Calculate the forward rates given the following zero rates.
Year |
Zero rate |
Forward rate |
1 |
3.5 |
|
2 |
3.75 |
|
3 |
4.5 |
|
4 |
5.0 |
1 Year Fwd rate = Same as Year Int Rate.
i.e 3.5%
1 Year Fwd Rate after 1 Year = [ (1 +YTM2)^2 / (1+YTM1) ] - 1
= [ ( 1 + 0.0375)^2 / ( 1 + 0.035) ] - 1
= [ (1.0375^2)/(1.035)] - 1
= [ 1.0764 / 1.035 ] - 1
= 1.04 - 1
= 0.04 i.e 4%
1 Year Fwd rate after 2 Years:
1 Year Fwd Rate after 2 Year = [ (1 +YTM3)^3 / (1+YTM2)^2 ] - 1
= [ ( 1 + 0.045)^3 / ( 1 + 0.0375)^2 ] - 1
= [ (1.045^3)/(1.0375)^2] - 1
= [ 1.1412 / 1.0764] - 1
= 1.0602 - 1
= 0.0602 i.e 6.02%
1 Year Fwd rate after 3 Years:
1 Year Fwd Rate after 3 Year = [ (1 +YTM4)^4 / (1+YTM3)^3 ] - 1
= [ ( 1 + 0.05)^4 / ( 1 + 0.045)^3 ] - 1
= [ (1.05^4)/(1.045)^3] - 1
= [ 1.2155 / 1.412] - 1
= 1.0651 - 1
= 0.0651 i.e 6.51%
Fwd Rates:
3.5%
4%
6.02%
6.51%
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