The current annualized yield on a 1-year STRIPS is 2.4% and the annualized yield on a...

The current annualized yield on a 1-year STRIPS is 2.4% and the annualized yield on a 2-year STRIPS is 2.6%. According to the expectations theory of interest rates, what will be the annualized yield on a 1-year STRIPS one year from now? What would you expect to pay for this STRIPS with a $1,000 face value?

Solutions

Expert Solution

Annual yield on 1 year strip = 2.4%, Annualized yield on 2 year strip = 2.6%

According expectation theory, investing in two year zero bond is equal to investing in a one zero bond and then investing in one year zero bond one year from now

Hence

( 1 + annual yield on 2 year STRIP)² = ( 1 + annual yield on 1 year STRIP)(1 + annualized yield on 1 year STRIP one year from now)

(1 + 2.6%)² = (1 + 2.4%)(1 + annualized yield on 1 year STRIP one year from now)

(1.026)² = (1.024)(1 + annualized yield on 1 year STRIP one year from now)

(1 + annualized yield on 1 year STRIP one year from now) = (1.026)² / 1.024

(1 + annualized yield on 1 year STRIP one year from now) = 1.052676 / 1.024 = 1.0280039

annualized yield on 1 year STRIP one year from now = 1.0280039 - 1 = 0.0280039 = 2.80039%

Face value of 1 year STRIP one year from now = 1000

Price of STRIP one year from now = 1000 / (1 + annualized yield on 1 year STRIP one year from now) = 1000 / (1 + 2.80039%) = 1000 / 1.0280039 = 972.758 = 972.76

Current price of STRIP = 1000 / (1 + annualized yield on 1 year STRIP one year from now) (1 + annual yield on 1 year STRIP)

= 1000 / ( 1 + annual yield on 2 year STRIP)²

= 1000 / (1 + 2.6%)² = 1000 / 1.026² = 1000 / 1.052676 = 949.959 = 949.96

jeff jeffy answered 1 year ago

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