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Standard deviation of returns

A measure of how far returns scatter around their own average: how much a typical period differs from the mean result.

Formula

\sigma = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}\left(r_i - \bar{r}\right)^2}

Returns are taken over equal periods and the sum of squared deviations is divided by the number of observations less one — the sample estimator, not the population one.

How to read the number

Two portfolios sharing this number did not give their owners the same experience: dispersion is symmetric, while only the downward half hurts.

When the metric lies

The measure assumes returns are close to normally distributed. Real markets regularly deliver moves of a size the normal curve treats as all but impossible.

Also known as: return dispersion

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