 # kurtosis

I did not understand the following question. Could you please explain about this percentage of deviations. A distribution of returns that has a greater percentage of small deviations from the mean and a greater percentage of large deviations from the mean compared to a normal distribution: A) has positive excess kurtosis. B) is positively skewed. C) is negatively skewed. D) has negative excess kurtosis. Your answer: B was incorrect. The correct answer was A) has positive excess kurtosis. A distribution that has a greater percentage of small deviations from the mean and a greater percentage of large deviations from the mean will be leptokurtic and will exhibit positive excess kurtosis. The distribution will be taller (more peaked) with fatter tails than a normal distribution.

It means that the distribution is more peaked around the mean but has fatter tails (more large deviation from the mean). This is a classic leptokurtic distribution. Consequently, because there are the same number of observations, the deviations that are kind of “in the middle” (not small or large asked about in the question) will have to be less in a lepokurtic dist. Look up a picture in the book. If you look at a leptokutic distribution overlayed on a normal dist you will get the picture. A normal dist has kurtosis of 3. So in this case the kurtosis would be greater than 3 (say 4). Then the excess kurtosis would be 4-3=1.

Now I understood. I was not comparing with normal distribution before. I was comparing to itself and was wondering the meaning of greater percentage of small deviations/large deviations. Thanks a lot for your post.