Question

PURE EXPECTATIONS THEORY The yield on 1-year Treasury securities is 6%, 2-year securities yield 6 2%, 3-year securities yield 6 3%, and 4-year securities yield 6 5%. There is no maturity risk premium. Using expectations theory and geometric averages, forecast the yields on the following securities: a. A 1-year security, 1 year from now b. A 1-year security, 2 years from now c. A 2-year security, 1 year from now d. A 3-year security, 1 year from now

Answer 1

A). 1-year security, 1 year from now =  [(1 + 2-year securities yield)^2 / (1 + 1-year securities yield)] - 1

= [(1.062)^2 / 1.06] - 1 = 6.40%

B). 1-year security, 2 years from now =  [(1 + 3-year securities yield)^3 / (1 + 2-year securities yield)^2] - 1

= [(1.063)^3 / (1.062)^2] - 1 = 6.50%

C). 2-year security, 1 year from now =  [(1 + 3-year securities yield)^3 / (1 + 1-year securities yield)]^[1/2] - 1

= [(1.063)^3 / (1.06)]^[1/2] - 1 = 6.45%

D). 3-year security, 1 year from now =  [(1 + 4-year securities yield)^4 / (1 + 1-year securities yield)]^[1/3] - 1

= [(1.065)^4 / (1.06)]^[1/3] - 1 = 6.67%