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Good Morning Sir.
Here’s the question I’ve been facing problems with.
A UK company expects to pay $700000 in 8months time. Current exchange rate 1.7550$/£ +/- 0.0003 4month exchange rate 1.7819$/£ +/- 0.0007 12 month exchange rate 1.8045 +/- 0.0007. Calculate receipts in £ if forward hedge is taken.
I took an algebraic approach to this and created two equations using the interest rate parity formula and using id as the annual interest rate in the US and ie as the annual interest rate in the UK. Here’s the first one (4month) :
1.7553 * ((1+(id/3))/ (1+(ie/3))) = 1.7826
The second one (12 month):
1.7553 * ((1+id)/(1+ie)) = 1.0284
I solved these equations but ended up with ie=143.75% which is impossible. As inconvenient as it sounds could you please tell me why this approach is wrong? (I’m terribly sorry about it but I’m kind of desperate?)
First, in your second equation you should have used 1.8052 (and not 1.0284).
Second, although 143.75% is obviously unlikely, it is not impossible 🙂However, this is not a maths exam, and you could therefore never be expected to do what you are trying to do!
What you are expected to do is simply apportion between the 4 month rate and the 12 month rate. 8 months is half way between 4 months and 12 months, and therefore you should simply estimate the 8 month forward rate as being half way between the 4 month and 12 month forward rates.
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