Fat Tailed distributions and the impact on VAR.

[Helen]

Fat Tailed distributions and the impact on VAR.

[Anonymous]

Hello:

The question below appeared in the simulated question list. The proposed answer given was c.

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 = 2
(b) A distribution with kurtosis = 0
(c) A distribution with kurtosis = 8
(d) A distribution with kurtosis = 3

The correct answer is choice ‘c’
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 ‘c’ is therefore the correct answer. Also refer to the tutorial about VaR and fat tails.

Based on the tutorial and the text (page 118), wouldn’t heavy tail (high +ve kurtosis level) underestimate the VAR instead? Please correct me if I am mistaken.

Thanks

[Anonymous]

HH,

Thank you for the question. Actually this question is not about over or underestimation of VaR, but simply which of the distributions will provide the highest estimate for VaR. In other words, this is not about comparing a leptokurtic distribution to a normal distribution – the context in which the question of over or underestimation would arise.

Since there are 4 distributions, the one with the fattest tail would have its last 1% (or whatever the confidence level is) at the maximum distance to the left of zero. Therefore the one with the highest kurtosis will have the highest VaR.
Hope this helps.

Mukul

[Anonymous]

I think that the question is quite awkward and create confusion. In short, higher kurtosis means fat-tail.Fat tail underestimates VaR at high confidence interval and overestimate VaR at low confidence interval . That should be enough for the exam.

[Author]

Posts