Question

Please calculate the forward rate between the two given spot rates.
(ex: if you have a 1y spot and a 5y spot, you are calculating the 4y forward)

3 year spot of 5.9%

8 year spot of 1.7%

Enter full (values rather than decimals. ex: enter 0.0325 as 3.25

Answer 1

Given

3 Year spot rate = 5.9%

8 Year spot rate = 1.7%

Let the 5 Year forward rate be x%

We know that

Expectation theory aims to predict what short term interest rate will be in future based on the long term interest rate.

( 1+0.059)^3 ( 1+x%)^5 = ( 1+0.017)^8

( 1.059)^3 ( 1+x% )^5 = ( 1.017)^8

1.187648( 1+x% )^5 = 1.144373

( 1+x%)^5 = 1.144373/1.187648

( 1+x%)^5 = 0.963562

( 1+x%) = 0.963562^1/5

( 1+x%) = 0.963562^0.2

( 1+x%) = 0.992604

x% = 0.992604-1

x% = -0.007396

Hence the 5 Year forward rate is -0.7396.