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Value at Risk Q&A Bank Q 3.6 (iii)

K

kylie jane

Member
Can someone help me out with the reasoning behind the solution:

Question: "Assuming a normal distribution, calcualte the VAR:
The 95% VAR for an investor with a $10m portfolio where the average annual return is 6% and there is a 5% chance that the value of the portfolio will fall by more than 10% over a year."

In the solution we have VAR = (0.06--0.1)*10m = 1.6m

I don't quite understand why... I get that if we ignore any return we have VAR_0.95 = 0.1*10m

I feel like I'm missing something really basic here! Any help would be great :)
 
In this case we are measuring the VaR relative to what we would expect our portfolio to grow to.

So, 5% chance of portfolio falling to $9m. We expect portfolio to grow to $10.6m. So VaR = $1.6m.
 
I think I'm convinced! In terms of the "formula" is this correct?

Var_0.95 = mu+ sigma*phi^-1(0.95)

mu = 10*0.06 =0.6
and from the question sigma*phi^-1(0.95) = 0.1*10 = 1
(i.e. we are assuming the loss is distributed N(0,sigma))

and Var_0.95 = 0.6+1 = 1.6
 
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