Fat tails and low even distributions is not enough....but if you get a good reading and have other means of confirmation then you can find high probability set ups which I will not discuss... This is a hard way to trade in my opinion. Hint: This is the best way to avoid flat tops with daily bars...This is a "must have" for statistical traders. Revealing Hint: A high Kurtosis with a MAE and MFE spreadsheet can make you money. Michael B.
I do pay attention to return kurtosis in my backtesting, though not as much as I do to skewness. I believe a low kurtosis is desirable, which is the opposite of fat tails. A return distribution with low kurtosis is one that is relatively predictable, with no outliers either positive or negative. Skewness I believe is more important -- I look for a positive skewness, meaning that the outliers that do exist are on the upside, rather than on the downside. This is essentially a long option profile. In reality there's nothing inherently good or bad about any skewness, but I think many strategies that have a negative expectancy but fool you for some time into thinking they have a positive expectancy have a negative skewness -- they make small returns very frequently and then suddenly lose it all. Think selling deep out-of-the-money put options on stock indices with any risk control and heavily overleveraging it.
Many so-called "arbitrage" strategies are actually stealth negative gamma, negatively skewed startegies - convert arb, stat arb, fixed income arb, soem relative value arb, etc. But of course most investors love these strategies because they have high Sharpe ratios..and that lead's to another point - the Sharpe Ratio is highly deficient as a risk-return measure. Never invest in strategies that have the potential to generate stable low positive returns but HIGH negative returns. Most of the high Sharpe ratio strategies/negative skewed strategies mentioned above fall in this category. I try to keep an open mind in the markets but as an investor, I would be very very reluctant to invest in the kind of strategies I mentioned above and certainly would NEVER invest in an option selling strategy. Finally, there are some great arbitrage stratgies. Don't ask me which ones.
Eventually, fat tails + low distributions = equal probabilities. How can you find high probability set ups with such a distribution? It's because you have made it into a dice game. What does MAE and MFE mean? Ditto for flat tops.