sims <- 1e6
n = 20

std <- c()

R <- rnorm(n*sims)
int <- seq(1,sims,20)
std <- sapply(int,function(i) sqrt(sum((R[i:(i+n-1)])**2)/19))
returns <- rnorm(sims)

f <- 1.1

VaR <- std*qnorm(0.99)*f
viostd <- mean(returns > f*std)
round(100*viostd,1)-round((1-pnorm(1))*100,1)

## [1] -2.3

viorate <- mean(returns > VaR)
round(viorate*100,1)

## [1] 0.8