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FRM Part II · FRM Exam Part II · Validating Bank Holding Companies' Value-at-Risk Models for Market Risk

A bank holding company's trading desk holds a portfolio whose 1-day 99% VaR is computed with a variance-covariance model assuming normally distributed returns with daily standard deviation of 1.5% on a position of USD 40 million and zero mean. Validators find that returns have fat tails, with a 99% quantile roughly 3.0 standard deviations instead of 2.33. What is the amount by which the normal-based VaR understates VaR using the fat-tailed quantile, in USD (to the nearest thousand)?

The normal-based VaR understates risk by USD 402,000. Dollar volatility is USD 600,000; normal VaR is 2.33 times that, or USD 1,398,000, while the fat-tailed VaR is 3.0 times, or USD 1,800,000. The difference is USD 402,000.

  1. AUSD 280,000
  2. BUSD 402,000Correct
  3. CUSD 600,000
  4. DUSD 1,398,000

Explanation

Daily sigma in dollars = 0.015 x 40,000,000 = 600,000. Normal VaR = 2.33 x 600,000 = 1,398,000. Fat-tailed VaR = 3.0 x 600,000 = 1,800,000. Understatement = 1,800,000 - 1,398,000 = 402,000. USD 600,000 is just one sigma, and USD 1,398,000 is the normal VaR itself.

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