Hi Brian,
 
Thanks for these precisions. I appreciate your help.
 
Regards,
 
Fabrice



> Date: Tue, 17 Jul 2007 12:13:52 -0500> From: brian@braverock.com> To: fabricemcshort@hotmail.com> CC: r-sig-finance@stat.math.ethz.ch> Subject: Re: [R-SIG-Finance] Multi-asset portfolio VaR> > Fabrice McShort wrote:> > I tried to calculate the VaR of a multi-assets portfolio.> > I have the historical data of the assets and their weights in the > portfolio.> > My impression is that the Performance Analytics Package calculate > only the> > VaR of each asset. Not the VaR of the portfolio. But, when I use > fPortfolio> > Package, I have the VaR (Historical simulation) of the portfolio. > Could you> > confirm my first impression or indicate me how to calculate the> > VaR of this portfolio with the Performance Analytics Package.> > Thanks for your help.> > Fabrice,> > You are correct. The parametric VaR methods in PerformanceAnalytics are > all univariate. fPortfolio calculates historical mean-VaR from the > quantiles of observed returns. The simplest method to do what you want > is to combine functions from the two packages.> > Use pfolioReturn() from fPortfolio to construct the return series of > your historical portfolio. Use this as the input to the parametric VaR > calculations in PerformanceAnalytics. This may be sufficient to answer > your requirements (it's how I calculate VaR of a historical portfolio in > most cases.)> > Now, a true multivariate parametric estimation is somewhat more > difficult. I'll take the case of traditional mean-VaR first, and then > extend that to the Cornish-Fisher expansion.> > In the case of traditional mean-VaR, to make a parametric estimate of > VaR that is multivariate, you need to construct the return series, > possibly using some robust estimator so that you get a more robust mean > to use as the input. The difficulty lies with the variance. You may in > this case wish to scale your observed component returns by the > historical weights and use one of the multivariate methods to come up > with a better multivariate covariance measure. See the Multivariate > Statistics CRAN Task view here:> > http://cran.r-project.org/src/contrib/Views/Multivariate.html> > Now, extending this to multivariate skewness and kurtosis is yet more > complex. PerformanceAnalytics provides functions for coskewness and > cokurtosis, but those aren't the actual inputs into the Cornish Fisher > expansion. The "moments" package provides slightly more options for > calculating skewness and kurtosis than those used in > PerformanceAnalytics and fBasics, but still doesn't provide a true > multivariate estimate of skewness and kurtosis. There is quite a lot of > literature on multivariate skewness and kurtosis, and if you're > interested, we would certainly welcome collaboration on creating a set > of functions for providing these in R.> > For most purposes, the univariate case seems to be sufficient, but I > wanted to make sure to cover the issues in the true multivariate case.> > Regards,> > - Brian
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