Chapter Eleven
Bond Pricing and Selection
KEY POINTS
Much of the material in this chapter will be a review. As with previous chapters, it
should be useful to almost everyone to read this material again. The important thing is
that trivial aspects of bonds (such as the dollar amount of interest a 7% coupon bond pays
annually) should be no-brainers.
There is much terminology here, and students may need some prodding to learn it all.
The test bank has over 70 questions from this chapter; this is sometimes sufficient
motivation to get them to go over this material carefully.
Dealing with semi-annual compounding is another important point in this chapter, as is
the reinvestment rate assumption associated with the bond’s yield to maturity. Stress that
it is not possible to “lock in” a yield to maturity with a bond that pays periodic interest.
Bond selection is a topic that often receives only minimal coverage in both textbooks and
literature from the trade. Bonds are important components of many portfolios, and the
selection of them should be by design. With bonds, the investor is concerned with
default risk and with interest rate risk. Reinvestment rate risk is a secondary concern, but
still an important one. As expected, there is a trade-off between yield and maturity.
What constitutes an adequate additional expected return for additional risk is an arguable
point about which investment managers probably will never reach consensus. It can be a
considerable inconvenience if a bond is called, particularly if the bond appears in many
managed portfolios. This is an example of a convenience risk.
TEACHING CONSIDERATIONS
Some instructors may want to assign some outside reading regarding theories of the yield
curve. The end of chapter references contain some good candidates.
It is also important to ensure that accrued interest gets covered and understood at this
point. This will become important in later chapters as portfolios are built and you seek to
avoid overspending. Spend some time on the distinction between interest rate risk and
reinvestment rate risk.
Introduce duration here; it will get more coverage later in the book. You can show that it
has two interpretations: 1) a measure of interest rate risk (incorporating Malkiel’s
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Chapter Eleven
Bond Pricing and Selection
theorems), and 2) the weighted average of time until the bond’s cash flow occur, but only
in the case of a bond without embedded options.
Take advantage of the “monthly retirement income” example at the end of this chapter.
This is a simple application exercise in portfolio management and well worth spending
class time to review the process of finding the right combination of dividends and interest
income to satisfy a client’s monthly income needs. Finance students often complain that
they “don't know how to do anything,” and building such a portfolio is something they
clearly can do right away. People routinely hire brokers and financial advisors to do this
for them.
Be sure to incorporate the BONDPORT file from the support materials at the
http://strong.swlearning.com website.
I usually assign a homework
assignment using this file. [Note: there is an occasional error arising with the
BONDPORT file. Interest payment months must be entered in chronological order. For
instance, a bond that pays interest in February and August must be entered with the “f”
first, followed by the “a.” As the file instructions indicate, letters can be either upper or
lower case.] I like to use a handout from the Standard & Poor's Bond Guide to augment
classroom discussion. This enables you to reinforce the notion of different interest
payment months and consider the higher yields associated with lower bond ratings. You
also can construct a monthly income schedule (or at least part of one) as with the
BONDPORT file.
ANSWERS TO QUESTIONS
1. No. As the cash flows are uncertain, you cannot calculate a precise yield to maturity.
2. If the two securities have the same coupon, the same degree of default risk, and the
same remaining time until maturity, they should sell for the same price because the
market would consider them identical securities.
3. The statement is true, everything else being equal.
4. Treasury bonds have an initial life of more than ten years. Treasury notes have an
initial life of up to 10 years.
5. Convenience risk refers to the possibility of “loss” due to added managerial time
necessary to properly manage the portfolio.
6. Bonds sometimes sell at a premium, in which case the bonds could be redeemed at a
loss if called. Capital gains are also determined relative to your purchase price, which
may be more or less than the call price. The call also may involve managerial
inconvenience that outweighs any call premium or capital gain.
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Chapter Eleven
Bond Pricing and Selection
7. If the interest rates associated with all maturities move up or down by the same
amount, this is a parallel shift. This assumes, for instance, that if T-bill rates rise by
one half point, so do 30-year bonds.
8. Arbitrage is present if a convertible bond sells for less than its conversion value. If it
did, people would buy the bond, convert it, sell the shares, and have more money than
when they started (ignoring transaction costs).
9. $20 per ounce: $1000 par /50 ounces
10. Accrued interest must be paid when the bond is purchased and is received when the
bond is sold. This amount is in actual dollars and the trade confirmation slip reflects
it.
11. The rating change from A to BBB represents an increase in default risk; as a
consequence, the bond price will fall and the bond yield will increase.
12. The realized compound yield is the same as the yield to maturity when interest is
compounded semi-annually.
13. This is because of reinvestment rate risk and because future reinvestment rates are
unknown.
14. The convertible bond’s conversion value.
15. Companies issue convertible bonds largely because they hope never to have to pay
them off. The firm wants the bondholder to convert, likes to see the number of
shareholders grow, and is not interested in having the debt reappear on the books.
This could cause a violation of other debt covenants and make short term financial
planning difficult.
16. There is no way to make a riskless dollar. Buying the bond, converting it, and selling
the stock would leave you with less money than when you started.
17. A primary objective of income means that the generation of income is paramount.
Therefore, the current yield (which is a direct function of the coupon rate) is more
important than yield to maturity.
18. Yes. Bonds with identical durations generally have the same yield to maturity unless
they have very different liquidity risk or other characteristics.
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Chapter Eleven
Bond Pricing and Selection
19. 1) Interest rates in the economy fell; 2) it sells at a discount and has moved closer to
maturity; 3) the bond rating was increased; 4) it is a convertible bond and the stock
price increased.
20. When bonds sell for a premium, it is because their coupon rate is higher than average,
so investors are willing to pay more for it. The yield to maturity is the factor that
matters long term. Some people, however, do not understand why you would buy
something that you know will go down in value. The fact that the income received
compensates for this can be overlooked. Some managers prefer to avoid having to
explain this fact of life.
21. It is an inconvenience having a bond called. Some people avoid buying a callable
bond because they want to avoid having to deal with replacement decisions or the
effort involved in doing so.
22. You can lose money if the call price is less than the price you paid.
23. There is no clear-cut answer to this one. Experience and personal opinion are very
relevant.
24. Many people would say no. Still, it is never a good idea to buy any security without
knowing a good deal about the issuer.
25. See the equation in footnote 3. Beta is directly related to the negative of duration.
26. They sometimes have a slightly higher yield to maturity than otherwise similar bonds
selling at par or at a discount.
27. Investors value the conversion option. They essentially buy a call option on the stock,
and the premium on the option takes the form of a reduced yield.
28. This depends on the covariance between the change in market interest rates and the
return on the market index. Often when interest rates rise, the stock market falls. If
this is the case, the beta will be negative.
29. Probably not. You cannot have your cake and eat it, too, so the rate at which funds
would be reinvested is not a concern.
30. The investment policy statement is important. It may contain constraints regarding
bond rating or maturity. Any selection should always be made with clear recognition
of the interest rate risk and credit risk involved, and the associated yield spreads over
other risk levels.
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Chapter Eleven
Bond Pricing and Selection
31. With regard to interest rate risk, the statement is fundamentally true, although many
investors are much more familiar with “maturity” than they are with “duration.” If
the policy statement specifically mentions maturity, it would not be smart to substitute
duration without discussing this with the client.
32. Many managers agree with this, although the magnitude of the credit spread changes
through time. It is not a good idea to make a sweeping generalization like this and
assume that it will always be true.
33. If the bond is selling near the call price, there would be a limitation on an increase in
the bond price because the issuer has the right to purchase the bond from the investor
at the call price. Thus, a decrease in interest rates would not increase the bond price
as much as duration would have indicated (i.e., negative convexity).
ANSWERS TO PROBLEMS
1. Five year:
FV  PV (1  R ) 2 N = $1000 (1 + .09/2)10 = $1,552.97
2
interest = FV – PV = $1,552.97 - $1,000 = $552.97
4.5 year:
FV  PV (1  R ) 2 N = $1000 (1 + .095/2)9 = $1,518.40
2
interest = FV – PV = $1,518.40 - $1,000 = $518.40
$552.97 - $518.40 = $34.57
14
2. Assume semi annual interest: P0  
t 1
40
1000

= $941.50
t
(1  .095 )
(1  .095 )14
2
2
 14

40
1000

t 
 14
14
.
0915
 t 1 (1  .095 ) t

(1 
)
2
2

 = 5.44 years
3. a. D 
941.50
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Chapter Eleven
Bond Pricing and Selection

.0915 )15  (1  .0915 )  .0915  14 
 (1 

2
2
1000  14
2
40


14
(.0915 ) 2 (1  .0915 )14

 (1  .0915 2 )
2
2


b. D  
941.50
1.956  1.046  .641 1000(14)
= 10.81 periods = 5.41 years

14
.002(1.871)

 (1.04575)
= 40
4. N = 8
P0 = 500 FV = 1000
a. Using the rule of 72, the value doubles in 8 years: 72/8 = 9%
b. PV 
FV
(1  R ) t
(1  R ) t 
FV
PV
R  ( FV
PV
)
1
t
1
R=2(1/8) – 1 = 9.05%
Using semi-annual periods:
R=2(1/16) – 1 = 4.43;
7
5. a. 800  
t 1
14
b. 800  
t 1
4.43 x 2 = 8.86%
80
1000
R = 12.44%

t
(1  R) (1  R) 7
40
1000

t
(1  R )
(1  R )14
2
2
R = 12.73%
6. Using the 365 day convention, 7 ¼%  .0725(1000)/365 = $0.1986 per day
$0.1986 x 43 = $8.54
7. First solve for R: R = 10.74%
42
PV of annuity:
t 1
PV of principal:
37.5
 (1  .0543)
t
 $632.75
1000
 $117.53
(1  .0543) 42
Interest: $632.75/$750 = 84.3%
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Chapter Eleven
Bond Pricing and Selection
8. You can use the DURATION file, set par=0 and N= 10000; this gives D = 17.67
9. Use equation 11-6:
effective annual rate = [1 + R/x]x – 1
=
[1 + .135/12]12 – 1 = 14.37%
10. conversion ratio = par value/conversion price = $1000/9.54 = 104.82 shares
11. conversion value = conversion ratio x stock price = 104.82 x $10 = $1048.20
12. Premium over conversion value = bond price – conversion value
= $1100 - $1048.20 = $51.80
13 – 14. Student response.
15. Smith has a compound yield of 10%; Jones has a simple yield of 10%.
16.
Accrued interest paid:
5 x 39 days x 70/365 =
Interest received:
Accrued interest received: 5 x 31days x 70/365 =
($37.40)
$175.00
29.73
$167.33
17. a. The point here is that once the short-term bond matures there is a reinvestment
rate issue. You cannot calculate a portfolio yield to maturity when maturities do
not coincide.
b. If both bonds have the same maturity and market rates equal 10.5%.
18. Student response.
19. Student response.
20. Student response.
21. Cost = principal + interest + commission
= (.99 x $5000) + ($5000 x .1025 x 73/365) + $40
= $4950 + 102.50 + 40 = $5092.50
22. $500,000 x .085 x 1/4 = $10,625
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Chapter Eleven
Bond Pricing and Selection
23 - 30. Student response.
31. Treasury bond after tax yield = 5.5% (1-0.28) = 3.96%
Corporate bond after tax yield = 6.5% (1-0.36) = 4.16%
Municipal bond after tax yield = 3.3%
The 6.5% Corporate bond has the highest after tax yield.
32. Student response.
33. Student response.
85