COLLATERAL : Calculation of Credit Support Amount

[ABSMOGHE]

Hi @David Harper CFA FRM ,
Firstly thanks a lot for replying to all of my previous questions. I have one more for you.
While going through the calculation for Credit Support Amount, I have the following Query.
In the Notes, the formula for Hypothetical Collateral Amount is stated as MAX(MTM- T, 0)- MAX(-MTM-T , 0) -C
However wouldn't the term MAX(-MTM-T, 0) always amount to 0, since threshold will always be positive ?
Is my interpretation correct ?

Also I have attached an Excel sheet detailing the above calculation. Would really appreciate if you could confirm the calculation and the formulas.

If it is correct, then the value of Portfolio on DAY 3 has fallen down to 800000. However the formula states the credit support amount to be 0.
Since our portfolio has already fallen below 1000000, wouldn't we re be required to deposit the collateral in this case ?

Thanks.

 

[David Harper CFA FRM]

Hi @ABSMOGHE The notes are notes of Gregory, so after I take the time to look it up (because you didn't supply any specific reference to help me save time), I can see that the formula is Gregory Chapter 6.1, see below.

Only one of the max(.) terms will have a positive value. Either the institution will have a gain (ie, MTM > 0) or a loss (ie, MTM < 0) in the position. BTW, don't forget: there is only credit exposure if the institution is sitting on a gain, as CE = Max(0, MtM).

• If MTM > 0, then the first max(.) will "kick in" as max(MTM - threshold_C, 0) will be positive; however
• If MTM < 0, then notice that the second max(.) will indeed kick in because -MTM will be positive! Say MTM = -3.0 million, which means the institution is underwater in the position, then the formula returns max(-3.0 - threshold_C, 0) - max(-(-3.0) - threshold_I) - C = 0 - max(+3.0 - threshold_I) - C.

Re the XLS, I can't seem to open it but honestly, I don't have leisure time to investigate, given we are near to the exam. Thanks,

 

[ABSMOGHE]

Hi @ABSMOGHE The notes are notes of Gregory, so after I take the time to look it up (because you didn't supply any specific reference to help me save time), I can see that the formula is Gregory Chapter 6.1, see below.

Only one of the max(.) terms will have a positive value. Either the institution will have a gain (ie, MTM > 0) or a loss (ie, MTM < 0) in the position. BTW, don't forget: there is only credit exposure if the institution is sitting on a gain, as CE = Max(0, MtM).

• If MTM > 0, then the first max(.) will "kick in" as max(MTM - threshold_I, 0) will be positive; however
• If MTM < 0, then notice that the second max(.) will indeed kick in because -MTM will be positive! Say MTM = -3.0 million, which means the institution is underwater in the position, then the formula returns max(-3.0 - threshold_c, 0) - max(-(-3.0) - threshold_I) - C = 0 - max(+3.0 - threshold_I) - C.

Re the XLS, I can't seem to open it but honestly, I don't have leisure time to investigate, given we are near to the exam. Thanks,

Got it. Appreciate your efforts

 

[thanhtam92]

@David Harper CFA FRM per the screenshot below, if I understand correct, the $775,000 can be returned to the counterparty since it is positive; however, on the next day, when MTM drops, the counterparty need to post $150,000 in collateral correct? Thanks a lot for your help

 

[David Harper CFA FRM]

Hi @thanhtam92 You are correct they go in opposite directions (because the "+" switches to a "-"), but I think it's the inverse of what you wrote. This exhibit replicates (and collapses) Gregory's Tables 6.3 and 6.4, as noted in the header. Assume we are the Financial Institution (FI) and our counterparty is the Counterparty; the exhibit is from our own perspective as the FI. In the first period, we are in-the-money as the Portfolio MTM is +1,754,858; aka, unrealized gain. The CSA of +775,000 indicates that we (the FI) call collateral (aka, make a collateral call) such our Counterparty must post collateral to us. Makes sense, right? We have the credit exposure to them, so they need to post the collateral to us. In the next period, the Portfolio's value drops to MTM = +1,623,920, but we are still very much in-the-money! However, the calculation shows that we are holding a bit too much collateral now: the -150,000 indicates that we (the FI) must return collateral of 150,000 to the Counterparty; after we return 150,000 we will hold 775,000 - 150,000 = 625,000 in collateral. (In fact, if there were only one period shows, the initial period or first day, and the Portfolio MTM were 1,623,920 instead of 1,774,858 then the CSA value would be "+625,000" indicating that we would start with a collateral call of 625,000). I hope that's helpful!

 

[bollengc]

Hi @thanhtam92 You are correct they go in opposite directions (because the "+" switches to a "-"), but I think it's the inverse of what you wrote. This exhibit replicates (and collapses) Gregory's Tables 6.3 and 6.4, as noted in the header. Assume we are the Financial Institution (FI) and our counterparty is the Counterparty; the exhibit is from our own perspective as the FI. In the first period, we are in-the-money as the Portfolio MTM is +1,754,858; aka, unrealized gain. The CSA of +775,000 indicates that we (the FI) call collateral (aka, make a collateral call) such our Counterparty must post collateral to us. Makes sense, right? We have the credit exposure to them, so they need to post the collateral to us. In the next period, the Portfolio's value drops to MTM = +1,623,920, but we are still very much in-the-money! However, the calculation shows that we are holding a bit too much collateral now: the -150,000 indicates that we (the FI) must return collateral of 150,000 to the Counterparty; after we return 150,000 we will hold 775,000 - 150,000 = 625,000 in collateral. (In fact, if there were only one period shows, the initial period or first day, and the Portfolio MTM were 1,623,920 instead of 1,774,858 then the CSA value would be "+625,000" indicating that we would start with a collateral call of 625,000). I hope that's helpful!

hi David,
I am on that same example in the video review of Gregory, Chapter 7 Margin (collateral) and settlement.

What I have troubles to understand is the sentence in yellow:



I understand that out net exposure is the MtM - CSA = 848 920$ and it is currently below the threshold of 1 000 000$.
I thought that nothing happened if the exposure amount is smaller than the threshold ( = level of MtM above which collateral is posted). so I do not get why there should be collateral returned.

and I have the same issue understanding example in the study notes (T6-R13-P2-Gregory-v15 page 35): (I guess it is similar mechanism but example taken from a most recent version of the book, so the values are different)


the portfolio being uncollateralized by 75, that is inferior to the threshold (and the threshold being the amount of uncollateralized exposure), I do not get why any collateral should be posted / returned.

thanks,
Camille

 

[David Harper CFA FRM]

Hi Camille (@bollengc ) Good question. You are correct that "nothing happen if the exposure amount is smaller than the threshold" but in the following sense: if you and myself enter into a CSA with a threshold (using the second of example) of $100, then if their zero initial margin, neither of us posts any collateral, so our margin accounts are zero. If the value goes up to +80 for you (so I am -80), it is under the threshold, and to your point, collateral is not called because the exposure is smaller than the threshold. Then per the example, it jumps to 350, then you will call the incremental 350 - 100 = 250, which I will post. Then, per the example, the value subsequently drops to 325 such that your exposure is +325 but your incremental (ie., above the threshold) exposure is only 325 - 100 = 225. But I've posted 250, which is 25 too much, so I get the extra 25 returned to me. We end up in the same place if the first step was the value increasing to 325, in which case I would post 325 - 100 = 225.

It is similar in the first example, when we get to the second period, the first counterparty has already posted $775,000 in margin (aka, collateral) but the incremental exposure (i.e., above the threshold) dropped from $754,858 (the basis for the rounded-up $775,000) to $1,623,920 value - $1.0 mm threshold = $623,920. The 775,000 is now too much such that a rounded 150,000 can be returned. I hope that's helpful,

 

[bollengc]

Thanks for your answer David.
I now understand the sentence in yellow. We cannot have a net exposure that is smaller than the threshold. So if the new MtM - collateral is below the threshold, we are over protected and we have to post back some collateral to maintain our exposure at the threshold level.

Small numerical example with threshold of 100: (illustrating affect of MtM falling back below threshold)
1st MtM = 80 below threshold, no call for collateral
2nd MtM = 120, call for 20 ( max(120-100,0) - max (-120-100,0) - 0)
3rd MtM = 90, max(90-100,0) - max(-90-100,0) - 20 = -20 I am posting back 20, we are back at 0 collateral (which makes sense as exposure is below threshold)