Question

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

Dealer	A	B	C	D	E
Japanese yen	108.98 - 109.00	109.02 - 109.06	108.99 - 109.02	109.01 - 109.05	108.97 - 109.01
British pounds	1.2374 - 1.2376	1.2376 - 1.2378	1.2378 - 1.2381	1.2376 - 1.2378	1.2373 - 1.2375

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.)

Answer 1

Yes, there is an arbitrage opportunity in Japanese Yen. Arbitrage can be done in two ways:

Suppose you initiated an arbitrage trade with $10.

Dealing only in Yen:

This will be done in 2 steps:

Step 1: Purchase $10 worth of Yen from Dealer B since the Ask price is the highest 109.02 Yen / US $. You’ll convert it to 1090.20 Yen.

Step 2: Sale convert these 1090.20 Yen to US $ at Dealer A since the Bid price is the lowest 109 Yen / US $ (which will maximise conversion value). You’ll get $10.00183486.

Profit     : $10.00183486 - $10 = $0.00183486

                : 0.0183486%

Dealing in both Yen & Pound:

Step 1: Purchase $10 worth of Pound from Dealer E since the Ask price is the lowest $1.2375 / Pound. You’ll convert it to 8.080808 Pounds.

Step 2: Convert these 8.080808 Pounds to US $ at Dealer C which is giving the highest conversion rate of $1.2378 / Pound. You’ll get $10.00242424.

Step 3: Convert $10.00242424 to Yen at Dealer B, since the Ask price is the highest 109.02 Yen / US $. You’ll convert it to 1090.4642909 Yen

Step 4: Convert these 1090.4642909 Yen to US $ at Dealer A since the Bid price is the lowest 109 Yen / US $ (which will maximise conversion value). You’ll get $10.00425955

Profit     : $10. 00425955 - $10 = $0.00425955

                : 0.0425955%

Do let me know if you have any doubts regarding any step or assumptions.

_{Note:Ask Price > Bid Price is based on the effective conversions.Try putting values in the equation you'll understand it better.}