Question

The £ spot exchange rate is $1.6135/£, the € spot exchange rate is $1.2021/€, and the £/€ spot rate is £0.7380/€.   

a) First show whether an arbitrage opportunity exists. (4 points)

b) Second, if arbitrage profits are available, describe a strategy to exploit the arbitrage opportunity and calculate the arbitrage profits you would earn. Start by borrowing 1,000 units in one currency and show that at the end of your trades you have more than you borrowed. (8 points)

Answer 1

a). The given £/€ is 0.7380.

First we need to calculate the cross rate as (£/$)*($/€) = (1/1.6135)*(1.2021) = £0.74503/€

This cross rate is not the same as the quoted rate of £0.7380/€ so there is an arbitrage opportunity here.

b). Applying the principal of buy low and sell high, we do the following:

1). Borrow 1,000 USD

2). Convert 1,000 USD to GBP @ $1.6135/£ to get 1,000/1.6135 = £ 619.77

3). Convert GBP to Euro @ £0.7380/€ to get 619.77/0.7380 = € 839.80

4). Finally, convert Euro to USD @ $1.2021/€ to get 839.80*1.2021 = $ 1,009.52

Net profit = 1,009.52 - 1,000 = USD 9.52