Attribution of Capital
- Thread starter ajsa
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Hi ajsa,
As usual, you raise an *interesting* point, I think there may be two ideas within your deceptively simple question...
in regard to aggregation, because the advantage of EC is a "common currency," we can refer to EC for credit risk or for the everything (EC for all risks). Each major risk bucket can have a EL and a UL. So, we can refer to either Credit VaR or EC for Credit risk or EC for all risks combined. EC can be aggregated horizontally accross risk types or up/down the organization
In regard to VaR, I think it gets confusing if we lose sight of fact that VaR is just a distributional quantile; i.e., total VaR is a challenging phrase, I think, because it implies we are combining the distributions (distributional losses) for credit, market and operational risk...
...but instead, Crouhy's RAROC has EC in the denominator which is a function of VaR for each major risk bucket. So we might have:
EC for Credit = Credit VaR = UL = WCL (confidence) - EL, and
EC for OpRisk = WCL(confidence); i.e., following Basel, we would include EL
and then we can aggregate the EC. Although Basel is regulatory capital (not economic capital), that's all it does with the three major risk buckets, it's uses a VaR quantile (market = 99.9% 10-day; credit and opRisk = 99% one year) and simply adds them up (no diversification benefit).
...so the VaR (IMO) is tricky in aggregation and easier to comprehend as the quantile associated with the distribution pertaining to the specific risk, but even here it depends on the definition. We can have absolute or relative VaR, so technically, we can include/exclude EL because given a quantile on the distribution we can be referring to either (i) the loss relative to zero or (ii) the loss relative to the mean of the distribution
e.g., CVaR = WCL - EL but even one of our basel readings shows CVaR as including the EL, which is not *wrong* it merely refers to an absolute VaR...and our DB LDA study has EC = VaR - EL ... and this in confusing unless and until (I think) we allow that VaR can be relative (to mean) or absolute (to today's zero)
...so the way i would think about it: we need to be specific (absolute or relative?) in regard to our meaning of VaR. One we do that, EC is a function of the VaR (or the WCL, if you like) and EC will depend on whether capital is needed for EL (i.e., for credit, answer is presumed to be "no" and for OpRisk, answer presumed to be "yes") ... then we aggregate the EC rather than the VaR.
David
append: about Crouchy's RAROC, there is no "magic" in excluding EL. The key point is ratio consistency: EL is excluded in the denominator because it is excluded in the numerator (returns net of EL on capital net of EL). Although it would be atypical, it would not be wrong to add EL to both numerator and denominator because you would have a consistent return against UL + EL
As usual, you raise an *interesting* point, I think there may be two ideas within your deceptively simple question...
in regard to aggregation, because the advantage of EC is a "common currency," we can refer to EC for credit risk or for the everything (EC for all risks). Each major risk bucket can have a EL and a UL. So, we can refer to either Credit VaR or EC for Credit risk or EC for all risks combined. EC can be aggregated horizontally accross risk types or up/down the organization
In regard to VaR, I think it gets confusing if we lose sight of fact that VaR is just a distributional quantile; i.e., total VaR is a challenging phrase, I think, because it implies we are combining the distributions (distributional losses) for credit, market and operational risk...
...but instead, Crouhy's RAROC has EC in the denominator which is a function of VaR for each major risk bucket. So we might have:
EC for Credit = Credit VaR = UL = WCL (confidence) - EL, and
EC for OpRisk = WCL(confidence); i.e., following Basel, we would include EL
and then we can aggregate the EC. Although Basel is regulatory capital (not economic capital), that's all it does with the three major risk buckets, it's uses a VaR quantile (market = 99.9% 10-day; credit and opRisk = 99% one year) and simply adds them up (no diversification benefit).
...so the VaR (IMO) is tricky in aggregation and easier to comprehend as the quantile associated with the distribution pertaining to the specific risk, but even here it depends on the definition. We can have absolute or relative VaR, so technically, we can include/exclude EL because given a quantile on the distribution we can be referring to either (i) the loss relative to zero or (ii) the loss relative to the mean of the distribution
e.g., CVaR = WCL - EL but even one of our basel readings shows CVaR as including the EL, which is not *wrong* it merely refers to an absolute VaR...and our DB LDA study has EC = VaR - EL ... and this in confusing unless and until (I think) we allow that VaR can be relative (to mean) or absolute (to today's zero)
...so the way i would think about it: we need to be specific (absolute or relative?) in regard to our meaning of VaR. One we do that, EC is a function of the VaR (or the WCL, if you like) and EC will depend on whether capital is needed for EL (i.e., for credit, answer is presumed to be "no" and for OpRisk, answer presumed to be "yes") ... then we aggregate the EC rather than the VaR.
David
append: about Crouchy's RAROC, there is no "magic" in excluding EL. The key point is ratio consistency: EL is excluded in the denominator because it is excluded in the numerator (returns net of EL on capital net of EL). Although it would be atypical, it would not be wrong to add EL to both numerator and denominator because you would have a consistent return against UL + EL
Hi asja,
I though i might count on you to notice that!
I mentioned b/c it showed up in a sample question, see (a) in question 33:
http://forum.bionicturtle.com/viewthread/1414/
....and from Basel itself in regard to OPERATIONAL RISK (advanced approach, AMA):
669(b). 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. That is, to base the minimum regulatory capital requirement on UL alone, the bank must be able to demonstrate to the satisfaction of its national supervisor that it has measured and accounted for its EL exposure
...so, the philosophy is the same as in credit: Basel wants EL and UL covered, of course. In credit, the presumption is that provisions/reserves cover the EL (but Basel specifically has a check for that, it "redirects" tier 1 capital to credit EL if the EL is not provisioned...although I can't imagine a bank would actually practice that). In OpRisk, the presumption is that EL is not already covered unless the bank can show otherwse.
David
I though i might count on you to notice that!
I mentioned b/c it showed up in a sample question, see (a) in question 33:
http://forum.bionicturtle.com/viewthread/1414/
....and from Basel itself in regard to OPERATIONAL RISK (advanced approach, AMA):
669(b). 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. That is, to base the minimum regulatory capital requirement on UL alone, the bank must be able to demonstrate to the satisfaction of its national supervisor that it has measured and accounted for its EL exposure
...so, the philosophy is the same as in credit: Basel wants EL and UL covered, of course. In credit, the presumption is that provisions/reserves cover the EL (but Basel specifically has a check for that, it "redirects" tier 1 capital to credit EL if the EL is not provisioned...although I can't imagine a bank would actually practice that). In OpRisk, the presumption is that EL is not already covered unless the bank can show otherwse.
David
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