Value at Risk and Tail VaR

My understanding is that:

Shortfall probability is P(x<L) and
VaR at k%=-L where P(x<L)=k%


Am I right in thinking that:

Tail VaR at k%=E[max(L-x,0)] where P(x<L)=k%

 

Yes, you're right!

Incidentally, I've attached a short note confirming this, which may be of interest (to you or others reading your post.)

Good luck on Wednesday.

 

thank you!

 

Negative TVaR

What if TVaR is negative? Does that mean zero since it is E(max L-t, 0)

 

As the TVaR tells us something about how far below the VaR level we are, it shouldn't ever be negative.

Remember that it is just the expected shortfall below the VaR level.

 

Thank you