Question

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

Answer 1

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%