1. Chapter 11
Bond Prices and Yields

2. 11.1 Bond Characteristics

3. Bond Characteristics Face or par value Coupon rate
Zero coupon bond
Compounding and payments
Accrued Interest
Indenture

4. Treasury Notes and Bonds
T Note maturities range up to 10 years
T bond maturities range from 10 – 30 years
Bid and ask price
Quoted in points and as a percent of par
Accrued interest
Quoted price does not include interest accrued

5. Listing of Treasury Issues

6. Treasury Notes and Bonds
Accrued interest
Interest that accrues between coupon payment dates
Accrued interest=(annual coupon payment)/2 *days since last coupon payment/days separating coupon payments, if semiannually paid
Example:
Coupon rate 8%, 40 days have passed since the last coupon payment, if semiannually paid
The accrued interest on the bond =8%*1000*0.5*40/182=8.79

7. Corporate Bonds Most bonds are traded over the counter
Registered (record)
Bearer bonds (without record)
Call provisions (price?)
Convertible provision (conversion value)
Put provision (putable bonds) (price?)
Floating rate bonds (yield spread fixed)
Preferred Stock (cumulate, not tax deductible, offsetting tax adv , 30% of dividend taxed)

8. Listing of Corporate Bonds

9. Corporate Bonds Coupon, maturity, price, yield to maturity, rating
Call provisions (price?)
Allowing the issuer to repurchase the bond at a specified call price before the maturity date
Refunding: retire high-coupon debt and issue new bonds at a lower coupon rate
Call option valuable to the firm, higher coupon and promised yields to maturity than non-callable bonds

10. Corporate Bonds Put provision (puttable bonds) (price?)
Give the option to the bondholder to extend the bond’s life, when the coupon rate exceeds current market yield
Floating rate bonds (yield spread fixed)
Interest payments tied to some measure of current market rate. Yield spread fixed if financial health kept.

11. Corporate Bonds Convertible provision (conversion value)
Give bondholders an option to exchange each bond for a specified number of shares of common stock
Conversion ratio, Market conversion value
Preferred Stock (cumulate, not tax deductible, offsetting tax adv)
International bonds
Foreign bonds: issued by a borrower from a country other than the one in which the bond is sold
Eurobonds: bonds issued in the currency of one country but sold in other national markets.

12. Corporate Bonds International Governments and Corporations
Foreign bonds
Foreign Issuer , Denominated in local currency
Yankee bonds (in USA)
Samurai bonds (in JAPAN)
Bulldog bonds (in UK)
Eurobonds
Foreign issuer, denominated in foreign currency

13. Innovative Bonds Inverse Floaters (suffer doubly and benefit doubly)
The coupon rate falls when market rate rises
Asset-backed bonds
Income from a specified group of assets is used to service the debt

14. Innovative Bonds Indexed Bonds
Payments are tied to a general price index or the price of a particular commodity
Example: Treasury inflation protected securities (TIPS), par value tied to general level of prices, coupon payments and final repayment of par value increase in direct proportion to the Consumer Price Index.
risk-free real rate

15. 11.2 BOND PRICING

16. Bond Pricing
Value a security, discount its expected cash flows by the appropriate discount rate
Bond value= present value of coupons + present value of par value

17. Bond Pricing PB = Price of the bond Ct = interest or coupon payments
T = number of periods to maturity
r = semi-annual discount rate or the semi-annual yield to maturity

18. Bond Pricing Price= coupon *annuity factor (r, T)
+ Par value * PV factor (r, T)
annuity factor (r, T)=
PV factor (r, T)=

19. Price of 8%, 10-yr. with yield at 6%20 1 1 å P = 40 +
1000 B ( 1 . 03 ) t ( 1 . 03 ) 20 t = 1 P = 1 ,
148 . 77 B
Coupon = 4%*1,000 = 40 (Semiannual)
Discount Rate = 3% (Semiannual)
Maturity = 10 years or 20 periods
Par Value = 1,000

20. Bond Prices and Yields
Prices and Yields (required rates of return) have an inverse relationship
When yields get very high the value of the bond will be very low
When yields approach zero, the value of the bond approaches the sum of the cash flows

21. Bond Prices and Yields Coupon rate=8%, semiannual, face value=1000
Maturity : 1-yr , 10-yr, 20-yr, 30-yr
Market interest rate, 4%--12%

22. Bond Prices and Yields TIME TO MATURITY MARKET INTEREST RATE 4% 6% 8%
10%
12% 1
￥-1,038.83
￥-1,019.13
￥-1,000.00 ￥ ￥ 10
￥-1,327.03
￥-1,148.77 ￥ ￥ 20
￥-1,547.11
￥-1,231.15 ￥ ￥ 30
￥-1,695.22
￥-1,276.76 ￥ ￥

23. The Inverse Relationship Between Bond Prices and Yields

24. Bond Prices and Yields Issued at par value
Secondary market, price move in accordance with market forces, fluctuate inversely with the market interest rate
Interest rate fluctuations, main source of risk in fixed-income market
Maturity, key factor of sensitivity
Longer maturity, greater sensitivity

25. Bond pricing between coupon dates
Invoice price= flat price + accrued interest

26. 11.3 BOND YIELDS

27. Yield to Maturity
Measure of rate of return that accounts for both current income and the price increase over the life
Total return: current income and price change
Average rate of return (bought now and held until maturity)
YTM is the discount rate that makes the present value of a bond’s payments equal to its price

28. Yield to Maturity
Solve the bond formula for r

29. Yield to Maturity Example
10 yr Maturity Coupon Rate = 7%
Price = $950
Solve for r = semiannual rate r = %

30. Yield to Maturity example
8% coupon, 30-year bond selling at $1,276.76:
r = 3%, semiannual rate

31. Yield Measures
Bond Equivalent Yield (semiannual yield doubled, YTM) 7.72% = 3.86% x 2; 6%=3%*2 Effective Annual Yield (accounts for compound interest) (1.0386)2 - 1 = 7.88%; (1.03)2 - 1 = 6.09% Current Yield (annual coupon payment divided by bond price) Annual Interest / Market Price $70 / $950 = 7.37 %; $80 / $ = 6.27 % Coupon rate 7% =70/1000; 8% =80/1000

32. Yield Measures YTM Premium bonds (selling above par)
internal rate of return
Compound rate of return over the life (assumption, all bond coupons can be reinvested at the yield)
Proxy for average return
Premium bonds (selling above par)
Coupon rate > current yield > YTM
Discount bonds (selling below par)
Coupon rate < current yield < YTM

33. Yield to Call if the bond is callable Example , Callable at $1100
The call provision allows the issuer to repurchase the bond at call price
Yield to Call
Call price replaces par
Time until call replaces time until maturity

34. Bond Prices: Callable and Straight Debt

35. Yield to Call example
8% coupon, 30-year bond selling at $1150, callable in 10 years at call price of 1100
yield to call
yield to maturity
coupon payment 40
number of semiannual periods 20 60
final payment
1100
1000
price
1150

36. Realized Compounded Yield versus YTM
Reinvestment Assumptions
All coupon are reinvested at an interest rate equal to YTM
With a reinvestment rate equal to YTM, the realized compound yield equal to YTM
Conventional YTM not equal realized compound return, if reinvestment rates can change over time
Example: 2 year, selling at par (1000), coupon rate 10%, annual pay

37. Growth of Invested Funds

38. Realized Compounded Yield versus YTM
If interest rate earned on the first coupon is less than 10%., the final value of the investment will be less than 1210, realized compound return will be less than 10%
Example:
if reinvest interest rate 8%

39. Realized Compounded Yield versus YTM
Horizon analysis
Forecasting the realized compound yield over various holding periods or investment horizons
Forecast of total return depends on forecasts of both the selling price of the bond and the rate to reinvest coupon income

40. Realized Compounded Yield versus YTM
Horizon analysis (Example)
30-year, 7.5% annual payment coupon bond, sell for 980, YTM is 7.67%, plan to hold for 20 years.
Forecast that YTM will be 8% when it is sold, reinvestment rate on the coupons will be 6%
At the end of your investment horizon, the bond will have 10 years remaining, the forecast sales price (when YTM is 8%) will be
20 coupon payments will grow with compound interest (6%)to
980 investment will grow in 20 years to =

42. Realized Compounded Yield versus YTM
When interest rates change, bond investors are subject to two sources of offsetting risk
Rate rise, bond prices fall, reduce the valued of the portfolio
Reinvested coupon income will compound more rapidly at those higher rates. The reinvestment rate risk will offset the impact of price risk

43. 11.4 BOND PRICES OVER TIME

44. Holding-Period Return
HPR = [ I + ( P1 - P0 )] / P0 where I = interest payment P1 = price in one period P0 = purchase price

45. Holding-Period Return
Requires actual calculation of reinvestment income
Solve for the Internal Rate of Return using the following:
Future Value: sales price + future value of coupons
Investment: purchase price

46. Premium and Discount Bonds
Par bond
Coupon rate equals market interest rate (fair compensation, no further capital gain)
Discount Bond
Coupon rate is lower than market rate (need to earn price appreciation, built-in capital gain)
Bond price will increase to par over its maturity
Yield to maturity exceeds coupon rate

47. Premium and Discount Bonds
Discount Bond Example
Market rate when issuing, 7% , annual coupon rate 7%. when the market rate is 8%
3 years left, Bond price= 70* annuity factor (8%, 3) * PV factor (8%,3)=974.23
2 years left, Bond price= 70* annuity factor (8%, 2) * PV factor (8%, 2)=982.17
HPR over this year
=( )/974.23=8%

48. Premium and Discount Bonds
Premium Bond
Coupon rate exceeds market rate (investors need to bid up the price above their par value, capital losses offset the large coupon payment, fair rate)
Coupon rate exceeds yield to maturity
Bond price will decline to par over its maturity

49. Premium and Discount Bonds over Time

50. YTM and HPR
YTM , measure of the average rate of return if the bond is held to maturity
If YTM is unchanged over the period, the HPR equals YTM
If YTM fluctuate, so will HPR.
Unanticipated changes in market rates will result in unanticipated changes in bond returns and HPR can be better or worse than YTM which it initially sells.

51. YTM and HPR
YTM depends on coupon, current price, par value. Observable today
HPR is a rate of return over a particular investment period and depends on the market price of the bond at the end of the holding period

52. Zero-coupon bond
No coupons and provides all returns in form of price appreciation
Provide only one cash flow on maturity date
US. Treasury bills
STRIPS (Treasury strips) :break down the cash flows of a Treasury coupon bond to be paid by the bond into a series of independent securities, each security is a claim to one of the payments of the original bond

53. Zero-coupon bond Prices of zeros over time On maturity dates, sell par
Before maturity, sell at discounts from par, approach par value

54. The Price of a Zero-Coupon Bond over Time

55. 11.5 DEFAULT RISK AND BOND PRICING

56. Default Risk and Ratings
Rating companies
Moody’s Investor Service
Standard & Poor’s
Fitch
Rating Categories
Investment grade
Speculative grade

57. Definitions of Each Bond Rating Class

58. Factors Used by Rating Companies
Coverage ratios
EBIT/INTEREST, ratio of earnings to all fixed cash obligations
Leverage ratios
D/E
Liquidity ratios
current asset/current liabilities
Profitability ratios
ROA, ROE
Cash flow to debt

59. Financial Ratios and Default Risk by Rating Class, Long-Term Debt

60. Factors Used by Rating Companies
Z-score
Edward Altman
Used discriminant analysis to predict bankruptcy, get a score based on financial financial ratio

61. Discriminant Analysis

62. Bond Indentures
Indenture, contract between the issuer and the bondholder (Protective covenants)
Set of restrictions that protect the rights of the bondholders
Provisions relating to collateral, sinking funds, dividend policy, further borrowing

63. Bond Indentures
Sinking funds- Help ensure the commitment of the par value payment at the end of the bond’s life, the firm agrees to establish a sinking fund to spread the payment burden over several years
The firm may repurchase a fraction of the outstanding bonds
May purchase a fraction of the outstanding at a special call price

64. Bond Indentures Subordination of future debt Dividend restrictions
Restrict the amount of additional borrowing. Additional debt might be required to be subordinated in priority to existing debt
Dividend restrictions
Collateral

65. Default Risk and YTM Promised yield and expected yield
The promised or stated yield will be realized only if the firm meets the obligations of the bond issue, maximum possible YTM
When a bond more subject to default risk, price will fall, its promised YTM will rise, default premium will rise.
Default premium is the difference between the promised yield on a corporate bond and the yield of an otherwise-identical government bond that is riskless in terms of default.

66. Default Risk and YTM Risk structure of interest rates Default premiums
Greater default risk, higher default premium
Default premiums
Yields compared to ratings
Yield spreads over business cycles

67. Yields on Long-Term Bonds, 1954 – 2006

68. Credit Risk and Collateralized Debt Obligations (CDOs)
Major mechanism to reallocate credit risk in the fixed-income markets
First establish a legally distinct entity to buy and later resell a portfolio of bonds or other loans (Structured Investment Vehicle, SIV, often used to create the CDO
Raise funds by issuing short-term commercial paper, using the proceeds to buy corporate bonds or other forms of debt
Loans are pooled together and then split into a series of classes (tranche)

69. Credit Risk and Collateralized Debt Obligations (CDOs)
Each tranche is given a different level of seniority in terms of its claims on the underlying loan pool, and each can be sold as a stand-alone security
Proceeds of the loans in the pool are distributed to pay interest to each tranche in order of seniority.
Priority structure implies the different exposure to credit risk.

70. Collateralized Debt Obligations

71. Collateralized Debt Obligations
Mortgage-backed CDOs were an Investment disaster in 2007
CDOs formed by pooling sub-prime mortgage loans made to individuals whose credit standing did not allow them to qualify for conventional mortgages. When home prices stalled in 2007, and interest rates on these typically adjustable-rate loans reset to market levels, mortgage delinquencies and home foreclosures soared, investors lost billions of dollars