BOND PRICES AND YIELDS

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BOND PRICES AND YIELDS

• CHAPTER 14

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Outline of the Chapter

• Bond Characteristics
• What is a bond?
• Types of bonds
• Bond Pricing
• Bond Yields
• Yield to Maturity
• Yield to Call
• How bond prices change over time.
• Default Risk
• How default risk affects bond prices.

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Bond Characteristics

• Debt securities (fixed-income securities) A
  claim on a specified periodic income.
• They promise either a fixed-stream of income or a
  stream of income that is determined according to
  a specified formula.
• A bond is a security that is issued in connection
  with a borrowing arrangement.
• The borrower issues (sells) a bond to the lender
  for some amount of cash.
• The arrangement obligates the issuer to make
  semiannual payments (coupon payments) of interest
  to the bondholder for the life of the bond.

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Bond Characteristics (Continued)

• The coupon rate of the bond serves to determine
  the interest payments to the bond holder
• the coupon ratethe bonds par value
• When the bond matures the issuer repays the debt
  by paying the par value (face value) of the bond
  to the bondholder.
• The coupon rate, maturity date, and par value of
  the bond are arranged in advance on the bond
  indenture
• The contract between the issuer and the
  bondholder.
• Types of Bonds
• Treasury bonds and notes
• Corporate bonds
• Preferred Stock
• International Bonds

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Bond Characteristics (Continued)

• Treasury bonds and notes
• Debt securities issued by the Treasury.
• Treasury notes matures in 10 years while bonds
  mature in 10 to 30 years.
• Issued in denominations of 1,000 or more (the
  minimum denomination was reduced to 100 in
  2008).
• Look at the figure 14.1
• Matures in January 2011
• n stands for notes
• Coupon rate is 4.25
• Note pays interest of 42.50 (1,0004.25) per
  year in two semiannual payments (21.25)

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Bond Characteristics (Continued)

• Bid and asked prices are quoted in points and a
  fraction of 1/32 of a point.
• Bid price 9807 of par value.
• 980798 7/32 98.219
• 1,0000.98219982.19
• Ask yield the yield to maturity on the bond
  based on the asked price.

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Bond Characteristics (Continued)

• Corporate Bonds
• Debt securities issued by corporations to borrow
  money from the investors.
• Call provisions
• Call provisions allow the issuer to repurchase
  the bond at a specified call price before the
  maturity date.
• Deferred callable bonds Callable bonds with a
  period of call protection, an initial time during
  which the bonds are not callable.
• The option to call a bond is valuable to the
  firm. The investor has to give up the high coupon
  rate when the bond is called. Thus in order to
  compensate for this risk, callable bonds are
  issued with higher coupons and promised yields to
  maturity than noncallable bonds.

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Bond Characteristics (Continued)

• Convertible bonds give bondholders an option to
  exchange each bond for a specified number of
  shares.
• Convertible bond holders benefit from price
  appreciation of the companys stock. Thus, the
  convertibel bonds offer lower coupon rates and
  yields ot maturity than do nonconvertible bonds.
• Puttable bonds gives the bondholder the option
  to extend or retire the bond.
• Floating-rate bonds tie interest payments to a
  measure of current market rates.

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Bond Characteristics (Continued)

• Preferred Stock Promises to pay specified stream
  of dividends like bonds although it is a stock.
• If dividends are not paid they cumulate.
• They have priority over common stock holders.
  They have to be paid first before the common
  stock holders receive any dividends.
• In case of bankruptcy their claims have higher
  priority over common stock holders but lower
  priority over bondholders.
• The dividend payments on preferred stocks are not
  tax deductable.

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Bond Characteristics (Continued)

• International Bonds
• Foreign bonds issued by a borrower from a
  country other than the one in which the bond is
  sold. The bond is denominated in the currency of
  the country in which it is marketed.
• e.g A German firm sells a dollar-denominated
  bond in the United States.
• Eurobonds issued in the currency of one country
  but sold in other national markets
• e.g Dollar denominated bonds sold outside the
  United States.

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Bond Characteristics (Continued)

• Indexed Bonds make payments that are tied to a
  general price index or the price of a particular
  commodity.
• e.g inflation-indexed bonds coupon payments
  and par value on the bonds increases in direct
  proportion to CPI.
• Time to maturity 3 years
• Par value 1,000
• Coupon rate 4 (annual payments)
• Inflation expectations for the three years are
  2, 3, and 1.

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Bond Characteristics (Continued)

• At the end of first year the par value becomes
  1,020 becuase of inflation.
• Coupon payment becomes 40.80 (4 of the new
  par)
• When the bond matures the investor will recieve
  the new par at the end of year three and the
  coupon payment computed by using the new par for
  third year.

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Bond Pricing

• Bond value Present value of coupons Present
  value of par value
• Market interest ratef(real risk-free rate of
  return, inflation premium, default risk premium,
  liquidity premium, call risk premium...)
• Price couponannuity factor (r, T) par value
  PV factor (r,T)

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Bond Pricing (Continued)

• This negative slope of the curve shows the
  inverse relationship between bond prices and
  yields (required rates of return on the bond).
• As the required rates increase the present value
  of the bonds payments (prices) decreases.
• An increase in the interest rate results in a
  price decline that is smaller than the price gain
  resulting from a decrease of equal magnitude in
  the interest rates.
• Convexity

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Bond Pricing (Continued)

• Main source of risk in fixed-income securities
  is the interest rate fluctuations.
• The sensitivity of the bond prices to market
  yields change with the maturity of the bond.
• Keeping all other factors the same, the longer
  the maturity of the bond, the greater the
  sensitivity of price to fluctuations in the
  interest rates.
• The force of discounting is greatest for the
  longest-term bonds.

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Bond Pricing (Continued)

• Bond pricing between coupon dates
• The formula we have employed to price the bonds
  assumes that the transaction happens at the
  coupon payment date.
• If the purchase date is between coupon dates then
  you should also compute the accrued interest.
• Accrued interest is the amount that the buyer
  must pay to the seller as a prorated share of the
  upcoming semiannual coupon.
• Thus the price of the bond becomes
• Invoice price flat priceaccrued interest
• Accrued interestannual coupon payment/2days
  since last coupon payment/days separating coupon
  payments

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Bond Yields

• Yield to Maturity
• Standard measure of total rate of return.
• Interest rate that makes the present value of a
  bonds payment equal to its price.
• Measure of the average rate of return that will
  be earned on a bond if it is bought now and held
  until maturity.
• The compound rate of return over the life of the
  bond under the assumption that all bond coupons
  can be reinvested at that yield.
• Current Yield
• Bonds annual coupon payment divided by the bond
  price

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Bond Yields (Continued)

• For premium bonds coupon rate is greater than
  current yield, which in turn greater than yield
  to maturity.
• For discount bonds coupon rate is smaller than
  current yield which in turn smaller than yield to
  maturity.
• Yield to Call
• Average rate of return for bonds subject to call
  provision.
• Interest rate that makes the present value of a
  bonds call price equal to its market price. The
  time frame is until the bond is called.

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Bond Yields (Continued)

• Realized compound return
• Yield to maturity will equal the rate of return
  realized over the life of the bond if all coupons
  are reinvested at an interest rate equal to the
  bonds yield to maturity.
• If reinvestment rate is equal to the yield to
  maturity then the realized compound return equals
  yield to maturity as well.
• Unfortunately the future interest rates are not
  certain so we can not know the rates at which the
  interim coupons will be reinvested.
• Reinvestment rate risk
• So we need forecasts. Forecasting the realized
  compound yield over various holding periods or
  investment horizons is called horizon analysis.

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Bond Prices Over Time

• If coupon ratemarket interest rate then a bond
  will sell at par.
• Investor receives fair compensation for the time
  value of money in the form of coupon payments.
• No further capital gain is necessary to provide
  fair compensation.
• If coupon rateltmarket rate then a bond will sell
  at discount.
• The coupon payments will not provide investors as
  high a return as they could earn in the market.
• Investors need to earn price appreciation. They
  provide built-in capital gain for fair
  compensation.

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Bond Prices Over Time (Continued)

• If coupon rategtmarket rate then a bond will sell
  at premium.
• The coupon payments will provide investors more
  return than they could earn in the market.
• Investors will bid up the price of these bonds
  above their par values. As the bond approach the
  maturity, the price will decrease since fewer of
  these above-market coupon payments remain.
• The capital losses due to decrease in prices will
  offset the large coupon payments and again the
  bondholders will receive fair rate of return.

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Bond Prices Over Time (Continued)

• Each bond offers investors the same total rate
  of return.
• The capital gain versus income components may
  differ but the price of each bond is set to offer
  competitive rates.

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Bond Prices Over Time (Continued)

• Yield to maturity versus holding-period return
• Yield to maturity depends on the bonds coupon,
  current price and par value at maturity.
• It is the average rate of return if the
  investment in the bond is held until the bond
  matures.
• Holding-period return is the rate of return over
  a particular investment period and depends on the
  market price of the bond at the end of that
  holding period
• The price at the end of period is not known from
  today and it will respond to unanticipated
  changes in interest rates.
• Holding-period return can at most be forecast.

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Bond Prices Over Time (Continued)

• Zero-Coupon Bonds
• Carries no coupons and provides all its return in
  the form of price appreciation.
• Provides only one cash flow on the maturity date
  of the bond.
• Zeros sell at discount before par and reaches
  their par value at the maturity.
• Their prices rise exponentially, not linearly.

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Default Risk and Bond Pricing

• There is always a risk that bond defaults, the
  company may bankrupt and may not pay the promised
  fixed flow of income.
• This bond default risk is called credit risk.
• Credit risk is usually measured by agencies such
  as Moodys Investor Services, StandardPoors
  Corporation, and Fitch Investor Services.
• They rate the firms.
• Investment Grade Bonds vs Speculative Grade Bonds
  (Junk Bonds)
• Those rates BBB or above (SP, Fitch) or Baa
  (Moodys are considered investment-grade while
  lower rated bonds are classified as
  speculative-grade ones.

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Default Risk and Bond Pricing (Continued)

• Determinants of Bond Safety
• Coverage ratio
• Times interest earned earnings before interest
  payments and taxes/interest expenses
  (obligations)
• Fixed-charge coverage ratio EBIT fixed charges
  (before taxes)/Fixed charges (before
  tax)Interest expense
• Low or decreasing coverage ratios signals
  possible cash flow difficulties.
• Leverage ratio
• Debt/equity ratio
• High ratio indicates excessive indebtedness.
• Signal the possibility that the firm will be
  unable to earn enough to satisfy the obligations
  on its bond.

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Default Risk and Bond Pricing (Continued)

• Liquidity ratios
• Current ratio current assets/current liabilities
• Quick ratio current assets-inventory/current
  liabilities
• Measures if firms can pay their bills with their
  liquid assets.
• Profitability ratios
• ROA, ROE
• Indicates overall health of the firm.
• Cash flow-to-debt ratio
• Indicates how firm can meet its debt obligations
  by using the cash flow.

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Default Risk and Bond Pricing (Continued)

• Bond Indentures
• It is the contract between the issuer and the
  bondholder.
• It sets some restrictions on the issuer to
  protect the rights of the bondholders.
• These protective covenants include sinking funds,
  dividend policy, further borrowing and
  collateral.
• Sinking Funds
• It is a fund used to spread the payment burden
  over several years.
• The fund may operate in two ways
• The firm may repurchase a fraction of the
  outstanding bonds in the open market each year.
• The firm may purchase a fraction of the
  outstanding bonds at a special call price.

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Default Risk and Bond Pricing (Continued)

• Subordination of Further Debt
• The amount of additional borrowing is restricted.
• Additional debt might be required to be
  subordinated in priority to existing debt.
• Dividend Restrictions
• Restricting the dividend payouts protect the
  bondholders since by this way the firm retain
  assets instead of paying them out to
  stockholders.
• Collateral
• Represents a particular asset of the firm that
  the bondholders receive if the firm defaults on
  the bond.
• Mortgage bond, Collateral trust bond, Equipment
  obligation bond

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Default Risk and Bond Pricing (Continued)

• Expected versus Promised yield to maturity
• Promised (stated) YTM is the maximum possible YTM
  of the bond.
• Expected YTM takes into account the possibility
  of default.
• Default Premium
• In order to compensate for the possiblity of
  default, corporate bonds must offer a default
  premium.
• Default premiumpromised yield-risk-free rate
• If the firm remains solvent then YTM on bond will
  be higher than YTM on government bond
• If the firm bankrupt then YTM on bond will be
  less than YTM on government bond.

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Default Risk and Bond Pricing (Continued)

• The corporate bond has the potential for both
  better and worse performance than the government
  bond.
• It is riskier.
• Collateralized Debt Obligations (CDO)
• Emplyed to reallocate risk in the fixed-income
  markets.
• e.g. mortgage-backed CDOs

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Default Risk and Bond Pricing (Continued)