I’m just wondering about the math behind this: sigma/(12^.5). Why does this formula work the way it does?
Variance is the determinant of volatility. You need to find the monthly variance. Since standard deviation is a square root of variance, dividing the standard deviation by the square root of 12 is the same as dividing the variance by 12 before finding standard deviation.
Assuming independence, variances are additive, so,
annual σ² = 12 × monthly σ²
Take the square root of both sides.