Question

You searched the foreign exchange market and got the following quotes:

In Ghana on Feb 23, 2010
Currency rate of U.S. Dollar Ghanaian cedi: 1 USD = GHS1.4299
Currency rate of Japanese Yen Ghanaian cedi: 1 JPY = GHS0.0156
In Japan on Feb 23, 2010
1. Currency rate of US dollar Japanese Yen: 1 USD = JPY89.37
2. Currency rate of Australian dollar Japanese Yen: 1 AUD = JPY80.13
3. Currency rate of Euro Japanese Yen: 1 EUR = JPY120.92
4. Currency rate of GBP Japanese Yen: 1 GBP = JPY137.17
5. Currency rate of Canadian dollar Japanese Yen: 1 CAD = JPY85.47
Required:
Explain whether a triangular arbitrage involving the cedi (domestic currency), US dollar and Japanese yen would be worthwhile using a starting amount of GH¢1,000. Back your answer with relevant computations and show all relevant workings.
b. Explain with relevant computations how a market trader in New York City with $1 million can make an arbitrage profit assuming the following rates:
a. Citibank quotes U.S. dollars per pound: $1.8400/£
b. National Westminster quotes euro per pound: £0.6849/€
c. Deutsche Bank quotes dollars per euro: €0.8475/$

Answer 1

Triangular arbitrage with Ghanaian cedi, US dollar, and Japanese yen using a starting amount of GH¢1,000 would not be profitable, ending with less than the starting amount. Similarly, an arbitrage opportunity in New York City with USD 1 million using rates involving USD, GBP, and EUR yields less than the starting amount, indicating no arbitrage profit.

Step-by-step explanation:

To determine whether a triangular arbitrage involving the Ghanaian cedi, US dollar, and Japanese yen is possible with the given rates, we need to calculate whether the process of exchanging these currencies can result in a profit due to discrepancies in currency exchange rates.

Starting with GH¢1,000, convert it to USD:

GH¢1,000 / 1.4299 USD/GHS = USD 699.44

Then convert USD to JPY:

USD 699.44 x 89.37 JPY/USD = JPY 62,492.65

Finally, convert JPY back to GHS:

JPY 62,492.65 x 0.0156 GHS/JPY = GH¢974.26

The final amount of GH¢974.26 is less than the starting amount, indicating that arbitrage would not be worthwhile.

For the arbitrage opportunity in New York City involving USD, GBP, and EUR, follow a similar process:

• Convert 1 million USD to GBP:
• USD 1,000,000 / 1.8400 USD/GBP = GBP 543,478.26
• Convert GBP to EUR:
• GBP 543,478.26 x 1/0.6849 GBP/EUR = EUR 793,391.13
• Finally, convert EUR back to USD:
• EUR 793,391.13 x 1/0.8475 EUR/USD = USD 935,679.42

The final amount of USD 935,679.42 is less than the starting amount, indicating no arbitrage profit can be made.