Question

The foreign exchange quotes are given below:

Braggart Bank 100.80 yen/$

Thrifty Bank 100.55 yen/$

• If we assume no transaction costs, there is evidently an opportunity for arbitrage here.

• If an arbitrageur started with $10,000, exactly how would she make profits and how much profit would she make?

• As many traders engage in arbitrage what do you expect to see in the above quotes at these two banks?

• If there is a 12.5 basis points transaction fee for each exchange is there still an opportunity for arbitrage?

Answer 1

The $10,000 would be converted into Yen with Braggart Bank. Yen received = $10,000 * 100.80 = 1,008,000 Yen

The 1,008,000 Yen would then be converted back into $ with Thrifty Bank. $ received = 1,008,000 / 100.55 = $10,024.86

Profit =  $10,024.86 - $10,000 = $24.86

As traders engage in arbitrage, dollars would be sold with Braggart Bank and dollars would be bought with Thrifty Bank. Hence, the exchange rate of Braggart Bank would decrease and the exchange rate of Thrifty Bank would increase until they are equal.

If there is a 12.5 basis point fee for exchange :

The $10,000 would be converted into Yen with Braggart Bank. Yen received = $10,000 * 100.80 * (1 - 0.125%) = 1,006,740 Yen

The 1,006,740 Yen would then be converted back into $ with Thrifty Bank. $ received = (1,006,740 / 100.55) * (1 - 0.125%) = $9,999.82

There is no opportunity for arbitrage when there is a fee for exchange