I figured it out. And it's entirely because of 1987. Using weekly 1987 data, I get a kurtosis of 3.3. If I change that week in 1987 from -12% to -22% (the daily loss), the kurtosis immediately jumps to 8.5. Obviously, the daily data has a much higher kurtosis than the weekly data.
There ya go newbunch, curtesy of GBOS. Looks like a very similar distribution to the DOW. GBOS, what's that software you're using please ?
There's been millions made by traders doing index-dispersion trades which are basically gamma index longs against a portfolio of short premium trades in the components......
That's actually a reverse dispersion / long correlation trade. You'd have to look at implied index correlation to see whether the conditions are right for that to be profitable now. When I last looked, it wasn't.
Why did you look at daily instead of hourly or minute by minute or tick by tick? What data to use obviously depends on your frequency of trading....
Not directly comparable results in this case, you are filtering out information. The weekly sigma for example is sqrt(5) times the daily sigma and the calculation formula will be affected cause kurt = E[((x-m)/sigma)^4] In the weekly case the kurt is around 3.46 (6.46 if you prefer the notation of normal distribution having kurt = 3). With monthly data the filtering is even more kurt = 2.51 (5.51 with the notation of normal distribution having kurt = 3). So if you are affected by prices only once a month and don't have any consequences by in between fluctuations (margin calls etc.) then monthly or even better yearly prices aproach the normal distribution.