CHAPTER 11: BOND YIELDS AND PRICES

1
CHAPTER 11 BOND YIELDS AND PRICES
2
Chapter Summary

• How are returns for fixed income securities
  determined?
• Bond Characteristics
• Bond Pricing and YTM
• Default Risk and Ratings

3
Definition Fixed Income Security

• A claim on a periodic income stream which is
  fixed
• Risk is minimal
• The easiest one is bonds

4
Bond Definitions

• Definition of a bond issuer borrows and makes
  specified pmts to bondholder on set dates
• Characteristics
• Face or par value
• Coupon rate (ie. Interest rate)
• Zero coupon bond
• Compounding and payments
• Accrued Interest
• Bond Indenture

5
Different Issuers of Bonds

• Canada bonds
• Provincial government bonds
• Corporations
• Municipalities
• International Governments and Corporations

RISK
6
Innovative Bonds

• Catastrophe bonds
• Eg. Electrolux tied to earthquake in Japan
• Asset-backed bonds
• Eg. Walt Disney bond value is tied to success of
  movie
• Indexed bonds
• Eg. Coupons tied to general price index
• Common in countries with high inflation
• Floaters
• Interest pmt tied to market rate (eg. Prime 2)
• Reverse floaters
• Coupon decreases when market rates increase

7
Summary Reminder

• ObjectiveTo review the principles of bond
  pricing and to examine the determinants of credit
  risk.
• Bond Characteristics
• Bond Pricing and YTM
• Default Risk and Ratings

8
Bond Pricing

• PB price of the bond
• Ct interest or coupon payments
• T number of periods to maturity
• r the appropriate semi-annual discount rate

9
Examples

• Zero-coupon bonds
• Regular bonds
• Sold at par
• Sold at premium
• Sold at a discount

10
Solving for Price 30-yr, 8 Coupon Bond, FV
1,000
Ct 40 (SA) P 1000 T 60 periods r 5 (SA)
PB 810.71
11
Bond Prices and Interest Rates

• Prices and market interest rates have an inverse
  relationship
• When interest rates get very high the value of
  the bond will be very low
• When rates approach zero, the value of the bond
  approaches the sum of the cash flows

12
Prices and Interest Rates
Convex curve an increase in interest rates has a
smaller price decline than the corresponding
price decrease
1
1
13
Bond prices

• You can look them up
• As interest rates inc gt price falls
• As interest rates dec gt price inc

14
Bond prices

• Bonds selling at par
• Price face value
• Coupon rate market rate
• Bonds selling at premium
• Price gt face value
• Coupon rate gt market rate

15
Bond prices

• Bonds selling at discount
• Price lt face value
• Coupon rate lt market rate
• Over timeprices will also move toward par value

16
Price Paths of Coupon Bonds
17
Excel Bond formulas

• PRICE(settlement, maturity, coupon ,YTD,
  redemption date, coupons/yr)

18
BOND YIELD DEFINITIONS

• YTM
• Effective annual yield
• Current yield
• Bond equivalent uield
• Bank discount yield
• Yield to call
• Realized compound yield
• Holding period return

19
Yield to Maturity

• Avg rate of return earned if you buy the bond
  today and hold it to maturity
• Interest rate that makes the present value of the
  bonds payments equal to its price
• Solve the bond price formula for r

20
Yield to Maturity Example
10 yr Maturity Coupon Rate 7 Price
950 Solve for r semiannual rate
r 3.8635
21
Excel formula for yield

• YIELD(settlement, maturity, coupon , flat
  price, redemption as par, coupons/yr)

22
Yield Measures

• Bond Equivalent Yield APR (simple interest)
• Yield reported in the newspaper
• 3.86 x 2 7.72
• 2) Effective Annual Yield (compound interest)
• (1.0386)2 - 1 7.88
• 3) Current Yield (Annual Interest/Market Price)
• 70 / 950 7.37

23
Yield to Call

• If bond is callable, what is the expected yield
  to call date?
• Then calculate the yield to this date.
• Eg. N10, pmt50, FV1100, PV1150
• Solution interest 3.99 x 2 7.98

24
Yield to Call
Price
1100
1000
Regular bond
Callable bond
8
YTM
25
Realized Yield versus YTM

• Reinvestment Assumptions of YTM
• YTM assumes coupons are reinvested at this rate
  until maturity
• Realized Yield
• Coupons are reinvested at the prevailing interest
  rates
• Holding Period Return

26
Realized Compound Yield vs. YTM

• Requires actual calculation of reinvestment
  income
• Solve for the Internal Rate of Return using the
  following
• Future Value sale price future value of
  coupons
• Investment purchase price

27
Example Realized Yield

• Two-year bond selling at par, 10 coupon paid
  once a year. First coupon is reinvested at 8.
  Then

28
Holding-Period Return Single Period
HPR Return over the total time period the
investor is holding the bond (ie. not annual)

• where
• I interest payment
• P1 price in one period
• P0 purchase price

29
Holding-Period Example

• CR 8 YTM 8 N10 years
• Semiannual Compounding P0 1000
• In 6M the rate falls to 7 P1 1068.55

HPR 10.85 (semiannual)
30
Special characteristics of Bonds

• Secured or unsecured
• Registered or bearer bonds (Canada)
• Call provision
• Convertible provision
• Retractable and extendible (putable) bonds
• Traded OTC

31
Summary Reminder

• ObjectiveTo review the principles of bond
  pricing and to examine the determinants of credit
  risk.
• Bond Characteristics
• Bond Pricing and YTM
• Default Risk and Ratings

32
Default Risk and Ratings

• Rating companies
• Moodys Investor Service
• Standard Poors
• Fitch IBCA
• Canadian Bond Rating Service (CBRS)
• Rating Categories
• Investment grade (BBB or above)
• Speculative grade (ie. junk bonds, high-yield
  bonds)

33
Factors Used by Rating Companies

• Coverage ratios
• Leverage ratio
• Liquidity ratios
• Profitability ratios
• Cash flow to debt

34
Protection Against Default

• Bond indenture
• Sinking funds
• Subordination of future debt
• Dividend restrictions
• Collateral