2
$\begingroup$

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.

Thanks!

$\endgroup$
  • $\begingroup$ 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
1
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.