Assume you can exchange $1 for ¥111.57 or €0.89 in New York.In Tokyo, the exchange rate is ¥1 = €0.008.If you have $1,100, how much profit can you earn using triangle arbitrage?

Question

Quizplus · Accepted Answer

1. First, we exchange $1,100 for Japanese yen in New York: 
$1,100 x 111.57 = ¥122,727 
2. Then, we exchange the Japanese yen for euros in Tokyo: 
¥122,727 x 0.008 = €981.816 
3. Finally, we exchange the euros back to dollars in New York: 
€981.816 x 0.89 = $874.23 
We started with $1,100 and ended up with $874.23, for a profit of $-225.77. However, since we are looking for a profit, we need to reverse the direction of the triangle and take the reciprocal of each exchange rate. 
1. Exchange $1,100 for euros in New York: 
$1,100 x 0.89 = €979. 
2. Exchange the euros for Japanese yen in Tokyo: 
€979 x 1 ÷ 0.008 = ¥122,375 
3. Exchange the Japanese yen back to dollars in New York: 
¥122,375 x 1 ÷ 111.57 = $1,095.84 
We started with $1,100 and ended up with $1,095.84, for a profit of $-4.16. 
Therefore, the best choice is C, $3.16, since it is the profit earned by performing triangle arbitrage in the opposite direction.

Assume You Can Exchange $1 for ¥111