Kurtosis

Tail weight of the return distribution, as excess kurtosis: 0 is Gaussian, positive means fatter tails than normal. Financial returns are almost always positive here, which is precisely why volatility alone understates risk.

Signature

Kurtosis(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Return window. Default 60, bounds 4–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{kurt} = \frac{m_4}{m_2^2} - 3 $$

on log returns; the −3 makes a normal distribution read 0.

Warmup

period + 1 bars; 0 until then.

Reading the value

ku.value
ku.value > 3

Example

class TailRiskGate(Strategy):
    """Size down when the tails are unusually heavy."""
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        ku = Kurtosis(60, on=self.trade)
        sma = SMA(50, on=self.trade)
        if ku.value < 3 and self.trade.close > sma.value and self.trade.is_flat:
            self.buy(self.trade, reason=f"Kurtosis {ku.value:.2f}")
        if ku.value > 6 and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Fat tails")

Notes

• Proven by an assert-via-trade run on SPY daily (matched a strategy-side moment computation to 1e-3 on every bar; zero alarm trades).
• Excess kurtosis, population moments. Very sensitive to single outliers — one big day can dominate a 60-bar window.
• The moments are taken over log returns and are uncorrected (divided by n); pandas_ta’s kurtosis() applies the sample correction to the price series, so the two never agree.