Question

The following spot and forward rates for the euro ($/euro) were reported:

Spot		1.6381
30-day forward		1.6380
90-day forward		1.6380
180-day forward		1.6387

a-1. Was the euro selling at a discount or premium in the forward market at 30 days.

• Discount

• Premium

a-2. Was the euro selling at a discount or premium in the forward market at 90 days.

• Premium

• Discount

a-3. Was the euro selling at a discount or premium in the forward market at 180 days.

• Premium

• Discount

b. What was the 30-day forward premium (or discount)? (Negative answer should be indicated by a minus sign. Do not round intermediate calculations. Round the final answer to 2 decimal places.)

30-day forward premium/discount            %

c. What was the 180-day forward premium (or discount)? (Do not round intermediate calculations. Round the final answer to 2 decimal places. Negative answer should be indicated by a minus sign.)

180-day forward premium/discount            %

d. Suppose you executed a 90-day forward contract to exchange 280,000 euros into Canadian dollars. How many dollars would you get 90 days hence?

Dollars for euros francs            $

e. Assume a French bank entered into a 180-day forward contract with TD Bank to buy $280,000. How many euros will the French bank deliver in six months to get the Canadian dollars? (Do not round intermediate calculations. Round the final answer to the nearest whole dollar.)

Euros francs for dollars          €

Answer 1

Solution to a1

The 30-day euro forward is trading at 1.6380 per Canadian dollar. That is lower than the spot rate of 1.6381. Hence, the euro was trading at a discount in the 30-day forward market

Solution to a2

The 90-day euro forward is trading at 1.6380 per Canadian dollar. That is lower than the spot rate of 1.6381. Hence, the euro was trading at a discount in the 90-day forward market

Solution to a3

The 180-day euro forward is trading at 1.6387 per Canadian dollar. That is higher than the spot rate of 1.6381. Hence, the euro was trading at a premium in the 180-day forward market

Solution to b

The formula for calculating 30-day forward premium/discount is [(30-day forward rate - spot rate) / spot rate] *100

Hence forward premium/discount = [(1.6380 - 1.6381)/ 1.6381 ] * 100

= -0.0001/1.6381 *100 = -0.0061%. Since this is negative, it is a forward discount

However, this is not an annualised rate. To find out the annualised forward discount, the formula is

[{(30-day forward rate - spot rate) / spot rate] *100} * 360/number of days for the forward]

[{(1.6380 - 1.6381)/ 1.6381 } * 100 ] * 360/30

=-0.0061% * 12 = -0.0732%

Solution to c

The formula for calculating 180-day forward premium/discount is [(180-day forward rate - spot rate) / spot rate] *100

Hence forward premium/discount = [(1.6387 - 1.6381)/ 1.6381 ] * 100

= 0.0006/1.6381 *100 = 0.0366%. Since this is positive, it is a forward premium

However, this is not an annualised rate. To find out the annualised forward discount, the formula is

[{(180-day forward rate - spot rate) / spot rate] *100} * 360/number of days for the forward]

[{(1.6387 - 1.6381)/ 1.6381 } * 100 ] * 360/180

=0.0366% * 2 = 0.0732%

Solution to d

The formula for converting euros into Canadian dollars using the 90-day rate is

Amount in euros * Canadian dollars per euro rate in 90 days

Hence, in 90 days, I will get, 280,000 euros * 1.6380 = Canadian $ 458,640

Solution to e

The formula for converting Canadian dollars into euros using the 180-day rate is

Amount in Canadian dollars / Canadian dollars per euro rate in 180 days

Hence, in 180 days, the French bank will get, Canadian $ 280,000 / 1.6387 = 170,867 Euros