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Assuming that we are talking about volatility as the standard deviation of uncorrelated random variables (in this case this would mean no autocorrelation) the variance is additive, which means that we get $\sqrt{.15^2+.2^2}=.25=25\%$. You can illustrate this result by simulation in R: > sd(rnorm(1e7,sd=.15)+rnorm(1e7,sd=.2)) [1] 0.2500001 If you want ...