Question

A Foreign currency trader at the bank’s FX desk calls to inform you that Bank of America is quoting $1.12/€1, and Citibank is offering $1.28/£1. The trader also noticed that Credit Agricole is making market in pound sterling and Euro at €1.18/£1.

a. What is the implied €/£ cross-rate for the two European currencies? Show this trader how you would use $1 million to conduct a triangular arbitrage to profit from the deviation (if any) of the implied cross rate of the €/£, from the rate quoted by Credit Agricole.

b. Suppose you observed that the 3-month forward rate quote from Bank of America is $1.21/€1, calculate the forward premium (discount) implied by the quote.

c. What do investors expect to happen to the value dollar in the next three months?

Answer 1

a]

Implied €/£ cross-rate =  €/$ rate * $/£ rate

€/$ rate = 1 / $/€ rate

Implied €/£ cross-rate = (1 / 1.12) * 1.28 = €1.14/£1

However, Credit Agricole is quoting €1.18/£1. Credit Agricole is offering a higher amount of € per £ than the implied cross rate.

The steps for triangular arbitrage are below :

• $1 million is converted into £ with Citibank.  £ received = $1 million / 1.28 = £781,250
• £781,250 is converted into € with Credit Agricole.  € received =  £781,250 * 1.18 = €921,875
• €921,875 is converted into $ with Bank of America. $ received = €921,875 * 1.12 = $1,032,500
• Arbitrage profit = $1,032,500 - $1,000,000 = $32,500

b]

The forward quote is higher than the spot quote. Hence, there is a forward premium.

Forward premium = 1.21 - 1.12 = $0.09/€1

Forward premium % = 0.09 / 1.12 = 8.04%

c]

As the dollar is trading at a premium in the forward market, investors are expecting the value of dollar to depreciate in the next three months. This is because in the forward market, each Euro can buy a higher quantity of dollars than in the spot market.