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Volatility drag

The gap between the arithmetic average return and the actual growth of capital: the more the result swings, the less compounding delivers for the same average.

Formula

g \approx \bar{r} - \frac{\sigma^2}{2}

An approximation: the geometric return is roughly the arithmetic mean less half the variance. Both quantities are stored as fractions rather than percentages.

How to read the number

Two consequences follow: reducing swings at an unchanged average return raises the final capital by itself, and a fall followed by a rise of equal size does not return you to where you started.

When the metric lies

Leverage amplifies the effect quadratically: doubling a position doubles the average return and quadruples the variance, so the deduction grows faster than the gain.

Also known as: variance drain

Related terms