# Fat tail question

Hi all, I’m a bit confused because in the books (CFAI and Schweser) it says that leptokurtic distributions are more “peaked” buz of excess kurtosis and hence have ‘fatter tails’ now fast forward a few readings and the books (CFAI and Schweser) says that T-distributions are flatter and have "fat tails’. aren’t the two contradictory? I mean if t-distribution is NOT leptokurtic buz it is not peaked, shouldn’t it NOT have fat tails? or put the other way around, shouldn’t leptokurtic distributions NOT have fat tails buz a t-distribution has fat tails and it is NOT leptokurtic? can someone plz clarify this? thanks!

leptokurtic thinner tails platokurtic fatter tails that’s my understanding

if you go to the end of the reading bullet point review in the Schweser notes for Kurtosis, i can guarantee you that It’ll say Leptokurtic = peaked = fat tails. you can even google it “A distribution with positive kurtosis is called leptokurtic, or leptokurtotic. In terms of shape, a leptokurtic distribution has a more acute “peak” around the mean (that is, a higher probability than a normally distributed variable of values near the mean) and “fat tails” (that is, a higher probability than a normally distributed variable of extreme values).”

florinpop, its the other way around lept is more peaked and fatter tails.

I think this is what it should be: Let’s name the ranges, 0, mid, infinity. (since it’s symmetrical) for positive kurtosis, (leptokurtic) it pushes up 0 and inf. while decreasing mid. resulting in a very peaked and very fat tail. kinda like someone pulls the distribution up from the middle, but holds down just the middle range so it doesn’t go up as much. for t-distribution, it pushes up mid. and inf. while decreasing 0 resulting in a distribution that is shorter than the normal distribution at the peak, while moving the distribution everywhere else. kinda like when someone pushes the distribution down from the middle and shifting some of the normal distribution peak over. make sense?

acwu Wrote: ------------------------------------------------------- > I think this is what it should be: > > Let’s name the ranges, 0, mid, infinity. (since > it’s symmetrical) > > for positive kurtosis, (leptokurtic) it pushes up > 0 and inf. while decreasing mid. resulting in a > very peaked and very fat tail. > > kinda like someone pulls the distribution up from > the middle, but holds down just the middle range > so it doesn’t go up as much. > > for t-distribution, it pushes up mid. and inf. > while decreasing 0 resulting in a distribution > that is shorter than the normal distribution at > the peak, while moving the distribution everywhere > else. > > kinda like when someone pushes the distribution > down from the middle and shifting some of the > normal distribution peak over. > > make sense? hi that makes sense, so graphically your saying that the t distribution is platokurtic at the center and leptokurtic at both ends (the tails) ? -thx

I’d say the t-distribution has characteristics of those (platokurtic and leptokurtic) in those ranges, but I wouldn’t say that’s what they are since kurtosis relate to the whole distribution and not individual sections. You can probably find the actual kurtosis of a t-distribution from google… since it’s just a number, the distribution can only either have <3 (plato), =3 (normal), or >3 (lepto).

kurtosis of t = 3 + 6/(df - 4) which isn’t all that fat-tailed…

I found fat-tail a very counter intuitive concept. I just remember when it is more peak ( leptokurtic), it actually has fatter tail, and more risk ( even though, intuitivly, it looks like a thinner tail, and seems to be less risky, coz most of the obs will be in the middle around 0). I cannot convince myself, so I just remembered it. As for t statistics, it is leptokurtic, to fatter tail. See the following link: http://en.wikipedia.org/wiki/Student’s_t-distribution

singlesong80 Wrote: ------------------------------------------------------- > I found fat-tail a very counter intuitive > concept. > I just remember when it is more peak ( > leptokurtic), it actually has fatter tail, and > more risk ( even though, intuitivly, it looks like > a thinner tail, and seems to be less risky, coz > most of the obs will be in the middle around 0). I > cannot convince myself, so I just remembered it. > As for t statistics, it is leptokurtic, to > fatter tail. See the following link: > http://en.wikipedia.org/wiki/Student’s_t-distribut > ion Here’s something that will make you feel better: After earning a Ph.D. in statistics and teaching it for 10 years at various colleges and universities, I cannot draw two distributions with the same variance and different kurtosis. I sort-of basically understand what kurtosis is, but I don’t know where the peak stops and the tails begin. I can generate all kinds of distributions with different kurtosis that I can’t order without calculating the kurtosis. I’ve never used kurtosis to do anything nor ever met anyone else who has. It’s a BS topic that gets taught all the time because platykurtic and leptokurtic are such cool words that you gotta teach them.

hahaha…that is funny. I earned stat master myself and getting a PhD Econ now. and I am constantly getting 58% on practice Econ section. How ironic… I hope the students won’t be on this page.

http://allaboutalpha.com/blog/2007/05/20/the-hedge-fund-metric-that-cried-wolf/ has some good stuff and interesting links about kurtosis (and how it is not particularly useful) and omega. Beyond the scope of level one though! I remember that “thin peaks” mean fat tails by considering the extreme cases. If you take an extremely leptokurtic distribution, you will end up with a really narrow peak that will have a really small area - and the area under the curve of a cdf function must be 1 - so less of the distributions area is in the peak, therefore more is in the tails.