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?
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 %
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