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Compute the margin, meaning the credit support amount, under a number of different scenarios.

FRM® Part II · Credit Risk Measurement and Management · Margin (Collateral) and Settlement · FRM2.CR.17.c

The idea

The standard sequence for a margin call starts with the collateral required. Required = Exposure + IA − Threshold. Here IA is the independent amount the pledgor posts in favour of the secured party, and the threshold is that of the pledgor. The result is floored at zero. Then compare it with the value of collateral already held. Value each asset at market value × (1 − haircut). If required exceeds held, the difference is a delivery (call) amount. If held exceeds required, it is a return amount. Apply the minimum transfer amount (MTA). If the amount is below it, nothing moves. Then round to the stated rounding multiple, delivery amounts up and return amounts down. Frequent errors are forgetting the haircut on securities, subtracting the threshold the wrong way, skipping the MTA test, and rounding in the wrong direction. Work through each step in order and the answer follows.

Formulas

Credit support amount required

Required = E + IA − K

E
the exposure to the pledgor
IA
the independent amount the pledgor must post
K
the pledgor's threshold

Floored at zero. Subtract collateral held to get the call, apply the minimum transfer amount, then round deliveries up and returns down.

Value credited for collateral after a haircut

Collateral value = MV × (1 − h)

MV
the market value of the asset
h
the haircut, as a decimal

Cash in the base currency usually carries no haircut. Forgetting the haircut on securities overstates the collateral held and understates the call.

A practice question

From the question bank, with the reason each wrong option is wrong.

A party has posted USD 5.0 million of collateral. Exposure falls to USD 3.5 million, the threshold is zero and the minimum transfer amount is USD 0.25 million. What is the result?

  1. The secured party returns USD 3.5 millionWhy not: Returns the exposure amount rather than the excess of collateral over exposure.
  2. The pledgor must post a further USD 1.5 millionWhy not: Gets the direction wrong: collateral held exceeds the requirement, so it is returned.
  3. The secured party returns USD 5.0 millionWhy not: Returns all collateral although exposure is still positive and must still be covered.
  4. The secured party returns USD 1.5 million - correct

Required = 3.5, held = 5.0, so the return amount = 5.0 - 3.5 = 1.5, above the MTA.

A harder one

Exposure is USD 6.2 million, the threshold is USD 5.0 million, the minimum transfer amount is USD 1.5 million and no collateral is held. What happens?

  1. A call for USD 1.2 millionWhy not: Ignores the minimum transfer amount test.
  2. A call for USD 1.5 millionWhy not: Calls the MTA itself instead of testing whether the requirement reaches it.
  3. No transfer, because the USD 1.2 million required is below the minimum transfer amount - correct
  4. A call for USD 6.2 millionWhy not: Ignores the threshold, which exempts the first USD 5.0 million.

Required = 6.2 - 5.0 = 1.2, which is less than the MTA of 1.5, so no call is made.

The hardest tier

Exposure is USD 18.0 million and the pledgor's threshold is USD 4.0 million. The pledgor has posted USD 6.0 million cash and bonds with market value USD 5.0 million subject to a 10% haircut. The MTA is USD 0.5 million and rounding is USD 0.5 million. What call is due?

  1. USD 3.0 millionWhy not: Values the bonds at full market value, omitting the haircut.
  2. USD 3.5 million - correct
  3. USD 2.5 millionWhy not: Grosses the bonds up by 1.10 instead of reducing by the haircut.
  4. USD 7.5 millionWhy not: Ignores the threshold: 18.0 less 10.5 of collateral.

Bond value = 5.0 x 0.90 = 4.5; collateral held = 6.0 + 4.5 = 10.5. Required = 18.0 - 4.0 = 14.0; call = 3.5, a multiple of 0.5 and above the MTA.

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