# Chapter 4. Risk Measures (in R/Julia)

Copyright 2011 - 2020 Jon Danielsson. This code is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. The GNU General Public License is available at: https://www.gnu.org/licenses/.

##### Listing 4.1/4.2: ES in R Last updated August 2016

p = c(0.5,0.1,0.05,0.025,0.01,0.001)
VaR = -qnorm(p)
ES = dnorm(qnorm(p))/p
cat("Probabilities:", paste0(p*100,"%"), "\n",
"VaR:", VaR, "\n",
"ES:", ES)

##### Listing 4.1/4.2: ES in Julia Last updated June 2018

using Distributions;
p = [0.5, 0.1, 0.05, 0.025, 0.01, 0.001]
VaR = quantile.(Normal(0,1), p)
ES = pdf.(Normal(0,1), quantile.(Normal(0,1),p))./p
println(ES)