending markets but falters constantly, producing whipsaws during sideways consolidation and trendless markets.

##### Construction

The formula for calculating Parabolic SAR for the current period is calculated on the previous periods value, using an exponential smoothing formula based on the so called Extreme Prices (EP) high/low price (depending on whether the direction of the trend is up or down). A smoothing constant called the Accelerating Factor (AF) is used in the formula, with the aim of increasing the speed of the indicator whenever the trend is accelerated in order for the SAR to follow the prices curve more effectively.

##### SAR_{t} = SAR_{t-1} + * [EP_{t-1} - SAR_{t-1}]

Where: SAR_{t} - is the current value of Parabolic SAR

SAR_{t-1} is the previous value of Parabolic SAR

EP_{t-1} is the latest “Extreme Point”: The highest high of the current uptrend or the lowest low of the current downtrend.

AF_{t-1} is the Acceleration Factor: Starting at 0.02, AF increases by 0.02 each time the extreme point makes a new high/low. However, the AF can reach a maximum of 0.20, no matter how long the trend extends. In terms of moving average days, the AF begins at 99-Days and increases its speed to a maximum of a 9-Day moving average.

In calculating the current value of the Parabolic SAR there are two exceptions:

- In an Uptrend, the SAR can never be above the prior two period’s lows. In case the SAR is higher than one of those lows, use the lower of the two instead.
- In a Downtrend, the SAR can never be below the prior two period’s highs. In case the SAR is lower than one of those highs, use the higher of the two instead.

For calculating Parabolic SAR one must assume that we are already holding a position (long or short). Since we don’t know what position we are in at the start of the data, for our excel example on this page, we assume we are in a long trade and therefore for day one the trend is UP. A full guide to the calculation and construction of the Parabolic SAR system is provided in excel format for your better understanding.

Be warned though that due to the fact that the formula is applied according to whether the underlying instrument is in an uptrend or a downtrend as well as the presence of the two exceptions that we have seen here, there is a fair amount of conditional statements involved. Nevertheless, this example will help you test the sensitivity of the system to different AFs.

Parabolic Stop & Reverse system (SAR)

##### Interpretation & Trade Signals

Despite the complexity of its calculations, the interpretation of Parabolic SAR is fairly straight forward. The SAR dots follow the prices like a trailing stop, progressively approaching the prices curve, as long as the trend continues in its original direction.

If however the prices curve intersects the SAR series, the system gives a “stop and reverse” signal, suggesting that the current trend has ended and a new one is resuming in the opposite direction. Following this signal, the SAR series of dots that have up to now been following the trend (e.g. from below in an uptrend or from above in a downtrend), moves to the other side of the prices chart assuming the Extreme Price (EP) of the past three days (highest high in a downtrend or lowest low in an uptrend).

Parabolic SAR signals should always be confirmed with the use of other indicators. For example, a reversal of the dots from below the price to above is much more convincing when a moving average also confirms the change in trend and when the prevailing longer-term trend is down.

##### Example

Utilising the ADX indicator to confirm the existence of a trend, we put the Parabolic SAR system to the test producing both the entry and exit signalling for a short trade. The trading signals produced by the SAR are also confirmed by the use of a moving average.

Existence of trending conditions: ADX>25 and since DI^{-} > DI^{+} the market is in a downtrend.

Short Entry signal: A buy signal is produced when Parabolic SAR crosses above the prices chart. A two-day filter is used to eliminate whipsaws.

Change of trend warning: Moving average line crosses to bearish territory a couple of bars before the signal to short is given.

Long Exit signal: Parabolic SAR crosses below the prices chart for two consecutive days. Confirmation also provided by the moving average line that simultaneously crosses below the prices chart confirming the reversal in trend.

##### Tips and ideas

Ignore Parabolic SAR signals when the market is ranging. A simple way to identify if the market is indeed ranging is to observe whether the underlying instrument chart intersects with a moving average multiple times on a small prices range.

If you are using the Parabolic SAR for opening and exiting positions, it may be advisable to stop trading if you are whipsawed twice or more in a row. It is most probably a sign that there is no trend or that a consolidation phase is on. Re-activate your trading only once you observe a breakout from the consolidation zone.

##### Strengths/Weaknesses

The SAR value is today’s, not tomorrow’s, stop level and it is calculated based on yesterday’s data. The advantage is that the stop level can be calculated in advance of the trade execution or even the market opening.

A big plus of the Parabolic SAR indicator is the simplicity and ease of implementation into any strategy – entry/exit, warning or stop trigger.

A major advantage of Parabolic SAR is that it reduces the lag that is inevitably built-in in most trend-following systems. It succeeds in doing so by increasing the speed of the system whenever the trend accelerates, thus “locking-in” profits with considerable success in comparison to its competitors.

As described before, Parabolic SAR works very well during trending markets but fails to produce reliable signals during sideways markets. Since more two thirds of the time markets are known to be trendless, Parabolic SAR should only be used in combination with other indicators capable of determining market conditions.

The SAR system assumes that the trend changes every time a stop has been hit. Nevertheless even in highly trending markets your stops may be hit several times while the trend continues. That is, prices retrace and then resume the up-trend, leaving you out of the market. Changing the Accelerator and Max. Accel. Factor according to market volatility can improve the system but this remains a weakness of the Parabolic SAR.

##### Suggested Combinations for EA development

Compliment Parabolic SAR trading signals by using other indicators such as the stochastic indicator, moving average crossovers and candlestick patterns.

Use in combination with the ADX for trend direction detection.

Support/Resistance levels, retracement zones.

Basic trend analysis.

##### Use in FxPro Quant

Parabolic SAR can be found under the ‘Indicators’ group in our FxPro Quant menu. With FxPro Quant, we do not have to worry about the calculations and definitions behind the indicator. We just need to drag & drop the indicator in the main window and set the parameters we want to test.

##### Parameters

###### Symbol

Input: e.g. EurUsd, GbpYen | Default: Current

If left empty, the instrument symbol used in the relevant chart in MT4 will relate by default.

###### Time Frame

Input:1m,5m,15m,30m,1h | Default: Current

If set to current, the time frame used in the relevant chart in MT4 will relate by default.

###### Step

Input: number | Default: 0.02

The increase of the Acceleration Factor (AF) added each time a new Extreme Price (EP) is recorded used in the calculation of SAR (see excel spread sheet attached).

###### Maximum

Input: number | Default: 0.2

The maximum value the Acceleration Factor (AF) can take, as used in the calculation of SAR (see excel spread sheet attached).

###### Shift Back

Input: Number | Default: “0”

Selects the data used for calculating the Indicator (Number of periods back or forth).

Please note that “Bands Shift”=1 means shifting the Bands one period backwards (in the past).

##### References

Welles Wilder - New Concepts in Trading Systems, in 1978.

Perry J. Kaufman – Trading Systems and Methods

John J. Murphy – Technical Analysis of the Financial Markets