Suppose that the yield on 1-year Treasury securities is 2.25%, 2-year securities

Question

Suppose that the yield on 1-year Treasury securities is 2.25%, 2-year securities yield 2.10%, 3year securities yield 2.05%, and 4-year securities yield 1.95%. There is no maturity risk premium.

a)Does this situation describe an upward sloping, downward sloping, or flat yield curve?

b)Based on the pure expectations theory of the yield curve, what do markets believe the yield on a 1-year Treasury security will be one year from now?

c)Based on the pure expectations theory of the yield curve, what do markets believe the yield on a 2-year Treasury security will be 2 years from now?

Explanation / Answer

Solution:

a. This is a case of downward sloping yield curve.

b. Let X be the yield on a 1-year Treasury security will be one year from now.

(1 + 0.0225) (1 + X) = (1.0210)^2

1 + X = (1.0210)^2/1.0225

1 + X = 1.0195

X = 1.95%

c. Let X be the yield on a 2-year Treasury security will be 2 years from now

(1 + 0.0210)^2 (1 + X)^2 = (1.0195)^4

(1 + X)^2 = (1.0195)^4/(1.0210)^2

(1 + X)^2 = 1.03633

1 + X = 1.018

X = 1.80%

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