Question

Suppose that the euro (€) is selling for 10.61 Swedish krona (SEK) in Stockholm while the British pound (£) is selling for 12.54 SEK in London. Use this data to answer the following questions:

(a) Calculate the cross-rate between the pound and the euro (i.e. calculate the €/£ cross-rate).

(b) Is this calculated cross-rate an equilibrium rate? Briefly explain.

(c) If the pound is selling for 1.31 euros in Frankfurt, the briefly discuss how you could make a profit assuming that you begin by holding 200 million euros.

(d) Calculate both the total profit and the profit per euro initially traded (ignoring transaction costs).

Answer 1

Suppose that the euro (€) is selling for 10.61 Swedish krona (SEK) in Stockholm while the British pound (£) is selling for 12.54 SEK in London. Use this data to answer the following questions:

(a) Calculate the cross-rate between the pound and the euro (i.e. calculate the €/£ cross-rate).

Swedish krona (SEK) / 1 Euro = 10.61 SEK / €

Swedish krona (SEK) / 1 Pound = 12.54 SEK / £

Cross-rate €/ 1 £ = 12.54 / 10.61 = 1.182 Euro / 1 Pound

(b) Is this calculated cross-rate an equilibrium rate? Briefly explain.

Cross rate is not the equilibrium rate. Equilibirum rate is the rate at which the demand for the currency will equal the supply of the currency. Cross rate is only a function of two different currencies with respect to a common currency and gets adjusted depending on supply or demand of the currencies involved.

(c) If the pound is selling for 1.31 euros in Frankfurt, the briefly discuss how you could make a profit assuming that you begin by holding 200 million euros.

Step 1: Convert 200 million euros in Stockholm at 10.61 Krona per Euro. Thus, you will get 2,122 million Krona (200 * 10.61)

Step 2: Convert the 2,122 million Krona in Stockholm into GBP at 12.54 krona per GBP. Thus, you will get 169.22 million GBP (2122 / 12.54)

Step 3: Convert the 169.22 million GBP in Frankfurt into Euro at 1.31 Euro per GBP. Thus, you will get 221.68 million euros (169.22*1.31)

Thus, with this 200 million euros becomes 221.68 million euros.

(d) Calculate both the total profit and the profit per euro initially traded (ignoring transaction costs).

The total profit earned = 221.68 million euros - 200 million euros = 21.68 million euros

Profit per euro = Difference in cross rate and actual spot rate / Cross rate = (1.31-1.182)/1.182 = 0.1082 Euro