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

A risk manager computes LVaR for a position of USD 50 million. Mid-price VaR is USD 1.0 million. The relative spread has mean 0.40% and standard deviation 0.10%; the spread-risk multiplier is 3.0. What is the LVaR, and what share of it is liquidity cost? Use LVaR = VaR + 0.5 × P × (mean + multiplier × standard deviation).

LVaR is USD 1.175 million. The liquidity cost is half of 50 million times a stressed spread of 0.7%, which is USD 175,000. That is about 14.9% of LVaR, since 175,000 divided by 1,175,000 is 0.149.

  1. AUSD 1.175 million; liquidity cost about 14.9%Correct
  2. BUSD 1.100 million; liquidity cost about 9.1%
  3. CUSD 1.175 million; liquidity cost about 17.5%
  4. DUSD 1.350 million; liquidity cost about 25.9%

Explanation

Spread term = 0.004 + 3 × 0.001 = 0.007. Cost = 0.5 × 50m × 0.007 = 175,000. LVaR = 1,000,000 + 175,000 = 1,175,000. Share = 175,000/1,175,000 = 14.9%. Option 3 divides by VaR instead of LVaR; option 2 uses only the mean spread.

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