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# Errors Found in Study Materials P2.T6. Credit Risk

##### New Member
Hi, i do not know if this has been reported, but default correlation formula in page 19 is confusing: square root of pi2(1-pi2) should not be squared 2 times.

regards

##### New Member
Not an error, but i am not able to find [CR-13] Counterparty Risk Intermediation study notes. Is it available or just can not find it?

#### David Harper CFA FRM

##### David Harper CFA FRM
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Hi @Carlos Madrid Apologies for the typo on page 19, indeed there is incorrectly shown an extra square root (this has been tagged for a fix and revision). In regard to CR-13 (aka, R45 Gregory), actually Deepa is currently working on the updated (2018) version including Gregory's XVA Chapter 9 (actually, it's an update to each of Chapter 4, 5, 6. 7. 9, 12, 14 and 17) so it's not currently available but will be fairly soon. Thank you!

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#### David Harper CFA FRM

##### David Harper CFA FRM
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HI @Karim_B Yes, absolutely you are correct, we mangled this (although I can see why, the source Stulz is confusing as usual). We will replace with this (cc: @Nicole Seaman ):
"If the debt is risky, there is no guarantee the principal amount will be repaid in full. Specifically, if the value of the firm falls below the principal amount, if V(T) < F, then the firm is insolvent and the debt holders can only recover the firm's value. Therefore, the payoff to debt holders is Min[V(T), F]; i.e., their payoff must be at least equal to the firm's value but cannot be greater than the principal amount. Further, Min[V(T), F] = F - Max[F - V(T), 0], which illustrates that the debt holders' payoff is economically equivalent to the debt principal minus the payoff of a put option on the firm's assets, V(T), with an exercise price equal to K. Consider the same example where F = $100. If V(T) =$120, then debt holders receive Min(100, 120) = 100 - Max(100 - 120, 0) = $100. But if V(T) =$80, then debt holders receive Min(100, 80) = 100 - Max(100 - 80, 0) = \$80."
Updated in Notes

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#### Nicole Seaman

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Hi @David Harper CFA FRM
R44.P2.T6 Malz Study Notes page 42:

I think the Default01 formula should have 1/20 multiplied by the difference in the next 2 terms rather than just being 1/20th of the 1st term.

Current formula:
View attachment 1510

What I think it should be:
Default01 = 1/20 * [(mean value/loss for Pi + 0.0010) − (mean value/loss for Pi − 00.0010)]

Thanks
Karim
@David Harper CFA FRM

Can you confirm that this is an error in the notes? Thank you! Nicole

#### David Harper CFA FRM

##### David Harper CFA FRM
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Thank you (again) @Karim_B ! @Nicole Seaman yes, as can be confirmed on page 333 of Malz (Chapter 9), Karim is correct. Thank you,

#### silver7

##### New Member
I am looking at the formulas for BCVA stress test. However, the notation is really confusing. Could anyone clarify which belongs to which (counterparty or the firm itself)?

For example, in the notes, it says S(I) is the counterparty's survival rate. (Topic 32, page 13) however, in the practice 708.3, according to the solution, C is correct, but it says S(I) is the Survival rate of the firm itself. So which notation is correct? Also, could someone clarify the notations for other variables as well?
Thank you.

#### David Harper CFA FRM

##### David Harper CFA FRM
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@silver7 I apologize but the Study Note appears to have a typo (it has been a struggle to cope with all of the different CVA assignments). cc @Nicole Seaman. The Study note page 13 should read "... so the probability that the counterparty has survived must enter into the calculation as S(n)."

Question 708.3 is correct: S(I) is the survival probability of the institution and S(n) is the survival probability of the counterparty. The first term is unilateral CVA such that we've basically got LGD*EE*PD each for the counterparty; i.e., LGD(counterparty)*EE(counterparty)*PD(counterparty). In BCVA the institution's own credit risk is added such that the two terms are (without respect to the +/-):
• CVA --> LGD(counterparty)*EE(counterparty)*PD(counterparty)
• DVA -->LGD(institution)*EE(institution)*PD(institution)
But these terms presume survival by the non-defaulting firm such that survivals enter as the following, where PS = probability of survival:
• CVA --> LGD(counterparty)*EE(counterparty)*PD(counterparty)*PS(institution)
• DVA -->LGD(institution)*EE(institution)*PD(institution)*PS(counterparty).
See Gregory below. #### rnavarro

##### New Member
From

P2.T6. Credit Risk Measurement & Management
Giacomo De Laurentis, Renato Maino, and Luca
Molteni: Developing, Validating and Using Internal
Ratings (p. 21)

N = the cumulated normal distribution operator
is missing in the probability of default. The text has this operator.

#### rnavarro

##### New Member
I have the 2018 GARP copy of De Laurentis and the normal cdf operator is present.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
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@rnavarro yes understood, but (per the link I shared to you) does it still also contain numerator ... µT + 1/2 σ(a)^2; i.e., missing the final "T"?
I don't know how many of the many errors we've contributed have been corrected

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#### JulioFRM

##### Member
Hi @David Harper CFA FRM , In the study notes of this topic, in page 4, it says that "If the debt is risky, that is, when the value of the firm falls below the principal amount to be paid back (V(t) < F) then the debt holders receive the maximum of F − V(t) or zero." However, I believe that when the value V falls below F, debt holders won't receive the maximum of F - V(t) and 0; debt holders will receive less than the loan amount F BY AN AMOUNT equal to F - V(t). But it is not that debt holders receive f-v. As a result, if the value of the firm is greater than f, then max is = to 0 and debt holders receive the whole loan amount back. If f is greater than v, then they receive less than the loan amount f by an amount f-v. Please let me know what you think. Thanks.

#### David Harper CFA FRM

##### David Harper CFA FRM
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Hi @JulioFRM Yes, I absolutely agree, it is our mistake in the text. Thank you, and apologies for any confusion. It can be difficult to follow Stulz's confusing language, but it should read:

"If the debt is risky, the debt holders are not guaranteed full repayment of the principal amount, F. Specifically, if the value of the firm falls below the debt's principal amount, then the debt holders can only be repaid the (reduced) value of the firm; i.e., if V(t) < F then debt repayment equals V(t). This can be restated in option terms: if the value of the firm falls below the principal amount to be repaid, then the debt holders receive the face value minus the difference, F - V(t). That is, if V(t) < F then debt repayment F - [F-V(t)] = V(t). In this way, we can express the repayment in option terms that accommodates any future V(t):

D(T) = F - Max[F - V(t). 0] = F - [Put option on firm's assets, V(t), with exercise price of debt principal, F]"

Thank you!

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#### Flashback

##### Active Member
The first one is correct. And same is used to answer correctly in GARP's Mocks.
In denominator, both calculations are the standard deviations of default probabilities of each variable.
In numerator the calculation is a covariance of PDs of both variables.

#### Nicole Seaman

Staff member
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default correlation should be like below I believe..

View attachment 1800

if you please see it is like below in the doc.

View attachment 1801
Hello @jaivipin

Can you post the specific reading that you are referring to and if possible the page that this is located on? This thread is for all readings in Topic 6, so it is helpful to know which reading you are referring to so I don't have to search through everything. I want to make sure this is fixed in the document. Thank you,

Nicole