Hello David,
I’ve seen the terms “covariance matrix” and “correlation matrix” a couple of times now, and I think I roughly know what they are and how they work, but I’m not sure as to how they apply and are being used in scenario analysis (stress testing). Also I am getting a bit overwhelmed by the covariance matrix concept used in Cholesky factorization. Can I ask for your suggestion on the readings that might help me get a solid understanding of the matrixes and how they are being used in both scenario analysis and cholesky factorization? I only read your 08’ note on “stress testing” and haven’t gone through the assigned readings for Jorion’s “stress testing” yet, so maybe that would be a start?

Thank you!

Hi Jack,

These are each big topics. Please note I uploaded a structured monte carlo @
http://www.bionicturtle.com/premium/spreadsheet/4.a.3_structured_monte_carlo/

This may helpful because I used a correlation matrix as input into the covariance matrix
(just as covariance embeds correlation per, COV = COR*VOL*VOL, it is true in matrix form too)
Then on the 2nd tab, I actually spent the time to hand-build a 5-factor Cholesky; the Cholesky is just matrix math; complex maybe but it’s role is straightforward: it uses information in the covariance matrix to convert a vector of random, independent returns into a vector of random, but correlated returns. (it is colored red b/c you don’t need to know for exam)

I attached two pdfs from my elibrary: the PRM matrix chapter is best I’ve got on Cholesky - really accessible!
And then a (free) article from 2007 Garp risk review that I found very helpful…Please see attached below

In regard to stressing the covariance matrix, this is a whole topic and can be a simple as: use an old crisis period, extract the covariance matrix from that period, and run of test of today’s portfolio through it. Many variations and details ensue…

Best i have on this, unsurprisingly, is Carol Alexander’s Vol IV on Value at Risk
http://www.amazon.com/Market-Risk-Analysis-Value-Models/dp/0470997885/ref=sr_1_3?ie=UTF8&s=books&qid=1246647336&sr=8-3

However, IMO, for purposes of sitting the full FRM, you probably don’t have time to take a deep dive on this…
e.g., Jorion’s Ch 12 on stress testing is *very* introductory, just a laundry list…

You raise a great point, though: it occurs to me only now that GARP has not “introduced” the covariance matrix in the readings (?!)
Since it is fashionable to beat up on it nowadays, maybe good idea to know why it’s getting dumped on

I will add, since you raised this point, a simple VaR XLS that uses convariance matrix maybe with a simple stress example…(I have an old version i can update)...I hope this is a helpful start…David

Hello David,
Thank you so much for the reply, I feel that I’m always getting more than I ask for from your resourceful replies!  THANKS!

Sure thing Jack, in all sincerity, as i said before, you’ve asked several questions that are relevant and often tend to hit common obstacles - so I do try to pull in answers that may be helpful (including to others) generally for the exam…(it keeps me fresh too, on topics, so i am benefitting too!) David