Suppose that the annual interest rate is 2.0 percent in the United States and 4 percent in Germany, and that the spot exchange rate is $1.60/€ and the forward exchange rate, with one-year maturity, is $1.58/€. Assume that an arbitrager can borrow up to $1,000,000 or €625,000. If an astute trader finds an arbitrage, what is the net cash flow in one year?

$7,000

Explanation:

Using the covered interest rate parity formula

No Arbitrage Forward rate = Spot Rate * (1 + RD)/ (1 + RF)

          = 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%) = $1,020,000

He converts 1,000,000 into Euros at the spot exchage rate of $1.60/€.

Thus he gets 1,000,000/1.6 = €625,000

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 at the end of 1 year into 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 the forward contract)

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

c.

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