"Some authors claim the distributions to be close to Paretian stable (McFarland et al. 1982), some to Student distributions (Boothe and Glassmann 1987), some reject any single distribution (Calderon-Rossel and Ben-Horim 1982)." Guillaume et al.
"Fact 1: Non stable, fat-tailed distribution."
"Fact 2: Finite variance."
"Fact 3: Symmetric distribution."
"Fact 4: Decreasing leptokurticity."
Guillaume et al.
"almost symmetric"
"For all time horizons, the empirically determined (excess) kurtosis exceeds the value 0, which is the theoretical value for a Gaussian distribution. For the shortest time intervals, the kurtosis values are extremely high. Another interesting feature is that all of the rates show the same general behavior, a decreasing kurtosis with increasing time intervals. At intervals of around 1 week, the kurtosis is rather close to the Gaussian value."
"the variance and the third moment are finite in the large-sample limit and that the fourth moment may not be finite."
Dacorogna et al. (2001) [book]
"the kurtosis of the stock returns is much larger than the kurtosis of the exchange rate returns, at both the daily and weekly sampling frequency. This may reflect the fact that central banks can intervene in the foreign exchange market, while there are virtually no such opportunities in stock markets."
Franses and van Dijk (2000) [book]