What Is the Parabolic SAR Indicator, and How Is It Calculated?

The parabolic SAR is a single price level, redrawn once per bar, that sits on the far side of price from the trade it follows — below the recent lows while long, above the recent highs while short, in the specification Park and Irwin tested — and closes part of the remaining distance on every bar. Sierra Chart's documentation for the study describes it as Welles Wilder's Parabolic SAR and expands the initials as stop and reversal. Park and Irwin, who write it stop and reverse, give the reason: at that price the trade is exited and flipped to the opposite side.

The level is one thing and the trading rule that acts on it is another: the first is a calculation on a chart, the second is something a person or a platform has to carry out. Park and Irwin's AgMAS report on US futures markets tested the rule, and the figures below are its figures.

What is the parabolic SAR indicator?

The parabolic SAR is a trailing level computed from the highs and lows of completed bars. In an uptrend it is pulled toward the highest high the move has produced; in a downtrend toward the lowest low. Sierra Chart calls that reference the extreme point, defined on its page as the extreme high while the chart is in an uptrend and the extreme low while it is in a downtrend. Park and Irwin define that reference from the position's side instead: the best price the open trade has reached, its high while long and its low while short.

Sierra Chart's study calculates the level and displays it, one value per bar. Park and Irwin add the constraint that gives the sequence its shape: for as long as a position is open the level travels one way only, upward in a long trade and downward in a short one, so the distance between it and the best price of the trade keeps closing.

Who created the parabolic SAR, and why is it called parabolic?

Welles Wilder published the parabolic system, and the AgMAS report's reference list gives the book as New Concepts in Technical Trading Systems, issued by Trend Research and Hunter Publishing of Greensboro, North Carolina, in 1978. The same report credits Wilder with two of the other systems it tests, directional movement and the directional parabolic combination. Wilder's directional movement system is the subject of our post on the ADX.

The name describes the shape the stops trace: plotted bar after bar, the sequence of levels curves like a parabola. For the reasoning the report quotes Pring, whose Technical Analysis Explained it dates to 2002, and the complaint the system was built to answer is the lag between the moment a market turns and the moment a trend-following rule reports it. Pring's words there, as the report prints them, are that "The Parabolic System is designed to address this problem by increasing the speed of the trend, so far as stops are concerned". Time counts against an open position, as the report relays the argument, and one that has stopped producing profit should be let go.

How is the parabolic SAR calculated?

The parabolic SAR for the next bar is this bar's level plus a fraction of the distance between this bar's extreme point and this bar's level. Sierra Chart prints the step as SAR plus alpha times the gap between the extreme point and the SAR, and states that the next bar's value is settled by the current bar's data. Park and Irwin write it with an absolute value, added when long and subtracted when short, which lands in the same place.

The fraction is the acceleration factor. It climbs by a fixed increment each time the extreme point moves, which is every time the position reaches a better price than it had before. Sierra Chart starts it at the Start Acceleration Factor input and caps it at the Max Acceleration Factor input; the report's version of Wilder's specification starts it at the increment itself, stops it at 0.20, keeps it there until the trade ends, and resets it at the next position.

A bar that sets no new extreme leaves the extreme point where it was, which Sierra Chart states explicitly, and the step still happens; the acceleration factor just does not grow that bar.

What do the acceleration factor settings change?

They change how fast the stop closes the gap between itself and the extreme point, and through that how soon price can reach it. Sierra Chart's Parabolic study exposes three of them — Start Acceleration Factor, Acceleration Increment and Max Acceleration Factor — along with the two price inputs it reads, which default to the bar's high and low, and an Adjust for Gap input that defaults to No and, when switched on, shifts the level by the size of an opening gap on a new day.

The page prints no figure for any of the three acceleration settings. Each is described as an input and nothing more, so there is no default to read off that page and no number on it to call standard.

The AgMAS report is more specific, because it had to be: it re-chose the increment every year from a grid of eleven values running from 0.014 to 0.024 in steps of 0.001, and it capped the factor at 0.20 throughout. That grid is the range one published test treated as plausible, and the value was re-selected each year on the previous three years of data rather than fixed, so the figures below belong to that annually re-optimised version of the rule and not to any single setting.

What happens when the parabolic SAR flips sides?

When price reaches the level, the rule closes the position and opens the opposite one, and the level jumps to the other side of price. Sierra Chart documents both halves of that jump: at a change from downtrend to uptrend the acceleration factor resets to its starting value and the new level is set to the lowest low of the downtrend that just ended, and at a change the other way it resets and takes the highest high of the uptrend just ended.

Park and Irwin give the same mechanic a name. The significant point is the extreme price reached during the previous trade in the opposite direction, and in their specification each trade's stop begins there. For the first trade in a sample their simulation works through the twenty trading days before entry, a method they credit to Wilder.

Their trading rules make every exit a reversal. The version they tested enters on the close of the first trading day on the side the market is already leaning, flips at the stop when it is reached within the day's range, flips on the close when the stop sits beyond the day's extreme, and offsets the position at the close of the final day of trade, which is the next rollover day.

Does the parabolic SAR move when price goes nowhere?

Yes. The step is a fraction of the remaining gap, so it closes some of the distance on every bar whether or not price advances. Hold the extreme point still at 40 points away and a factor of 0.02 moves the level 0.8 points on the next bar; at 0.20 the same gap moves 8 points. After n bars of no new extreme the gap left is the original gap multiplied by one minus the factor, n times over — it shrinks toward zero without ever reaching it by arithmetic alone.

That is the mechanical reason a stalling market eventually meets its own stop, and why the system's exits do not wait for a reversal to become visible.

Park and Irwin's specification adds one guard rail. The stop may not be moved into the current day's range or the previous day's, and where the formula would put it there, their rule substitutes the more distant of the two days' lows for a long position, or the two days' highs for a short, and continues the calculation from that figure.

Is the parabolic SAR the same thing as a trailing stop order?

No. The parabolic SAR is a number a chart study calculates; a trailing stop is an order that something has to hold and move. Sierra Chart documents the Parabolic as a study with a description, a set of inputs and a downloadable spreadsheet of the formulas, which is what a chart calculation looks like in documentation. Nothing on that page concerns placing or working an order.

The distinction matters more in futures than it looks. CME Group's client-systems wiki, under its order-type heading, names five order types as supported for iLink order entry — market with protection, limit, stop with protection, stop limit and market limit — and a trail is not one of them, so whatever moves a trailing stop sits between the trader and the exchange. Our post on trailing stops in futures works through who holds that order and what happens when the software holding it closes.

As a trading system the parabolic rule is a reversal rule: the same price that ends the long opens the short. Using the level as an exit and leaving the reversal out is half the system, and that half is not what the figures below were measured on.

Has the parabolic SAR been tested on futures data?

It has. Park and Irwin's AgMAS report of May 2005 re-ran twelve technical trading systems across twelve US futures markets, the parabolic time and price system among them under the label PAR. Those markets were corn and soybeans at the CBOT; live cattle, pork bellies, lumber, the British pound, the Deutsche mark and US T-bills at the CME; silver and copper at COMEX; and world sugar and cocoa at the CSCE. Daily data ran from 1975 to 2003, shorter for the three financials, and results are out of sample from 1978.

The assumptions matter as much as the figures. Costs were $100 per contract per round turn across the sample, commission and bid-ask spread together, with a cheaper scenario of $75 from 1985 and $50 from 1995. Parameters were re-chosen yearly from the previous three years by highest mean net return. Trades were one contract at a time, with no pyramiding and no reinvestment.

In the first out-of-sample stretch — 1978 to 1984 for the commodities and metals, 1980 to 1984 for the three financials — PAR's annual mean net return across the twelve-market portfolio was 2.24%, with a Sharpe ratio of 0.21 and no statistical significance. Three individual markets were significant for it: silver at 49.13% at the 1% level, T-bills at 4.05% at 5%, and the mark at 8.03% at 10%. Against that, live cattle lost 17.79% a year and cocoa 14.32%.

What happened to those returns after 1984?

They went negative, for the parabolic system and for the other eleven alongside it. Park and Irwin's later period, 1985 to 2003, left PAR with an annual mean net return of −7.80% on the twelve-market portfolio and a Sharpe ratio of −0.93, and the report records no positive net return for any of the twelve systems on that twelve-market portfolio. One PAR result kept its star: T-bills at 0.47% a year, significant at the 10% level, on a series the report notes ends in 1996.

Two cautions on that table. PAR was not the weakest column in the later period — the outside price channel system came in at −8.08% — and the five systems that did earn significant portfolio returns in the earlier period did not include it. The collapse is also not specific to this rule: in the same tables the dual moving average crossover system goes from 3.48% on the twelve-market portfolio in the earlier period to −7.79% in the later one, which our post on moving average crossovers covers. On the lower-cost scenario the full-period aggregate improves to −1.67% and stays negative.

What is a parabolic SAR distance worth per contract?

The gap between price and the level is worth whatever the contract's point value makes it. Our instrument table gives the E-mini S&P 500 contract a unit of $50 times the index and the micro a unit of $5 times the index, so a ten-point gap between price and the level is $500 on one E-mini and $50 on one micro.

Run the step arithmetic through those multipliers and the settings stop being abstract. The 0.8-point move from the example above is $40 per E-mini contract; the 8-point move at a factor of 0.20 is $400. On four contracts that one bar of catch-up at the higher factor takes $1,600 out of the distance to the stop. The same two moves on one micro contract are $4 and $40, so the multiplier is what turns a distance in index points into a figure comparable across instruments.

What does the parabolic SAR mean on a funded account?

On a simulated funded account what matters is the distance in dollars against the loss line. Our help article on how drawdown works says where that line sits and how it moves, and the arithmetic to do is how many stop distances of the size your settings produce fit between your balance and it.

Two features of the system matter before it is used that way. In the version tested every exit is a reversal, so the position replacing the one it closed is live from the same day. The acceleration also means the stop distance changes through a trade, far away early on and close after a run of new extremes, which moves the loss a single adverse bar can cause from one day to the next. Our post on position sizing works through how many stops of a given size an account absorbs.

What the settings cannot tell you is whether the distance is worth risking: the AgMAS test of the rule on twelve markets over twenty-six years was negative on the portfolio in two of its three periods.

FAQ

What are the standard parabolic SAR settings?

Sierra Chart's Parabolic study prints no figure for the start factor, the increment or the maximum, so there is no platform default to quote from that page. The specification in Park and Irwin's report caps the acceleration factor at 0.20 and starts it at the increment, and their test re-chose that increment yearly from eleven values between 0.014 and 0.024. The numbers are a choice, and in that test the choice was remade every year on the previous three years of data rather than fixed once.

Does the parabolic SAR work in a sideways market?

The arithmetic closes the level in whether or not price moves, so a market that stalls meets its stop and the rule flips. What that costs is a question for the evidence. Across 1985 to 2003, Park and Irwin found the parabolic system returned −7.80% a year on a twelve-market futures portfolio, and no system in their set was positive on it. Their earlier period, 1978 to 1984, gave it 2.24% without statistical significance.

Is a parabolic SAR flip a buy signal?

In the system as tested it is both an exit and an entry: Park and Irwin's trading rules close the existing position at the stop and open the opposite one, with no flat period between. Sierra Chart's documentation describes the calculation and its inputs without stating any reading rule. Whether a flip is worth acting on is the question the report's figures address, and over 1978 to 2003 the system's twelve-market portfolio return was −5.10% a year.

Can you use the parabolic SAR on an intraday futures chart?

The calculation needs a high and a low per bar, and Sierra Chart's study takes those from inputs that default to the bar's high and low, so it can be computed on any bar that has both. The evidence is a different matter: Park and Irwin's test ran on daily prices from 1975 to 2003, so their figures say nothing about the rule on a five-minute chart. Every number in this post is a measurement of the daily version of the rule.