CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A stock's annual return is normally distributed with a mean of 12% and a standard deviation of 15%. An investor requires a return of at least 0%. Given that the cumulative probability for z = -0.80 is 0.2119, the probability that the stock's return falls below 0% is closest to:
The probability of a return below 0% is about 21.2%. The z-score is (0 − 12)/15 = −0.80, and the cumulative probability at that value is 0.2119. The 78.8% figure is the chance of earning above 0%, not below.
- A12.0%
- B21.2%Correct
- C78.8%
Explanation
z = (0 − 12)/15 = −0.80, so P(R < 0%) = 0.2119, or about 21.2%. The 78.8% result is the probability of exceeding 0%, which is the complement and answers a different question.
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