9. The spot exchange rate in New York is 1.650 dollars per British d. The 360 da

Question

9. The spot exchange rate in New York is 1.650 dollars per British d. The 360 day forward exchange rate is 1.680 dollars per pound. The one-year interest rate in the United States is 4%. a. What should the one-year interest rate be in the U.K. according to the interest rate parity theory? (Assume investors can borrow and lend at the same rate.) b. If the one-year interest rate n the UK is 3%. An American investor with $100,000 decides to take advantage of the differences in rates. Ignoring transaction costs, how can the American investor exploit the disequilibrium? (Assume investors can borrow and lend at the same rate.)

Explanation / Answer

According to the interest rate parity,

(1+ US interest rate) = Expected Future Spot Rate/Current Spot rate * (1+ UK interest rate)

Part (a)

US interest rate = 4%

Expected future spot = 1.680 $/Pound

Current Spot exchange rate = 1.650$/Pound

So, we need to find out the UK interest rate.

Applying these values to interest rate parity equation,

(1+0.04) = 1.680/1.650 * (1+ UK interest rate)

Solving the above equation, we get

UK interest rate = 2.14%

Part (b)

An American investor can exploit this equilibrium by doing an arbitage. This opportunity is available because the interest rate in UK is 3% as opposed to the 2.14% which is the equilibrium interest rate. The arbitrage can be done as follows:

1. He should convert $100,000 to pounds at current spot rate i.e. 100,000/1.650 = 60,606.06 pounds

2. Invest these pounds @ 3% in the UK market. So, the interest earned at the end of 360 days = 60,606.06*3%*360/365 = 1793.2 pounds

3. Total pounds that he has at the end of 360 days period = 60,606.06 + 1793.2 = 62399.2 pounds

4. Covert these pounds back to US $ at the forward rate = 62,399.2 * 1.68 = $104830.656

Therefore, he will have $104830.656 at the end of 360 days period.

Now, if he would have invested in the US market itself, he would have earned an interest equal to

= $100000 * 4% * 360/365 = $3945.2

Hence, total dollars he would have at the end of the 360 days period if he invests in the US market = 100000 + 3945.2 which is equal to $103945.2

Therefore, by using arbitrage, he will earn a profit of $104830.656 - $103945.2 = $885.4

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