## R

where RS is the nominal risk-free rate in Switzerland. The period is one year, so F1 is the 360-day forward rate.

Do you see an arbitrage opportunity here? There is one. Suppose you have \$1 to invest, and you want a riskless investment. One option you have is to invest the \$1 in a riskless U.S. investment such as a 360-day T-bill. If you do this, then, in one period, your \$1 will be worth:

Alternatively, you can invest in the Swiss risk-free investment. To do this, you need to convert your \$1 to Swiss francs and simultaneously execute a forward trade to convert francs back to dollars in one year. The necessary steps would be as follows:

2. At the same time, enter into a forward agreement to convert Swiss francs back to dollars in one year. Because the forward rate is SF 1.90, you will get \$1 for every SF 1.90 that you have in one year.

3. Invest your SF 2.00 in Switzerland at RS. In one year, you will have:

SF value in 1 year = SF 2.00 X (1 + RS) = SF 2.00 X 1.05 = SF 2.10

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4. Convert your SF 2.10 back to dollars at the agreed-upon rate of SF 1.90 = \$1. You end up with:

Notice that the value in one year resulting from this strategy can be written as:

\$ value in 1 year = \$1 X S0 X (1 + RS)/F1 = \$1 X 2 X 1.05/1.90 = \$1.1053

The return on this investment is apparently 10.53 percent. This is higher than the 10 percent we get from investing in the United States. Because both investments are risk-free, there is an arbitrage opportunity.

To exploit the difference in interest rates, you need to borrow, say, \$5 million at the lower U.S. rate and invest it at the higher Swiss rate. What is the round-trip profit from doing this? To find out, we can work through the steps outlined previously:

1. Convert the \$5 million at SF 2 = \$1 to get SF 10 million.

2. Agree to exchange Swiss francs for dollars in one year at SF 1.90 to the dollar.

3. Invest the SF 10 million for one year at RS = 5%. You end up with SF 10.5 million.

4. Convert the SF 10.5 million back to dollars to fulfill the forward contract. You receive SF 10.5 million/1.90 = \$5,526,316.

5. Repay the loan with interest. You owe \$5 million plus 10 percent interest, for a total of \$5.5 million. You have \$5,526,316, so your round-trip profit is a risk-free \$26,316.

The activity that we have illustrated here goes by the name of covered interest arbitrage. The term covered refers to the fact that we are covered in the event of a change in the exchange rate because we lock in the forward exchange rate today.

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