According to the expectations theory, what is the expected one-year treasury security rate (i.e. forward rate,...

According to the expectations theory, what is the expected one-year treasury security rate (i.e. forward rate, f) three years from today if today’s rates on treasury securities of different maturities are as follows:

One-year US Treasury Note: 4.5%

Two-year US Treasury Note: 4.8%

Three-year US Treasury Note: 5.2%

Four-year US Treasury Note: 5.3%

Five-year US Treasury Note: 5.3%

Expert Solution

1 Year after 3 year from Today Rate = [ [ (1 + YTM 4 ) ^ 4 / ( 1 + YTM 3 ) ^ 3 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1 + 0.053 ) ^ 4 / ( 1 + 0.052 ) ^ 3 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1.053 ) ^ 4 / ( 1.052 ) ^ 3 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.2295 / 1.1643 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.056 ] ^ ( 1 / 1 ) ] - 1
= [ 1.056 ] - 1
= 0.056
= I.e 5.6 %
YTM 4 - Spot Rate for 4 Years

YTM 3 - Spot Rate for 3 Years

As requested forward Rate for Year 3:

1 Year after 2 year from Today Rate = [ [ (1 + YTM 3 ) ^ 3 / ( 1 + YTM 2 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1 + 0.052 ) ^ 3 / ( 1 + 0.048 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ ( 1.052 ) ^ 3 / ( 1.048 ) ^ 2 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.1643 / 1.0983 ] ^ ( 1 / 1 ) ] - 1
= [ [ 1.06 ] ^ ( 1 / 1 ) ] - 1
= [ 1.06 ] - 1
= 0.06
= I.e 6 %

jeff jeffy answered 2 years ago

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