Question

One-year Treasury securities yield 4%. The market anticipates that 1-year from now 1-year Treasury securities will yield 4.4%. If the pure expectations theory is correct, what should be the yield today for 2-year Treasury securities?

Answer 1

Answer-

Given

One-year treasury securities yield = 4 %
The 1-year treasury securities 1-year from now = 4.4 %

As per pure expectations theory

[1+i (2)]² = [ 1+i(1) ] x [ 1 + i(1)(exp) ]

I(2) = 2-year treasury securities
i (1) = 1-year treasury securities yield = 4 % = 0.04
i (1)exp) = 1-year Treasury securities 1 year from now= 4.4 % = 0.044

by substituting the values in above equation we get

[1+i (2)]² = (1+0.04) x ( 1+0.044)
= (1.04) x (1.044)
1 + i(2) = [ (1.04) x (1.044) ]^1/2
i (2) = [ (1.04) x (1.044) ]^1/2 - 1
i (2) = ( 1.08576)^1/2 - 1
i (2) = 1.04199 - 1
i (2) = 0.04199
i (2) = 4.199 %

Therefore the 2-year treasury securities yield today = 4.199 %