Question

Consider the following spot rate curve: 6-month spot rate: 7%. 12-month spot rate: 10%. 18-month spot rate: 13%. What is the forward rate for a 6-month zero coupon bond issued one year from today? Equivalently, the question asks for f12, where 1 time period consists of 6 months. Remember, like spot rates, forward rates are expressed as bond-equivalent yields. Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Answer 1

Given that,

1-year spot rate r1 = 10%

18 month spot rate r1.5 = 13%

So, 6 month forward rate 1 year from now = 2*((((1+r1.5/2)^3)/((1+r1/2)^2)) - 1) = 2*((((1+0.13/2)^3)/((1+0.1/2)^2)) - 1)

=> 6 month forward rate 1 year from now = 19.13% or 0.1913