VaRs

Can someone please explain the difference between VaR, TVaR and X-TVaR?

Thank you!

 

VaR is the minimum amount (it's a lower bound) you will lose if you have a bad day.

Tail-VaR is the expectation of the amount you will lose *given* you are having a bad day.

Excess Tail VaR is the expected difference between Tail VaR and VaR.

I am not 100% certain without checking, but I think I am correct in saying that excess tail VaR is not equal to tail VaR minus VaR.

 

X-TVaR is actually the difference between the TVaR and the mean.

 

Correct. Well spotted.

Have to admit I'm not sure about the intellectual coherence of a measure of an expected value under two different filtrations...but who ever said VaR made sense?

 

Not quite sure I understand what you mean by "two different filtrations." X-TVaR is certainly not coherent in the formal sense.

 

Thank you both!