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No Arbitrage Forward rate = Spot Rate * (1 + RD)/ (1 + RF)
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Question 36 of 40
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where Rp is the interest rate in the domestic country, in this case United States
RF is the interest rate in the foreign country, in this case Germany
The SF/$ 180-day forward exchange rate is SF1.30/$ and the 180 day forward premium is 8 percent. What is the outright spot exchange rate?
A. None of these.
B. SF1.35/$
C. SF1.25/$
D. SF1.30/$
Thus, using this formula, the no arbitrage forward rate should be = 1.6 * (1 + 2%)/ (1 + 4%) = 1.6 * 1.02 / 1.04 = $1.57 approximately However, the actual forward rate = $1.58/€Hence, there is an arbitrage opportunity.
Suppose an arbitrager borrows 1,000,000 in the United States at 2%.
Thus, after one year, he has to pay back 1,000,000 * (1 + 2%) = $1,020,000He converts 1,000,000 into Euros at the spot exchage rate of $1.60/€.Thus he gets 1,000,000/1.6 = €625,000
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The arbitrager now invests this money in Germany at 4%.At the same time, he enters into a forward contract to convert the money that he will get US Dollars at a forward rate of $1.58/€
After 1 year, he gets 625,000 * (1 + 4%) = €650,000
He converts this money into USD at the exchange rate of $1.58/€ (at which he entered th Thus he gets 650,000 * 1.58 = $1,027,000
Amount he has to pay back = $1,000,000 * (1 + 2%) = $1,020,000
Net cash flow for the year through this arbitrage = $1,027,000 - $1,020,000 = $7,000
8:45 AM
11/9/2022
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