IAI Actuarial Core Principles · Economic Modelling · Measures of investment risk
A fund's annual return is normally distributed with mean 9% and standard deviation 12%. What is the probability that the return is below 0%? (Use Φ(0.75)=0.7734.)
The shortfall probability is 22.66%. The standardised value is (0-9)/12 = -0.75, and Φ(-0.75) = 1 - 0.7734 = 0.2266. The 77.34% figure is the probability of a positive return, which is the opposite tail.
- A12.66%
- B22.66%Correct
- C27.34%
- D7.50%
- 77.34%
Explanation
z=(0-9)/12=-0.75. P(R<0)=Φ(-0.75)=1-0.7734=0.2266. The 77.34% option is the probability of exceeding zero, the wrong tail. The 27.34% option arises from wrongly using 1-0.7266.
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