1.Spot rates of interest for zero-coupon Government of Canada bonds are observed for different terms to maturity as follows:

Term to maturity

Rate (r_i)

1 year from today

5.75%

2 years from today

6.25%

3 years from today

6.35%

4 years from today

6.25%

5 years from today

6.40%

a)What is the forward rate of interest from year 2 to year 3, i.e., what is f₃?

b)What is the forward rate of interest from year 3 to year 4, i.e., what is f₄?

c)If you believe in the pure expectations theory, what does your answer to (a) imply about E[₂r₃]? If you believe in the augmented expectations theory, what does your answer to (a) imply about E[₂r₃]?

d)If you believe in the pure expectations theory, what does your answer to (b) imply about E[₃r₄]? If you believe in the augmented expectations theory, what does your answer to (b) imply about E[₃r₄]?

e)Suppose a zero-coupon bond has a face value of $1,000 and matures 5 years from today.

i)What is its price today?

ii)If you believe in the pure expectations theory, then what do you expect its price to be four years from today?

f)Suppose a bond has a 6% annual coupon, a face value of $1,000 and matures in 2 years. Use the same spot rates of interest as those of zero coupon bonds.

i)What is its price today?

ii)What is the yield to maturity, expressed as an effective annual rate, of this bond?