Question

Interest rates on 4-year Treasury securities are currently 6.5 percent, while 6-year Treasury securities yield 6.8 percent. If the pure expectations theory is correct, what does the market believe that 2-year securities will be yielding 4 years from now?

Answer 1

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($^{j+k}$) = (1+Sj) ^$^{j}$ 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

$\frac{1.068^6}{1.065^4}$ = (1 + f4,2)^2

1.1535 = (1 +f4,2)^2

f4,2 = $\sqrt{1.1535} -1$

f,2 = 7.4%