Short term (one year) interest years over the next 6 years will be0.9, 1.7, 1.1,...

Short term (one year) interest years over the next 6 years will be 0.9, 1.7, 1.1, 2.6, 3.2, and 3.9. Using the expectations theory, what will be the interest rates on 5-year bonds?

Solutions

Expert Solution

Spot 5 Year Rate = [ [ ( 1 + r1)( 1 +r2) ( 1 + r3) ( 1 + r4) ( 1 +r5) ] ^ ( 1 / 5 ) ] - 1

= [ [ ( 1 + 0.009 ) ( 1 +0.017 ) ( 1 + 0.011 ) ( 1 + 0.026 ) ( 1 + 0.032 ) ] ^ ( 1 / 5 ) ] - 1

= [ [ ( 1.009 ) ( 1.017 ) ( 1.011 ) ( 1.026 ) ( 1.032 ) ] ^ ( 1 / 5 ) ] - 1

= 1.0985 ^ ( 1 / 5 ) - 1

= 1.0190 - 1

= 0.0190 I.e 1.90%

r1 - short term rate in Year 1

r2 - short term rate in Year 2

r3 - short term rate in Year 3

r4 - short term rate in Year 4

r5 - short term rate in Year 5

5 Year spotRate is 1.90%

jeff jeffy answered 1 year ago

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