Question

Assume that the expectations theory holds, and that liquidity and maturity risk premiums are zero. If...

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?

Homework Answers

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 %

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