# Forward Rates and Arbitrage

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?

d. Reconcile your answers to parts (a). and (c).

https://brainmass.com/business/finance/forward-rates-and-arbitrage-121682

#### Solution Preview

Please see the attached file.

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.

Investment Science (Arbitrage; Bonds; Forward Rate; Return): 1. Is there any other arbitrage opportunity? 2. Given above bonds, what are the implied forward rates? 3. If one was to invest $1,000 two years from now for one year. Which would be the best strategy (what forward rate to use)? What is the return?

Please see attachment for tables and pre-question information.

Questions:

Data:

Suppose the following coupon info

Maturity (year) Coupon Rate price

1 0% 97

2 3.00% 99

2 0% 91

3 4.00% 98

3 0% 87

Please note there are arbitrage opportunities (shown below).

The 1-yr rate implied by the 1-yr zero coupon bound is

= 100/97 - 1 = 3.09%

The 2-yr rate implied by the 2-yr zero coupon bound is

91 = 100/ = - 1 = 4.828%

The 2-yr rate implied by the 2-yr coupon bound is

99 = = 3.5%

The 3-yr rate implied by the 3-yr zero coupon bound is

87 = 100/ = - 1 = 4.75%

The 3-yr rate implied by the 3-yr coupon bound is

98 = = 4.75%

The 2-year rates implied by coupon bond is different to those implied by zero coupon bonds. Hence there is arbitrage opportunity for this segment of term structure.

Questions:

1. Is there any other arbitrage opportunity?

2. Given above bonds, what are the implied forward rates?

3. If one was to invest $1,000 two years from now for one year. Which would be the best strategy (what forward rate to use)? What is the return?