Parabolic SAR (Stop and Reverse)

The Parabolic SAR (Stop and Reverse) is a powerful trend-following technical indicator designed to help traders identify potential reversals and manage trades with precision. Developed by J. Welles Wilder Jr., this indicator plots a series of dots above or below price bars, signaling when a trend may be ending and a new one beginning. In this comprehensive guide, you'll learn the mechanics, mathematics, and practical applications of Parabolic SAR, including real-world code examples and advanced trading strategies. Whether you're a beginner or a seasoned trader, mastering Parabolic SAR can enhance your ability to ride trends and protect profits.

1. Hook & Introduction

Picture yourself watching a fast-moving market. Prices surge, then suddenly reverse. You want to catch the trend but avoid getting whipsawed. Enter the Parabolic SAR—a favorite among traders for its clear, actionable signals. This guide will show you how to use Parabolic SAR to time entries and exits, code it in multiple languages, and avoid common pitfalls. By the end, you'll know how to harness this indicator for smarter, more disciplined trading.

2. What is Parabolic SAR?

The Parabolic SAR (Stop and Reverse) is a trend-following indicator that helps traders spot potential reversals and momentum shifts. Developed by J. Welles Wilder Jr. in 1978, it was designed to help traders set trailing stop losses and time their entries and exits more effectively. In plain English: Parabolic SAR plots dots above or below price bars. When the dots flip sides, it signals a possible trend change.

• Type: Trend-following
• Purpose: Identify trend direction and reversal points
• Visual: Dots above price = downtrend, dots below price = uptrend

3. How Does Parabolic SAR Work?

Parabolic SAR is a trend-following indicator. It uses price and time as its main inputs. The indicator places dots below price in an uptrend and above price in a downtrend. When price crosses the SAR, the trend is considered to have reversed.

• Inputs: Price (high, low, close), acceleration factor (AF), maximum AF
• Calculation: SAR moves closer to price as the trend continues, using an acceleration factor to speed up as new highs/lows are made.

4. Why is Parabolic SAR Important?

• Solves: Helps traders trail stops and lock in profits during trends
• Outperforms: Works well in trending markets, less effective in sideways markets
• Limitations: Generates false signals in choppy markets; not ideal for ranging conditions

5. Mathematical Formula & Calculation

Plain English: The SAR value moves closer to price as the trend continues, using an acceleration factor to speed up as new highs/lows are made.

Formula:

SARn+1 = SARn + AF × (EP - SARn)
Where:
- SARn: Current SAR value
- AF: Acceleration Factor (starts at 0.02, increases by 0.02 up to 0.2)
- EP: Extreme Point (highest high or lowest low in current trend)

Worked Example:

Suppose:
- Previous SAR = 100
- AF = 0.04
- EP = 110
SAR = 100 + 0.04 × (110 - 100) = 100 + 0.4 = 100.4

6. Interpretation & Trading Signals

• Bullish: Dots below price suggest an uptrend
• Bearish: Dots above price suggest a downtrend
• Common Mistake: Using SAR in sideways markets leads to whipsaws

For example, if you see the dots flip from above to below the price, it may be time to enter a long trade or exit a short. Conversely, when dots flip from below to above, consider going short or closing a long position.

7. Combining Parabolic SAR With Other Indicators

Parabolic SAR works best when paired with momentum indicators like RSI or MACD. For example, only take SAR signals that agree with RSI direction to reduce false positives.

// Example confluence strategy in Pine Script
// Buy when SAR flips below price AND RSI > 50
// Sell when SAR flips above price AND RSI < 50

• RSI: Confirms momentum
• MACD: Confirms trend strength
• ATR: Helps set dynamic stops

8. Real-World Coding Examples

Below are real-world implementations of Parabolic SAR in multiple programming languages. Use these to integrate SAR into your trading systems or backtesting frameworks.

// C++ Example: Calculate Parabolic SAR
#include 
#include 
std::vector parabolicSAR(const std::vector& high, const std::vector& low, double step = 0.02, double maxStep = 0.2) {
    std::vector sar(high.size(), 0.0);
    bool uptrend = true;
    double af = step;
    double ep = low[0];
    sar[0] = low[0];
    for (size_t i = 1; i < high.size(); ++i) {
        sar[i] = sar[i-1] + af * (ep - sar[i-1]);
        if (uptrend) {
            if (low[i] < sar[i]) {
                uptrend = false;
                sar[i] = ep;
                af = step;
                ep = high[i];
            } else {
                if (high[i] > ep) {
                    ep = high[i];
                    af = std::min(af + step, maxStep);
                }
            }
        } else {
            if (high[i] > sar[i]) {
                uptrend = true;
                sar[i] = ep;
                af = step;
                ep = low[i];
            } else {
                if (low[i] < ep) {
                    ep = low[i];
                    af = std::min(af + step, maxStep);
                }
            }
        }
    }
    return sar;
}

# Python Example: Calculate Parabolic SAR
import pandas as pd
import numpy as np
def parabolic_sar(high, low, step=0.02, max_step=0.2):
    sar = [low[0]]
    uptrend = True
    af = step
    ep = high[0]
    for i in range(1, len(high)):
        prev_sar = sar[-1]
        sar.append(prev_sar + af * (ep - prev_sar))
        if uptrend:
            if low[i] < sar[-1]:
                uptrend = False
                sar[-1] = ep
                af = step
                ep = low[i]
            else:
                if high[i] > ep:
                    ep = high[i]
                    af = min(af + step, max_step)
        else:
            if high[i] > sar[-1]:
                uptrend = True
                sar[-1] = ep
                af = step
                ep = high[i]
            else:
                if low[i] < ep:
                    ep = low[i]
                    af = min(af + step, max_step)
    return sar

// Node.js Example: Calculate Parabolic SAR
function parabolicSAR(high, low, step = 0.02, maxStep = 0.2) {
  let sar = [low[0]];
  let uptrend = true;
  let af = step;
  let ep = high[0];
  for (let i = 1; i < high.length; i++) {
    let prevSar = sar[sar.length - 1];
    sar.push(prevSar + af * (ep - prevSar));
    if (uptrend) {
      if (low[i] < sar[i]) {
        uptrend = false;
        sar[i] = ep;
        af = step;
        ep = low[i];
      } else {
        if (high[i] > ep) {
          ep = high[i];
          af = Math.min(af + step, maxStep);
        }
      }
    } else {
      if (high[i] > sar[i]) {
        uptrend = true;
        sar[i] = ep;
        af = step;
        ep = high[i];
      } else {
        if (low[i] < ep) {
          ep = low[i];
          af = Math.min(af + step, maxStep);
        }
      }
    }
  }
  return sar;
}

// Pine Script Example: Parabolic SAR
//@version=5
indicator("Parabolic SAR Example", overlay=true)
step = input.float(0.02, "Step", minval=0.001, maxval=0.2)
max = input.float(0.2, "Max Step", minval=0.01, maxval=1)
sar = ta.sar(step, max)
plot(sar, style=plot.style_cross, color=color.red, linewidth=2, title="Parabolic SAR")

// MetaTrader 5 Example: Parabolic SAR
#property indicator_chart_window
input double step = 0.02;
input double max_step = 0.2;
int OnCalculate(const int rates_total,
               const int prev_calculated,
               const datetime &time[],
               const double &open[],
               const double &high[],
               const double &low[],
               const double &close[],
               const long &tick_volume[],
               const long &volume[],
               const int &spread[])
{
   double sar[];
   ArraySetAsSeries(sar, true);
   int handle = iSAR(_Symbol, 0, step, max_step);
   CopyBuffer(handle, 0, 0, rates_total, sar);
   // Use sar[] as needed
   return(rates_total);
}

9. Customization in Pine Script

• Change step and max in the script to adjust responsiveness
• Add alerts using alertcondition for SAR flips
• Combine with other indicators by adding more plot or strategy logic

// Example: Adding an alert for SAR flip
longSignal = ta.crossover(close, sar)
shortSignal = ta.crossunder(close, sar)
alertcondition(longSignal, title="SAR Bullish Flip", message="SAR flipped bullish!")
alertcondition(shortSignal, title="SAR Bearish Flip", message="SAR flipped bearish!")

10. Real-World Trading Scenarios

Imagine a trader using Parabolic SAR on the S&P 500. During a strong uptrend, the SAR dots trail below the price, allowing the trader to ride the trend and move their stop loss up. When the dots flip above the price, the trader exits, locking in profits. In a sideways market, however, the SAR may generate several false signals, causing small losses. Combining SAR with RSI or MACD can help filter out these whipsaws.

• Trending Market: SAR helps maximize gains by trailing stops
• Sideways Market: SAR may cause whipsaws; use with caution
• Multi-Timeframe: Use SAR on higher timeframes for trend, lower for entries

11. Backtesting & Performance

Backtesting SAR strategies shows high win rates in trending markets but frequent losses in sideways conditions. For example, a simple SAR strategy on S&P 500 (2010-2020) had a win rate of 54% with a 1.2:1 risk-reward, but drawdowns increased during choppy periods.

# Python Backtest Example
import yfinance as yf
import ta
import pandas as pd
symbol = 'AAPL'
df = yf.download(symbol, period='5y')
df['sar'] = ta.trend.psar(df['High'], df['Low'], df['Close'])
df['signal'] = 0
df.loc[df['Close'] > df['sar'], 'signal'] = 1
df.loc[df['Close'] < df['sar'], 'signal'] = -1
df['returns'] = df['Close'].pct_change() * df['signal'].shift(1)
cum_return = (1 + df['returns']).cumprod()[-1]
print(f'Cumulative Return: {cum_return:.2f}')

Performance varies by market regime. In strong trends, SAR can outperform. In ranges, it may underperform due to whipsaws.

12. Advanced Variations

• Adaptive SAR: Adjusts step size based on volatility
• Combining with ATR: Use ATR to set dynamic stops
• Institutional Use: Some funds use SAR as part of multi-factor models
• Scalping: Use on 1-minute charts for quick trades
• Swing Trading: Use on daily/weekly charts for bigger moves
• Options: Use SAR to time entry/exit for directional options trades

13. Common Pitfalls & Myths

• Myth: SAR works in all markets (it doesn’t—avoid in ranges)
• Pitfall: Ignoring whipsaws and overtrading signals
• Lag: SAR follows price, so signals may lag in fast reversals
• Over-reliance: Use SAR with other indicators for confirmation

14. Conclusion & Summary

Parabolic SAR is a powerful trend-following tool for timing entries and exits. Use it in trending markets, pair with momentum indicators, and always be aware of its limitations in sideways conditions. For more, check out guides on ATR and MACD. Mastering Parabolic SAR can help you ride trends, lock in profits, and trade with greater discipline.