ECON 435: Bond features & pricing

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ECON 435 > ECON 435: Bond features & pricing

Definations

• Face value
  • the principal amount of the bond that is paid back at maturity.
• Coupon rate
  • When coupons are in fixed amounts, the annual coupon divided by the face value of the bond (is the interest rate?)
  • Note sometimes coupons are indexed to other events, like inflation or income of company
• Default
  • When the issuar of the bond fails to either pay the coupons or pay back the face value of the bond at maturity
• market value of the bond
  • Depends on the face value of bond, number of periods until maturity, the coupon, the frequency with which coupons are paid, and the market rate of return require of securities with similar risk features
• Yield-to-maturity (YTM)
  • DIFFERENT THAN THE DISCOUNT RATE
  • Something that is given by a price
  • When is priced at its fair price, r=YTM

Bond pricing

• Pbond = [C / r] x {1-(1+r)^-t} + F x (1+r)^-t (FOR CONSTANT PAYMENTS, C)

• • Note, t = number of years (ACTUALLY PAYMENTS), F = value of bonds, C = constant payments, r = market interest rates
  • This determines the present value of the payments (first part) and the present value of the principal paid back at maturity
  • NOTE: a newly issued bond with a coupon rate of 5% would have a present value of exactly $1,000

Yied-to-maturity

• When YTM rises, the market price of bonds falls and vice-versa
  • Why? In perfect market r=YTM (in a perfect market) and as such we are just studying the behavior of a present value when r changes...
  • In other words, the relationship between bond prices and YTMs is a inverse one
  • The relationship turns out to be convex
  • Example, bond expiring in 1 year & paying two semi-annual coupons, face value of $1,000, and a market price of $981
    • NOTE, you can't find interest rate in equation on slides
    • look at slides for more info
• REMEMBER THIS BY HEART
  • Approx. YTM = [C + (F-Pbond)/t] / [(F + P)/3]
• EXCELLENT QUESTION FOR EXAM:
  • if yield to maturity is 0%, the value of the bond is just the principal plus the sum of all interest payments.
  • If the bond is $1000 and pays three $100 payments and YTM=0%, value = $1,300

Interest rate risk

• the risk that arises when interest rates change, causing a change in bond prices.
• Therefore, if a bond does not force you to reinvest any prices & you are certain of holding the bond until maturity, there is no interest rate risk.
• NOTE, the interest rate risk declines when the coupon rate goes down
  • this is because, a high coupon rate means that the bond's price is comprised more of coupons

Bonds vs. Equitys

• Main differences:
  • Bonds are debt, and not ownership
  • Interests paid on bonds are tax deductable
  • bondholders have a claim on the asset of the firm before shareholders.

Lecture slides

• Get lecture slides [here]