[R-SIG-Finance] PCA in Risk Control with R

[Benji Famel]

Hello,

my apologies if I do something wrong - first posting for me.

I am trying to apply PCA on the daily history of a bunch of forward
curves and run into my depths of ignorance.  I would appreciate some
help...

My aim is to use PCA for risk control.  I.e. estimate the
eigenverctors and eigenvalues and build the principal components at
some confidence level, e.g. 95%.  If, for example, we were looking at
the first 3 components only, I would
- estimate PC1up, PC1dn, PC2up, PC2dn, PC3up and PC3dn.

Let's assume that
- PC1up is worse for my position than PC1dn,
- PC2up is worse than PC2dn and
- PC3dn is worse than PC3up
I would then 'add' these worse for me components (PC1up, PC2up and
PC3dn) and run my position through them to get a measure of risk at
that confidence level.

To do the PCA, I first foundthe log returns, let's call them Returns.
I then do:
pcdat <-princomp(Returns, cor=TRUE)
and calculate the principal components like this (this is where I am
very foggy...):

PC <- exp(someQuantile*t(pcdat[[2]])*sqrt(pcdat[[1]])*sd(Returns))   #
somQuantile = 1.64 for a 95% CL


As much as I looked around, people discuss the benefits of PC but not
how to recombine the principal components at some confidence interval
to get a shocked curve.

Could anyone help?

Thank you,
Benji