David,

thanks for answer. First I don't know why my mail was sent in Spam and
sorry if i made some mistake for that. I accept your suggestion and use
mvrnorm form MASS.

l<-list("vector",10)
mu<-apply(sh,2,mean)
sigma<-cov(sh)
#generate 10 scenatrios
l<-list("vector",10)
for (i in 1:10)
{
l[[i]]<-mvrnorm(10,mu,sigma)
}

But after this I still don't know what to do in order to estimate VaR from
this generated 10 scenatrios.
Is this a good way or not:

mc<-sapply(l,function(x) mean(x%*%w))
quantile(mc,p=0.05)

Thanks for help and sorry if this is a too simple or begginer question but
I not so experienced with this.

Andrija




On Fri, Nov 18, 2011 at 3:51 PM, David Reiner <David.Reiner@xrtrading.com>wrote:

> I'm guessing that you would want to specify the correlation as given as
> you have the volatilities,
> hence use a covariance matrix in MASS::mvrnorm to generate your 'sh'.
> That shuld get you started anyway.
> Rolling your own with use of Cholesky is OK, too, of course, but others
> have done lots of hard work do give you better results.
>
> (
> There are many other functions in various packages to generate
> multivariate normal samples if you look; e.g.,
> > require(sos)
> > ???"random multivariate normal "
> found 532 matches;  retrieving 20 pages, 400 matches.
> 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
> )
>
> HTH,
> -- David
>
>
> -----Original Message-----
> From: r-sig-finance-bounces@r-project.org [mailto:
> r-sig-finance-bounces@r-project.org] On Behalf Of andrija djurovic
> Sent: Friday, November 18, 2011 3:02 AM
> To: r-sig-finance@r-project.org
> Subject: [SPAM] - [R-SIG-Finance] Monte Carlo simulation for VaR
> estimation - Email found in subject
>
> Dear users,
> I need help in understanding steps of Monte Carlo simulation for VaR
> estimation. Here is the simplified example of what i was trying to do, but
> I suppose this is not appropriate way for performing MC simulation.
>
> Suppose that our portfolio consist of x1 and x2 (with equal weights),
> which returns are given:
>
> sh<-matrix(c(rnorm(100,0,0.01),rnorm(100,0,0.015)),ncol=2)
> colnames(sh)<-c("x1","x2")
> w<-matrix(c(0.5,0.5),ncol=1)
>
> >From this I calculated portfolio returns, mean and variance:
>
> pr<-sh%*%w
> pmu<-mean(pr)
> sigma<-cov(sh)
> pvar<-t(w)%*%sigma%*%w
>
> Now I was trying to generate 10 scenarios (keeping the correlation between
> x1 and x2). Then calculate portfolio mean for each scenario and from that
> mean distribution  calculate 95% VaR. Here I am sure  these aren't good
> steps and I that I am missing something in part of keeping a correlation
> between x1 and x2:
>
> l<-list("vector",10)
> cd<-chol(cov2cor(sigma))
> #generate 10 scenarios#
> mu<-apply(sh,2,mean)
> sd<-apply(sh,2,sd)
> for (i in 1:10)
> {
> l[[i]]<-matrix(c(rnorm(10,mu[1],sd[1]),rnorm(10,mu[2],sd[2])),ncol=2)%*%cd
> }
>
> mc<-sapply(l,function(x) mean(x%*%w))
>
> quantile(mc,p=0.05)
>
>
> Thanks in advance and any help is really appreciated.
>
> Andrija
>
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