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Bond Prices and Yields - Chapter 10

10.1 Bond Characteristics

  • Bond

    • Definition: A security that obligates the issuer to make payments to the bondholder over time.

  • Face Value (Par Value, Future Value)

    • Definition: The payment to the bondholder at the maturity of the bond, typically set at issuance.

  • Coupon Rate

    • Definition: The bond's annual interest payment per dollar of par value.

  • Zero-Coupon Bond

    • Definition: A bond that pays no coupons; it sells at a discount and provides only the payment of par value at maturity.

Example: Treasury Bonds and Notes

  • Accrued Interest and Quoted Bond Prices

    • Quoted prices for bonds do not include interest accruing between payment dates.

    • Accrued Interest Calculation:
      ext{Accrued Interest} = rac{ ext{Annual Coupon Payment}}{2} imes rac{ ext{Days Since Last Coupon Payment}}{ ext{Days Separating Coupon Payments}}

10.1 Bond Characteristics (Corporate Bonds)

  • Call Provisions on Corporate Bonds

    • Definition: Callable bonds may be repurchased by the issuer at a specified call price during the call period.

  • Convertible Bonds

    • Definition: Allow bondholders to exchange bonds for a specified number of shares of common stock.

  • Puttable Bonds

    • Definition: Allows the holder to either exchange for par value or to extend the bond for a given number of years, particularly when coupon rates exceed market rates.

  • Floating-rate Bonds

    • Definition: Coupon rates that periodically reset according to a specified market index (e.g., adjusted to T-Bill rates).

10.1 Bond Characteristics (Preferred Stock)

  • Preferred Stock

    • Definition: Commonly pays fixed dividends and is categorized as equity, included within the fixed-income universe.

    • Floating-rate preferred stock is becoming more popular.

    • Tax Implications: Dividends are not typically tax-deductible for corporations. Corporations buying preferred stock from other firms are taxed on only 30% of received dividends.

10.1 Bond Characteristics (Domestic Issuers)

  • Types of bonds issued by domestic entities include:

    • State and local governments (Municipal Bonds)

    • Federal Home Loan Bank Board

    • Farm Credit agencies

    • Ginnie Mae, Fannie Mae, Freddie Mac

10.1 Bond Characteristics (International Bonds)

  • Foreign Bonds

    • Definition: Issued by a borrower in a different country than where the bond is sold and denominated in the currency of the market country.

  • Eurobonds

    • Definition: Denominated in a currency, usually that of the issuing country, different from that of the market.

10.1 Bond Market Innovations

  • Indexed Bonds

    • Definition: Payments tied to a general price index or the price of a particular commodity.

    • Treasury Inflation-Protected Securities (TIPS): The par value of the bond increases with the consumer price index, thus providing both interest payments and price appreciation.

    • Nominal and Real Return Formulas:
      ext{Nominal Return} = rac{ ext{Initial Price}}{1+ ext{Nominal Return}}; ext{Real Return} = rac{1}{1+ ext{Inflation}} - 1

10.2 Bond Pricing

  • Bond Value Calculation

    • Formula:
      ext{Bond Value} = ext{Present Value of Coupons} + ext{Present Value of Par Value}
      ext{Bond Value} = ext{Σ} rac{ ext{Coupon}}{(1+r)^t} + rac{ ext{Par Value}}{(1+r)^T}

    • Where:

    • $T$ = Maturity date

    • $r$ = Discount rate

  • Price Sensitivity

    • Prices fall as market interest rates rise. Interest rate fluctuations are identified as the primary source of bond market risk.

    • Longer maturity bonds are more sensitive to interest rate changes.

Figure 10.3: Inverse Relationship between Bond Prices and Yields

  • Visual representation indicating that as interest rates rise (x-axis), bond prices (y-axis) fall, illustrating the inverse relationship.

  • Example Graph Data:

    • At 0% interest rate, bond price = $3,500

    • At 5% interest rate, bond price = $3,000

    • At 10% interest rate, bond price = $2,500

    • Continuing down to nearly $0 at higher interest rates.

10.2 Bond Pricing between Coupon Dates

  • Invoice Price Calculation

    • Formula:
      ext{Invoice Price} = ext{Flat Price} + ext{Accrued Interest}

10.3 Bond Yields

  • Yield to Maturity (YTM)

    • Definition: The discount rate that makes the present value of the bond's payments equal to the current price of the bond.

  • Current Yield Calculation

    • Formula:
      ext{Current Yield} = rac{ ext{Annual Coupon}}{ ext{Bond Price}}

  • Premium and Discount Bonds

    • Premium Bonds:

    • Definition: Bonds selling above par value (Coupon rate > YTM).

    • Discount Bonds:

    • Definition: Bonds selling below par value (Coupon rate < YTM).

10.3 Yield to Call (YTC)

  • Definition: Calculated similarly to yield to maturity, but time until call replaces time until maturity, and the call price replaces the par value. Premium bonds are more likely to be called than discount bonds.

10.3 Realized Compound Returns vs. Yield to Maturity

  • Realized Compound Return

    • Definition: The compound rate of return on a bond with all coupons reinvested until maturity.

  • Horizon Analysis

    • Definition: Analysis of bond returns over a multiyear horizon, based on forecasts of the bond's yield to maturity and other investment options.

  • Reinvestment Rate Risk

    • Definition: The uncertainty surrounding the cumulative future value of reinvested coupon payments.

10.4 Bond Prices Over Time

  • Zero-Coupon Bonds and Treasury STRIPS

    • Definition: Zero-coupon bonds carry no coupons and provide all return in the form of price appreciation.

    • STRIPS (Separate Trading of Registered Interest and Principal of Securities): Oversees the creation of zero-coupon bonds from coupon-bearing notes and bonds. Each payment is treated as an independent security with its own CUSIP number.

10.5 Default Risk and Bond Pricing

  • Investment Grade Bonds

    • Definition: Rated BBB and above by Standard & Poor's (S&P) or Baa and above by Moody’s.

  • Speculative Grade or Junk Bonds

    • Definition: Rated BB or lower by S&P, Ba or lower by Moody’s, or unrated.

Figure 10.8: Bond Rating Classes

  • Visual representation of bond ratings categorized into four classes based on quality (Highest to Lowest):

    • AAA (Aaa) => Very High Quality

    • AA (Aa)

    • A (Baa) => High Quality

    • BBB (Baa)

    • BB, B, CCC, D => Very Speculative, Poor Quality.

  • Rating Adjustments: S&P uses plus and minus signs for ratings (A+ is strongest, A- is weakest) while Moody's employs a 1, 2, or 3 designation (1 indicates strongest).

10.5 Bond Indentures

  • Bond Indenture

    • Definition: Contract between issuer and holder that protects the rights of the bondholder.

  • Sinking Fund

    • Definition: Indenture provision requiring the issuer to periodically repurchase a proportion of outstanding bonds before maturity.

  • Subordination Clause

    • Definition: Restrictions on additional borrowing ensuring senior bondholders are paid first in bankruptcy scenarios.

  • Collateral

    • Definition: A specific asset pledged as security against possible default.

  • Debenture

    • Definition: A bond not backed by specific collateral.

10.5 Yield to Maturity and Default Risk

  • Stated Yield

    • Definition: It represents the maximum possible yield to maturity of the bond.

  • Default Premium

    • Definition: An increment to the promised yield that compensates investors for the risk of default.

Homework Chapter 10

  • Problem Sets: 4, 5, 6, 9, 12, 16, 17

  • CFA Problems: 1a, 1b, 1c, 1d.