Question

Assume that the rate on a 1-year bond is now 6%, but all investors expect 1-year rates to be 7% one year from now and then to rise to 8% two years from now. Assume also that the pure expectations theory holds, hence the maturity risk premium equals zero. Which of the following statements is CORRECT?
A. The yield curve should be downward sloping, with the rate on a 1-year bond at 6%.
B. The interest rate today on a 2-year bond should be approximately 6%.
C. The interest rate today on a 2-year bond should be approximately 7%.
D. The interest rate today on a 3-year bond should be approximately 7%.
E. The interest rate today on a 3-year bond should be approximately 8%.

Answer 1

Answer:

Option (D) is correct.

Explanation:

Given that,

Rate on a 1-year bond, now = 6%

Expected rate on a 1-year bond, one year from now = 7%

Expected rate on a 1-year bond, two years from now = 8%

Maturity risk premium = 0

Therefore, the interest rate today on a 3-year bond should be approximately:

= (Rate on a 1 year bond, now + Rate on a 1 year bond, one year from now + Rate on a 1 year bond, two years from now) ÷ Number of years

= (6% + 7% + 8%) ÷ 3

= 21% ÷ 3

= 7%