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FRM Part II · FRM Exam Part II · Liquidity Risk

A fund must liquidate USD 80 million of a bond. Assume the mid-price is constant and the half-spread is 0.15% for the first USD 20 million, and the price impact beyond that is linear so that each additional USD 20 million block is sold at a half-spread 0.10% wider than the previous block (blocks 2, 3, 4 have half-spreads 0.25%, 0.35%, 0.45%). What is the total expected liquidation cost relative to mid-value?

Block costs are 0.03, 0.05, 0.07 and 0.09 million, since each USD 20 million block is multiplied by its half-spread. They sum to USD 0.24 million, equal to 0.30% average half-spread times USD 80 million.

  1. AUSD 0.12 million
  2. BUSD 0.24 million
  3. CUSD 0.48 millionCorrect
  4. DUSD 0.96 million

Explanation

Each block is USD 20 million. Costs: 20 x 0.0015 = 0.03; 20 x 0.0025 = 0.05; 20 x 0.0035 = 0.07; 20 x 0.0045 = 0.09. Total = 0.24 million. Check via average half-spread (0.15+0.25+0.35+0.45)/4 = 0.30%; 80 x 0.003 = 0.24. Correct is USD 0.24 million; 0.48 would double count the half-spread as a full spread.

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