Operational VaR includes EL?

[hsuwang]

Hello David,

When we talk about 99.9% Operational VaR, does that value include EL or do we subtract out EL? It is a bit confusing because usually when we talk about VaR, it is stdev x alpha, but for Operational VaR, it seems like we have to subtract out EL and treat it like Unexpected loss only. It would be more intuitive to think (99.9% Op VaR) -(EL) = UL = economic capital for Operational Risk, but it seems like when we talk about 99.9% Op VaR, we're talking about UL instead of the actual 99.9% VaR value.

Thanks.

 

[David Harper CFA FRM]

Hi Jack,

This is an area that suffers from various approaches. Can I first convince you that subtracting EL out of OpVaR is actually consistent with (std dev * alpha), as these are both *relative* VaRs?

e.g., for market risk, if expected return = 10%, vol = 20%, relative VaR = 20%*alpha. Say the period is one year, this *relative* VaR actually does exclude the drift! If we include the drift, we get an absolute VaR = -exp return + 20%*alpha = absolute VaR (i.e., the loss relative to where we started or zero).

for op risk, the analog to absolute market risk VaR = EL + UL because that is the exp. worst loss relative to where we started.

so:
relative market risk VaR = vol * deviate; i.e., loss relative to future expected value
relative oprisk VaR = UL

absolute market risk VaR = -drift + vol * deviate; i.e., loss relative to initial/zero
absolue oprisk VaR = UL + EL

therefore, technically speaking, as VaR can be relative or absolute, so too OpRisk VaR and it really should be specified
e.g., this is a bogus question: http://forum.bionicturtle.com/viewthread/2032/
...for assuming exclude EL without stating
this is bogus for including EL (!) without stating: http://forum.bionicturtle.com/viewthread/1422/

...but, please keep in mind the *substantive* issue when it comes to capital, where the semantics of the defintion shouldn't get in the way. Basel II AMA OpRisk has a *default* assumption that the capital charge includes the EL. Why? because unlike loans which are loss reserved, the bank probably doesn't reserve for EL of operational risks. Therefore, the capital charge needs to cover the EL because nothing else does. But Basel says, if the bank does cover the EL, then the capital only refers to the UL...either way, they just want to ensure both EL and UL are covered

(the credit risk is essentially no different: of course the credit charge is UL, but basel has an override concerning the EL. If provisions don't cover it, the the capital charge needs to cover UL + EL, too...it's just not expected to be needed).

The key reason that OpRisk tends to "default" to UL + EL is due to the "modern" nature of op risk (i.e., it's not historically common to provision for OpRisk). But credit risk, we expect any banking business knows to provision for the EL.

Hope that helps, David

 

[hsuwang]

Hello David,

If the exam states that it is looking for "absolute" Op VaR, then it will be: Op Var @ 99.9% (which includes EL), and if it asks for "relative", then the 99.9% VaR will need to be subtracted by EL, is this correct?

Thanks.

 

[David Harper CFA FRM]

Hi Jack,

Yes, correct, but the exam is more likely to say "includes EL" or "excludes EL" (I was more trying to draw the comparison). Thanks, David

 

[ajsa]

Hi David,

Can we have the following rule of thumb in the exam without having specific statement of "include" or "exclude" in the question?
1. Op risk VAR includes EL
2. Market or Credit risk VAR excludes EL

Also for delta-normal approach to calculating VAR, is it true that UL=vol*deviate and (-exp return (or -drift) = EL)?

Many thanks.

 

[David Harper CFA FRM]

Hi ajsa,

You probably know my caveat: these are among the definitions i've asked GARP to "standardize" for exam purposes, but to date, have not been; therefore, include/exclude should be specified. However, as for rules of thumb:

1. OpRisk includes EL: Yes, agreed b/c it follows Basel's default, so that seems like the best default
2. CreditRisk excludes EL: Yes, agreed b/c it follows Basel's default
3. Market Risk: GARP certainly knows this needs to be specified, they exam should be well aware of the relative/absolute distinction. IMO, the safest and most correct is to follow Dowd with the proper:
absolute market risk VaR = -drift + vol * deviate; i.e., loss relative to initial/zero
...and under daily period, it is okay to assume drift = 0 where there is no difference

Re: "for delta-normal approach to calculating VAR, is it true that UL=vol*deviate and (-exp return (or -drift) = EL)?"
(the use of EL/UL is awkward for market risk VaR b/c the drift is an expected gain not loss; EL & UL connote oprisk or credit risk where the "drift" is negative... market risk does not typically have an expected loss)

but more imporantly, "delta-normal approach" is one of our big three approaches (in Jorion's terms: delta-normal, HS, MCS) or i prefer (1. parametric, 2. HS, MCS) ... delta-normal is an approach used to generate the distribution ... it connotes market risk due to "normality" ... but beyond that is just giving us an approach to market risk ... it doesn't necessarily imply absolute/relative VaR.

key point:
* the three approaches to VaR (1. parametric/delta-normal/analytical, 2. HS, 3. MCS) are methods to generate the distribution
* AFTER we have a distribution: VaR, EL, UL concern quantiles (or averages) on the distribution or differences btwn same; they are measures that utilize the distribution and they do not need to be aware of (they are independent of) how the distribution is generated

David