Question

Assume current 1 year bond rate is 1%, 2 year bond rate is 1.5% and 3 year bond rate is 2%. Using pure expectation theory, calculate the expected 1- year rate one year from now? Using pure expectation theory, calculate expected 1-year rate two years from now?

Answer 1

Formula :

According to expectation theory we have :

R_n = (r₀ + r₁ + r₂ --------------r_n-1)/n

where R_n = n year bond rate and r_n = expected 1-year rate n years from now

According to above formula we have :

R₁ = (r₀)/1 => r₀ = R₁ = 1%

Now, R₂ = (r₀ + r₁)/2 => 1.5 = (1 + r₁)/2 => r₁ = 2%

Similarly, R₃ = (r₀ + r₁ + r₂)/3 => 2 = (1 + 2 + r₂)/3 => r₂ = 3%

Thus, Expected 1-year rate two years from now = r₂ = 3%

Hence, Expected 1-year rate two years from now = 3%