P1.T4 "Valuation & Risk Model" EOC 10.14.

[AUola2165]

Question:

Answer:


the forward rate between 1 and 1.5 years is stated as 4.4013% which seems to come from 0.0220066 x 2. However, shouldn't it be (1.00220066^2)-1= 4.4497%?

 

[David Harper CFA FRM]

Hi @AUola2165 I get their answer, because (1 + z_1.0/2)^2*(1 + f/2) = (1 + z_1.5/2)^3:
(1 + f/2) = (1 + z_1.5/2)^3 / (1 + z_1.0/2)^2,
f/2 = (1 + z_1.5/2)^3 / (1 + z_1.0/2)^2 - 1,
f = [(1 + z_1.5/2)^3 / (1 + z_1.0/2)^2 - 1] * 2; i.e.,
f = [(1 + 3.80%/2)^3 / (1 + 3.50%/2)^2 - 1] * 2 = 2.20066% * 2 = 4.40133% = f(1.0, 1.5).
... nit: it's awkward to write "the forward rate per six months ...". Thanks,