The most interesting thing is when the return distribution has a skewness lower than -1 and an excess kurtosis higher than 1. In this case, the probability to have sudden high negative returns increases. For a distribution with a skewness of -1 and an excess kurtosis of 5 (for example, technology stocks, media stocks, telecom stocks or hedge funds in arbitrage strategies), a claasical approach will conclude that the investor will not lose more than -3.5% in the next 1 day with 99% probability. An approach, accounting for skewness and kurtosis, shows a -7.4% loss in the next 1 day with 99% probability. This is exactly what one observes on the equity market. The difference is large: an underestimation of 111% of the downside risks (i.e. 7.4%/3.5%-1=111%) when using volatility only to measure the risk.
To conclude, for optimization and simulation, the technique must account for volatility, skewness, and kurtosis as soon as they are significant and as soon as the investor is risk averse.