Financial Risk Manager Part 1
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Which of the following is incorrect about kurtosis?
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NNikitesh
A
Excess kurtosis is a measure relative to the uniform distribution, which has a kurtosis of 3
B
Excess kurtosis that's negative indicates a platykurtic distribution
C
Excess kurtosis that's positive indicates a leptokurtic distribution
D
The normal distribution has a kurtosis equal to 3
Explanation:
Explanation
Kurtosis measures the peakedness of a distribution and the heaviness of its tails. The key concepts are:
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Kurtosis of Normal Distribution: The normal distribution has a kurtosis of exactly 3.
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Excess Kurtosis: This is defined as kurtosis minus 3 (the kurtosis of the normal distribution). Therefore, excess kurtosis is measured relative to the normal distribution, not the uniform distribution.
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Types of Distributions:
- Leptokurtic: Excess kurtosis > 0 (positive) - distribution has fatter tails and higher peak than normal
- Platykurtic: Excess kurtosis < 0 (negative) - distribution has thinner tails and flatter peak than normal
- Mesokurtic: Excess kurtosis = 0 - distribution has same kurtosis as normal
Why Option A is incorrect:
- Excess kurtosis is measured relative to the normal distribution (kurtosis = 3), not the uniform distribution.
- The uniform distribution actually has a kurtosis of 1.8, not 3.
Correct statements:
- Option B: Correct - Negative excess kurtosis indicates platykurtic distribution
- Option C: Correct - Positive excess kurtosis indicates leptokurtic distribution
- Option D: Correct - Normal distribution has kurtosis equal to 3
This question tests understanding of kurtosis measurement and the reference point for excess kurtosis calculations.
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