FRM Part I · FRM Exam Part I · Sample Moments
A risk analyst estimates the kurtosis of a portfolio's daily returns as 5.2. Which statement is the most accurate description relative to a normal distribution?
The distribution is leptokurtic. A normal distribution has kurtosis of 3, so a value of 5.2 means excess kurtosis of 2.2, indicating fatter tails and more frequent extreme returns. Kurtosis says nothing about the direction of asymmetry, which is measured by skewness.
- AThe distribution is leptokurtic, with fatter tails and a higher chance of extreme outcomes than the normalCorrect
- BThe distribution is platykurtic, with thinner tails than the normal
- CThe distribution is negatively skewed, with a longer left tail
- DThe distribution is mesokurtic, because kurtosis exceeds zero
Explanation
A normal distribution has kurtosis of 3, so excess kurtosis here is 2.2. Kurtosis above 3 means leptokurtic, with fat tails. Kurtosis measures tail heaviness, not asymmetry, so skewness cannot be inferred from it.
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