Outline how margin and default funds are applied and estimated under central clearing.
The idea
Variation margin passes daily mark-to-market gains and losses between members through the CCP, so exposure does not accumulate. Initial margin is posted by each member against potential future loss on its own portfolio over the margin period of risk, the time needed to close out after a default. In a typical estimate, z comes from a high confidence level such as 99 percent, σ is daily volatility and MPOR is the margin period in days. For a portfolio, σ uses correlations, so offsetting positions need less margin than the sum of the separate positions. Initial margin, written IM, then combines these inputs with the size of the position. IM = z × σ × √MPOR × Position. The default fund is a pool contributed by members and used when a defaulter's own resources are insufficient. It is sized from stress tests, commonly so that the default of the two members with the largest stressed losses (cover-2) can be absorbed. The common error is scaling the margin period linearly instead of with its square root.
Formulas
Initial margin on a position
IM = z × σ × √MPOR × Position
- z
- the normal quantile for the confidence level, 2.326 at 99%
- σ
- the daily volatility of the position, or of the portfolio with correlations
- MPOR
- the margin period of risk, in days
- Position
- the size of the position
Normal, independent daily returns. Scale by the square root of the margin period, never linearly; offsetting positions in a portfolio need less than their separate margins.
A practice question
Which statement best describes the roles of variation margin (VM) and initial margin (IM) at a CCP?
- IM passes daily gains and losses between members through the CCP; VM covers potential future losses that could arise during the close-out of a defaulted member.Why not: Reverses the two roles: IM is the buffer for future losses, VM settles current gains and losses.
- VM is the member's contribution to the mutualised default fund; IM is a fee returned at year end.Why not: Confuses VM with default fund contributions; IM is collateral, not a fee.
- VM passes daily gains and losses between members; IM covers potential future losses on the member's portfolio during the period needed to close it out after default. - correct
- Both cover the same current exposure, and IM is only called if VM payments fail.Why not: Treats IM as a back-up to VM; IM is posted up front against future movements.
VM settles current exposure each day; IM is a buffer sized for potential future exposure over the margin period of risk.
A harder one
A CCP sets initial margin for a USD 200 million position with daily volatility of 0.8%, using a 99% confidence level (z = 2.326), a 5-day margin period of risk and normally distributed returns. The initial margin is closest to:
- USD 8.32 million - correct
- USD 3.72 millionWhy not: Uses a one-day horizon and ignores the 5-day margin period of risk.
- USD 18.61 millionWhy not: Scales the one-day figure linearly by 5 instead of by the square root of 5.
- USD 5.88 millionWhy not: Uses the 95% quantile (1.645) instead of the 99% quantile (2.326).
IM = z x sigma x sqrt(MPOR) x position = 2.326 x 0.008 x 2.236 x 200 = USD 8.32 million.
The hardest tier
A CCP margins a member's portfolio as a whole at a 99% confidence level (z = 2.326) and a 5-day margin period of risk. The member is long USD 100 million of asset X (daily volatility 1.0%) and short USD 60 million of asset Y (daily volatility 0.9%). The correlation of daily returns is 0.7. Assuming normal returns, the initial margin is closest to:
- USD 8.01 millionWhy not: Adds the stand-alone margins of the two positions and gives no credit for the hedge.
- USD 5.91 millionWhy not: Assumes zero correlation, so the hedge benefit of the short position is ignored.
- USD 3.81 million - correct
- USD 2.39 millionWhy not: Assumes correlation of 1, which overstates the hedge benefit of the short position.
Daily portfolio sigma = sqrt(1.0² + 0.54² - 2 x 0.7 x 1.0 x 0.54) = 0.7318 (USD million). IM = 2.326 x 2.236 x 0.7318 = USD 3.81 million.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
Start free →More in Central Clearing
- State what a central counterparty (CCP) is and outline how central clearing works.
- Account for novation as it applies in central clearing.
- Explain multilateral offset, compression and netting, illustrating each with a case.
- Discuss the exposures a CCP bears and how it controls them.
- Show a loss waterfall at work through illustrations.
- Account for the ways losses are absorbed and the default of one or more CCP members is handled.
- Contrast clearing done bilaterally with clearing done through a central counterparty.
- Contrast the initial margin and default fund contributions asked of clearing members, with respect to how losses are covered, what clearing costs and the moral hazard created.
- Outline the strengths and weaknesses of central clearing.