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Hello,

I'm having trouble understanding much of the content (bolded) for this AIM. Can someone explain the following ?

"The first desirable attribute is unbiasedness. Specifically, we require that the VaR estimate be the x% tail. Put differently, we require that the average of the indicator variable I(t) should be x%: This attribute alone is an insufficient benchmark.

How is a VaR constant through time ?

- Does this just mean that the VaR estimate was the same over multiple time series ie: yesterday my 10 day VaR was X, today my 10 day VaR is X, each day for the past week my 10 day VaR was x ?

What is a VaR probability, tail probability, cyclical tail probability (Googling tail probability didn't help) ?

"the second attribute which we require of a VaR estimate is that

Am I correct in my understanding that by "extreme events" the author means losses in excess of VaR ?

Thanks !!

I'm having trouble understanding much of the content (bolded) for this AIM. Can someone explain the following ?

"The first desirable attribute is unbiasedness. Specifically, we require that the VaR estimate be the x% tail. Put differently, we require that the average of the indicator variable I(t) should be x%: This attribute alone is an insufficient benchmark.

**To see this, consider the case of a VaR estimate which is constant through time, but is also highly precise unconditionally (i.e., achieves an average VaR probability which is close to x%). To the extent that tail probability is cyclical, the occurrences of violations of the VaR estimate will be “bunched up”. This is a very undesirable property, since we require dynamic updating which is sensitive to market**

conditions"conditions

How is a VaR constant through time ?

- Does this just mean that the VaR estimate was the same over multiple time series ie: yesterday my 10 day VaR was X, today my 10 day VaR is X, each day for the past week my 10 day VaR was x ?

What is a VaR probability, tail probability, cyclical tail probability (Googling tail probability didn't help) ?

"the second attribute which we require of a VaR estimate is that

**extreme events do not “bunch up”. Put differently, a VaR estimate should increase as the tail of the distribution rises. If a large return is observed today, the VaR should rise to make the probability of another tail event exactly x% tomorrow.**"Am I correct in my understanding that by "extreme events" the author means losses in excess of VaR ?

Thanks !!

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