CFA Level I · CFA Level I Exam · Statistical Distributions for Financial Asset Prices and Returns
An analyst models the price of a share as lognormally distributed. Which statement about the distribution of the share price is most accurate?
A lognormal price distribution is bounded below by zero and positively skewed. Because the price is the exponential of a normally distributed variable, it can never be negative, and large upward outcomes stretch the right tail, unlike the symmetric normal distribution.
- AIt is symmetric around its mean and can take negative values.
- BIt is bounded below by zero and positively skewed.Correct
- CIt is bounded above by zero and negatively skewed.
Explanation
If the natural log of price is normal, price equals e raised to a normal variable, so it is always positive and has a long right tail (positive skew). The symmetric option describes the normal distribution, which allows negative values.
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