# Calculating the Forward Rate Model Simplistically

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?

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Why not?

Simplify the complicated side; don't complify the simplicated side.

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Well that is the question I have! Is there any downside to doing so?

Could the exam throw a question at us which will be significantly easier to do an iteration of Equation 4 vs 6?

Memorize this…

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.

¯\_(ツ)_/¯ It be like that sometimes.

CEO10K-DAY wrote:
Memorize Understand this…

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.

Much better.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams
http://financialexamhelp123.com/

CEO10K-DAY wrote:

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)

I definitely grasp the concept and process. I’m possibly trying to unnecessarily complicate the issue based on the long-winded CFAI text…