September 2007 Q7(i)

[?????]

Hi

Can someone help with the following:

The Normal approximation for the VaR for Investor 2:

The solution says the mean is 0.04*1000. Why is the mean not 0.96*1000? The probability of default is 0.04 and hence the probability of actually receiving 1 at the end of the year is 0.96?

Tks

 

[Anna Bishop]

Yes, this is confusing. I think it depends on how you interpret the question.

The way you have interpreted it, as I also did to start with, is by considering only the payoff X on the bonds at maturity:

X is Bin(1000, 0.96).

However, if you interpret the question as looking at the net return Y, taking into account the price paid for the bonds, then:

Y is Bin(1000, 0.04)

The examiners have gone for the second approach. Note that they did the same thing in April 2007 - ie there was a distinction between payoff and net return.

 

[Lewin]

Even with the idea of 'looking at net returns' i still dont understand why bin(1000,0.4) is used as basis of calculating expected return for 2
can anyone clarify this??

 

[Edwin]

Anna Bishop, I was wondering why working with net returns will make us look at the right tail of the probabilty distribution?Isn't it because we are looking at the distribution of losses.


Plus I think what the examiner's have done in the April VaR is more of a technique of integration as they are still working with the left tail of the distribution of net net gains.

Lewin, If you think about the whole thing as a sum of independent Bernolii trials you should arrive at a Bin(n,p). However the examiner's switched to Bin(n,q).