Question

You have the following information about the current one-year spot rate and the expected one-year T-note rates during the next three years. The one year spot rate is 1.66%. The expected rate in year 2 is 2.45%, the expected rate in year 3 is 2.86%, and the expected rate in year 4 is 3.64%. What are current rates for the 1, 2, 3, and 4 year maturities for these treasury securities

Answer 1

Current 1 Years rate = 1.66%

Spot 2 year Rate = [ (1 + 1R1)(1+2R1) ] ^ ( 1 / 2 ) - 1

= [ ( 1 + 0.0166)(1 + 0.0245) ] ^ ( 1 / 2 ) - 1

= [ 1.0166 * 1.0245 ] ^ ( 1 / 2 ) - 1

= 1.0415 ^ ( 1 / 2 ) - 1

= 1.0205 - 1

= 0.0205 I.e 2.05%

Spot 3 year Rate = [ (1 + 1R1)(1+2R1) ( 1 + 3R1) ] ^ ( 1 / 3 ) - 1

= [ ( 1 + 0.0166)(1 + 0.0245) ( 1 + 0.0286 )] ^ ( 1 / 3 ) - 1

= [ 1.0166 * 1.0245 * 1.0286 ] ^ ( 1 / 3 ) - 1

= 1.0713 ^ ( 1 / 3 ) - 1

= 1.0232 - 1

= 0.0232 I.e 2.32%

Spot 34year Rate = [ (1 + 1R1)(1+2R1) ( 1 + 3R1) ( 1 +4R1) ] ^ ( 1 / 4 ) - 1

= [ ( 1 + 0.0166)(1 + 0.0245) ( 1 + 0.0286 ) ( 1 + 0.0364) ] ^ ( 1 / 4 ) - 1

= [ 1.0166 * 1.0245 * 1.0286 * 1.0364 ] ^ ( 1 / 4 ) - 1

= 1.1103 ^ ( 1 / 4 ) - 1

= 1.0265 - 1

= 0.0265 I.e 2.65%