Answer:
7.4%
Explanation:
We are looking for the rate of a 2 year security beginning four years from now. denoted with f4,2.
Using the forward rate model.
1 + S([tex]^{j+k}[/tex]) = (1+Sj) ^[tex]^{j}[/tex] x (1+f(j,k) ^k
where
j; starting date of the loan = 4 years
k; duration of the loan = 2 years
S; given spot rates = four year treasury (S4) 6.5%, six year treasury yield = 68%.
f(j,k); a k duration loan, starting j period from now. (f4,2)
(1 + S6) ^ 6 = (1 + S4)^4 x (1 + f4,2) ^ 2
(1.068)^6 = (1.065)^4 x (1 + f4,2) ^ 2
[tex]\frac{1.068^6}{1.065^4}[/tex] = (1 + f4,2)^2
1.1535 = (1 +f4,2)^2
f4,2 = [tex]\sqrt{1.1535} -1[/tex]
f,2 = 7.4%
