Question

Interest rates on 4-year Treasury securities are currently 6.4%, while 6-year Treasury securities yield 7.55%. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now? Calculate the yield using a geometric average. Do not round intermediate calculations. Round your answer to two decimal places.

Answer 1

2 Year after 4 year from Today Rate = [ [ (1 + YTM 6 ) ^ 6 / ( 1 + YTM 4 ) ^ 4 ] ^ ( 1 / 2 ) ] - 1
= [ [ ( 1 + 0.0755 ) ^ 6 / ( 1 + 0.064 ) ^ 4 ] ^ ( 1 / 2 ) ] - 1
= [ [ ( 1.0755 ) ^ 6 / ( 1.064 ) ^ 4 ] ^ ( 1 / 2 ) ] - 1
= [ [ 1.5476 / 1.2816 ] ^ ( 1 / 2 ) ] - 1
= [ [ 1.2075 ] ^ ( 1 / 2 ) ] - 1
= [ 1.0989 ] - 1
= 0.0989
= I.e 9.89 %

Expected Rate after 4 Years for 2 years is 9.89% per anum