P.2 Credit VaR

[chopin]

Hi David,

I did the FRM part 2 exam in November 2016 but unfortunately I falsed. I remembered one questios about Credit Var, which I was not able to get the solution. Please could you help me?
question:
Bank has a basket of 500 short CDS. Each CDS for $1.000.000 bond, which has a 4% probability of default. RR equals 0%. There is a 5% probability that at least 25 bonds go to default. Calculate credit VaR.


Thanks in advance,

 

[David Harper CFA FRM]

Hi @chopin I think they were looking for 95% CVaR = 95% UL = 95% quantile - EL = 25 defaults - (4%*500) = 5 defaults * $1 mm * 100% LGD = $5.0 mm; ie, probably just needed to subtract the expected loss. Sorry to hear about the outcome But I hope you are still enjoying the journey! Thanks,

 

[emilioalzamora1]

Hi David,

I am fully aware that have already been an exorbitant number of discussions in the forum about Credit VaR. I am referring to your post from 2 Sept 2015 saying:

Hi @afterworkguinness I disagree that any of the answers say that Credit VaR is "Expected Loss - Unexpected loss". The source Q&A is located here (https://forum.bionicturtle.com/threads/p2-t6-305-credit-value-at-risk-cvar.6816). Strictly speaking CVaR can be either UL+EL (e.g., some Basel references) or, more typically, CVaR = UL. So just to be careful, because Basel refers to CVaR as UL+EL. A fair question must specifically state that is assumes CVaR is net of EL (or not).

1. Malz uses: CVaR = UL

while

2. per Basel Definition CVaR = UL + EL

Basel II distinguishes between expected loss and unexpected loss. The former (UL) directly charges equity whereas for the latter (EL) banks have to keep the appropriate capital requirements.

There is a BIS document from 2004 by. R. Hibino (as I can't attach files anymore without being blocked from the forum) I simply copied the link, please see on page 45 how Basel treats the EL and UL under the Internal-Ratings-based approach:

http://www.bis.org/publ/qtrpdf/r_qt0409e.pdf

It says that risk-weighted assets (RWA) are calibrated to cover EL and UL while the EL is offset by provisioning (this is the outdated version apparently, titled CP3 in the Hibino paper).

having: (Capital)/(UL+EL - specific provisions)*12.5 >> 8%

However, since the Basel 2004 Framework RWA's are calibrated to cover UL only

having: Capital + (provisions - EL)/ UL*12.5 >>8%

Looking forward to a discussion.

 

[David Harper CFA FRM]

Hi @emilioalzamora1 Yes, thank you, I agree with both of CVaR definitions. With respect to Malz, clearly her defines CVaR = UL; aka, CVaR is a relative VaR. See below, where, it is interesting how he confirms this by contrasting the relative CVaR to an absolute MVaR (emphasis mine):

"6.9.1 Expected and Unexpected Loss: Credit losses can be decomposed into three components: expected loss, unexpected loss, and the loss “in the tail,” that is, beyond the unexpected. Unexpected loss (UL) is a quantile of the credit loss in excess of theexpected loss. It is sometimes defined as the standard deviation, and some times as the 99th or 99.9th percentile of the loss in excess of the expected loss. The standard definition of credit Value-at-Risk is cast in terms of UL: It is the worst case loss on a portfolio with a specific confidence level over a specific holding period, minus the expected loss.

This is quite different from the standard definition of VaR for market risk. The market risk VaR is defined in terms of P&L. It therefore compares a future value with a current value. The credit risk VaR is defined in terms of differences from EL. It therefore compares two future values."

This sort of thing is why I say VaR can be either relative (e.g., rMVaR = σ*α) or absolute (aMVaR = -µ+σ*α). With respect to Basel, I'm not sure to which document you refer, but I am fond of referring to their excellent guidance on the IRB function (here at http://trtl.bz/2phtPgf ) which even includes visual "confirmation" of CVaR = EL + UL:

The only thing I would say about that is that I don't think VaR is an "official" term in the capital requirements. In my recollection, it has always been the case that the OpRisk regulatory requirement has been framed with respect to expected losses (which are expected, pun intended, or presumed to be provisioned as a periodic expense [e.g., cost of goods sold]) versus unexpected losses, UL; and the regulatory capital charge has always been required only of the unexpected losses conditional on the expected loss being adequately covered as expense(s). I hope that's additive!

 

[emilioalzamora1]

For sure, every single line is of help! Thanks, @David Harper CFA FRM ! Will not be the last here...

 

[bpdulog]

Hi David,

I did the FRM part 2 exam in November 2016 but unfortunately I falsed. I remembered one questios about Credit Var, which I was not able to get the solution. Please could you help me?
question:
Bank has a basket of 500 short CDS. Each CDS for $1.000.000 bond, which has a 4% probability of default. RR equals 0%. There is a 5% probability that at least 25 bonds go to default. Calculate credit VaR.


Thanks in advance,

Based on how this question is presenting this information, this is what I get:

EL = .04*1000000*500 = 20000000

25 losses = 25*1000000 = 25000000

CVaR = 25000000 -20000000 = 5000000

Is there any official guidance from GARP?

 

[jagbrar]

Based on how this question is presenting this information, this is what I get:

EL = .04*1000000*500 = 20000000

25 losses = 25*1000000 = 25000000

CVaR = 25000000 -20000000 = 5000000

Is there any official guidance from GARP?

Your method here is correct, also confirmed by David's first response at the top on how to tackle the question. Looks like the trick here was that question provided the 5% PD and asked for a 95% Credit VAR, so really not much calculation was needed .... Tricky, tricky GARP

 

[David Harper CFA FRM]

@bpdulog Yes, I agree with that solution, I feel like it's almost the only calculation you can make with that information, including (i) assume it's a 95.0% CVaR and (ii) assume CVaR = UL. RE: official guidance from GARP? I don't know what you mean, exactly, sorry. Primarily I "upload feedback" (e.g., ask for consistency in definitions). Thanks,