VAR - Help!

[Nicholas.Campbell]

Hello,

In question 4.11 of the notes, it poses the following distribution of returns

X P
-7 0.04
5.5 0.96

It says the 95% VAR is 5.5, since
P(X< -7)=0 and P(X< 5.5) = 0.04. Hence VAR=5.5

However, in a near identical question in S2012 exams, Q1,

It has

X P
0 0.018
106 0.982

It says the 95% VAR is 0.

But these questions are virtually identical.

The definition of discrete VAR in core reading is
VaR(X) = -t, t=max(x : P(X<x) <= p

So going by the definition, the first question is correct. But to me, the exam question 'feels' more correct.

Kind regards,

Nick

 

[Graham Aylott]

They are both correct, as intuitively the VaR always just corresponds to the 5%/95% lower tail value of the distribution of investment returns.

In the first case, this corresponds to a return of 5.5% and hence a VaR equal to -5.5% * 100m = -£5.5m compared to the initial investment.

In the second case, it corresponds to £106, ie getting all of your money back, which can be interpreted as a VaR of -£6m compared to the initial investment. However, there are also other possible ways of expressing the VaR here, as shown in the attached extract from the CT8 ASET.

 

[Nicholas.Campbell]

Aaaaahhhhhh!! I geddit!

I missed the part saying it could be measure relative to various benchmarks - and consequently those two questions completely threw me.

Thanks a lot, Graham.

Nick