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No Arbitrage Forward rate = Spot Rate * (1 + RD)/ (1 + RF)
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Question 22 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
When a currency trades at a premium in the forward market
A. the exchange rate is more than one dollar (e.g., €1.00 = $1.28).
B. the forward rate is more than the spot rate.
C. the exchange rate is less than one dollar.
D. the forward rate is less than the spot rate.
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
8:44 AM
11/9/2022
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