Question

Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If the annual rate of interest on a 5-year Treasury bond is 2.0 percent and the rate on a 3-year Treasury bond is 1.5 percent, what rate of interest should you expect on a 2-year Treasury bond, three years from now?

Answer 1

As per expectations hypothesis, the long-term rate is determined by current and future expected short-term rates.

(1+r₃)³ x (1+r₂)² = (1+r₅)⁵

(1+ 0.015)³ x (1+r₂)² = (1+0.02)⁵

(1.015)³ x (1+r₂)² = (1.02)⁵

1.045678375 x (1+r₂)² = 1.1040808032

(1+r₂)² = 1.1040808032/1.045678375

            = 1.0558512345634

1+r₂ = √ (1.0558512345634)

            = 1.02754622015917

r₂ = 1.02754622015917 – 1

    = 0.02754622015917 or 2.775 %

Expected rate on 2-year treasury bond, three year from now is 2.775 %