ES @ 97.5% vs. VaR @ 99%

[Ken Abbott]

Hey, all. I could use some help with the exact comparison of these two. I'm simply not smart enough to do the math. I know the 99% normal is 2.32634787404084. With 1,000,000 Monte Carlo draws, I get a 97.5% ES of 2.33717879512072. I tried doing this with 100,000,000 on my Mac in Excel and it choked.

It occurred to me that someone here could probably do the actual math. A million draws is probably enough, but then I'm relying on Excel's random number generator. It probably uses Box-Mueller as per Numerical Recipes in C, but I'm not sure.

 

[Dimitri Vulis]

What do you assume about the distribution of the payoffs of the P&L - do you assume linear (e.g. just cash positions in some stocks or foreign currencies) or do you allow option-like instruments with non-linear P&Ls?