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30 July, 18:57

Suppose that the one-year interest rate is 5.0 percent in the United States and 3.5 percent in Germany, and that the spot exchange rate is $1.12/€ and the one-year forward exchange rate, is $1.16/€. Assume that an arbitrageur can borrow up to $1,000,000. If an astute trader finds an arbitrage, what is the net cash flow in one year? A. $10,690 B. $15,000 C. $46,207 D. $21,964.29

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  1. 30 July, 22:29
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    Spot x (1+domestic interest rate) / (1+foreign interest rate) = Forward rate

    1.12 * (1+0.05) / (1+0.035) = 1.136

    The forward rate should be $1.136/€ but is $1.16/€ so we have an arbitrage opportunity.

    Because we believe that $ is being undervalued and € is over valued (one euro should be have a forward rate of $1.136/€ but has a rate of $1.16/€)

    We will borrow 1,000,000 at a 5% interest rate which means that at the end of the year we will have to pay = $1,050,000, this will be our negative cash flow.

    We will then buy 1,000,000/1.12=€ 892,857 and Earn an interest of 3.5% on the Euros. At the end of the year we will get payed 924,107. This will be our positive cash flow. At the start of the year we will get into a forward contract in which we will sell the €924,107 for $1,071,964 (924,107*1,16). Because the forward rate is $1,16/€ we will get 1.16 dollars for every euro.

    At the end of the year we will have $1,071,964 from our forward contract and will have to pay 1,050,000 as our loan payment so we will be left with (1,071,964-1,050,000) = $21,964

    D. $21,964.29 will be our net cash flow from this Arbitrage opportunity.
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