# I am once again asking for your help

Scheweser book 4 fixed income, LOS 32F swap rate curve. I am stuck on how to calculate this and its driving me nuts.

Can someone break down the mathematical sequence to solve the swap fixed rate tenor of 2 years and get their answer 3.98%? The answer is #2 below, but I have no idea how to get solve for it.

Problem starts:

Example: Swap rate curve

Given the following Libor spot rate curve, compute the swap fixed rate for a tenor of 1, 2 and 3 years (i.e., compute the swap rate curve).

Maturity Spot Rate

1 3.00%

2 4.00%

3 5.00%

Answer:

1) SFR_{1} can be computed using the equation:

SFR_{1}/(1+S_{1}) + 1/(1+S_{1}) = 1

SFR_{1}/1.03 +1/1.03 = 1; SFR_{1} = 3.00%

2) SFR_{2} can be similarly computed:

SFR_{2}/(1+S_{1}) + SFR_{2}/(1+S_{2})^{2} +1/(1+S_{2})^{2} =1

SFR_{2}/1.03 + SFR_{2}/(1.04)^{2}+ 1/(1.04)^{2} =1; SFR_{2} = 3.98%

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Try this:

SFR

_{2}/1.03 + SFR_{2}/(1.04)^{2}+ 1/(1.04)^{2}= 1(1/1.03)SFR

_{2}+ (1/1.04^{2})SFR_{2}= 1 − 1/(1.04)^{2}= 1 – 0.9246 = 0.07540.9709SFR

_{2}+ 0.9246SFR_{2}= 1 − 1/(1.04)^{2}= 1 – 0.9246 = 0.0754(0.9709 + 0.9246)SFR

_{2}= 0.07541.8955SFR

_{2}= 0.0754SFR

_{2}= 0.0754 / 1.8955 = 0.0398 = 3.98%Simplify the complicated side; don't complify the simplicated side.

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you need to first calculate the implied forward rate given the spot rates

let i

_{t}^{s}^{ }be the spot rate of interest for t years,i

_{t1,t2}^{f }be the implied forward rate of interest from years t_{1 }to t_{2. }i

_{t1,t2}^{f }= (1+ i_{t2})^{t2}_{ }/ (1 + i_{t1})^{t1 }- 1(a proper financial math book explains in detail how to get to this formula, which is fundamental in finance. if scheweser book doesnt show this, maybe you deserve a refund). it should also be noted that this formula is only applicable for single periods. multi-period implied forward rate is slightly different)

the implied forward rate for year 0 to 1 is just the spot rate, so i

_{1}^{f }= i_{1}^{s }= .03the implied forward rate for year 1 to 2 is:

i

_{2}^{f }= (1.04^{2 }/ 1.03^{1}) - 1 = .050097087the swap rate is calculated as follows:

sum from t = 1 to n of [i

_{t1,t2}^{f }x (1 + i_{t }^{s})^{-t}] / [sum from t = 1 to n of ( 1+ i_{t}^{s })^{-t}]thus:

(.03 x 1.03

^{-1 }+ .050097087 x 1.04^{ -2 }) / (1.03^{-1 }+ 1.04^{-2 }) = .039802993 = 3.980%Studying With

Hey S2000Magician, thanks for this. It worked! Do you know why it doesn’t work when I do it this way? Is it the order or operations? Many thanks.

SFR

_{2}/1.03 + SFR_{2}/(1.04)^{2}+ 1/(1.04)^{2}= 1SFR

_{2}/1.03 + SFR_{2}/(1.04)^{2}= 0.0754SFR

_{2}/1.03 + SFR_{2}= 0.0754 * (1.04)^{2}SFR

_{2}/1.03 + SFR_{2} = .08155SFR

_{2}+ SFR_{2} = .08155 * 1.03SFR

_{2}+ SFR_{2} = .084SFR

_{2 }= .042 Studying With

Hey Thanks for this, but its too complex for me to understand.. S2000Magician way worked for me. Thanks Again

Whatever you do to one side of an equation, ya hafta do to the other!!! have a look at where you multiplied the left hand side by 1.04

^{2 }and later by 1.03.“Mmmmmm, something…” - H. Simpson

Breadmaker nailed it!

Here, for example, you forgot to multiply SFR

_{2}/1.03 by 1.04^{2}. If you multiply one term by something, you have to multiply every other term by that same something.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/

Studying With

thank you

Studying With

Hey thanks for this, and for the foresight to know I have no idea what @breadmaker meant when he said I have to do it to the other side of the equation lol. I now feel like I’ve been doing math wrong for my entire life lolol.