The question asks for calculation of regulatory capital.
I understand the theory of VaR but find it tricky in use.
In the question, investment returns are expected to be 4%. Std Dev is 25% of mean. And 0.5th percentile is 2.2 Std Devs from mean.
Firstly, why is VaR not Min (0; L - Z)
where Z = L[1+(25% x 4% x 2.2)]
L = lump sum invested at start of year.
My reasoning is 0.5th percentile in this case is 1.8% returns (4% x 2.2 x 25%), hence does not result in a loss of any of the initial investment and therefore should be reserved for.
Alternatively, why is it not
(1.04 x L x 25% x 2.2) - 0.04 x L
My reasoning here is expected value at end of period is 1.04 x L. 0.5th percentile is 2.2 x 25% of this. But since this reduction includes the returns gained on the initial investment, then x L should be deducted from the result to find the value that is at risk of loss within the year. Why is the VaR not lump-sum at start x 1.04 x 2.2 x 25%
The model answer says VaR = 4% x 25% x 2.2 x L. In my mind, this is a positive return of 1.8%, not a loss, although lower than the 4% we expected.
Help find the lost brother.
I understand the theory of VaR but find it tricky in use.
In the question, investment returns are expected to be 4%. Std Dev is 25% of mean. And 0.5th percentile is 2.2 Std Devs from mean.
Firstly, why is VaR not Min (0; L - Z)
where Z = L[1+(25% x 4% x 2.2)]
L = lump sum invested at start of year.
My reasoning is 0.5th percentile in this case is 1.8% returns (4% x 2.2 x 25%), hence does not result in a loss of any of the initial investment and therefore should be reserved for.
Alternatively, why is it not
(1.04 x L x 25% x 2.2) - 0.04 x L
My reasoning here is expected value at end of period is 1.04 x L. 0.5th percentile is 2.2 x 25% of this. But since this reduction includes the returns gained on the initial investment, then x L should be deducted from the result to find the value that is at risk of loss within the year. Why is the VaR not lump-sum at start x 1.04 x 2.2 x 25%
The model answer says VaR = 4% x 25% x 2.2 x L. In my mind, this is a positive return of 1.8%, not a loss, although lower than the 4% we expected.
Help find the lost brother.