I’m working through the Fixed Income section on calculating Forward Rates and want to simplify how to approach these questions with a minimal amount of formulas.
I’ll write out the formulas below with including the page numbers. To help I’ve used X to denote multiply.
The CFAI text gives an initial formula: Equation 4 (pg 8) as [1 + r(T* + T)](T*+T) = [1 + r(T*)]T* X [1 + f(T*,T)](T)
Later they ‘consolidate’ knowledge into Equation 6 (pg 11) as { [1 + r(T*+T)] / [1 + r(T*)]}(T*/T) X [1 + r(T*+T)] = [1 + f(T*,T)].
I’ve worked through the examples boxes and both result the same answer (as expected). SO, for simplicity’s sake, can I just put Equation 6 on the list to remember as the more flexible version?
a three period spot rate (cubed) is equal to a two period spot rate (squared) multiplied by a 1 year forward rate two years from now.
as long as you always have that formula down, you can always just chug and plug for whatever value they ask you to give. and the relation never changes… so…
(1+s4)4 = (1+s3)3 * (1+1-year forward rate THREE years from now)
in this example if they asked you to calculate the 3 period spot rate you would take the four period spot rate (remember to compound it 4 times) divided by the 1 year forward rate three years from now, and THEN take the cubed root of that number to get the 3 period spot rate.