TailVar

Question: Suppose hypothetically returns ~ Uniform(-5%,10%).

1) What is the Var at a 95% confidence level for portfolio worth only £100?
I get £4.25.

2) What is the TailVar at a 95% confidence level?

Is it just the expected shortfall below benchmark -4.25 from part (1)? hmmmmmm........?

 

i think what you said is correct, so the tVaR is 5.1478.

 

thanks i agree, however my answer is not the same:

TVar(95%)=ESF(Var(95%))= ESF(-4.25)
= integral(-5;-4.25) (-4.25-x).1/15 dx
= 0.01875

Please let me know how u got your answer. It is quite possible I can't integrate properly anymore. Thanks.....

 

I'm starting to think I'm wrong because what I did was integrating (-5, t) x/15.dx = 0.05 and solving for t, but i guess this is wrong.

I look at your formula and redid the integration, from (-5, -4.25) over (-4.25-x)/15 .dx and i got 4.1979. I'm suspicious of this answer because it is positive instead of negative.

Any clue?

 

Even if your answer was -4.1979 it does not exceed the original Var value of -4.25 (TVar must be more conservative than Var i think). I'm not sure, think a tutor needs to help out here please....

 

I think the answer is -4.625. I think the core reading is misleading.

They say E[X!X<L]=integral(-inf:L)(L-x)f(x)dx

I think E[X!X<L]=1/F(L) integral(-inf:L) x f(x) dx

Using the second formula things make sense:

E[X!X<-4.25]= 1/0.05 integral (-5,-4.25) x 1/15 = -4.625 = TailVar(95%)

i.e the average of all losses exceeding the 95% Value at Risk..

If we take 0.01875 from earlier post then 0.01875/0.05=0.375 is the expected shortfall relative to benchmark -4.25 and -4.25-0.375=-4.625.
Hopefully a tutor can clarify this before the April exam because I don't feel like having to fumble around in the exam when its probably only worth 3 marks.

 

I read somewhere that tVaR>VaR and technically, -4.1979 IS larger than -4.25!

regarding the formula you recommended with the 1/F(L), i'm not sure about that cause i dont have the core reading. I have the CMP and i dont see that formula anywhere.

 

I mean exceed as in more towards the tail i.e more conservative risk measure.
-4.19 is not 'more towards the tail' so it must be wrong.

Also, the CR is very wrong I researched the topic.

 

funny how it's just the two of us replying to this issue...

 

whoops... looks like it's me who can't integrate properly :S