FRM Part I · FRM Exam Part I · Calculating and Applying VaR
A risk manager has a 1-day 95% VaR of USD 3.0 million for a portfolio with normally distributed returns and zero mean. Using z-values of 1.645 for 95% and 2.326 for 99%, what is the approximate 1-day 99% VaR?
With normal zero-mean returns, VaR scales with the z-value, so the 99% VaR equals USD 3.0 million times 2.326 divided by 1.645, about USD 4.24 million. Higher confidence means a larger quantile and therefore a larger VaR.
- AUSD 3.00 million
- BUSD 4.24 millionCorrect
- CUSD 3.95 million
- DUSD 2.12 million
Explanation
Under normality with zero mean, VaR is proportional to z. 99% VaR = 3.0 × 2.326 / 1.645 = 3.0 × 1.4140 = USD 4.24 million. USD 3.95 million results from wrongly using the ratio 99/95 style scaling of confidence levels, and 2.12 inverts the ratio.
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