Question

The annualized risk-free rate in the eurozone is 3% and the annualized UK risk-free rate is 5%. The spot quote is €1.20/£ while the one year forward quote is €1.25/£. You can borrow either €1,000,000 or £833,333.33. According to interest rate parity, is the forward quote correct? If not, what should it be? If the forward quote is not correct, how much money would you profit if you implemented the proper arbitrage?

Multiple Choice:

Forward rate should be €1.2643/£; arbitrage would net you €73,950

Forward rate should be €1.2643/£; arbitrage would net you €93,750

Forward rate should be €1.1771/£; arbitrage would net you €83,600

Forward rate should be €1.1771/£; arbitrage would net you €57,500

Forward rate should be €1.1771/£; arbitrage would net you €63,750

Answer 1

The correct answer is last option: Forward rate should be €1.1771/£; arbitrage would net you €63,750.

i_euro = 3%; i_uk = 5%

Spot quote = S = €1.20/£

According to interest rate parity, forward quite should be F = S x (1 + i_euro) / (1 + i_uk) = 1.20 x (1 + 3%) / (1 + 5%) = €1.177142857/£

According to interest rate parity, the forward quote is not correct? It should be €1.1771/£

• I will borrow €1,000,000; convert it into £833,333.33 and lend it. Thus initial outflow for me = 0
• My liability on borrowed money after one year = €1,000,000 x (1 + i_euro) = €1,000,000 x (1 + 3%) =  €1,030,000
• My money receipt on lent amount of £833,333.33 after 1 year = £833,333.33 x (1 + i_uk) = £833,333.33 x (1 + 5%) = £875,000
• I will convert £875,000 in € at the forward rate of €1.25 / £. At actual forward rate of €1.20/£, my maturity amount = €1.25/£ x £875,000 = €1,093,750
• Hence, my gain = arbitrage profit = €1,093,750 - €1,030,000 = € 63,750

Hence, the correct answer is last option: Forward rate should be €1.1771/£; arbitrage would net you €63,750.