StdDev — Rolling Standard Deviation

Standard deviation of the input over the last N bars. The volatility primitive.

Signature

StdDev(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Lookback.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \bar{x} = \frac{1}{N} \sum_{i=0}^{N-1} \text{close}{t-i}, \qquad \text{StdDev} = \sqrt{\frac{1}{N} \sum{i=0}^{N-1} (\text{close}_{t-i} - \bar{x})^2} $$

Population standard deviation (divide-by-N), not sample. Returns 0 until the period-bar window is full.

Warmup

period bars.

Reading the value

sd.value
sd > some_threshold

Example — Bollinger Bands

class BollingerBounce(Strategy):
    """Mean reversion on Bollinger Band touches."""
    period = Param(20, min=10, max=50)
    num_std = Param(2, min=1, max=3)
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        sma = SMA(self.period, on=self.trade)
        sd = StdDev(self.period, on=self.trade)

        lower = sma.value - self.num_std * sd.value
        upper = sma.value + self.num_std * sd.value

        self.stop_loss(3.0)

        if self.trade.close < lower and self.trade.is_flat:
            self.buy(self.trade, reason="Touch lower band")

        if self.trade.close > upper and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Touch upper band")

Notes

• StdDev is unbounded — values scale with the source. To compare across instruments, normalize by price (sd.value / self.trade.close).
• Want the classic bands directly? Use the built-in BollingerBands — the SMA + StdDev composition above is the same math, useful when you need custom band logic.
• For volatility regimes (“am I in a calm or noisy market?”), compare current StdDev to historical: e.g. is sd.value > sd.value_at(20)?