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Significant Level


New Member
If I have a significant level of 2% and a list of historical return: 0.012, 0.024, 0.033, 0.045, 0.057 and 0.071 why do I need to take the 5th lowest return? How do I come up with the 5th lowest return from the 2% significant level? and how the logic works for other significant levels?

I know that for VaR(99%) I need to take the 1st VaR(98%) the 2sd and so on, so for the 2% significant level I would take the 2sd lowest not the 5th?

See question in the image



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New Member
Hi Samuel,

You are absolutely right for 100 values, in case of this question, the manager ranked 250 daily returns, so 2% of that is 5.

All the best!!

David Harper CFA FRM

David Harper CFA FRM
Staff member
It is also okay to use the 6th worst return here (consistent with Dowd who is assigned). That means that, yes, in the case of a simple historical simulation based on sorting discrete returns, there are two valid answers! The reason being that 2%*250 = 5.0 worst returns occupy the 2.0% tail, such that we can validly say that "with 2% probability, we expect the loss to exceed the VaR (in this case the 6th worst return)." I happen to like this (Dowd's) approach because it locates the VaR "immedately" adjacent to the tail rather than in the tail. But just wanted to say that GARP accepts two answers here! Thanks,