In: Finance
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?
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