Financial Risk Manager Part 1
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All of the following statements are true, except:
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NNikitesh
A
If the return distributions of two investments have the same mean and standard deviation, the one which has more a negatively skewed distribution will be considered to be riskier
B
Distributions with positive excess kurtosis are known as leptokurtic
C
If two investments have the same mean, standard deviation and skewness, then the one with the lower kurtosis will be considered riskier
D
The normal distribution has a kurtosis of 3
Explanation:
The correct answer is C because:
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Statement A is TRUE: Negative skewness indicates more frequent large negative returns (losses), making the investment riskier when mean and standard deviation are equal.
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Statement B is TRUE: Leptokurtic distributions have positive excess kurtosis (kurtosis > 3), meaning they have fatter tails and more extreme values than the normal distribution.
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Statement C is FALSE: When two investments have the same mean, standard deviation, and skewness, the one with higher kurtosis (not lower) is riskier. Higher kurtosis indicates more extreme returns (both positive and negative), which increases risk due to greater probability of extreme losses.
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Statement D is TRUE: The normal distribution has a kurtosis of exactly 3. Excess kurtosis is calculated as kurtosis minus 3.
Key Insight: Higher kurtosis means fatter tails in the distribution, which implies greater probability of extreme returns. In risk management, extreme negative returns are particularly concerning, making investments with higher kurtosis riskier when other distribution characteristics are equal.
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