Question

FI ($/E) 4 1.9975 5% 16% 2.0000

Answer 1

(a) Investment should be done in pounds as the same provides a greater interest rate of 6% per annum (or 1.5 % for 3 months)

(b) Borrowing should be done in $ as the same provides a lower interest rate of 5 % per annum (or 1.25 % for 3 months)

(c) Current Spot Rate = $ 2 / GBP and 3-month Forward Rate = $ 1.9975 / GBP

Expected 3-month Forward Rate as per Interest Rate Parity = [1.0125 / 1.015] x 2 = $ 1.9951 / GBP

Arbitrage can be executed as descibed below:

- Borrow $ 1 at the $ rate of 5% per annum for 3-months

- Convert $ into GBP at the current spot rate of $ 2 / GBP to yield (1/2) = 0.5 GBP

- Invest 0.5 GBP at the UK interest Rate of 6 % per annum to yield (0.5 x 1.015) = 0.5075 GBP

- Convert the Investment Yield at the given forward rate (and not expected forward rate) of $ 1.9975 / GBP to yield (0.5075 x 1.9975) ~ $ 1.0137

- The initiallly borrowed $ 1 would have a repayment liability of (1 x 1.0125) ~ $ 1.0125

- Arbitrage Profit = 1.0137 - 1.0125 ~ $ 0.0012

(d) As calculated in part(c), $ 1 borrowed provided an arbitrage profit of $ 0.0012