Question

Suppose that:

1) The interest rate on a one-year bond today is 3%;

2) The interest rate on a one-year bond starting one year from now is expected to be 4% per year;

3) The interest rate on a one-year bond starting two years from now is expected to be 5% per year;

4) The risk premium on a two-year bond is 0.5%; and

5) The risk premium on a three-year bond is 1%.

Use that information to answer the following questions:

a) According to the expectations theory, what is the interest rate today on a two-year bond? Show your work.

b) According to the expectations theory, what is the interest rate today on a three-year bond? Show your work.

c) Plot the yield curve.

Answer 1

The Expectations theory says that the forward rates in current long term bonds are closely related to bond market's expectation about future short-term interest rates i.e long run rates are averages of expected future short terms. The key assumption behind this theory is that for buyers bonds with different maturities are substitutes.

i_nt = i_t + i^e_i+(n-1) / n

Risk premium is not considered in expectations theory.

a) interest rate today on a two-year bond = (0.03+0.04)/2 = 0.07/2 = 0.035

b) interest rate today on a three-year bond = (0.03+0.04+0.05)/3 = 0.12/3 = 0.04

c) Yield curve