# 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)

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. s2 = 1.9139%, so 1f1 = 1.0191392 / 1.015 − 1 = 2.3296%)

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.

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.

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.

I also did calculation and found that it is not a 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!

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!

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:

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

(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?

Question 2: Could someone please explain to me what the paragraph below means? I can’t get it.

“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.