Question

1. Currently the spot exchange rate is $1.50/£ and the three month forward exchange rate is $1.52/£. The three month interest rate is 8.0% per annum in the US and 5.8% per annum in the UK. Assume that you can borrow as much as $1M. or £1M.

1. Is there a covered interest arbitrage opportunity for a US multinational? What is the payoff if they conducted CIA?
2. Is there a covered interest arbitrage opportunity for a UK multinational? What would be their payoff if they conducted CIA?
3. How will the covered interest rate parity be restored?
4. What should have been the “correct” forward exchange rate?

Answer 1

a]

Yes there is CIA opportunity. The steps are :

• Borrow $1 million. Convert into £ at the spot exchange rate.  £ received =  $1 million / 1.50 =  £666,666.67.
• Sell the £ forward at the forward rate of $1.52/£.
• Invest £666,666.67 in UK for 3 months.  £ received after 3 months =  £666,666.67 * (1 + (5.8% * (3/12)) =  £676,333.33
• Convert £ into $ using the forward contract. $ received = £676,333.33 * 1.52 = $1,028,026.67.
• Repay the $ loan. $ to repay = $1,000,000 * (1 + 8%*(3/12)) = $1,020,000.
• Profit =  $1,028,026.67 - $1,020,000 = $8,026.67.

b]

No, CIA is not available for the UK multinational as the arbitrage is available for the US multinational. That is, the arbitrage opportunity is available for the US multinational as it can borrow in $, and not available for the UK multinational as it has to borrow in £.

c]

As investors/speculators/arbitrageurs engage in CIA, £ will be bought and $ sold. This process will go on until the exchange rate is restored to its equilibrium arbitrage-free level.

d]

Correct forward exchange rate = spot rate * ((1 + US interest rate) / (1 + UK interest rate))^{time in years}

Correct forward exchange rate = 1.50 * ((1 + 8%) / (1 + 5.8%))^3/12

Correct forward exchange rate = $1.51/£