Parabolic Sar (Trend)

Wilder's Parabolic SAR: buys when price closes above the stop-and-reverse dot and sells when price closes back below it — a trailing stop that accelerates toward price as the trend runs.

How It Works

1. Track the parabolic stop from each bar's high and low: it trails below price while the trend is up, creeping closer every bar and faster with each new high.
2. Buy when the close is above the stop — the trend has flipped up and the stop has moved beneath price to trail it.
3. Sell when the close falls back through the stop. Because the stop accelerates, a long-running trend gets stopped out on a much smaller pullback than a young one would.

Worked example. The stop flips below price at 100 and the strategy buys. As the rally extends the stop climbs from 90 toward 118, tightening with each new high, until a pullback to 118 touches it and closes the trade — the gain is kept because the stop had ratcheted up behind it, not because the trend was called at the top.

The Math Behind The Indicators

Everything runs on closing prices of the traded timeframe: P is a close, P_t today's close, and N counts bars — one bar is one candle of that timeframe, so 20 bars on a 1h chart is 20 hours.

Parabolic SAR

A trailing stop that tightens as a trend runs. It starts far below a rising market and steps toward price each bar, covering a fraction of the remaining distance to the highest high reached so far. That fraction — the acceleration factor — begins at 0.02 and rises by 0.02 every time the trend posts a new extreme, capped at 0.2, so a long quiet trend is given room early and squeezed later. When price finally touches the stop, it flips to the other side of price and the trend is considered over — the stop and reverse the name refers to.

\[\mathrm{SAR}_{t+1} = \mathrm{SAR}_t + \alpha\left(\mathrm{EP} - \mathrm{SAR}_t\right), \quad \alpha = \min\left(0.02\,n,\ 0.2\right)\]

Example: In a rising market the stop sits at 90 with the highest high (EP) at 100 and α still 0.02, so the next stop is 90 + 0.02·(100 − 90) = 90.2. After several new highs α has grown to 0.10 and the same 10-point gap pulls the stop a full point per bar — the longer the trend lasts, the less room it is given.

Example Chart

Real Data31/ 100Composite score

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Resampled Data35/ 100Composite score

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