I'm not sure where to put this question, so I apologize if it's in the wrong thread. I read that default correlation has no influence on EL. I don't understand that. For a portfolio, EL is a simple product of EAD, PD, and LGD. In this case, PD is the combined default probability of the entire portfolio and that is affected by default correlations. Isn't that right? Or are we assuming that for a portfolio, we would calculate EL separately for each instrument and then simply add them up to get EL of the portfolio (which is equivalent of assuming default correlation of 1)
Default correlation in expected loss?
- Thread starter frm_prep
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Hi @frm_prep No worries. For an individual position, of course EL = PD*LGD*EAD and this is arguably the most fundamental formula in credit risk. This is obviously a product and, although it is rarely mentioned, implicitly it assumes that PD and LGD are uncorrelated, ρ(PD,LGD) = 0, because if ρ(PD,LGD) > 0, then EL > PD*LGD*EAD.
Expect loss (EL) is a mean and portfolio expected loss (EL) is the sum of individual (aka, component) expected losses, EL(P) = EL(1) + EL(2) + .... + EL(N), and such a summation has no role for default correlation, so we say "Portfolio EL is invariant to default correlation" where default correlation refers to pairwise default correlation between the positions (this is a typical correlation matrix but instead of pairwise correlation between returns, the cells are pairwise correlations of defaults).
The portfolio UL is a standard deviation (not a summation) and, just like the tradition portfolio variance, does have a role for the default correlation matrix such that portfolio UL is highly variant to default correlations. I hope that's helpful,
Expect loss (EL) is a mean and portfolio expected loss (EL) is the sum of individual (aka, component) expected losses, EL(P) = EL(1) + EL(2) + .... + EL(N), and such a summation has no role for default correlation, so we say "Portfolio EL is invariant to default correlation" where default correlation refers to pairwise default correlation between the positions (this is a typical correlation matrix but instead of pairwise correlation between returns, the cells are pairwise correlations of defaults).
The portfolio UL is a standard deviation (not a summation) and, just like the tradition portfolio variance, does have a role for the default correlation matrix such that portfolio UL is highly variant to default correlations. I hope that's helpful,
Yes, it definitely helps. Thanks David.
Regarding the last example (GARP practice question number 76) on the CVA chapter from Gregory, I followed all the calculations and I think I understand them. But, what I don't understand is that CVA could have been approximated by simply using the spreads from every year and multiplying them by the EPE. Since the question mentioned that EE remains same for all the years, average of EE, i.e. EPE remains the same (in the example, 15-13=2). When I do a sum-product that way, my answer comes to 0.18 AUD. If I used that approach, I would have selected the option B (0.172 AUD) as being the closest answer. Can you please help me understand what am I missing here?
Regarding the last example (GARP practice question number 76) on the CVA chapter from Gregory, I followed all the calculations and I think I understand them. But, what I don't understand is that CVA could have been approximated by simply using the spreads from every year and multiplying them by the EPE. Since the question mentioned that EE remains same for all the years, average of EE, i.e. EPE remains the same (in the example, 15-13=2). When I do a sum-product that way, my answer comes to 0.18 AUD. If I used that approach, I would have selected the option B (0.172 AUD) as being the closest answer. Can you please help me understand what am I missing here?
@David Harper CFA FRM - I will appreciate if you can help me understand the above.
Hi @frm_prep GARP's practice question 76 was deeply flawed, and required us to submit at least three corrections (informing revisions) over several years; the original author apparently did not understand CVA mechanics. At first glance, let me say: if your approximation generated 0.18 and if the exact answer is nearby, that sounds like an approximation. I do not understand to which version you refer, my 2020 paper gives the following answers: A. AUD 0.214 million, B. AUD 0.253 million, C. AUD 0.520 million, D. AUD 0.998 million. So I don't know to what you refer, actually. But the point is that your approximation will not match the exact solution, but it should be close.
If GARP's choices are too proximate, that's their mistake actually!
See https://forum.bionicturtle.com/threads/garp-2017-p2-76.10344/
tag https://forum.bionicturtle.com/tags/garp17-p2-76/
note: please don't follow-up like you did today, i do my best and don't need to be nagged. Believe it or not, my whole life is not this forum
I'm taking the weekend off, so you can follow up next week with me on this if you like (or post to general, hopefully others can help). Talk to you soon, thanks,
If GARP's choices are too proximate, that's their mistake actually!
See https://forum.bionicturtle.com/threads/garp-2017-p2-76.10344/
tag https://forum.bionicturtle.com/tags/garp17-p2-76/
note: please don't follow-up like you did today, i do my best and don't need to be nagged. Believe it or not, my whole life is not this forum
I'm taking the weekend off, so you can follow up next week with me on this if you like (or post to general, hopefully others can help). Talk to you soon, thanks,Thanks for the detailed explanation, David. I didn't intend to nag you. I apologize for the inconvenience. I just wasn't sure whether you got my question. I haven't used the forum as much, in either part 1 or part 2 until very recently and hence not well versed. Have an excellent long weekend and enjoy your time off .
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