Question

2. Consider the following quotes:

Yen per Pound: 256

Yen per dollar: 180

Dollar per pound: 1.5

Suppose 1 million dollars invested Is there any possibility of triangular arbitrage? Why or why not? If yes, what is the arbitrage profit? Use $1,000,000.

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Answer 1

Triangular arbitrage is the method of gaining from the differences between the rates quoted of three different currencies in the foreign exchange market.

Buying in one currency whose rates are smaller than converting and selling in the higher rate currency is the fundamental principal in the triangular arbitrage.

Information given in the question-

Rates as quoted

Japanese Yen per Pound= 256

this means 1 pound = 256 Yen

Japanese Yen per dollar:=180

this means 1 dollar = 180 Yen

US Dollar per pound= 1.5

this means 1 pound= 1.5 Dollars

Now there are 2 scenarios of doing the transactions in the 3 currencies.

A- Converting Dollars into Pounds ,

converting the received Pounds into yen and

converting Yen into Dollars.

B- Converting Dollars into Yen,

converting the received Yen into Pounds and

converting Pounds into Dollars.

option A- Starting from Pounds

Suppose 1 million dollars are invested in pound today

1 pound= 1.5 Dollars

pounds received = 1000000 /1.5

pounds received = 666666.67 Pounds (approx)

converting pounds into Yen

1 pound = 256 Yen

666666.67 Dollar = 256* 666666.67 Yen

Yen received =1706666667.52 (approx)

converting Yen into Dollars

1 dollar = 180 Yen

1706666667.52 Yen

=1706666667.52 / 180 Dollars

Dollars received= 948148.15 dollars (approx)

which is less than the initially invested 1000000 dollars , so there is no arbitrage opportunities.

Option B- Starting from Yen

Suppose 1000000 dollars are invested in Yen today

1 dollar = 180 Yen

1000000 Dollar= 180* 1000000 Yen

Yen received = 180000000

Converting Yen into Pound

1 pound = 256 Yen

180000000 Yen = 180000000 / 256 pound

Pounds received =703125

converting Pound into dollars

1 pound= 1.5 Dollars

703125 pound = 1.5 * 703125 Dollars

Dollars received = 1054687.50

Since this amount is more than the amount invested of $1000000 there exists an arbitrage opportunity.

Arbitrage gain = amount received from conversion - amount initially invested

=1054687.50 - 1000000

Arbitrage gain = $ 54687.50