You run a hedge fund with a line of credit that allows you to borrow $100...

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?

Solutions

Expert Solution

$/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

jeff jeffy answered 1 year ago

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