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FRM Part II · FRM Exam Part II · Liquidity Risk

A portfolio holds USD 20 million of a bond. Its 99% one-day VaR is USD 600,000. The bond's mean relative bid-ask spread is 0.50% and the spread's standard deviation is 0.20%. Using a constant-spread-plus-exogenous-spread approach with a 99% spread multiplier of 2.33, and the common formula LVaR = VaR + 0.5 × V × (mean spread + k × spread std dev), what is the LVaR?

LVaR equals USD 696,600. The spread term is 0.5% plus 2.33 times 0.2%, giving 0.966%. Half of that on USD 20 million is USD 96,600, which is added to the USD 600,000 VaR. Using the full spread instead of half would double the liquidity cost.

  1. AUSD 600,000 plus USD 96,600 = USD 696,600Correct
  2. BUSD 600,000 plus USD 193,200 = USD 793,200
  3. CUSD 600,000 plus USD 46,600 = USD 646,600
  4. DUSD 600,000 plus USD 100,000 = USD 700,000

Explanation

Spread term = 0.005 + 2.33 × 0.002 = 0.00966. Half of that is 0.00483, multiplied by 20 million gives 96,600. LVaR = 600,000 + 96,600 = 696,600. The 793,200 option forgets the 0.5 factor; 646,600 uses only the volatility term; 700,000 uses the mean spread alone with no half factor.

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