This page presents the most well known financial time series fitted by the skew lognormal cascade distribution. The fat tails are so clear under this microscope.

For a fat tail distribution to make sense, it will need at least 4000 data points. That means you need at least 15 years of daily data to start with. I'd like to use this distribution to fit all kinds of real-world statistical data. If you have something that I can try, please let me know.

Here are what I got so far... I tried to sort them by kurtosis (or eta more or less)...

You must have noticed that the mean is typically very small compared to the wide distribution for the daily returns. This means that the long-term growth rate is almost negligible when compared to the daily fluctuation. This is an evidence that the (day) traders live in a totally different world from the long-term investors.

Fat Tails Sorted By Kurtosis

(Note: Kurtosis scales up with total duration, while scales down with sampling interval.)

Kurtosis	Asset Type	(hover on to preview the charts)
> 20.0	STOCK IDX	Dow Daily Log Return for 80 years (1928-2008) - Most Prominent Fat Tails
10-20	STOCK IDX	Dow Weekly Log Return for 80 years (1928-2008)
	COMMODITY	WTI Oil (Cushing, OK) Spot Price (1986-2008)
	COMMODITY	Gold vs USD London (AM) Fixing Daily Log Return Fit (1972-2009)
	STOCK IDX	Nasdaq Index Daily Log Return Fit (1971-2009)
	STOCK IDX	Dow Monthly Log Return for 80 years (1928-2008)
~10	US STOCKS	Collection of Blue Chip Stock's Daily Log Return Fit (1980-2010)
5-10	STOCK IDX	Russell 2000 Index Daily Log Return Fit (1988-2008)
	STOCK IDX	Nikkei 225 Daily Log Return Fit (1984-2009)
	COMMODITY	XAU Index Daily Log Return Fit (1983-2008) (PHLX Gold and Silver Sector Index)
2-5	BOND	10-Year Treasury Daily Log Return (1962-2008)
	VOLATILITY	VIX Volatility Index Daily Log Return Fit (1990-2008)
	CURRENCY	Japanese Yen vs US Dollar Daily Log Return for 30 years
	CURRENCY	Swiss Franc vs US Dollar Daily Log Return Fit (1975-2008)