VAR mapping and stress testing

[ajsa]

David,

Could you elaborate how it works?

"The stress test consists of decreasing all bonds by their VaR"
Does it mean the portfolio's value is decreased by the total VAR? Any special point/concept this AIM trying to deliever other than aggregating each zero's VAR to get a total VAR?

Thanks.

 

[David Harper CFA FRM]

Hi ajsa,

It refers to Table 11-3 in Jorion Chapter 11. I recreated the XLS here @
http://www.bionicturtle.com/premium/spreadsheet/5.c.2._jorion_mapping_fi/

Jorion intent is to compare this stress testing of the zero rates as inferior to the matrix b/c the matrix uses correlations
in his example:

http://learn.bionicturtle.com/images/f/jorion_t11.3.png

each of the five zero rates in the term structure is "stressed" by a return VaR; e.g., 1 year spot @ 4% is "stressed" or "shocked" by a +0.47% and so the cash flow for that "vertex" is reduced to $105.27. And, just as you suggest, they are added to produce the undiversified VaR of $2.63 which Jorion says is inferior because it assumes the zero rates are perfectly correlated (and the correlation matrix overcomes this to produce a smaller "diversified VaR")

David

 

[ajsa]

Hi David,

So Jorion's point is the stress testing using VAR mapping is inferior to the matrix?

Meanwhile I feel VAR mapping can also introduce correlations, right?

Thanks again!

 

[David Harper CFA FRM]

Hi asja,

Re: "Meanwhile I feel VAR mapping can also introduce correlations, right?"
Absolutely, mapping can and does seek to introduce correlations....

...in this instance (of the bond portfolio), for some reason, Jorion seems to be distinquishing between:
1. Stress testing to generate undiversified VaR; as illustrated above, stress all of the spot rates simultaneously and therefore assume perfect correlation. Consequently, only undiversified VaR can be produced under this "stress test" versus
2. VaR mapping with the matrix, which incorporates correlations and therefore can produce a diversified VaR.

David

 

[babu]

hi David

what is diversified VAR and undiversified VAR

 

[David Harper CFA FRM]

Babu,

this is from Jorion Ch 7...undiversified VaR (naively) adds the position (component) VaRs together and is the equivalent of assuming perfect correlation. Diversified VaR tries to account for imperfect correlation between positions and therefore Diversified VaR < Undiversified VaR

David

 

[BahaSD]

Hi David.
I want calculate diversified VaR (delta-normal) for portfolio consisting of
- USD, GBP, EUR cash
- GDR (equity)
- eurobonds
- forward on currency

I can calculate individual VaR for cash, equity, eurobonds (map to duration) and forwards (map to currency, interest rates).
But I can't imagine how to calculate diversified VaR for portfolio, using delta-normal method.
Can you give me great idea.

Bakhyt