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

An analyst lengthens the assumed liquidation horizon of a position from 1 day to 4 days to reflect the time needed to sell without moving the market. Daily VaR at 99% is USD 1.5 million and returns are i.i.d. normal. Ignoring the spread cost, what is the VaR over the liquidation horizon, and how does it compare with selling in 1 day?

VaR over four days is USD 3.0 million. With independent, identically distributed normal returns, VaR scales with the square root of time, so 1.5 million times the square root of four equals 3.0 million, double the one-day figure.

  1. AUSD 3.0 million, because VaR scales with the square root of timeCorrect
  2. BUSD 6.0 million, because VaR scales linearly with time
  3. CUSD 1.5 million, because VaR is independent of horizon
  4. DUSD 0.75 million, because longer horizons reduce risk

Explanation

Under i.i.d. normal returns, VaR scales with the square root of time: 1.5 × √4 = 3.0 million. Linear scaling gives 6.0 million, which wrongly assumes perfect serial correlation of returns. The longer horizon doubles the market risk borne while liquidating.

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