Conditional EL

[ajsa]

Hi David,

"Conditional EL – EL: Conditional EL includes EL and UL, the difference between
conditional EL and EL results in the necessary capital for UL only. Regulatory guidelines
require EL to be covered by provisions and earnings"

I wonder if Conditional EL is (credit) VAR since VAR=EL+UL?

BTW is provision the same as "reserve"?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

Yes, in Basel that is correct, CVaR = EL + UL
...but keeping in mind or other thread ...

I think it helps avoid confusion if we are mindful that VaR can be absolute or relative, so you will see some authors define CVaR as UL (i.e., excluding the EL) and that's not incorrect b/c that's a "relative" VaR as in "relative to the expected portfolio in the future" as opposed to "absolute" CVAR = EL + UL which is VaR "relative to today or zero"

re reserves vs. provisions, see this.

I think "reserves" is out of fashion owing to ambiguity (but not 100% sure about that). I think best terms are: provision vs. allowance

basically, management estimates losses to accrue for the period (year): that's an income statement PROVISION for loan losses (e.g., $1 MM)
then the $1 MM increases the cumulative balance sheet ALLOWANCE (reserve) for loan losses, which is a contra asset account

e.g.,
gross loans = $10 MM
allowance for losses = $2 MM
net loans = $8 MM

so each period the provision (a flow) is increasing the allowance (a stock)

David

 

[ajsa]

thanks David. Just to double confirm, is Conditional EL the same as absolute CVaR?

Thanks..

 

[David Harper CFA FRM]

Hi asja,

Terrific, yes, your sentence pretty much summarizes the challenging IRB. From the doc (p 5):

"The conditional expected loss for an exposure is estimated as the product of the conditional PD and the “downturn” LGD for that exposure. Under the ASRF model the total economic resources (capital plus provisions and write-offs) that a bank must hold to cover the sum of UL and EL for an exposure is equal to that exposure’s conditional expected loss. Adding up these resources across all exposures yields sufficient resources to meet a portfolio-wide Value-at-Risk target."

in other words, in terms of our other readings, they want a worst case loss (WCL) with 99.9% confidence, or absolute CVaR(99.9%). The confusing part, IMO, is that they use EL to find the UL; i.e., to get the absolute CVaR/WCL, where UL = CVaR - EL.

a normal start with: EL = PD * LGD

then the PD and LGD are "reused" to get:
conditional EL = conditional PD * downturn LGD
(and the correlation is the key paramater that achieves this "stretching" of an EL into a conditional EL)

such that:
conditional EL - EL = UL, or
CVaR = EL + UL = EL + (conditional EL - EL) = conditional EL (nice!)

David

 

[ajsa]

Hi David,

Could you take a look the following question? Does it mean the Op risk capital can include EL as well, and so different from credit risk capital calculation?

Thanks.

30. According to the Basel Committee which of the options below is NOT a quantitative
standard that a bank must meet before it is permitted to use the Advanced Measurement
Approach (AMA) for operational risk capital:
a. A bank’s risk measurement system should be sufficiently ‘granular’ to capture the
major drivers of operational risk affecting the shape of the tail of the loss estimates
b. Supervisors will require the bank to calculate its regulatory capital as the Unexpected
Loss (UL), disregarding the Expected Losses (EL)
c. Internally generated operational risk measures used for regulatory capital purposes
must be based on a minimum 5-year observation period of loss data. When the bank
first moves to the AMA a 3-year historical data window is acceptable.
d. The tracking of internal loss data
ANSWER: B
‘B’ is not a quantitative standard. According to the Basel Committee,
“Supervisors will require the bank to calculate its regulatory capital requirement
as the sum of expected loss (EL) and unexpected loss (UL), unless the bank can
demonstrate that it is adequately capturing EL in its internal business practices.”
Basel II: International Convergence of Capital Measurement and Capital
Standards: A Revised Framework, Bank for International Settlements, 2005.

 

[ajsa]

Hi David,

I have found a similar question here. could you clarify?

http://forum.bionicturtle.com/viewthread/1414/

BTW, it also seems to have nothing to do with Op VaR, since OpVaR is not part of Basel II, right?

Thanks.

 

[David Harper CFA FRM]

Hi asja,

I stand by my view in our previous thread: http://forum.bionicturtle.com/viewthread/1837/
Consistent with that view, please note this 2009 sample LII Q40
...the first question is GARP's; "what is the 95% VaR?"
...and their answer includes EL as this is OpRisk

Re: "OpVaR is not part of Basel II, right?"
Yes, OpVaR is part of Basel II: VaR is just a quantile, the quantiative criteria is 99.9% one-year horizon. Ergo, Basel II AMA is a 99.9% one-year OpRisk VaR or OpVaR

Re: does OpRisk VaR include or exclude EL?
Jus like credit risk, it can be either "relative" or "absolute" VaR (can include or exclude EL)

Re: does regulatory capital requirement include/exclude EL?
Unlike credit risk, which (by default) presumes EL is covered by loan pricing, Basel II (note the answer above) presumes that EL is not elsewhere covered
(to add to the confusion, Crouhy assumes differently for EC: he has EC covereing UL, assuming the OpRisk EL is priced into cost of doing business)

Re: Does it mean the Op risk capital can include EL as well, and so different from credit risk capital calculation?
They are only different in the "default presumption," but they are not different ultimately because: if the bank has not provisioned for EL (in both), then capital must be used to cover the EL "deficit"

David