1. Chapter 12 Bond Pricing and Selection
Portfolio Construction, Management, & Protection, 5e, Robert A. Strong
Copyright ©2009 by South-Western, a division of Thomson Business & Economics. All rights reserved.

2. We cannot gamble with anything
so sacred as money.
William McKinley

3. Introduction
The investment characteristics of bonds range completely across the risk/return spectrum
As part of a portfolio, bonds provide both stability and periodic income
Capital appreciation is not usually a motive for acquiring bonds

4. Identification of Bonds
A bond is identified by:
The issuer
The coupon
The maturity
For example, five Household Finance “eights of 10” means $5,000 par Household Finance bonds with an 8 percent coupon rate and maturing in 2010

5. Indenture The bond indenture describes the details of a bond issue:
Description of the loan
Terms of repayment
Collateral
Protective covenants
Default provisions

6. Issuer
Bonds can be classified by the nature of the organizations initially selling them:
Corporation
Federal, state, and local governments
Government agencies
Foreign corporations or governments

7. Bond Security
The security of a bond refers to what backs the bond (what collateral reduces the risk of the loan)

8. Unsecured Debt Governments:
A full faith and credit issue (general obligation issue) is government debt without specific assets pledged against it
e.g., U.S. Treasury bills, notes, and bonds

9. Unsecured Debt (cont’d)
Corporations:
Debentures are signature loans backed by the good name of the company
Subordinated debentures are paid off after original debentures

10. Secured Debt Municipalities issue: Revenue bonds Assessment bonds
Interest and principal are repaid from revenue generated by the project financed by the bond
Assessment bonds
Benefit a specific group of people, who pay an assessment to help pay principal and interest

11. Secured Debt (cont’d) Corporations issue: Mortgages
Well-known securities that use land and buildings as collateral
Collateral trust bonds
Backed by other securities
Equipment trust certificates
Provide physical assets as collateral

12. Term The term is the original life of the debt security
Short-term securities have a term of one year or less
Intermediate-term securities have terms ranging from one year to ten years
Long-term securities have terms longer than ten years

13. Terms of Repayment
Interest Only
Sinking Fund
Balloon
Income Bonds

14. Interest Only Periodic payments are entirely interest
The principal amount of the loan is repaid at maturity

15. Sinking Fund
A sinking fund requires the establishment of a cash reserve for the ultimate repayment of the bond principal
The borrower can:
Set aside a potion of the principal amount of the debt each year
Call a certain number of bonds each year

16. Balloon
Balloon loans partially amortize the debt with each payment but repay the bulk of the principal at the end of the life of the debt
Most balloon loans are not marketable

17. Income Bonds Income bonds pay interest only if the firm earns it
For example, an income bond may be issued to finance an income-producing project

18. Bond Cash Flows Annuities Zero Coupon Bonds Variable Rate Bonds
Consols

19. Annuities
An annuity promises a fixed amount on a regular periodic schedule for a finite length of time
Most bonds are annuities plus an ultimate repayment of principal

20. Zero Coupon Bonds
A zero coupon bond has a specific maturity date when it returns the bond principal
A zero coupon bond pays no periodic income
The only cash inflow is the par value at maturity

21. Variable Rate Bonds
Variable rate bonds allow the rate to fluctuate in accordance with a market index
For example, U.S. Series EE savings bonds

22. Consols Consols pay a level rate of interest perpetually:
The bond never matures
The income stream lasts forever
Consols are not very prevalent in the U.S.

23. Convertible Bonds
A convertible bond gives the bondholder the right to exchange them for another security or for some physical asset
Once conversion occurs, the holder cannot elect to reconvert and regain the original debt security

24. Security-Backed and Commodity-Backed Bonds
Security-backed convertible bonds are convertible into other securities
Typically common stock of the company that issued the bonds
Commodity-backed bonds are convertible into a tangible asset
For example, silver or gold

25. Registration
Bearer Bonds
Registered Bonds
Book Entry Bonds

26. Bearer Bonds Bearer bonds:
Do not have the name of the bondholder printed on them
Belong to whoever legally holds them
Are also called coupon bonds
The bond contains coupons that must be clipped
Are no longer issued in the U.S.

27. Registered Bonds Registered bonds show the bondholder’s name
Registered bondholders receive interest checks in the mail from the issuer

28. Book Entry Bonds
The U.S. Treasury and some corporations issue bonds in book entry form only
Holders do not take actual delivery of the bond
Potential holders can:
Open an account through the Treasury Direct System at a Federal Reserve Bank
Purchase a bond through a broker

29. Bond Pricing and Returns
The current price of a bond is the market’s estimation of what the expected cash flows are worth in today’s dollars
There is a relationship between:
The current bond price
The bond’s promised future cash flows
The riskiness of the cash flows

30. Valuation of Annuities
For a semiannual bond:

31. Valuation of Annuities (cont’d)
Separating interest and principal components:

32. Valuation of Annuities (cont’d)
Example
A bond currently sells for $870, pays $70 per year (paid semiannually), and has a par value of $1,000. The bond has a term to maturity of ten years.
What is the yield to maturity?

33. Valuaton of Annuities (cont’d)
Example (cont’d)
Solution: Using a financial calculator and the following input provides the solution:
N = 20
PV = $870
PMT = $35
FV = $1,000
CPT I = 4.50
This bond’s yield to maturity is 4.50% × 2 = 9.00%.

34. Valuation of Zero Coupon Bonds
For a zero-coupon bond (annual and semiannual compounding):

35. Valuation of Zero Coupon Bonds (cont’d)
Example
A zero coupon bond has a par value of $1,000 and currently sells for $400. The term to maturity is twenty years.
What is the yield to maturity (assuming semiannual compounding)?

36. Valuation of Zero Coupon Bonds (cont’d)
Example (cont’d)
Solution:

37. Valuation of Variable Rate Bonds
The valuation equation must allow for variable cash flows
You cannot determine the precise present value of the cash flows because they are unknown:

38. Valuation of Consols
Consols are perpetuities:

39. Valuation of Consols (cont’d)
Example
A consol is selling for $900 and pays $60 annually in perpetuity.
What is this consol’s rate of return?

40. Valuation of Consols (cont’d)
Example (cont’d)
Solution:

41. Yield to Maturity
Yield to maturity captures the total return from an investment
Includes income
Includes capital gains/losses
The yield to maturity is equivalent to the internal rate of return in corporate finance

42. Realized Compound Yield
The effective annual rate is useful in comparing bonds to investments generating income on a different time schedule

43. Realized Compound Yield (cont’d)
Example
A bond has a yield to maturity of 9.00% and pays interest semiannually.
What is this bond’s effective annual rate?

44. Realized Compound Yield (cont’d)
Example (cont’d)
Solution:
Effective annual rate = [1 + (R/x)]x - 1
= [1 + (0.09/2)]2 – 1
= [1.045]2 – 1
= 9.2%

45. Current Yield The current yield:
Measures only the return associated with the interest payments
Does not include the anticipated capital gain or loss resulting from the difference between par value and the purchase price

46. Current Yield (cont’d)
For a discount bond, the yield to maturity is greater than the current yield
For a premium bond, the yield to maturity is less than the current yield

47. Current Yield (cont’d)
Example
A bond pays annual interest of $70 and has a current price of $870.
What is this bond’s current yield?

48. Current Yield (cont’d)
Example (cont’d)
Solution:
Current yield = $70/$870 = 8.17%

49. Yield Curve The yield curve:
Is a graphical representation of the term structure of interest rates
Relates years until maturity to the yield to maturity
Long-term interest rates are usually higher than rates for shorter terms, and the yield curve typically gets flatter the farther out in time we go.

50. Information Used to Build a Yield Curve

51. Theories of Interest Rate Structure
Expectations Theory
Liquidity Preference Theory
Inflation Premium Theory

52. Expectations Theory
The essence of the expectations theory of interest rates is that wealth-maximizing people are smart enough to figure out how to earn a maximum return on their investment:

53. Expectations Theory (cont’d)
Example
An investor can purchase a two-year CD at a rate of 5 percent. Alternatively, the investor can purchase two consecutive one-year CDs. The current rate on a one-year CD is 4.50 percent.
According to the expectations theory, what is the expected one-year CD rate one year from now?

54. Expectations Theory (cont’d)
Example (cont’d)
Solution:

55. Liquidity Preference Theory
Proponents of the liquidity preference theory believe that, in general:
Investors prefer to invest short term rather than long term
Borrowers must entice lenders to lengthen their investment horizon by paying a premium for long-term money (the liquidity premium)
The liquidity premium means that forward rates are higher than the expected interest rate in a year

56. Inflation Premium Theory
The inflation premium theory states that risk comes from the uncertainty associated with future inflation rates
Investors who commit funds for long periods are bearing more purchasing power risk than short-term investors
More inflation risk means longer-term investments will carry a higher yield

57. Spot Rates
Spot rates:
Are the yields to maturity of a zero coupon security
Are used by the market to value bonds
The yield to maturity is calculated only after learning the bond price
The yield to maturity is an average of the various spot rates over a security’s life

58. Spot Rates (cont’d) Spot Rate Curve Yield to Maturity Interest Rate
Time Until the Cash Flow

59. Spot Rates (cont’d) Example
A six-month T-bill currently has a yield of 3.00%. A one-year T-note with a 4.20% coupon sells for 102.
Use bootstrapping to find the spot rate six months from now.

60. Spot Rates (cont’d) Example (cont’d)
Solution: Use the T-bill rate as the spot rate for the first six months in the valuation equation for the T-note:

61. The Conversion Feature
Convertible bonds give their owners the right to exchange the bonds for a pre-specified number of shares of stock
The conversion ratio measures the number of shares the bondholder receives when the bond is converted
The par value divided by the conversion ratio is the conversion price
The current stock price multiplied by the conversion ratio is the conversion value

62. The Conversion Feature (cont’d)
The market price of a bond can never be less than its conversion value
The difference between the bond price and the conversion value is the premium over conversion value
Reflects the potential for future increases in the common stock price
Mandatory convertibles convert automatically into common stock after three or four years

63. The Matter of Accrued Interest
Bondholders earn interest each calendar day they hold a bond
Firms mail interest payment checks only twice a year
Accrued interest refers to interest that has accumulated since the last interest payment date but which has not yet been paid

64. The Matter of Accrued Interest (cont’d)
At the end of a payment period, the issuer sends one check for the entire interest to the current bondholder
The bond buyer pays the accrued interest to the seller
The bond seller receives accrued interest from the bond buyer

65. The Matter of Accrued Interest (cont’d)
Example
A bond with an 8% coupon rate pays interest on June 1 and December 1. The bond currently sells for $920.
What is the total purchase price, including accrued interest, that the buyer of the bond must pay if he purchases the bond on August 10?

66. The Matter of Accrued Interest (cont’d)
Example (cont’d)
Solution: The accrued interest for 71 days is:
$80/365 × 71 = $15.56
Therefore, the total purchase price is:
$920 + $15.56 = $935.56

67. Bond Risk Bondholders face price risks and convenience risks
Price risks include:
Interest rate risk
Default risk
Convenience risks include:
Call risk
Reinvestment rate risk
Marketability risk

68. Interest Rate Risk
Interest rate risk is the chance of loss because of changing interest rates
The relationship between bond prices and interest rates is inverse
If market interest rates rise, the market price of bonds will fall

69. Default Risk
Default risk measures the likelihood that a firm will be unable to pay the principal and interest on a bond in accordance with the bond indenture
Standard & Poor’s Corporation is one of several advisory services monitoring default risk

70. Default Risk (cont’d)
Investment grade bonds are bonds rated BBB or above
Junk bonds are rated below BBB
The lower the grade of a bond, the higher its yield to maturity

71. Convenience Risk
Convenience risk refers to added demands on management time because of:
Bond calls
The need to reinvest coupon payments
The difficulty in trading a bond at a reasonable price because of low marketability

72. Call Risk If a company calls its bonds, it retires its debt early
Call risk refers to the inconvenience to bondholders associated with a company retiring a bond early
Bonds are usually called when interest rates are low

73. Call Risk (cont’d) Many bond issues have: Call protection
A period of time after the issuance of a bond when the issuer cannot call it
A call premium if the issuer calls the bond
Typically begins with an amount equal to one year’s interest and then gradually declines to zero as the bond approaches maturity

74. Reinvestment Rate Risk
Reinvestment rate risk refers to the uncertainty surrounding the rate at which coupon proceeds can be invested
The higher the coupon rate on a bond, the higher its reinvestment rate risk

75. Marketability Risk
Marketability risk refers to the difficulty of trading a bond:
Most bonds do not trade in an active secondary market
The majority of bond buyers hold bonds until maturity
Low marketability bonds usually carry a wider bid-ask spread

76. Malkiel’s Interest Rate Theorems
Provide information about how bond prices change as interest rates change
Any good portfolio manager knows Malkiel’s theorems

77. Theorem 1 Bond prices move inversely with yields:
If interest rates rise, the price of an existing bond declines
If interest rates decline, the price of an existing bond increases

78. Theorem 2
Bonds with longer maturities will fluctuate more if interest rates change
Long-term bonds have more interest rate risk

79. Theorem 3 Higher coupon bonds have less interest rate risk
Money in hand is a sure thing while the present value of an anticipated future receipt is risky

80. Theorem 4
When comparing two bonds, the relative importance of Theorem 2 diminishes as the maturities of the two bonds increase
A given time difference in maturities is more important with shorter-term bonds

81. Theorem 5
Capital gains from an interest rate decline exceed the capital loss from an equivalent interest rate increase

82. The Concept of Duration
Duration is a measure of interest rate risk
For a noncallable security:
Duration is the weighted average number of years necessary to recover the initial cost of the bond where the weights reflect the time value of money
Duration is a direct measure of interest rate risk:
The higher the duration, the higher the interest rate risk

83. Calculating Duration
The traditional duration calculation:

84. Calculating Duration (cont’d)
The closed-end formula for duration:

85. Calculating Duration (cont’d)
Example
Consider a bond that pays $100 annual interest and has a remaining life of 15 years. The bond currently sells for $985 and has a yield to maturity of 10.40%.
What is this bond’s duration?

86. Calculating Duration (cont’d)
Example (cont’d)
Solution: Using the closed-form formula for duration:

87. Bond Diversification It is important to diversify a bond portfolio
Diversification of a bond portfolio is different from diversification of an equity portfolio
Two types of risk are important:
Default risk
Interest rate risk

88. Default Risk
Default risk refers to the likelihood that a firm will be unable to repay the principal and interest of a loan as agreed in the bond indenture
Equivalent to credit risk for consumers
Rating agencies such as Standard & Poor’s function as credit bureaus for credit issuers

89. Default Risk (cont’d) To diversify default risk:
Purchase bonds from a number of different issuers
Do not purchase various bond issues from a single issuer
e.g., Enron had 20 bond issues when it went bankrupt

90. Dealing With the Yield Curve
The yield curve is typically upward sloping
The longer a fixed-income security has until maturity, the higher the return it will have to compensate investors
The longer the average duration of a fund, the higher its expected return and the higher its interest rate risk

91. Dealing With the Yield Curve (cont’d)
A portfolio manager in conjunction with the client and the statement of investment policy needs to determine the appropriate level of interest rate risk that the portfolio should carry

92. Bond Betas The concept of bond betas:
States that the market prices a bond according to its level of risk relative to the market average
Has never become fully accepted
Market risk does affect bonds, but most investors are much more concerned with default risk and interest rate risk

93. Client Psychology and Bonds Selling at a Premium
Premium bonds held to maturity are expected to pay higher coupon rates than the market rate of interest
There is nothing wrong with buying bonds selling at a premium
Premium bonds held to maturity will decline in value toward par value as the bond moves towards its maturity date
Clients may not want to buy something they know will decline in value

94. Call Risk If a bond is called:
The funds must be reinvested
The fund manager runs the risk of having to make simultaneous adjustments to many portfolios
There is no reason to exclude callable bonds categorically from the list of eligible securities
Avoid making extensive use of a single callable bond issue

95. Possible Client-Initiated Constraints to Bond Purchase
Specifying Return
Specifying Grade
Specifying Average Maturity
Periodic Income
Maturity Timing
Socially Responsible Investing

96. Specifying Return To increase the expected return on a bond portfolio:
Choose bonds with lower S&P ratings
Choose bonds with longer maturities
Or both

97. Specifying Grade
A legal list specifies securities that are eligible investments
e.g., investment grade only
Portfolio managers should take the added risk of noninvestment grade bonds only if the yield pickup is substantial
Conservative organizations will accept only U.S. government or AAA-rated corporate bonds
A fund may be limited to no more than a certain percentage of non-AAA bonds

98. Specifying Average Maturity
Average maturity is a common bond portfolio constraint
The motivation is concern about rising interest rates
Specifying a maximum average duration would be an alternative approach

99. Periodic Income
Some funds have periodic income needs that allow little or no flexibility
Clients will want to receive interest checks frequently
The portfolio manager should carefully select the bonds in the portfolio

100. Maturity Timing Maturity timing generates income as needed
Sometimes a manager needs to construct a bond portfolio that matches a particular investment horizon
e.g., assemble securities to fund a specific set of payment obligations over the next ten years
Assemble a portfolio that generates income and principal repayments to satisfy the income needs

101. Socially Responsible Investing
Some clients will ask that certain types of companies not be included in the portfolio
Examples are nuclear power, military hardware, “vice” products

102. The Problem
Unspecified Constraints
Using S&P’s Bond Guide
Solving the Problem

103. Example: Monthly Retirement Income
A client has:
Primary objective: growth of income
Secondary objective: income
$1,100,000 to invest
NOTE: This is about half of the amount listed in the text in order to present a slightly different problem!
Income needs of $4,000 per month
NOTE: As with the investment, this is also a fraction of that presented in the textbook’s Monthly Retirement Income Example

104. Monthly Retirement Income Example (cont’d)
You decide:
To invest the funds 50–50 between common stocks and debt securities
To invest in ten common stock in the equity portion (see next slide)
You incur $1,500 in brokerage commissions

105. Monthly Retirement Income Example (cont’d)
Stock
Value
Quarterly Dividend
Payment Month
3,000 AAC
$51,000
$380
Jan/April/July/Oct
1,000 BBL
50,000
370
2,000 XXQ
49,000
400
Feb/May/Aug/Nov
5,000 XZ
52,000
270
March/June/Sept/Dec
7,000 MCDL
53,000 —
1,000 ME
Feb/May/Aug./Nov
2,000 LN
51,000
500
4,000 STU
47,000
260
3,000 LLZ
290
6,000 MZN
43,000
170
Total
$494,000
$3,010

106. Monthly Retirement Income Example (cont’d)
Characteristics of the fund:
Quarterly dividends total $3,010 ($12,040 annually)
The dividend yield on the equity portfolio is 2.44 percent
Total annual income required is $48,000 or 4.36 percent of fund
Bonds need to have a current yield of at least 6.28 percent
[4.36% - 0.5(2.44%)] ÷ 0.5 = 6.28%

107. Unspecified Constraints
The task is meeting the minimum required expected return with the least possible risk
You don’t want to choose CC-rated bonds
You don’t want the longest maturity bonds you can find

108. Using S&P’s NetAdvantage Service
Identifies the bond by issuer, coupon, and maturity
Indicates when interest is paid
Provides S&P ratings
Provides recent market price, current yield based on this market price and the yield to maturity

109. Solving the Problem Setup
Dealing with Accrued Interest and Commissions
Choosing the Bonds
Overspending
What about Convertible Bonds?

110. Setup You have two constraints:
Include only bonds rated BBB or higher
Keep the average maturities below fifteen years
Set up a worksheet that enables you to pick bonds to generate approximately $4,000 per month (see next slides)

111. Setup (cont’d) Security Price Jan. Feb. March April May June 3,000 AAC
$51,000
$380
1,000 BBL
50,000
370
2,000 XXQ
49,000
$400
5,000 XZ
52,000
$270
7,000 MCDL
53,000
1,000 ME
2,000 LN
51,000
500
4,000 STU
47,000
260
3,000 LLZ
290
6,000 MZN
43,000
170
Equities
$494,000
$1,420
$1,060
$530

112. Dealing with Accrued Interest and Commissions
Brokerage firms often maintain an inventory of bonds for resale to their customers and do so on a “net” basis (includes a markup representing compensation to the broker)
Calculate accrued interest using the mid-term heuristic
Assume every bond’s accrued interest is half of one interest check

113. Choosing the Bonds The following slide shows one possible solution:
Stock cost: $494,000
Bond cost: $557,130
Accrued interest: $9,350
Stock commissions: $1,500
Do you think this solution could be improved?

114. Bonds Security Price Jan. Feb. March April May June
$80,000 Empire 71/2s02
$86,400
$3,000
$80,000 Energen 8s07
82,900
$3,200
$100,000 Enhance 61/4s03
105,500
$3,370
$80,000 Enron 65/8s03
84,500
$2,650
$90,000 Enron 6.7s06
97,200
$3,010
$100,000 Englehard 6.95s28
100,630
$3,470
Bonds subtotal
$557,130
Total income
$4,420
$4,260
$3,900
$4,070
$4,000

115. Overspending
The total of all costs associated with the portfolio should not exceed the amount given to you by the client to invest
The money the client gives you establishes another constraint

116. What About Convertible Bonds?
Convertible bonds can be included in a portfolio
Useful for a growth of income objective
People buy convertible bonds in hopes of price appreciation
Useful if you otherwise meet your income constraints