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Exchange USD 1,200,000 into EUR 1,000,000
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Buy EUR 1,000,000 worth of euro-denominated bonds
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Sell EUR 1,025,000 via a 1 year forward contract, to receive USD 1,260,750, i.e. agree to exchange the euros back into US dollars in 1 year at today’s forward price.
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At the expiry of one year, two transactions occur consecutively. First, the euro-denominated bond delivers EUR 1,025,000. Secondly, the forward contract turns the EUR 1,025,000 into USD 1,260,750. So, the earning is USD 60,750. Had the investment been made in dollar, the return would have been only 4%. But, in this case, the two transactions can be viewed as resulting in an effective dollar interest rate of (1,260,750/1,200,000)-1 = 5.1%
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The above discussion does not consider the cost of capital. Alternatively, if the USD 1,200,000 were borrowed at 4%, USD 1,248,000 would be owed in 1 year, leaving an arbitrage profit of 1,260,750 – 1,248,000 = USD 12,750 in 1 year.
Covered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency. The proceeds of the investment are only known exactly if the financial instrument is risk-free and only pays interest once, on the date of the forward sale of foreign currency. Otherwise, some foreign exchange risk remains.
Similar trades using risky foreign currency bonds or even foreign stock may be made, but the hedging trades may actually add risk to the transaction, e.g. if the bond defaults the investor may lose on both the bond and the forward contract.
Example
In this example the investor is based in the United States and assumes the following prices and rates: spot USD/EUR = $1.2000, forward USD/EUR for 1 year delivery = $1.2300, dollar interest rate = 4.0%, euro interest rate = 2.5%.
Models
Financial models such as interest rate parity and the cost of carry model assume that no such arbitrage profits could exist in equilibrium, thus the effective dollar interest rate of investing in any currency will equal the effective dollar rate for any other currency, for risk-free instruments.