CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
A portfolio manager's monthly returns are normally distributed with a mean of 1.0% and a standard deviation of 4.0%. The z-score for a monthly return of 9.0% is closest to:
The z-score is 2.00. It is found by subtracting the mean of 1.0% from the observed 9.0% return to get 8.0%, then dividing by the 4.0% standard deviation. Skipping the mean subtraction would give 2.25, which is incorrect.
- A1.00
- B2.00Correct
- C2.25
Explanation
z = (9.0 − 1.0)/4.0 = 2.00. The value 2.25 results from dividing 9.0 by 4.0 without subtracting the mean, so the mean adjustment is missed.
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