CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
An asset's continuously compounded return over a year is normally distributed with a mean of 8% and a standard deviation of 20%. The expected holding period return, which equals e^(μ+σ²/2) − 1, is closest to:
The expected holding period return is e^(0.08 + 0.02) − 1 = e^0.10 − 1, about 10.5%. The variance term σ²/2 raises the expected price relative above the exponential of the mean log return, so using only 8% would understate it at 8.3%.
- A8.3%
- B10.5%Correct
- C27.5%
Explanation
μ + σ²/2 = 0.08 + 0.04/2 = 0.10. e^0.10 − 1 = 0.1052, or about 10.5%. Using e^0.08 − 1 = 8.3% omits the variance adjustment.
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