T distribution/Fat Tails

[sucheta_isi]

David,

I have a doubt.

Leptokurtic distributions always have fat tails?

Is T distribution leptokurtic? I know that it has the property of fat tails. But I am little confused about Schweser notes. It says that the greater the DF , the greater the % of observations near the center of the distribution and the lower the % of observations in the tails. So as DF increases it tends toNormal distribution. But leptokurtic means it should be more peaked than Normal. I am really confused. Please clear this doubt.

Returns of being LONG a call option: Positively/Negatively skewed? Why?

Thanks

 

[David Harper CFA FRM]

sray,

The student's t is always heavy-tailed b/c excess kurtosis is always > 0.
http://en.wikipedia.org/wiki/Student's_t-distribution
... and, in fact, it is always more peaked than the normal, but you almost never see it drawn that way because it's typically compared to a standard normal rather than a comparable normal. I have come to view leptokurtosis as only a tail property (i.e., heavy or dense tails) where the higher peakedness is a byproduct in unimodal distributions. So, your text here looks correct, only that you may be looking at a typical "optical illusion" comparison that deceives by implying shorter peaks

Re: Returns of being LONG a call option
I'm not sure that has an unambiguous answer (i think it's more complex than it looks; e.g., FMV/discount/premium; further, mark to market returns?) but probably is looking for positive skew. The easiest intuition IMO is something like:
* about 1/2 the time you'll lose the CAPPED premium
* the other 1/2 you'll exercise for UNLIIMITED gain
Ergo: mean > median and that probably implies positive skew.


David