Question

Suppose that the current 1-year rate (1-year spot rate) and expected 1-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows: 1R1 = 1%, E(2r1) = 4.25%, E(3r1) = 4.75%, E(4r1) = 6.25% Using the unbiased expectations theory, calculate the current (longterm) rates for 1-, 2-, 3-, and 4-year-maturity Treasury securities. Plot the resulting yield curve. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

1 Year Rate = 1R1 i.e 1%

2 Years Rate = Square Root [ (1+1R1) * (1+E(2r1)) ] - 1

= Square root [ (1+0.01)* (1+0.0425) ] - 1

= Square Root [ (1.01)*(1.0425) ] - 1

= Square Root [ 1.0529 ] - 1

= 1.0261 - 1

= 0.0261 i.e 02.61%

3 Years rate :

3 Years Rate = [ (1+1R1) *(1+(E(3r1))² ]^1/3 - 1

= [ (1+0.01) *(1+0.0475)² ]^1/3 - 1

= [ (1.01) *(1.0475)² ]^1/3 - 1

= [ (1.01) *1.0973]^1/3 - 1

= [ (1.01) *1.0973]^1/3 - 1

= 1.1083^1/3 - 1

= 1.0349 - 1

= 0.0349 i.e 3.49%

4 Years rate :

4 Years Rate = [ (1+1R1) *(1+(E(4r1))³ ]^1/4 - 1

= [ (1+0.01) *(1+0.0625)³ ]^1/4 - 1

= [ (1.01) *(1.0625)³ ]^1/4 - 1

= [ (1.01) *1.1995 ]^1/4 - 1

= [ 1.2115 ]^1/4 - 1

= 1.0491 - 1

= 0.0491 i.e 04.91%

Yield Curve: