Name who takes part in derivatives collateralization and outline how collateral is used.
The idea
Collateralisation involves a collateral giver who posts assets when its position is out of the money, a collateral taker who holds them when exposed, and often a custodian or triparty agent. The custodian holds and values the collateral under a margin agreement such as an ISDA Credit Support Annex. Variation margin tracks the current mark-to-market and cuts present exposure. Let E be the exposure, T the threshold and C the collateral already held. Once the exposure is measured, the call amount to ask the counterparty for is roughly given by: Call = E − T − C. The call is made only if it exceeds the minimum transfer amount, which stops very small transfers. Collateral is valued after a haircut, so a 10 percent haircut means a bond counts for 90 percent of its price. Risk remains because default is followed by a margin period of risk of several days in which the position moves, and eligible collateral can lose value. Exam point: collateral reduces but does not remove exposure.
Formulas
Collateral call under a threshold
Collateral call = E − K − C
- E
- the current exposure to the counterparty
- K
- the threshold left uncollateralised
- C
- the collateral already held, valued after haircuts
Made only if the result reaches the minimum transfer amount. Forgetting to deduct collateral already held is the usual slip.
Market value of securities needed after a haircut
Market value to post = required ÷ (1 − h)
- required
- the collateral value needed after haircut
- h
- the haircut, as a decimal
Divide by one minus the haircut; multiplying the requirement by one plus the haircut understates what must be posted.
Exposure left over the margin period of risk
Residual exposure = z × σ × √MPR
- z
- the standard normal quantile for the confidence level, 2.326 at 99%
- σ
- the daily standard deviation of the portfolio's mark-to-market change, in currency
- MPR
- the margin period of risk in days
Assumes normal, independent daily changes and no threshold. Even daily margining leaves this exposure; scale by the square root of the days, not the days.
A practice question
In a bilateral collateral arrangement for derivatives, which parties typically take part?
- A collateral giver and a rating agency that decides how much collateral must be posted each dayWhy not: Rating agencies do not set margin calls; the amount follows the agreement's exposure formula.
- A collateral taker only, because collateral in a Credit Support Annex always flows in one directionWhy not: Ignores two-way agreements, where either party posts depending on who is out of the money.
- A clearing house and a trade repository that jointly hold the collateral in a segregated accountWhy not: Confuses a trade repository, which only records trades, with a custodian, and applies a cleared set-up to bilateral trades.
- A collateral giver, a collateral taker, and often a custodian or triparty agent - correct
Collateral is posted by the party that is out of the money to the party that is exposed, frequently held by a custodian or triparty agent under the terms of a margin agreement.
A harder one
A one-way collateral agreement has a threshold of USD 3.0 million and a minimum transfer amount of USD 0.5 million. The collateral taker's exposure is USD 9.0 million and it already holds USD 4.7 million of collateral. The call it can make is closest to:
- USD 4.3 millionWhy not: Ignores the threshold: 9.0 - 4.7.
- USD 1.3 million - correct
- USD 6.0 millionWhy not: Subtracts the threshold but ignores the collateral already held: 9.0 - 3.0.
- USD 1.8 millionWhy not: Adds the minimum transfer amount to the call instead of using it as a floor.
Required collateral = 9.0 - 3.0 = 6.0 million; call = 6.0 - 4.7 = 1.3 million, which exceeds the 0.5 million minimum transfer amount, so the call is made.
The hardest tier
Collateral worth USD 30 million after haircut is required. The collateral will be government bonds with a 15 percent haircut. The market value of bonds that must be posted is closest to:
- USD 34.5 millionWhy not: Treats the haircut as a mark-up: 30 x 1.15.
- USD 25.5 millionWhy not: Applies the haircut to the required value instead of dividing the requirement by (1 - haircut).
- USD 30.0 millionWhy not: Ignores the haircut entirely.
- USD 35.3 million - correct
Bonds count for 85 percent of market value, so the market value needed = 30 / 0.85 = 35.29 million.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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