This is explained in the textbook. Vol 5, P.243-244

As far as I know, the inputs & intermediate processes are different. But the final calculations between Historical VAR and Monte Carlo VAR are same. That is, the ranked output shall be examined in the same way to calculate VAR. The expected return & standard deviation can be calculated by Analytical-variance method under the normality assumption but they are irrelevant here because the focus is Monte Carlo VAR.

On P. 243. Last three sentence… We rank order the data and find the 15th-lowest outcome, which is a portfolio value of $34.25m, corresponding to a loss of $15.75m. This value is higher than the annual VAR est. using the analytical method ($13.4m). THESE VALUE WOULD BE IDENTICAL (or nearly so) IF WE HAD EMPLOYED SUFFICIENTLY LARGE SAMPLE SIZE IN THE MONTE CARLO SIMULATION so that the sample VAR would converge to the true population VAR. => This suggests that if the sample is large enough, the final calculation of analytical method and MC VAR will be the same, right?

B_C, Yes, if the sample is large enough, the final calculation of analytical method and MC VAR will be the same. But the question raised here is why Mc is given but they have solved using historical Var. It is because though the inputs & intermediate processes are different, the final step (calculation) of Historical VAR and Monte Carlo VAR is same. That is, the ranked output shall be examined in the same way to calculate VAR. Am I wrong ?

You are not wrong. Given the sample size in question 12 (700) is so small, you can’t use analytical method (even if the inputs are normally distributed) to calculate Monte Carlo VAR. You rank the output to find the worst 5% result, just like the usual historical method. But if the sample size is million (large enough), you can calculate Monte Carlo VAR the same way as analytical method. ie. E® - 1.65(std dev) for 5% significance level.

Yes, I guess that’s why the expected return & standard deviation are irrelevant here. Do you think so ?

It is irrelevant if the sample size is small (just like Q12) It is relevant if the sample size is large enough.

B_C Wrote: ------------------------------------------------------- > It is irrelevant if the sample size is small (just > like Q12) > > It is relevant if the sample size is large enough. I think so. But how to define if the sample size is small or large enough ?

The book say you get close to normal distributions when simulations are done in hundreds of thousands or millions.

Ya. this is what I am thinking. If the output distribution is normal or nearly normal, then Analytical-variance method. But I will like to hear comments from others.