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FRM Part II · FRM Exam Part II · Liquidity Risk

A desk holds USD 20 million of a bond. Daily return volatility is 1.0% and the 99% z-value is 2.33. The desk can only liquidate the position evenly over 4 days. To approximate LVaR for the holding period, the risk manager uses the liquidation-horizon approach: VaR for the full position is scaled by the square root of the liquidation horizon as though the whole position were held for 4 days. Ignoring spread costs, what is that VaR, and what is the reason it is conservative?

The 4-day VaR is USD 932,000: one-day VaR of USD 466,000 times the square root of four. It is conservative because it assumes the full position stays exposed for the whole period, although the position actually shrinks as it is sold.

  1. AUSD 466,000; it is conservative because it assumes the whole position is held for all 4 days rather than being sold downCorrect
  2. BUSD 932,000; it is conservative because it ignores correlation across days
  3. CUSD 233,000; it is conservative because it uses only 1 day
  4. DUSD 466,000; it is conservative because it uses a 95% confidence level

Explanation

1-day VaR = 2.33 x 1% x 20,000,000 = USD 466,000. Scaling by sqrt(4) = 2 gives USD 932,000. So the number is 932,000. Assuming the whole position is exposed for 4 days overstates risk since the position shrinks as it is sold. Option B has the right number and the right logic of conservatism is the full-exposure assumption, not ignoring correlation.

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