# Reading 23 - Implied forward yield

Pg. 147 of Book 4 on Fixed Income Portfolio Management

Year 1; Coupon 1.50; Par Value: 100

Year 2: Coupon 1.91: Par Value: 100

Year 3: Coupon 2.23: Par Value: 100

Implied forward yield on Year 1 = 2.33% (1.0191)^{2} divided by 1.015. This part I get.

Implied forward yield on Year 2 =2.61%. How do they get 2.61%? (Do we need to derive it using the spot zero curve)

Anyone please?

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I’m still waiting for my books to arrive, but when I calculate the implied forward rate for year 2 I get 2.8962%.

You’re correct: you have to compute the spot rates first (from the par rates), then compute the forward rates from the spot rates.

(Note: your calculation for year 1 forward rate is not correct, because you’re using the par rates instead of the spot rates.

s_{2}= 1.9139%, so_{1}f_{1}= 1.019139^{2}/ 1.015 − 1 = 2.3296%)Simplify the complicated side; don't complify the simplicated side.

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I got the same as you did. 2.3296% for Year 1 and 2.8962% for Year 2. The book shows 2.61% for Year 2, which I believe it’s a mistake. Let me know when you get your books.

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The 2018 CFAI book gives the implied forward yield as 2.61%, maybe a mistake

There’s nothing in the Level III errata about it … yet.

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

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I dont think you need to know the calculation? I think you just need to be able to look at the table and identify the appropriate positioning based on the numbers given.

SG

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I also did calculation and found that it is

nota mistake. Initially i also got 2.89% and thought the same way.It is the yield on 2 year bond 1 year from now (and not the yield on 1 year bond 2 years from now). If you do that way, you will get 2.61%

Hope that helps!

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sqrt of (1.0233 x 1.02896= 1.0261.

Is that how you got your 2.61?

So for 3 Year Maturity: I got 1.1046 from the spot zero curve and divided by 1.015 to get 1.0883, which i then cubic root it to get 1.0286. Is that what you got as well to get the 3 year bond 1 year from now? Thanks!

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I used below calculations

(1.015) * (1 + f)

^{2}= (1.0224)^{3}so f = 2.61%

for 2.86% I used this calculations

(1.015) * (1+f)

^{3}= (1.02519)^{4}f = 2.86%

Hi everyone, could someone help me out with the following questions:

I tried performing the same calculations for the bond maturing at Year 4 (ie. 5 year bond 1 year from now)Question 1:(1+0.015)*(1+f)

^{4}= (1.027706)^{5}f = 3.09%

This does not tie to the figure in the book which states 3.07%. Am I missing something?

Could someone please explain to me what the paragraph below means? I can’t get it.Question 2:“Notice an important interpretation of the forward rate: Any bond maturing in n periods that trades at its implied forward rate in one year, when it is an n – 1 to remaining maturity bond, will have the same realized return as today’s 1-year (one-period) bond. If all bonds trade at their forward rates in one year, all bonds will have had the same realized return as today’s 1-year bond: 1.50%.”

Thank you.