FRM Part I · FRM Exam Part I · Random Variables
Daily P&L of a trading desk is normally distributed with mean USD 0 and standard deviation USD 2 million. Using z-values of 1.645 for the 95th percentile and 2.326 for the 99th percentile, what is the one-day 99% VaR, and how does it compare with the 95% VaR?
With a zero mean, VaR equals the z-value times the standard deviation. At 99% that is 2.326 x USD 2 million, about USD 4.65 million, and at 95% it is 1.645 x 2, about USD 3.29 million. The higher confidence level gives the larger VaR.
- AUSD 3.29 million at 99%; 95% VaR is USD 4.65 million
- BUSD 4.65 million at 99%; 95% VaR is USD 3.29 millionCorrect
- CUSD 4.65 million at 99%; 95% VaR is USD 1.645 million
- DUSD 2.33 million at 99%; 95% VaR is USD 1.65 million
Explanation
With zero mean, VaR = z x sigma. 99%: 2.326 x 2 = 4.652 million. 95%: 1.645 x 2 = 3.29 million. The 95% figure of 1.645 million forgets to multiply by sigma, and the 2.33/1.65 option uses z-values without scaling.
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