Question

Suppose the interest rate on a 1-year T-bond is 2.0%, that on a 2-year T-bond is 3.0%, and that on a 3-year T-bond is 5.0%. Assuming the pure expectations theory, what does this mean for expected 1-year rates investors can expect to receive during year the second and third years?

Answer 1

Based on the Pure Expectations Theory,

(1 + 2 Yr rate)2 = (1 + 1 Yr rate) * (1 + 1 Yr rate 1 Yr from now)

(1 +3%)2 = (1 + 2%) * (1 + 1 Yr rate 1 Yr from now)

1.0609 = 1.02 * (1 + 1 Yr rate 1 Yr from now)

(1 + 1 Yr rate 1 Yr from now) = 1.04009

1 Yr Rate 1 yr from now = 0.04 = 4.01%

(1 + 3 Yr rate)3 = (1 + 2 Yr rate)2 * (1 + 1 Yr rate 2 Yr from now)

(1 +5%)3 = (1 + 3%)2 * (1 + 1 Yr rate 2 Yr from now)

1.157625 = 1.0609 * (1 + 1 Yr rate 2 Yr from now)

(1 + 1 Yr rate 2 Yr from now) = 1.091173

1 Yr Rate 2 Yr from now = 0.0912 = 9.12%