Bond Prices and Yields

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Chapter 11

• Bond Prices and Yields

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11.1 Bond Characteristics
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Bond Characteristics

• Face or par value
• Coupon rate
• Zero coupon bond
• Compounding and payments
• Accrued Interest
• Indenture

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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

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Listing of Treasury Issues
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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
  810000.540/1828.79

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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)

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Listing of Corporate Bonds
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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

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Corporate Bonds

• Put provision (puttable bonds) (price?)
• Give the option to the bondholder to extend the
  bonds 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.

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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.

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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

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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

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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

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11.2 BOND PRICING
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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

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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

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Bond Pricing

• Price coupon annuity factor (r, T)
• Par value PV factor (r, T)
• annuity factor (r, T)
• PV factor (r, T)

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Price of 8, 10-yr. with yield at 6
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Coupon 41,000 40 (Semiannual) Discount Rate
3 (Semiannual) Maturity 10 years or 20
periods Par Value 1,000
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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

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Bond Prices and Yields

• Coupon rate8, semiannual, face value1000
• Maturity 1-yr , 10-yr, 20-yr, 30-yr
• Market interest rate, 4--12

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Bond Prices and Yields
TIME TO MATURITY MARKET INTEREST RATE MARKET INTEREST RATE MARKET INTEREST RATE MARKET INTEREST RATE MARKET INTEREST RATE
TIME TO MATURITY 4 6 8 10 12
1 ?-1,038.83 ?-1,019.13 ?-1,000.00 ?-981.41 ?-963.33
10 ?-1,327.03 ?-1,148.77 ?-1,000.00 ?-875.38 ?-770.60
20 ?-1,547.11 ?-1,231.15 ?-1,000.00 ?-828.41 ?-699.07
30 ?-1,695.22 ?-1,276.76 ?-1,000.00 ?-810.71 ?-676.77
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The Inverse Relationship Between Bond Prices and
Yields
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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

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Bond pricing between coupon dates

• Invoice price flat price accrued interest

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11.3 BOND YIELDS
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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 bonds payments equal to its price

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Yield to Maturity

• Solve the bond formula for r

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Yield to Maturity Example

• 10 yr Maturity Coupon Rate 7
• Price 950
• Solve for r semiannual rate r 3.8635

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Yield to Maturity example

• 8 coupon, 30-year bond selling at 1,276.76

r 3, semiannual rate
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Yield Measures

• Bond Equivalent Yield (semiannual yield doubled,
  YTM)
• 7.72 3.86 x 2 632
• 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 / 1276.76 6.27
• Coupon rate
• 7 70/1000 8 80/1000

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Yield Measures

• YTM
• 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 gt current yield gt YTM
• Discount bonds (selling below par)
• Coupon rate lt current yield lt YTM

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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

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Bond Prices Callable and Straight Debt
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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 40
number of semiannual periods 20 60
final payment 1100 1000
price 1150 1150
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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

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Growth of Invested Funds
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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

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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

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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 966.45.
• 20 coupon payments will grow with compound
  interest (6)to 2758.92
• 980 investment will grow in 20 years to
  966.452758.923725.37

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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

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11.4 BOND PRICES OVER TIME
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Holding-Period Return

• HPR I ( P1 - P0 ) / P0
• where
• I interest payment
• P1 price in one period
• P0 purchase price

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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

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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

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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) 1000 PV factor (8,3)974.23
• 2 years left, Bond price 70 annuity factor
  (8, 2) 1000 PV factor (8, 2)982.17
• HPR over this year
• (982.17-974.2370)/974.238

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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

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Premium and Discount Bonds over Time
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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.

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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

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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

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Zero-coupon bond

• Prices of zeros over time
• On maturity dates, sell par
• Before maturity, sell at discounts from par,
  approach par value

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The Price of a Zero-Coupon Bond over Time
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11.5 DEFAULT RISK AND BOND PRICING
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Default Risk and Ratings

• Rating companies
• Moodys Investor Service
• Standard Poors
• Fitch
• Rating Categories
• Investment grade
• Speculative grade

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Definitions of Each Bond Rating Class
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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

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Financial Ratios and Default Risk by Rating
Class, Long-Term Debt
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Factors Used by Rating Companies

• Z-score
• Edward Altman
• Used discriminant analysis to predict bankruptcy,
  get a score based on financial financial ratio

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Discriminant Analysis
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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

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Bond Indentures

• Sinking funds- Help ensure the commitment of the
  par value payment at the end of the bonds 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

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Bond Indentures

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

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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.

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Default Risk and YTM

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

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Yields on Long-Term Bonds, 1954 2006
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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)

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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.

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Collateralized Debt Obligations
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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