prices <- read.table('/media/alourme/GERMAIN/DSPEG/2016-17/master/bfni/data/price02.csv',header=FALSE,sep=',',dec='.')
returns <- log(prices[-1,]/prices[-251,])

# paramètres standards
mu=colMeans(returns)
sigma=var(returns)

# paramètres RiskMetrics
lambda=0.9
weights = (1-lambda)*lambda^(250-(1:250))
sigmaRM <- matrix(0,nrow=3,ncol=3)
for (i in 1:250){
centeredreturn=as.matrix(returns[i,]-mu)
sigmaRM <- sigmaRM + as.numeric(weights[i])*(t(centeredreturn)%*%(centeredreturn))
}

# structure du portefeuille
theta=rep(1,3)/3*1000

cat('----------','\n')
cat('moyenne des rendements','\n')
cat(mu,'\n')
cat('----------','\n')
cat('covariances standard des rendements','\n')
print(sigma)
cat('----------','\n')
cat('covariances RiskMetrics','\n')
print(sigmaRM)

theta=rep(1,3)/3*100 # structure du portefeuille

var = - theta%*%mu-qnorm(0.01)*sqrt(theta%*%sigma%*%theta)
cat('----------','\n')
cat('value-at-risk 1% Gaussienne : ',var,'\n')

var = - theta%*%mu-qnorm(0.01)*sqrt(theta%*%sigmaRM%*%theta)
cat('----------','\n')
cat('value-at-risk 1% RiskMetrics : ',var,'\n')