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# concept behind credit and operational var

#### hamu4ok

##### Active Member
CVaR = UL - EL
OpVaR =UL + EL
The logic behind, deducting EL from CVaR is, I understand, because EL is projected by the bank as bad loans charge/ provision, and to avoid double counting for Basel capital charge (bad loans provision on P&L is effectively reduces Retained Earnings, and thus Regulatory Capital)
OpVaR on the other hand, one has to add expected operational loss, as it is not normally provisioned for specifically.Instead banks allocate budget to cover for operational losses. In this case, bank is exempted from Basel operational risk charge.
Correct me or confirm, if logic above is correct.

CVaR (for exam purposes) can be calculated in two ways. ( in all cases EL = LGD * PD* EAD)
1.Merton model, when the debt of company is assumed to be one zero coupon bond, CVaR =Bond Parvalue - bond value at quantile - EL.
2.Portfolio of credit risk sensitive assets (Loans). You'RE given in such case N - number of assets, V-equal size of each position in portfolio, and simplifying assumptions of zero correlation.
in such case UL = (1-Conf.level)*N*V
And the CVaR = UL - EL.

OpVaR on the other hand can be calculated only in LDA approach, with frequency and severity distribution given.
EL is then equal to product of weighted averages of freq and severity distro.
UL, we need to multiply expected frequency (weighted ave) multiply with prob of each severity and calculate cumulative probability ranked from most severe to less severe loss. The loss at which (1-conf.level) is crossed is our UL. The rest is obvious.
Am I correct, or is there any other cases?
How about Ong's way of calculating UL? In what cases we need to apply Ong's UL?

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @hamu4ok

While I've been long requesting that GARP adopt Jorion's "absolute vs. relative" terms to distinguish, I agree with your CVaR and OpVaR. It's confusing because Basel occasionally refers to CVaR = UL + EL, but the most conventional use of CVaR is how you show it, under a theory it refers to a need for capital (i.e., balance sheet buffer for the unexpected) rather than an expense (ongoing P/L cost of the expected).

Can you see my summary here @ https://www.bionicturtle.com/forum/threads/frm-fun-13-absolute-versus-relative-var-versus-ul.6020
Under Basel II advanced approaches (IRB for credit risk, IMA for market risk and AMA for operational risk), the defaults are:
• Credit risk capital charge is relative CVaR since it is a charge for UL which excludes EL (in credit, EL is an ongoing expense that Basel expects to be expensed by provisions. If, however, there is a gap, capital must first address the gap)
• Market risk capital charge can be argued as either, IMO, because the drift is uniquely positive: maybe better is Absolute VaR where the drift is assumed to be zero; or, if you like, relative VaR where the drift is omitted.
• Operational risk capital is absolute OpVaR because, unlike credit, otherwise coverage of EL is not presumed (i.e., it is not ordinary practice to expense OpRisk EL):
This is exactly correct, well done with a difficult idea in Malz:
• Merton model, when the debt of company is assumed to be one zero coupon bond, CVaR =Bond Parvalue - bond value at quantile - EL;
• and because: Expected future value of debt = bond value at quantile - actuarial EL, this is equivalent to:
• CVaR = (Expected future value of debt) - (bond value at quantile)
Finally, you are also correct about easily the exam's most likely approach to OpVaR (i.e., by tabulation/convolution of frequency and severity). I've written several practice question testing this. Ong's UL is a special case of a one standard deviation unexpected loss; it's like a "statistical UL." But this will correspond to a lower-than-typical confidence (e.g., if the credit distribution were normal, which is definitely is not but i'm lazy, Ong's UL would correspond to =NORM.S.DIST(z = 1, cdf = true) = only 84% confidence). So, that's a statistical UL, not a CVaR. In Ong, he needs a capital multiplier, say X: CVaR = X*UL, to get to the higher confidence implied by a capital buffer. I hope that's help, thanks for your awesome and generous infographic contributions Thanks! David

#### hamu4ok

##### Active Member
Hi David,
Thanks for confirming my recapping views. CVaR was for me a very difficult thing not to picture about, but to handle it with actual problems. Different set of problems also took different take on CVaR , which was confusing, at least for me.
OpsVaR being treating differently from CVaR forced me to think more for the reason As I had some accounting background (ACCA member since some time, although moved to risk management in banking few years ago), I tried to link ideas together.

Re slides: I like to generalize things, finding common thing and differences, searching for the common sense, an bird's-eye-view. And as one clever person once said the best way to learn is through teaching someone. Slides allow me to achieve the both, I hope.