Question

Suppose that the six-month interest rate in the United Kingdom is 0.5% per annum the sixmonth interest rate in Germany is 1.2% per annum. If the spot exchange rate is GBP/EUR 1.1286 and the six-month forward exchange rate is GBP/EUR 1.1312. Assume that the arbitrager can borrow up to EUR 1,000,000 or the equivalent GBP amount, at the spot rate.

a. Can the arbitrager make a covered interest arbitrage (CIA) profit, justify your answer?

b. If yes, determine how much profit can be realised. Show all your calculations.

Answer 1

GIVEN

six-month interest rate

United Kingdom = 0.5% per annum

Germany = 1.2% per annum

spot rate GBP/EUR = 1.1286

six-month forward rate GBP/EUR = 1.1312

All the rates are given for 6 months, so no need to change

a) ANSWER

covered interest arbitrage (CIA)

(1+ Interest rate in UK) = (six-month forward rate / spot rate) * (1+ interest rate in germany)

(1+0.005) = (1.1312/1.1286) * (1+0.012)

1+0.005 = 1.01433

0.005 is not equal to 0.01433

it is less

so, the arbitrager can make a covered interest arbitrage (CIA) profit.

b) ANSWER

Domestic country (UK)

Assume that the arbitrager can borrow up to EUR 1,000,000 or the equivalent GBP amount, at the spot rate.

spot rate GBP/EUR = 1.1286

1000000 EUR = 1000000/1.1286 GBP

= 886053.517 GBP

means he will take 886053.517 GBP loan at interest rate of 0.5% pa

after 6 months he has to pay Interest = 0.5%*886053.517 = 4430.26

Invest 1000000 EUR in Germany receive 1.2% interest

= 12000 EUR

after 6 month he will receive 1012000 EUR

six-month forward rate GBP/EUR = 1.1312

therefore, 1012000*1.1312 GBP

=1144774.4 GBP

PROFIT = 1144774.4 GBP - ( loan + interest)

= 1144774.4-(886053.517+4430.267)

= 1144774.4 - 890483.784

= 254290.616

Means he can earn profit of 254290 GBP