Question

1.       Suppose at 11am this morning, the following rates are obtained from the FX markets:

In New York €1 =$1.09251

In Frankfurt £1 = €1.1234

In London $1 = £0.85

(a)   Determine if there is a currency arbitrage opportunity in this 3-currency situation.

(b)  If there is an arbitrage opportunity to be exploited, show how you may be able to capture this profit. YOU NEED TO ILLUSTRATE YOUR PROFITABLE ROAD MAP WITH A NUMERICAL EXAMPLE.

Answer 1

(a) Given,

€1 = $1.09251

£1 = €1.1234 => £1 = €1.1234*$1.09251/€ = $1.22733

$1 = £0.85 => £1 = $1/0.85 = $1.17647

As the above-calculated exchange values do not match, there is indeed an arbitrage opportunity in the given FX market.

(b) Let us assume that we start with $1 and exchange it for £0.85 in the London FX market

Sell £0.85 for obtaining euros in the Frankfurt FX market and obtain £0.85*€1.1234/£ = €0.95489

Sell euros in the New York FX market to obtain back dollars and obtain €0.95489*$1.09251/€ = $1.04323

Therefore, one would be able to obtain $1.04323 from $1 from the arbitrage opportunity. By converting the USD into different currencies, as shown above, the arbitrage can be used to obtain profit from the different FX market exchange rates.