From Reading 35, the forward rate model is relatively straightforward, or so I thought. I am doing the EOC questions in the CFAI textbook. On question 17, we take the square root of (1.06^3/1.04) to solve the answer. In question 18, the answer provided doesn’t square root it. Can someone tell me when and when not to square root the term (1+r(T*+T)^T*+T/1+r(T*)^T*).This is equation 4 solving for f(T*,T)^T. I know this is a simple concept and I am probably just forgetting something very basic, but obviously I need a reminder. Thanks in advance!
Question 17 asks for a 2-year forward rate. Rates are quoted annually, so after you compute the effective rate for the 2-year period based on the spot rates, you have to take the 2-year effective rate and uncompound (via (1 + r1,eff) = (1 + r2, eff)1/2) it to get the 1-year effective rate.
Question 18 asks for a 1-year forward rate. You compute the effective rate for the 1-year period based on the spot rates, and you’re done.
If there’d been a question asking for a 3-year forward rate, you’d compute the effective rate for the 3-year period, then uncompound it (via (1 + r1,eff) = (1 + r3, eff)1/3) to get the 1-year effective rate.
If there’d been a question asking for a 7-year forward rate, you’d compute the effective rate for the 7-year period, then uncompound it (via (1 + r1,eff) = (1 + r7, eff)1/7) to get the 1-year effective rate.
And so on.