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# Forward Rates and Arbitrage

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1. Deriving the Forward Rate: Assume that annual interest rates in the U.S. are 4 percent, while interest rates in France are 6 percent.

a. According to IRP, what should the forward rate premium or discount of the euro be?

b. If the euro's spot rate is \$1.10, what should the one-year forward rate of the euro be?

2. Covered Interest Arbitrage in Both Directions: The following information is available:

? You have \$500,000 to invest
? The current spot rate of the Moroccan dirham is \$.110.
? The 60-day forward rate of the Moroccan dirham is \$.108.
? The 60-day interest rate in the U.S. is 1 percent.
? The 60-day interest rate in Morocco is 2 percent.

a. What is the yield to a U.S. investor who conducts covered interest arbitrage? Did covered interest arbitrage work for the investor in this case?
b. Would covered interest arbitrage be possible for a Moroccan investor in this case?

3. Testing IRP: The one-year interest rate in Singapore is 11 percent. The one-year interest rate in the U.S. is 6 percent. The spot rate of the Singapore dollar (S\$) is \$.50 and the forward rate of the S\$ is \$.46. Assume zero transactions costs.

a. Does interest rate parity exist?

b. Can a U.S. firm benefit from investing funds in Singapore using covered interest arbitrage?

4. Deriving Forecasts of the Future Spot Rate. As of today, assume the following information is available:
U.S. Mexico
Real rate of interest required
by investors 2% 2%
Nominal interest rate 11% 15%
Spot rate ? \$.20
One year forward rate ? \$.19

a. Use the forward rate to forecast the percentage change in the Mexican peso over the next year.

b. Use the differential in expected inflation to forecast the percentage change in the Mexican peso over the next year.

c. Use the spot rate to forecast the percentage change in the Mexican peso over the next year.

5. Integrating IRP and IFE. Assume the following information is available for the U.S. and Europe:

U.S. Europe
Nominal interest rate 4% 6%
Expected inflation 2% 5%
Spot rate ----- \$1.13
One-year forward rate ----- \$1.10

a. Does IRP hold?
b. According to PPP, what is the expected spot rate of the euro in one year?
c. According to the IFE, what is the expected spot rate of the euro in one year?

#### Solution Preview

1. Deriving the Forward Rate: Assume that annual interest rates in the U.S. are 4 percent, while interest rates in France are 6 percent.

a. According to IRP, what should the forward rate premium or discount of the euro be?
F1/e0 = (1+rd)/(1+rf)
rd=4%
rf=6%
F1/e0=(1.04)/(1.06)= 0.9811
Thus the euro will sell at a forward discount of (1-0.9811)=0.0189 or 1.89% against US\$.

b. If the euro's spot rate is \$1.10, what should the one-year forward rate of the euro be?
F1= (1+rd)/(1+rf)*e0
rd=4%
rf=6%
F1=(1.04)/(1.06)*1.10=\$1.0792
The one year forward rate is \$1.0792 per Euro.

2. Covered Interest Arbitrage in Both Directions: The following information is available:

? You have \$500,000 to invest
? The current spot rate of the Moroccan dirham is \$.110.
? The 60-day forward rate of the Moroccan dirham is \$.108.
? The 60-day interest rate in the U.S. is 1 percent.
? The 60-day interest rate in Morocco is 2 percent.

a. What is the yield to a U.S. investor who conducts covered interest arbitrage? Did covered interest arbitrage work for the investor in this case?

Borrow 1US\$ at 1%. Convert into Moroccan dirham to receive Moroccan dirham 9.0909. Invest in Moroccan at the rate of 2%, to receive Moroccan dirham 9.2727. Convert them into US\$ ...

#### Solution Summary

The solution calculates forward rates and arbitrage opportunities.

\$2.19