I know leptokurtic distributions have excess kurtosis greater than 3 and it results in more returns around the mean and more returns in the tails. The events in the tails is increased risk (ie higher probability of a large deviation). Can someone paint the picture of platykurtic distributions?

A picture is worth a thousand words http://en.wikipedia.org/wiki/Image:Standard_symmetric_pdfs.png the platykurtic distributions are the negative excess kurtosis numbers Hope it helps

"leptokurtic distributions have excess kurtosis greater than 3 " be careful about excess kurtosis / kurtosis - - leptokurtic distributions have excess kurtosis greater than 0, and kurtosis greater than 3 for normal distributions, kurtosis is equal to 3 and excess kurtosis is equal to 0.

platykurtic —> less peaked + thin tails --> kurtosis < 3 leptokurtic —> more peaked + fat tails --> kurtosis > 3

Fat tails equals more risk since large deviations exist in the tails. Does thin tails mean few large deviations from the mean?