# Parabolic SAR A Trend concept (Trend-following systems) in the LuxAlgo Library, with 2 indicator implementations. ## What is the Parabolic SAR? The Parabolic SAR (stop and reverse) is a trailing stop system introduced by J. Welles Wilder in his 1978 book New Concepts in Technical Trading Systems. It plots one dot per bar: below price while the system is long, above price while it is short. Each bar the dot advances toward price by an acceleration factor (AF) times the distance between the trend's extreme point and the current SAR. The AF starts at 0.02, increases by 0.02 each time the trend prints a new extreme, and caps at 0.20; that accelerating step is what bends the trail into its parabola. When price touches the dot, the system stops and reverses: the SAR flips to the other side, restarting at the prior extreme with the AF reset. By construction it is always in the market, which makes it a stop-placement method as much as a signal generator. It behaves well in sustained trends, tightening as the move accelerates, and poorly in ranges, where it flips repeatedly. Wilder himself positioned it as a tool for trending markets and pointed to his [ADX/DMI system](https://www.luxalgo.com/library/concept/adx-dmi-system/) as the filter for deciding when to run it. ## How to read Parabolic SAR The plot is a dotted trail that switches sides of price. To read it: 1. Check which side the dots are on: below price marks an uptrend regime (system long), above price a downtrend regime (system short). 2. Watch the gap between dot and price: dots accelerating toward price mean the trend keeps printing new extremes and the trailing stop is tightening. 3. Treat a touch as a flip: the dots jump to the opposite side at the prior extreme, and the acceleration count restarts at its minimum. 4. Grade flips by context: in a trending tape a flip is meaningful, while in sideways chop flips fire constantly and most fail, so require a [higher-timeframe trend filter](https://www.luxalgo.com/library/concept/higher-timeframe-trend-filter/) or an ADX-style gate first. ## How it's calculated Parabolic SAR trails price with a stop-and-reverse level that accelerates toward the trend's extreme and flips sides when price touches it. ``` SAR_(t+1) = SAR_t + AF_t × (EP_t - SAR_t) Uptrend: EP_t = highest H since the uptrend began, then clamp SAR_(t+1) = min(SAR_(t+1), L_t, L_(t-1)) Downtrend: EP_t = lowest L since the downtrend began, then clamp SAR_(t+1) = max(SAR_(t+1), H_t, H_(t-1)) AF_t starts at AF_start and rises by AF_step each bar that EP_t makes a new extreme, capped at AF_max Reversal: if the next bar touches or crosses SAR_(t+1), flip the trend, set the new SAR to the old trend's EP_t, and reset AF_t to AF_start SAR_t: stop-and-reverse level plotted for bar t EP_t: extreme point of the current trend (highest high in an uptrend, lowest low in a downtrend) AF_t: acceleration factor in effect at bar t AF_start: initial acceleration factor (default 0.02) AF_step: acceleration increment (default 0.02) AF_max: acceleration cap (default 0.2) H_t: high of bar t L_t: low of bar t t: bar index; t-1 is the prior bar and t+1 the next ``` Wilder's defaults are 0.02 step and 0.2 maximum; a larger step tightens the stop, a larger cap lets it accelerate longer. The first SAR must be seeded from an assumed starting trend and its extreme, so early values differ slightly across platforms. ## How traders use it - As a trailing stop for open positions, its original job: the dot is the exit level, and it only ratchets in the trade's favor. The broader [trailing method taxonomy](https://www.luxalgo.com/library/concept/trailing-method-taxonomy/) shows where it sits among alternatives. - As an always-in [stop-and-reverse](https://www.luxalgo.com/library/concept/stop-and-reverse/) system, flipping long and short on every touch; usually only viable with a regime filter screening out ranges. - As a one-glance trend read for dashboards and multi-symbol screens: which side the dots sit on is a compact regime label. - As a time-based tightening template: the SAR keeps stepping toward price every bar even when no new extreme prints, so it closes out stalls sooner than fixed-distance [volatility stops](https://www.luxalgo.com/library/concept/volatility-stop/), which suits traders who want stagnant trades closed. ## Parabolic SAR vs other trailing systems - **Supertrend** (https://www.luxalgo.com/library/concept/supertrend/): Both are flip-on-touch trailing systems. Supertrend offsets its stop by a multiple of ATR, so the distance scales with volatility; the SAR's distance shrinks with time and new extremes regardless of volatility, so it tightens even when the market goes quiet. - **Chandelier Stop** (https://www.luxalgo.com/library/concept/chandelier-stop/): The chandelier trails an ATR multiple from the extreme high or low and is a stop only. The SAR is a full stop-and-reverse system that is always positioned, with tightening driven by acceleration rather than a fixed ATR multiple. - **Stop and Reverse** (https://www.luxalgo.com/library/concept/stop-and-reverse/): Stop and reverse is the general always-in concept: every exit is also the next entry. The Parabolic SAR is its most famous concrete implementation, with Wilder's acceleration schedule deciding where the reversal point sits. ## FAQ ### What are the standard Parabolic SAR settings? Wilder's published defaults: the acceleration factor starts at 0.02, steps up by 0.02 each time the trend makes a new extreme, and caps at 0.20. Lowering the step or the cap loosens the trail and slows flips; raising them tightens the trail and increases whipsaw. Most platforms ship these defaults, and any change should be tested per market. ### Does Parabolic SAR work in sideways markets? Poorly, and Wilder said as much. Because the SAR is always in the market and converges on price bar by bar, a range produces a steady stream of losing flips. The common remedy is a regime gate: honor SAR signals only when a trend filter such as ADX agrees, and stand aside or switch tools in chop. ### Is the Parabolic SAR an entry signal or a stop? By construction it is both: stop and reverse means the exit of one position is the entry of the opposite one. In practice many traders use only half of it, taking entries from separate logic and using the SAR purely as a trailing stop, which sidesteps the always-in whipsaw problem in ranging conditions. ## Implementations in the Library - Parabolic SAR Oscillator (LuxAlgo): https://www.luxalgo.com/library/indicator/parabolic-sar-oscillator/ - Parabolic SAR (LuxAlgo, the standard build of the classic formula): https://www.luxalgo.com/library/indicator/parabolic-sar/ ## Related concepts - Supertrend: https://www.luxalgo.com/library/concept/supertrend/ - Chandelier Stop: https://www.luxalgo.com/library/concept/chandelier-stop/ - Donchian Trend Rules: https://www.luxalgo.com/library/concept/donchian-trend-rules/ - ATR Trailing Regime: https://www.luxalgo.com/library/concept/atr-trailing-regime/ - Gann HiLo Activator: https://www.luxalgo.com/library/concept/gann-hilo-activator/ - Alligator: https://www.luxalgo.com/library/concept/alligator/ - NRTR: https://www.luxalgo.com/library/concept/nrtr/ - Chande Kroll Stop: https://www.luxalgo.com/library/concept/chande-kroll-stop/ - Halftrend: https://www.luxalgo.com/library/concept/halftrend/ - Trend Magic: https://www.luxalgo.com/library/concept/trend-magic/ --- Source: https://www.luxalgo.com/library/concept/parabolic-sar/ (LuxAlgo Library, the encyclopedia of trading & technical analysis). Free to use with attribution: https://www.luxalgo.com/library/license/