Bonds

Bond Terminology

Bond Indenture

• A statement of the terms of a bond as well as the amounts and dates of all payments to be made

Maturity Date

• The final repayment date of a bond

Term

• The time remaining until the final repayment date of a bond

Face Value

• AKA par value or principal amount
• Notional amount used to compute interest payments

Coupons

• The promised interest payments of a bond
• Paid periodically until the maturity date of the bond

Coupon Rate

• Set by the issuer and stated on the bond certificate
• By convention, expressed as an APR, so the amount of each coupon payment, CPN, is

Zero-Coupon Bonds

Only two cash flows

• The bond’s market price at the time of purchase
• The bond’s face value at maturity
  Treasury bills are zero-coupon government bonds with maturity of up to one year

Risk-Free Interest Rates

A default-free zero-coupon bond that matures on date $n$ provides a risk-free return over the same period

• Law of One Price guarantees that the risk-free interest rate equals the yield to maturity on such a bond
• Refer to the YTM of such bond as risk-free interest rate

Spot Interest Rates

Default-free, zero-coupon yields

Coupon Bonds

• Pay face value at maturity
• Also make regular coupon interest payments
  Return on a coupon bond comes from:
• Any difference between the purchase price and the face value
• Periodic coupon payments

YTM of a Coupon Bond

• The coupon payments represent an annuity, so the yield to maturity is the interest rate $YT{M}_n$ that equates the bond’s price, $P$, to the present value of an annuity of coupons plus the present value of the bond’s face value, FV:
  

Why Bond Prices Change

• Zero-coupon bonds always trade for a discount
• Coupon bonds may trade at a discount or at a premium
• Most issuers of coupon bonds choose a coupon rate so that the bonds will initially trade at, or very close to, par
• After the issue date, the market price of a bond changes over time

Interest Rate Changes and Bond Prices

• If a bond sells at par, the only return investors will earn is from the coupons that the bond pays
  • The bond’s coupon rate will exactly equal its yield to maturity
• As interest rates in the economy fluctuate, the yields that investors demand will also change
• Longer term bonds are more sensitive to interest rate changes
  • More risky
• Bond with smaller coupon payments is more sensitive to interest rate changes
  • More risky

Key Terms

Premium:

• A price at which coupon bonds trade that is greater than their face value
  Discount:
• A price at which coupon bonds trade that is lower than their face value
  Par:
• A price at which coupon bonds trade that is equal to their face value

Corporate Bonds

Credit Risk

• The risk of default by the issuer of any bond that is not default free
  • Indication that the bond’s cash flows are not known with certainty
• Corporations with higher default risk will need to pay higher coupons to attract buyers to their bonds

Corporate Bond Yields

• Yield to maturity of a defaultable bond is not equal to the expected return of investing in the bond
• A higher yield to maturity does not necessarily imply that a bond’s expected return is higher

Bond Ratings

Several companies rate the creditworthiness of bonds

1. Investment-grade bonds
2. Speculative bonds
   1. Junk bonds
   2. High-yield bonds

• The rating depends on
  • The risk of bankruptcy
  • Bondholders’ claim to assets in the event of bankruptcy

Corporate and Provincial Yield Curves

The credit spread is the difference between the various bonds and the Government of Canada