Right now 1 year maturity Tbonds sell for 2 yield 2year matu

Right now, 1 year maturity T-bonds sell for 2% yield, 2-year maturity bonds sell for 2.5% yeild and 3-year maturity bonds sell for 3% yield.

a. Compute the expected 1-year interest rate in the second year, i.e., one year from now?

b. What is the exoected 1-year interest rate two years from now, i.e., in the third year?

Solution

According to the expectation theory,

the one year interest rate, compounded over the next year , will give us the same return as the return compounded over 2 years by a 2 year bond.

a. 1 year maturity T bonds for 2% yield ,

( 1.02) (1 + x ) = (1.025)^2

( 1.02) (1+x) = 1.0506,

(1+x ) = 1.03

x = 3%

the 1 year interest rate 1 year from now is 3%\'

b. (1.025)^2 (1 +x ) = ( 1.03)^3

or, (1+x ) = 1.0927/1.0506

(1+x) = 1.0401

x = 4%

therefore, the one year treasury bond expected interest rate two years from now is 4%