I need to compare VaR before and after the recession.

I have a series of market returns for a period before, and a series of market returns for the period immediately after.

Both have been bootstrapped 500+ times, allowing me to generate 500+ VaR's.

I have put these VaRs in a histogram, and I was wondering if I could do a T-Test to find out if the difference is significant?

I have a feeling I cannot, as the distribution of VaR's is not normal, however this doesn't matter as the T-test takes means which are normally distributed?

Can anyone clarify what I could to do?

Apologies for my lack of knowledge, I'm grateful for your patience.


  • $\begingroup$ Is there any special reason why you unnaccepted my answer? $\endgroup$ – vonjd Apr 12 '15 at 6:11
  • $\begingroup$ Sorry, I thought I replied stating why it's wrong, but I didn't. I will now. $\endgroup$ – Harry Apr 12 '15 at 11:16

Using a t-test should be ok because even when the underlying distribution is not normal you have a large enough sample size which justifies the assumption that the distribution of the sample means should be approximately normal due to the Central Limit Theorem.

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  • $\begingroup$ Thanks, I will do this. Is there any other test you would recommend that I can use? Perhaps something that gives me other information I can comment about? $\endgroup$ – Harry Jan 1 '15 at 17:33
  • $\begingroup$ Also, to clarify, the null that means are equal is rejected if the T-stat lies between the + and - of the Critical 2-tail? Or do I only consider P values? Or a mixture of both $\endgroup$ – Harry Jan 1 '15 at 17:39
  • $\begingroup$ if you want to be 95% confident you just look at the p-value: If it is below 5% the difference is significant. $\endgroup$ – vonjd Jan 1 '15 at 18:54
  • $\begingroup$ Update - basically, central limit theorem is only applicable if you want to use a T-test to compare the means of two samples. This question is interested in the sample VaR (which is the left-side tail of the sample), and hence this method is flawed. $\endgroup$ – Harry Apr 12 '15 at 11:17

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