FRM Part I · FRM Exam Part I · Random Variables
A portfolio's annual return is normally distributed with mean 8% and standard deviation 12%. Using N(0.5)=0.6915, N(1.0)=0.8413, N(1.5)=0.9332, N(2.0)=0.9772, what is the probability that the return is below −4%?
The probability is 0.1587. The standardized value is (−4% − 8%)/12% = −1.0, and the normal probability below −1 standard deviation is 1 − 0.8413 = 0.1587.
- A0.1587Correct
- B0.0668
- C0.0228
- D0.8413
Explanation
z = (−4 − 8)/12 = −1.0. P(Z < −1) = 1 − N(1.0) = 1 − 0.8413 = 0.1587. Option B is the probability for z = −1.5, from a wrong standardization. Option D is the upper-tail complement, a sign error.
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