For identical mean and variance, which of the following distribution assumptions will provide a higher estimate of VaR at a high level of confidence?

For identical mean and variance, which of the following distribution assumptions will provide a higher estimate of VaR at a high level of confidence?
A . A distribution with kurtosis = 8
B . A distribution with kurtosis = 0
C . A distribution with kurtosis = 2
D . A distribution with kurtosis = 3

View Answer

Answer: A

Explanation:

A fat tailed distribution has more weight in the tails, and therefore at a high level of confidence the VaR estimate will be higher for a distribution with heavier tails. At relatively lower levels of confidence however, the situation is reversed as the heavier tailed distribution will have a VaR estimate lower than a thinner tailed distribution.

A higher level of kurtosis implies a ‘peaked’ distribution with fatter tails. Among the given choices, a distribution with kurtosis equal to 8 will have the heaviest tails, and therefore a higher VaR estimate. Choice ‘a’ is therefore the correct answer. Also refer to the tutorial about VaR and fat tails.