I have a question in regard to how I should think about kurtosis. My understanding of Kurtosis is that it’s a measurment of the fatness of a distributions tails and the level of a distributions peakness. A leptokurtic distribution has excess kurtosis compared to a normal distribution because it has fatter tails. The fatter tails are a result of relatively more scores farther from the mean and more scores that are tightly concentrated around the mean. The tighter concentration of scores near the mean result in a leptokurtic distributions haveing more peak. This makes sense except when it comes to a T Distribution which has fatter tails then a Normal Distribution but less peak. Is it correct to say that the T Distribution is Leptokurtic? If so then isn’t it more appropriate to think of Kurtosis as the fattness of a distributions tails as opposed to it’s level of peakness?
kurtosis is a measure of tail fatness. don’t worry about the peak - it can be higher or lower than the one of a normal distribution.
Thanks, I don’t think CFAI or Schweser does a great job of explaining that.
Kurtosis is a measure of the likelihood that an event occurring is extreme in relation to a given distribution. The higher the kurtosis coefficient is above the normal level, the more likely that future returns will be either extremely large or extremely small.
leptokurtosis – to be clear – is GOOD. Less variance around mean, you want this is you are analyzing a portfolio of stock returns, for example. That is where the “peak” comes from – rtns are concentrated around the mean. This can be construed as “lower risk”
daj224, you might want to be careful in making conclusions. When you analyze portfolio returns, you really care about tails. A high peak is not good news if it comes with a fat left tail.
“daj224, you might want to be careful in making conclusions. When you analyze portfolio returns, you really care about tails. A high peak is not good news if it comes with a fat left tail.” YOU ARE RIGHT – THX FOR CLARIFYING