Bonds

Bonds

• An interest-bearing security that pays a “face value” at a future maturity date
  • Redemption value: the date you turn in the bond; usually the same as the maturity date
  • If the bond has a redemption date < maturity date, the bond is considered callable
    • You can turn in your money for it before it matures
    • The trade-off is that you may not get the entire face value
• Two types:
  • Accumulation bond
    • The interest is included in the redemption value
    • Like compound interest in a fund
  • Coupon bonds
    • Payments are received at various dates before redemption
    • Like an annuity but with a bank deposit
    • The minimal rate of return occurs when you cash in the bond earliest

Coupon Bond

• $P$: Price of the bond
  • Present value of all the coupons and redemption value
• $F$: Face value of the bond
• $C$: Redemption value of the bond
• $r$: coupon rate (percentage of the face value)
  • Coupon amount for each time period: $Fr$
• $i$: yield rate

Premiums and Discount

• $P > C$: premium
  • amortization of premium
    • Value is marked down to the “book value” after each payment
      • Book value is the PV of all future payments
• If $P < $C$: discount
  • accumulation of discount
    • The book value is “written up” at each coupon date