Economic Capital = Unexpected Loss? and RAROC
- Thread starter ajsa
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Hi ajsa,
okay, sorry i didn't get to it...maybe this thread from last week helps:
http://forum.bionicturtle.com/viewthread/1734/
I do tend to think of EC = UL = WCL (confidence) - EL = CVaR (confidence), where Ong's UL is the special case of low confidence corresponding to one standard deviation...
where CVaR (confidence) here *excludes* EL but that is definitional; just as market VaR can be relative to zero (initial value) or expected future value, CVaR can be relative to starting value (zero) or expected future value (i.e., minus EL).
but i suppose beyond the math, there have different connotations:
You might like the PPT presentation (by Jennifer Lang) I attached to the practice question:
http://www.bionicturtle.com/learn/article/economic_capital_practice_ops/
Note that GARP asserts as true, from the question above:
"I. Economic capital is designed to provide a cushion against unexpected losses at a specified confidence level over a set time horizon."
couple of thoughts about that ...
* Ms Lang's presentation notes that EC is *not* a captial resource but rather a risk currency (!)
* such that my perspective would be: UL is a measure of EC (UL = EC and they differ only in application/context), where the UL is generically WCL(alpha) - EL and, as such, is a usable measure in both regulatory (external) and internal...so UL is like the generic metric
e.g., Basel's capital adequay ratio is calibrated by UL (e.g., IRB Credit is a UL @ 99.9% one-year),
but so is EC an *internal* risk measure also calibrated by UL (i.e., EC = UL but calibrated to keep us solvent)...
...and as EC is a risk measure, like VaR, then RAROC = risk-adj return / EC (EC in the denominator) but it can just as well be:
RAROC = risk -adj return / UL
David
okay, sorry i didn't get to it...maybe this thread from last week helps:
http://forum.bionicturtle.com/viewthread/1734/
I do tend to think of EC = UL = WCL (confidence) - EL = CVaR (confidence), where Ong's UL is the special case of low confidence corresponding to one standard deviation...
where CVaR (confidence) here *excludes* EL but that is definitional; just as market VaR can be relative to zero (initial value) or expected future value, CVaR can be relative to starting value (zero) or expected future value (i.e., minus EL).
but i suppose beyond the math, there have different connotations:
You might like the PPT presentation (by Jennifer Lang) I attached to the practice question:
http://www.bionicturtle.com/learn/article/economic_capital_practice_ops/
Note that GARP asserts as true, from the question above:
"I. Economic capital is designed to provide a cushion against unexpected losses at a specified confidence level over a set time horizon."
couple of thoughts about that ...
* Ms Lang's presentation notes that EC is *not* a captial resource but rather a risk currency (!)
* such that my perspective would be: UL is a measure of EC (UL = EC and they differ only in application/context), where the UL is generically WCL(alpha) - EL and, as such, is a usable measure in both regulatory (external) and internal...so UL is like the generic metric
e.g., Basel's capital adequay ratio is calibrated by UL (e.g., IRB Credit is a UL @ 99.9% one-year),
but so is EC an *internal* risk measure also calibrated by UL (i.e., EC = UL but calibrated to keep us solvent)...
...and as EC is a risk measure, like VaR, then RAROC = risk-adj return / EC (EC in the denominator) but it can just as well be:
RAROC = risk -adj return / UL
David
...sorry to belabour, just wanted to share link to Jennifer's article on EC, which is the best-clearest I've read:
http://ozrisk.net/2009/04/20/economic-capital-a-common-currency-of-risk/
David
http://ozrisk.net/2009/04/20/economic-capital-a-common-currency-of-risk/
David
Thanks David..
below is how Schweser defined them:
EC = EV -P(c)
EL = FV-EV
UL= deviation of EL
FV: fwd portfolio value with promised return
EV: expected portfolio value with expected return
P(c): portfolio value in the worst case at (1-c) confidence level
so it does not seem to be consistent with yours.. I agree you explainations make a lot of sense but I am just a little confused.
thanks.
//BTW, I posted several question in Credit Risk forum. If you get chance, could you pls take a look? I feel this part requires a lot of good understandings.. Thanks again!
below is how Schweser defined them:
EC = EV -P(c)
EL = FV-EV
UL= deviation of EL
FV: fwd portfolio value with promised return
EV: expected portfolio value with expected return
P(c): portfolio value in the worst case at (1-c) confidence level
so it does not seem to be consistent with yours.. I agree you explainations make a lot of sense but I am just a little confused.
thanks.
//BTW, I posted several question in Credit Risk forum. If you get chance, could you pls take a look? I feel this part requires a lot of good understandings.. Thanks again!
Hi asja,
Interesting, thanks for sharing...it's just different terminology (I am not sure which reading these terms refer to, but these definitions comport with mine, which I got from the readings)...
distribution runs from no credit losses (FV) to expected losses (EL = FV - EV) to unexpected losses (UL = WCL - EL).
Such that EL + UL = Worst case Loss (WCL)
there are two issues, i can see:
1. aside from their definitions, I probably should not use CVaR to include the EL, because CVaR confuses (i.e., the CVaR, like any VaR, can be absolute or relative; so there are two version of this). So i replaced my CVaR with WCL(alpha) to avoid confusion...
2. UL= deviation of EL. Recall Ong defines UL as one standard deviation, it's the special case of UL = WCL(alpha) - EL, where that distance will correspond to some multiple of standard deviation. Put again:
Ong's UL = 1 Std Dev; a special case of
UL = WCL - EL = multiple*1 StdDev, such that
EC = multiple * (Ong's UL) = general UL (confidence)
...I really recommend focusing on the credit risk distribution...the terms may vary a bit, but we are just talking about the distance between quantiles on the distribution: from [0 losses] to [FV - EV =EL] to [WCL]. Three quantiles on a skewed distribution.
re credit risk forum, yes, I saw, will get to ASAP.
David
Interesting, thanks for sharing...it's just different terminology (I am not sure which reading these terms refer to, but these definitions comport with mine, which I got from the readings)...
distribution runs from no credit losses (FV) to expected losses (EL = FV - EV) to unexpected losses (UL = WCL - EL).
Such that EL + UL = Worst case Loss (WCL)
there are two issues, i can see:
1. aside from their definitions, I probably should not use CVaR to include the EL, because CVaR confuses (i.e., the CVaR, like any VaR, can be absolute or relative; so there are two version of this). So i replaced my CVaR with WCL(alpha) to avoid confusion...
2. UL= deviation of EL. Recall Ong defines UL as one standard deviation, it's the special case of UL = WCL(alpha) - EL, where that distance will correspond to some multiple of standard deviation. Put again:
Ong's UL = 1 Std Dev; a special case of
UL = WCL - EL = multiple*1 StdDev, such that
EC = multiple * (Ong's UL) = general UL (confidence)
...I really recommend focusing on the credit risk distribution...the terms may vary a bit, but we are just talking about the distance between quantiles on the distribution: from [0 losses] to [FV - EV =EL] to [WCL]. Three quantiles on a skewed distribution.
re credit risk forum, yes, I saw, will get to ASAP.
David
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