Question

Suppose you are a currency trader for BRADESCO and you see the following currency quotes from CITI Bank, ITAU, and CAIXA Economica Federal Banks.

Bank	Quotation Description	Quote
CITI Bank	Exchange rate of Singapore dollar in U.S. $	$0.32
ITAU	Exchange rate of pound in U.S. $	$1.50
CAIXA Economica Federal Banks	Exchange rate of pound in Singapore dollars	S$4.50

a. (8 pts) Calculate the no arbitrage cross exchange rate for S$/£, and determine whether there is and arbitrage opportunity. Make sure you explain your answer fully.

b. (10 pts) If there is an arbitrage opportunity, assuming you have $100 million to use for trading currencies, detail all the steps you will take to make arbitrage profit in a triangular arbitrage case. Indicate how much money you will get for each transaction, and show your ending profit. Please note that you have to end up in the currency you start off with which is the US $. If your answer to a is that there is no arbitrage opportunity then please just indicate so as the answer for

Answer 1

a. Cross exchange rate of dollar to pound

=USD/Singapore dollars*Singapore dollars/pound

A person has one dollar

He can convert it to 3.125 (1/.32) Singapore dollars from Citi bank.

He can further convert it to .69 (3.125/4.5) pounds from CAIXA Economica Federal Banks

He can convert it back to 1.04(.69*1.5) dollars from ITAU bank

So there is an arbitrage opportunity. The person started with one dollar and at the end got 1.04 dollars earning a profit of .04 dollars.

b. An investor had 100000000 dollars

He can convert it to 3.12500000000 (1/.32) Singapore dollars from Citi bank.

He can further convert it to 69000000 (3.125/4.5) pounds from CAIXA Economica Federal Banks

He can convert it back to 104000000(.69*1.5) dollars from ITAU bank

The investor can make a profit of (104000000-100000000) or 4000000 dollars.