FRM Part I · FRM Exam Part I · Measures of Financial Risk
A portfolio's annual returns are normally distributed with a mean of 8% and a standard deviation of 12%. Using the normal approximation, what is the 95% one-year VaR (z = 1.645) expressed as a loss relative to the initial value, with the mean taken into account?
The 95% VaR is 11.74%. It equals 1.645 times the 12% standard deviation (19.74%) minus the 8% expected return, because the mean offsets part of the potential loss when VaR is measured against the initial value.
- A11.74%Correct
- B19.74%
- C27.74%
- D8.00%
Explanation
VaR relative to zero return = z*sigma - mu = 1.645*12% - 8% = 19.74% - 8% = 11.74%. The 19.74% option ignores the expected return (it is VaR relative to the mean). The 27.74% option adds the mean instead of subtracting it.
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