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FRM Part II · FRM Exam Part II · Derivatives

A dealer's exposure to a counterparty under a daily-margined CSA is assessed using a margin period of risk (MPOR). The dealer's risk team increases the assumed MPOR from 10 to 20 business days because of illiquid, hard-to-value trades and frequent collateral disputes. Assuming exposure changes follow a random walk with constant volatility, by approximately what factor does the potential exposure on the collateralized portfolio change?

Potential exposure rises by about 1.41 times. With random-walk dynamics, exposure over the margin period of risk scales with the square root of time, so doubling the MPOR from 10 to 20 days multiplies it by root two, not by two.

  1. AIt rises by about 1.41 timesCorrect
  2. BIt doubles
  3. CIt rises by about 1.19 times
  4. DIt is unchanged because collateral is posted daily

Explanation

Under a random walk, exposure over the MPOR scales with the square root of time. sqrt(20/10) = sqrt(2) = about 1.41. Doubling would imply linear scaling. Daily margining does not remove the exposure that builds during the MPOR.

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