Variance and standard deviation
What do variance and standard deviation measure, and why do traders quote the second one?
In plain words
Both describe dispersion: how far a set of returns spreads out around its average. Variance is the average squared deviation, measured in squared units. Standard deviation is the square root of variance, putting the measure back into the same units as the returns themselves.
Why it matters
Because variance is expressed in squared units, traders quote risk in standard deviation, the measure that shares the returns' own units. Annualised standard deviation, reported as a percentage, sets position sizes, margin levels and the width of risk bands, and lets volatility across different assets and periods be compared.
In a real week: ETH, week of 3 February 2025
For ETH in the week of 3 February 2025, annualised realised volatility, a standard deviation of returns scaled to a year, was 140.8%. The week's return was -8.45%, its range 37.46%, and its largest one-hour move -11.74% at 01:00 UTC on Monday. The same swings, expressed as variance, would be in squared percentage units, which is why the 140.8% figure is quoted.
A common mistake
Treating variance and standard deviation as interchangeable measures. They rank dispersion identically, but only standard deviation shares the returns' units, so raw variance cannot be read as a percentage move.