[R-SIG-Finance] Multi-asset portfolio VaR

[Brian G. Peterson]

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