Question

In what way do skewness and excess kurtosis affect the relationship between VaR and Expected Shortfall?

Answer 1

VaR and expected shortfall (ES) are industry standards for measuring downside risks. Now skewness and excess kurtosis affect the relationship between VaR and Expected Shortfall by reducing the variations from the out-of-sample observations. Incorporating and taking into consideration skewness and excess kurtosis into the downside risk estimates positively impacts the relationship between VaR and Expected Shortfall as it leads to a more accurate risk forecasts.

Thus incorporating asymmetry and thickness of tails of the density function into the downside risk estimates will lead to more accurate forecasts.