Question

1. You run a hedge fund with a line of credit that allows you to borrow $100 million at an annual interest rate of 5%. The minimum amount of time that you can borrow for is one day. There are 365 days in a year. The spot rate for a euro is $1.20. The spot rate for a yen is $0.0094. The spot rate between yen and euros is ¥125/€. Which currencies should you buy or sell to take advantage of arbitrage opportunities? How much money can you make in one roundtrip in one day if prices don’t change?

Answer 1

$/Euro = 1.2

$/Yen = 0.0094

Therefore, Yen/Euro = Yen/$*$/Euro = [1/($/Yen)]*$/Euro = 1.2/0.0094 = 127.6596

Whereas, Cross Rate of Yen/Euro = 125

Therefore, Euro should be Bought via Cross Rate and Sold via $ Rate

Therefore, For Arbitrage,

(i) Sell the borrowed $ and Buy Yen at $/Yen Rate

(ii) Sell above Yen and Buy Euros at Yen/Euro Rate

(iii) Sell above Euros and Buy Back $ at $/Yen Rate

Money that can be made using $100 Million

(i) Yens Received = 100,000,000/($/Yen) = 100,000,000/0.0094 = Yen 10,638,297,872.34

(ii) Euros Received = 10,638,297,872.34/(Yen/Euro) = 10,638,297,872.34/125 = Euros 85,106,382.98

(iii) $ Received = 85,106,382.98*($/Euro) = 85,106,382.98*1.2= $102,127,659.57

Money Made in 1 Roundtrip = $ Received Back in Step (iii) - Initial Borrowing - Interest for 1 day = 102,127,659.57-100,000,000-[100,000,000*5%*1/365]

= 2,127,659.57-13,698.63

= $2,113,960.94