# Bond Valuation using nodes and Trees

How do you know whether to add the coupon or not when valuing bonds using the nodes and decision trees?

Top Instructors, Best-in-Class Content, Partner Until You Pass Guarantee

If I’m recalling the material correctly: the coupon amount is always taken into account as a component of a bond’s pv at a particular node (at least in the case of the problems presented and discussed in the curriculum). There are instances where you might adjust the coupon amount at a particular node if the bond you’re valuing contains an embedded floor or ceiling.

"Between stimulus and response there is a space. In that space is our power to choose our response. In our response lies our growth and our freedom." -Viktor Frankl

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

Note that, for the time being, there’s a 33% discount on the subscription rate.

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/

I have been battling with this same issue for weeks. It seems about 50% of the BB and EOC’s I’m doing require you to add the coupon and the rest don’t. I can’t seem to identify the difference in the questions.

Here is an example for you Bill, Reading 36 EOC #13.

Based on Exhibits 3 and 4, the value of Bond C at the upper node at Time 1 is closest to:

1. 97.1957.

2. 99.6255.

3. 102.1255.

Now exhibit 4 just shows that the bond we are working with has 2 years to maturity and pays a 2.5% coupon. (The title of exhibit 4 says this is an annual pay bond. This debunks my initial thoughts on this discrepancy being due to coupon paying vs zeros. Even this coupon paying bond won’t use the coupon in calculating the value.)

Exhibit 3 is the rate tree. Math goes:

(102.5/1.02885)+(102.5/1.02885)/2 then +2.5 gives us the value of 102.1255. This is the answer I chose, which was wrong. The answer is 99.6255, which is my answer -3. In other examples though the coupon is added to calculate the value, except when calculating the value at T=0 because there is no coupon at initiation. (Like EOC #14 right below this question) What is the difference??????? I’m going crazy. Thanks for the help!

Time 0
Time 1
Time 2

2.7183%

2.8853%

1.500%

1.6487%

1.7500%

1.0000%.

I bathe in Lake Superior Returns

S2000magician wrote:

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

Note that, for the time being, there’s a 33% discount on the subscription rate.

Please see my example above if you would. Thank You.

I bathe in Lake Superior Returns

In any pricing model based on binomial or trinomial trees, in the nodes of the tree you put all the cashflows you want to price. So if the goal is to price the bond as a whole (not stripped of its coupon), you must include all the coupons in the nodes.

asrmek wrote:
S2000magician wrote:

What might change is whether you’re interested in the value of the bond by itself or the value of the bond and the coupon together.

Do you have a specific example that’s vexing you?

I wrote a series of articles on creating and using binomial trees for fixed income: http://www.financialexamhelp123.com/binomial-trees-for-fixed-income/.

(Full disclosure: as of 4/25/16 there is a charge to read the articles on my website.  You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)

Note that, for the time being, there’s a 33% discount on the subscription rate.

Please see my example above if you would. Thank You.

The key here is that the question asks you to value the bond, not the bond and the coupon payment that occurs on that date; that’s why you don’t add the coupon.  You would want to know the value of the bond alone if, for example, it is callable or putable and you’re trying to determine whether the option holder would exercise the option at that time; as the coupon has to be paid whether or not the option is exercised, the decision to exercise depends only on the value of the bond, not on the value of the bond plus the coupon.

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/

It looks like the April 10 errata corrected this. The CFAI has changed to correct answer on the questions discussed above from B to C. It now includes the coupon at the node. Is it safe to assume I should always add the current coupon when answering questions of bond value at a particular node?

yyzz wrote:
It looks like the April 10 errata corrected this.

Do you have the link to the errata page?  I cannot seem to find it.

yyzz wrote:
The CFAI has changed to correct answer on the questions discussed above from B to C. It now includes the coupon at the node.

They shouldn’t have; once it’s paid, the coupon is not part of the value of the bond.

yyzz wrote:
Is it safe to assume I should always add the current coupon when answering questions of bond value at a particular node?

I wouldn’t.

But I’d like to see the errata before I tell you what CFA Institute considers safe.  And if they got this one wrong, they’ll be hearing from me.

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/

Here is a link to the April 10 errata:

https://www.cfainstitute.org/-/media/documents/support/programs/cfa/2018...

You’ll see the change in red under Reading 36

Got it.

They’re wrong.

I’ll e-mail them.

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/

What if the question asks for the bond price at a particular node as oppose to value? I’ve come across a question in the curriculum almost identical to the one above only it asks for the bond price and the CFAI includes the coupon in their answer.

Bond price and bond value are (or, at least, should be) the same thing.

I haven’t heard back from CFA Institute yet.

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/

This discrepancy in bond value/price at a particular node only seems to arise in reading 36 where they first introduce the backward induction valuation methodology via straight bonds. I don’t know if you have access to the curriculum but practice problem 4 in this section is a prime example of the confusion they’re creating. Exhibit 4 is labeled “implied values” when it is in fact the “implied value plus the cash flow” at each node. Having said all that, from what I understand, this section is more for practice anyway as it preps you for the next section, “bonds with embedded options”.

The value Maalouf estimates for the three-year bond using the binomial tree in Exhibit 2 is closest to? This is all the question asks for so why am I adding the coupon?

EXHIBIT 2

CALIBRATED BINOMIAL INTEREST RATE TREE

Steinerja29 wrote:
The value Maalouf estimates for the three-year bond using the binomial tree in Exhibit 2 is closest to? This is all the question asks for so why am I adding the coupon?

You add the coupon because you get coupon payments; the value of an investment is the present value of its future cash flows.

What’s the coupon rate?

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/

its 2.8 %. I just dont get why the CF is 100 (Par) + 2.8(Coupon) but then you also add the coupon again each time.

Steinerja29 wrote:
its 2.8 %. I just dont get why the CF is 100 (Par) + 2.8(Coupon) but then you also add the coupon again each time.

You add the coupon at each node because the bond pays coupons at the time of each node.

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/

use method in schweser u will get same answer as curriculum

New errata came out May 21 and this still has not changed… bond value at a node includes the current coupon. Hmmm

I have noticed the following during my humble experience in this topic. When the problem asks bond value, the answer does not include the coupon, but when it asks the value at a particular node (without explicit words “bond value”), the answer does include the coupon. Although I have no explanation for this, I wonder whether this might be the key to the elimination of all of the confusions. Correct me if this is not true.

This is what I noticed, although my experience does not have depth, but 2 days of reading R36 and solving EOC problems.

Think wise and act!