Ch 11. Bond Prices and Yields

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Ch 11. Bond Prices and Yields

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

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1. Bond Characteristics

• Bond Typically a bond issuer makes semi-annual
  coupon payments and pays the bonds par value at
  maturity.
• Face or par value
• Coupon rate
• Zero coupon bond
• Indenture loan contract between the bond issuer
  and bondholder.

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• Accured interest
• invoice price flat (stated, quoted) price
  accrued interest
• Example 10 coupon. 90 days have passed since
  the last coupon payment. There are 182 days
  between two coupon payment dates.
• Accrued interest100(90/365)24.66, or
• 50(90/182) 24.73

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Issuers of Bonds

• Canada bonds
• Provincial government bonds
• Corporate bonds
• International bonds
• Foreign bonds and Eurobonds
• Recent innovations in the market
• Indexed Bonds
• RRB (Real Return Bonds)
• TIPS (Treasury Inflation Protected Security)
• Floaters and Reverse Floaters

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Provisions of Bonds

• Secured or unsecured
• Registered or bearer bonds (Canada)
• Call provision and deferred callable bonds
• Convertible provision
• Retractable and extendible (putable) bonds
• Floating rate bond

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2. Bond Pricing

• P price of the bond
• Ct interest or coupon payments
• F face value
• T number of periods to maturity
• r the appropriate discount rate for a period

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Example bond price
30-yr, 8 semiannual oupon Bond, F 1,000,
with ytm10 p.a.
Ct 40 (semiannual payment) P 1000 T 60
periods r 5 (semiannual rate)
P 810.71
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Bond Prices and Interest Rates

• Prices and yields (required rates of return) have
  an inverse relation
• When yields get high the value of the bond will
  be low
• The longer the maturity is, the bond price is
  more sensitive to changes in interest rates.
• To a large extent, treasury bill is default free
  and interest rate risk free.

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Prices and Interest Rates
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3. Yield to maturity (ytm)

• Interest rate that makes the present value of the
  bonds payments equal to its price. It is the
  solution r

Example 10 year, 7 coupon bond, P950. Solve
for r semiannual rate 950??t1,20 35/(1r)t
1000/(1r)20 r3.8635 for 6 months
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Yield Measures

• Bond equivalent yield 3.8627.72 p.a.
• Effective annual yield(1.0386)2 -17.88 p.a.
• Current yield (annual interest/market price)
• 70/950 7.37
• Current yield does not consider price changes in
  the future. The ytm does.
• The ytm is the average return over the life of
  the bond, assuming that all coupons are
  reinvested at the bonds ytm.

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Realized yield and ytm

• Consider a bond current price100, 10 coupon,
  2-year bond.
• 100 10/(1r) 110/(1r)2
• which is 100(1r)210(1r) 110.
• Definition of ytm assumes the reinvestment of
  coupon at a rate of ytm.
• Suppose the appropriate reinvestment rate is z
  instead of r. Then we have
• 100(1y)2 10(1z) 110.
• Solution y is called the realized compound yield.

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Example Realized yield vs. ytm

• Two-year bond selling at par, 10 coupon paid
  once a year. First coupon is reinvested at 8.
  Then
• 1000(1y)2 100(10.08) 1100.
• Solving for y results in y9.91 p.a.

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Bond prices over time
Price Paths of Coupon Bonds
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Holding period return

• HPR (Interest P1)/P0 - 1
• Example Consider 10-year 8 semiannual coupon
  bond selling at par. Suppose that the yield
  falls to 7 in six months. What is holding
  period return?
• P11068.55 (i.e., PV of coupons and par value)
• HPR 40 (1068.55-1000)/1000
• 10.85 semiannual

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Zero coupon bonds

• For constant yields, discount bond prices rise
  over time and premium bond prices decline over
  time.
• Strips Synthetically created zero-coupon bond
  by selling the rights to a single payment backed
  by a coupon-paying Treasury bond.

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Zero-coupon bonds and taxation issues

• Original issue discount bond bonds that are
  issued intentionally with low coupon rates.
• The price appreciation of original issue discount
  bonds (based on constant yield) is taxed as
  ordinary income
• Price changes due to yield changes are taxed as
  capital gains if the bond is sold

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Example

• 30-year 4 coupon bond with an 8 YTM. Suppose
  you sold the bond one year later when YTM7.
  Assume a 36 income tax and a 20 capital gains
  tax.
• P0549.69 P1(8)553.66
• P1(7)631.67.
• ?P at 8 yield 553.66 - 549.69 3.97 (1)
• ?P due to ?(yield) 631.67 - 553.6678.01 (2)
• income tax on (1)40 36(3.9740)15.83
• capital gains tax on (2) 2078.0115.6
• total tax 15.8315.6 31.43
• After tax rate of return
• (40631.67-549.69-31.43)/549.69 1 0.165

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5. Default Risk

• Rating companies
• Dominion Bond Rating Service (DBRS) in Canada,
  and in U.S. Moodys Investor Service and Standard
  Poors
• Rating Categories
• Investment grade (BBB and above)
• speculative (junk bond) grade bonds
• Factors used by rating companies
• Coverage Leverage Liquidity
  Profitability Cash flow to debt

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Financial ratios by rating class
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Altman discriminant analysis method

• Compare bankrupt firms one year prior to default
  with solvent (control) firms.
• Find a line to separate bankrupt and solvent firms

• Firms with Zgt1.626 were safe, and firms with
  Zlt1.626 were in risk of default

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• Indenture Protection against default
• Sinking funds
• Subordination of future debt (me-first rule)
• Dividend restrictions
• Collateral
• Ytm and default risk
• Expected yield vs promised yield on corporate
  bonds would be different due to default risk.
  Promised yield is the maximum possible yield.

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• Ytm and default risk
• Default premiums The difference between the
  promised yield on a corporate bond and the yield
  of comparable T-bond.
• Risk structure of interest rates pattern of
  default premiums on risky bonds
• Yield spreads tend to be wider during economic
  recession (Flight to quality)