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# L1.T4.14. Yield to maturity (YTM)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
AIMs: Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing. Compute a bond's YTM given a bond structure and price. Establish the relationship between spot rates and YTM. Understand the relationship between coupon rate, YTM, and bond prices. Define and describe: Discount bond; Premium bond; Coupon effect; Pull-to-par.

Questions:

14.1. A three (3)-year bond with a current price of $105.90 pays a semi-annual coupon with a coupon rate of 5.0% per annum. What is the bond's yield-to-maturity (YTM) on a bond-equivalent basis? a. 1.97% b. 2.25% c. 2.93% d. 3.56% 14.2. An eight (8)-year bond with a current price of$975.00 pays an annual coupon of 6.0%. What is the bond's yield-to-maturity (YTM)?
a. 5.88%
b. 6.41%
c. 6.89%
d. 7.14%

14.3. Each of the following is necessarily TRUE about a bond's yield-to-maturity (YTM) EXCEPT:
a. A bond that sells at a premium to par has a yield (YTM) that is less than its coupon rate
b. A bond that sells at a discount to par has a yield (YTM) that is greater than its coupon rate
c. The yield (YTM) of a zero-coupon bond equals the spot (zero) rate of the bond's maturity
d. If the same term structure of spot rates applies to two bonds with identical maturities, the bond with the higher yield (YTM) is a superior investment

14.4. Assume the two-year term structure of spot rates is upward-sloping as follows: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, 4.0% at 2.0 years. Consider the following two statements:

I. The yield (YTM) of a two-year bond must be less than 4.0%
II. Given a two-year bond, an increase in the coupon rate implies an increase in the yield (YTM)

Which of the above statements is (are) TRUE?
a. Neither
b. I. only
c. II. only
d. Both I. and II.

14.5. Which of the following bonds offers the highest yield (YTM)?
a. 7-year bond with a 3% coupon trading at par
b. 20-year bond with a 4% coupon trading at a 15% premium to par
c. 10-year bond with 4% coupon trading at a 15% discount to par
d. 15-year bond with a 4% coupon 15% trading at a 15% discount to par

14.6. A ten (10)-year bond pays a semi-annual coupon with a coupon rate of 7.0% and the bond's yield (YTM) is 6.0%. If the yield remains unchanged, what happens to the price of the bond in six months?
a. Lower price
b. Same price
c. Higher price

14.7. Each of the following is necessarily true about a bond's yield (YTM) EXCEPT:
a. If the term structure of spot rates is flat at X%, a bond's yield must be also be X%
b. Regardless of the slope of the term structure (e.g., upward- or downward-sloping) and number of spot rates, the yield (YTM) is a single value
c. The yield on a coupon-paying bond is sensitive to (i.e., will change in response to) a change in spot rates at specific maturities
d. For a given bond with a fixed coupon rate, an increase in the bond's maturity implies a decrease in the bond's yield (YTM)

14.8. You just purchased a ten (10)-year bond at a discount to par. The bond pays a quarterly coupon with a coupon rate of 4.0% per annum; i.e., 1% each quarter. The bond's yield is 8.0% per annum. Your broker says to you, "The 8% yield-to-maturity represents the return you will realize--that is, your realized return--on this bond." Which qualifier or caveat is BEST attached to this assertion?
a. This statement is already true: realized return will equal yield (YTM)
b. The statement is only true if there is no shift in the term structure of spot rates
c. This statement is true if you (the bondholder) hold the bond to maturity: realized return will equal yield (YTM) if the bond is held to maturity
d. This statement is true only if both the bond is held to maturity and the coupons (interim cash flows) are reinvested at the same yield (YTM)

#### Hend Abuenein

##### Active Member
Hi David,
I don't want to be pushy, but you haven't posted any quizzes today or yesterday.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi Hend, It is great to be wanted, I did miss yesterday .... for what it's worth, the main reason is: i now that I finished the T8. Investment set (yipee), as I start a new section, with respect to those new questions, I need to shift my attention to 2012: new questions that I write need to be "durable" to to the 2012 exam year (it's not really ideal to write fresh questions today that may not apply to 2012!).

So, I wanted/needed to get confirmation that the Stock & Watson text will remain in 2012 (which I am told, it will remain: I wish they would go back to Gujarati but i guess it ain't gonna happen ... buggers) ... so that I can start a fresh econometric set (today). But the next four weeks or so are the one time of the year where i may not be perfect with respect to the daily discipline (i.e., 2011 is now primarily a support job for me; and, I start the considerable work of orienting question sets toward the 2012 exam).

Actually, fwiw to 2012 candidates: since our question database has grown so large, much of my work will be consolidating the question database so the Study Planner contains fewer, but consolidated question sets for each topic. Organizing & streamlining for easier retrieval, basically. And, yes: mock exams, baby!!

Thank you so much for liking the daily questions that you would miss a day!!

David

#### Hend Abuenein

##### Active Member
You're doing a lot of work that is very very much appreciated.
I really thought the time between exams and the new cycle is your time off...This is probably out of line, but if it isn't so, then when DO YOU take time off??!!

(You can delete this post if you wish)

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hend, Thank you, I really really appreciate that, and your support generally. By design, I take off the week, mostly, of Nov 21st to 26th (Thanksgiving week). Right after the exam, as the week before the exam will be busy with forum support (in the week before the exam, the forum can approach full time duty). So I am headed to my brother's in Paso Robles, CA where I can play with, and generally dote on, my four wonderful nephews and niece. Thanks for asking!

(I would not delete your post: as a policy, b/c we always wanted transparency, we've never ever deleted or edited a member's post [least of all when they are citing an error] with the only exception being logistical: delete a duplicate or move to the right section. I do occasionally have private offlines, to request a behavior change, but i never edit/delete somebody else's non-spam post). thanks,

David

#### goturtlego

##### New Member
14.4 C
14.5 C
14.6 A

These were fun questions. I'm not familiar with the term structure of spot rates. I guess I need to look that up and study that. I'm curious to know what the answers are. I did get a little help from this YTM Calculator.

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
14.4 C
14.5 C
14.6 A

These were fun questions. I'm not familiar with the term structure of spot rates. I guess I need to look that up and study that. I'm curious to know what the answers are. I did get a little help from this YTM Calculator.
Hello @goturtlego

The answers to our daily practice questions are only available to our paid members, as these questions are part of our practice question sets in the study planner. If you would like access to the answers and in-depth explanations, these are the study packages that we offer: https://www.bionicturtle.com/features-pricing/.

Thank you,

Nicole

Thanks Nicole!

#### flex

##### Member
AIMs: ...
Questions:
14.4. Assume the two-year term structure of spot rates is upward-sloping as follows: 1.0% at 0.5 years, 2.0% at 1.0 years, 3.0% at 1.5 years, 4.0% at 2.0 years. Consider the following two statements:

I. The yield (YTM) of a two-year bond must be less than 4.0%
II. Given a two-year bond, an increase in the coupon rate implies an increase in the yield (YTM)

Which of the above statements is (are) TRUE?
a. Neither
b. I. only
c. II. only
d. Both I. and II.
hi, everybody. hi, @David Harper CFA FRM
there is GARP's convention (like) concerning to bond typology when it (zero/non-zero cpn, etc)'s missed at qstn text? thx

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@flex I don't understand the question. You quoted question 14.4 but I don't see any terms that are unusual: term structure, spot rates, yield (aka, YTM), coupon. Yes, these are all conventional bond terms, if that's what you are asking.

#### flex

##### Member
@flex I don't understand the question. You quoted question 14.4 but I don't see any terms that are unusual: term structure, spot rates, yield (aka, YTM), coupon. Yes, these are all conventional bond terms, if that's what you are asking.
sorry, @David Harper CFA FRM
i've implied situation, when bond type isn't specified (by/at 'quality qstn text' (particulary, 14.4)). that make 'I' statement incorrect, when z-coupon take in consideration, or i am stupid))

ps: must be 'concerning ab. bond type specifing'

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@flex i don't understand, i'm sorry. The full Q&A (at http://www.bionicturtle.com/forum/threads/l1-t4-14-yield-to-maturity-ytm.4940/) has two pages of discussion, question 14.4 has survived so far. If the term structure of spot rates is upward sloping, with 2-year spot (aka, zero) equal to 4.0%, then i think it's true that any bond's 2-year yield must be less than or equal to 4.0%. Statement (II) is considered false (not necessarily true). Thanks,

#### flex

##### Member
@flex i don't understand, i'm sorry. The full Q&A (at http://www.bionicturtle.com/forum/threads/l1-t4-14-yield-to-maturity-ytm.4940/) has two pages of discussion, question 14.4 has survived so far. If the term structure of spot rates is upward sloping, with 2-year spot (aka, zero) equal to 4.0%, then i think it's true that any bond's 2-year yield must be less than or equal to 4.0%. Statement (II) is considered false (not necessarily true). Thanks,

thx so much, @David Harper CFA FRM .
i cleary understand, that the qstn's target (arround 'I' statement) is checking of 'YTM-z.i relations on different fwd curve sloping' knowledge.
(especially, when '+slope' given )) quantitatively). it's first YTM property which remember after qstn was read
, but condition 'YTM<z(2) or 'YTM<z(maturity)' (for generally) is stricly and true for non-z-coupon security). i am concerned about GARP look on that uncertainty.

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@flex I recently recorded youtube videos that review yield to maturity concept, hopefully this is is helpful (my point #3 mentions that YTM is complex average of the spot rates, which implies that it must be bound by the min/max spot rates):
... it is part of the a playlist https://www.youtube.com/playlist?list=PLCBifSfCnx3tQuvaS-lG-8ZqUh7NvxRDg
... hopefully this may be helpful