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

A risk manager adds a liquidity cost to the standard VaR of a single-asset position using the constant-spread approach. Which expression correctly gives the liquidity-adjusted VaR (LVaR) when the position value is P, the mean relative bid-ask spread is S, and the VaR is computed on the mid-price?

LVaR equals VaR plus half the position value times the relative spread. Liquidation occurs at the bid, which sits half a spread below the mid-price, so only half the spread is the liquidity cost. Adding the full spread would overstate the cost.

  1. ALVaR = VaR + 0.5 × P × SCorrect
  2. BLVaR = VaR + P × S
  3. CLVaR = VaR − 0.5 × P × S
  4. DLVaR = VaR × (1 + S)

Explanation

Liquidating at the bid rather than the mid-price costs half the quoted spread, so the exogenous liquidity cost is 0.5 × P × S. This is added to the mid-price VaR. Using the full spread overstates the cost because the position is only sold, not bought and sold.

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