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# COLLATERAL : Calculation of Credit Support Amount

#### ABSMOGHE

##### New Member
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.

#### Attachments

• Ch26_Collateral Example.xlsx
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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
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, Last edited:

#### ABSMOGHE

##### New Member
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 #### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
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!