Question

2.. Assume the Pound sterling is worth 9.80 Danish Kroner in Denmark and 5.40 Swiss francs in Zurich.

a. Show how British arbitrageurs can make profits, given that the Swiss franc is worth two Danish Kroner. What would be the profit per pound transacted?

b. What would be the eventual outcome on exchange rates in Denmark and Zurich given these arbitrage activities?

c. Rework step (a) assuming that transaction costs amount to 0.06 percent of the amount transacted. What would be the profit per Pound transacted?

show all calculation and explain

Answer 1

a) 1 pound = 9.80 Kroner, 1 pound = 5.40 francs and 1 franc = 2 Kroner

You start with 100 pound and convert it into franc at 5.40. You get 540 franc which you convert into Kroner and have

540 x 2 = 1080 Kroner. Now you convert Kroner back into pound, you get = 1080 / 9.80 = 110.20 pounds.

Hence, your profit per pound = 110.20 / 100 - 1 = 10.20%

b) The value of pound in Denmark will increase and the value of pound in Zurich will decrease so that the arbitrage not be possible.

c) You conver 100 pounds to franc and now you will have 100 x 5.40 x (1 - 0.06) = 507.6 franc

No. of Kroners = 507.6 x 2 x (1 - 6%) = $954.29 kroners

No. of pounds = 954.29 x (1 - 6%) / 9.80 = 91.53 pounds

Profit per pound = 91.53 / 100 - 1 = -8.47%