Stress Testing, Extreme Value Theory and VAR

[Liming]

Dear David,


I was reading http://www.bionicturtle.com/learn/article/value_at_risk_var_2007_frm_part_6_structured_monte_carlo/: The worst-case scenario (WCS) helps "plug the hole" in VaR; i.e., that VaR does not say anything about the loss distribution in excess of VaR. (Note: so does extreme value theory).

This left me confused about the Extreme value theory, which I always thought to be able to describe the loss distribution in excess of VAR. So can I clarify with you whether EVT describes the loss distribution beyond VAR? Thanks

Cheers
Liming
04/10/2009

 

[David Harper CFA FRM]

Hi Liming,

It is a good question. In a way, they are different things and therefore not exclusive. EVT gives us a parametric distribution for the extreme tail. You will note in the assigned case study, Deutche Bank characterizes losses:

up to $50 million: empirical distribution
>$50 million: POT (EVT)

so, in a typical approach, the EVT "grafts on" or replaces the extreme tail with it's own distribution...

VaR simply returns a quantile on the distribution. If we want the 99.9% VaR, we are looking for the loss at this quantile. Maybe or maybe not EVT has given us a distribution that applies here...

e.g., here are the key examples from Dowd:
http://www.bionicturtle.com/premium/spreadsheet/5.d.3._dowd_evt/

note these are all EVT, so EVT is used to characterize the extreme tail
...and then VaR is calculated (e.g., VaR @ 99.9%)

please further note, the same criticism of VaR can be levied here. Although EVT is used to produce the 99.9% VaR, the VaR is giving us no information about losses in excess of the 99.9% (the EVT distribution contains the information, but VaR is not using it...)

...so that is why Dowd also calculates exp shortfall (ES), see H25
...so what do we have here? We have both a VaR and an ES calculated for a distribution with is characterized by an EVT (POT) tail approach

(in this way, we can calculate VaR with or without EVT. And EVT does not require/imply VaR; e.g., we can use EVT just to get straight to ES, if we like)

hope that helps, David