Question

7. Triangular arbitrage Please refer to Table 2 in the datafile. Which of the triangles below results in profitable arbitrage? (Note: you should use bid and ask rates for this question) a) USD --> JPY --> EUR --> USD b) JPY --> USD --> EUR --> JPY c) EUR --> JPY --> GBP --> EUR d) none of the them

Answer 1

Answer:

First of all when any one buy any currency pair in market, they buy at the ask rate quoted and sell at the bid rate quoted.

For example, If anyone buying EURUSD in market, he will get the EURUSD ask rate 1.0554. Similarly anyone selling EURUSD in market, he will get the EURUSD bid rate 1.0532 in the market.

In this answer, we will take 1000 unit of each currency pair to check the examples:

Option A:

USD > JPY > EUR > USD

1000 USD if converted in JPY, one is selling USD and buying JPY (i.e selling USDJPY) @ 102.33. Hence I get 1000*102.33 JPY = JPY 102,330

JPY 102,330 to be converted in EUR (i.e selling JPY and Buying EUR that means buying EURJPY) @108.10

Hence amount of EUR received =102330/108.10 = 946.62

946.62 EUR to be converted to USD @1.0532 = 996.98

Hence option A is not a profitable arbitrage as 1000 USD resulted to lesser 996.98 USD.

Option B

JPY > USD > EUR > JPY

1000 JPY = 1000/102.77 USD = 9.73 USD

9.73 USD = 9.73/1.0554 EUR = 9.22 EUR

9.22 EUR = 107.60*9.22 JPY = 992.04 JPY which is < 1000 JPY, it is not a profitable arbitrage.

Option C

EUR > JPY > GBP > EUR

1000 EUR = 108.10*1000 JPY = 108100 JPY

108100 JPY = 108100/120.13 GBP = 899.86 GBP

899.86 GBP = 899.86*1.1075 EUR = 996.63 EUR which is < 1000 EUR, it is not a profitable arbitrage.

Hence answer is d) none of them.