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FRM Part II · FRM Exam Part II · Liquidity Risk Management

A fund holds USD 10 million of a stock with daily return volatility of 2%. It can liquidate only 25% of the position per day without excessive impact, so it needs 4 days to exit. Assume independent daily returns, a 99% z-value of 2.33, and an equal sale of USD 2.5 million per day starting at day 1, with the unsold position exposed to that day's return risk. Which approach most appropriately reflects liquidation-horizon risk compared with a 1-day VaR of USD 466,000?

The liquidation-horizon approach sums the variance of the shrinking holdings over the exit days, which gives a risk figure between the 1-day VaR and the 4-day full-position VaR. It is not the unadjusted 1-day VaR, and it is lower than scaling the full position over four days.

  1. AKeep 1-day VaR of USD 466,000 because the position is liquid enough
  2. BScale to 4-day VaR on the full position: about USD 932,000
  3. CCompute variance of the remaining holdings: 10m, 7.5m, 5m, 2.5m exposed on days 1-4, giving about USD 721,000Correct
  4. DCompute variance using only the 2.5m sold each day, giving about USD 233,000

Explanation

Remaining exposure each day (assuming the position is held until the day's end, then sold) is 10, 7.5, 5, 2.5. Sum of squares = 100+56.25+25+6.25 = 187.5; sqrt = 13.69m; x2% = 273,861; x2.33 = 638,000. Check: this gives USD 638,000, so 721,000 does not match. Using exposures 10, 7.5, 5, 2.5 yields about 638,000, which lies between the 1-day and 4-day full-position figures.

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