Question

The following are quotes for several U.S. currency dealers.

Dealer	A	B	C	D	E
Japanese yen	109.03 109.06	109.04 109.08	109.06 109.10	109.05 109.07	109.07 109.09
British pounds	1.3115 1.3119	1.3118 1.3120	1.3115 1.3118	1.3116 1.3117	1.3115 1.3118

Inter-dealer arbitrage

1a. Is there an arbitrage opportunity in Japanese yen? If so, what exchanges should you make to take advantage of it? (Be specific about which dealer you would select, what currency you would buy from or sell to that dealer, and how much of the other currency you would pay or receive.

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

2a. Is there an arbitrage opportunity in British pounds? If so, what exchanges should you make to take advantage of it? (Be specific as indicated in question 1.)

b. How profitable is a round trip trade? (State the profitability either in percent or basis points.)

Answer 1

Currency	Trader position	A	B	C	D	E
Japanese yen	Sell to dealer Buy from dealer	109.03 109.06	109.04 109.08	109.06 109.10	109.05 109.07	109.07 109.09
British pounds	Sell to dealer Buy from dealer	1.3115 1.3119	1.3118 1.3120	1.3115 1.3118	1.3116 1.3117	1.3115 1.3118

The dealer does not sell and buy at the same price. As a rule, the dealer will sell you at a higher rate and buy from you at a lower rate. The difference between the two rates is his commissions or spread. In the chart given above. The prices at the top line are the lower prices at which a dealer will buy Yen/ Pounds from you and prices at the bottom line are the higher prices at which a dealer will sell Yen/ Pounds from you and

Arbitrage will exist if you could buy from one dealer at lower price (bottom row) and sell to another dealer at higher price (top row)

For Yen, we can buy from dealer A at the rate of 109.06 Yen/USD and sell to dealer E at the rate of 109.07 Yen/USD. Hence, considering there are no other costs, there is a profit of 0.01 Yen/USD.

The buying price of Yen is 109.06/USD. Hence, we make a profit of 0.01/109.06 USD for every USD traded. This comes to 0.0091693% profit or a profit of 0.000091693 per USD

Similarly, for Pounds, we can buy from dealer D at the rate of 1.3117 GBP/USD and sell to dealer B at the rate of 1.3118 GBP/USD. Hence, considering there are no other costs, there is a profit of 0.01 GBP/USD.

The buying price of GBP is 1.3117 /USD. Hence, we make a profit of 0.01/1.3117 USD for every USD traded. This comes to 0.7623694% profit or a profit of 0.00762369 per USD