January 23, 2004
Coupon Bonds
To calculate the value of a coupon bond, we add up the values of all the individual payments. Tables A and C are a great help in this endeavor.
To confirm the logic of these calculations, we can prove that a $1000 bank deposit at 10% interest can recreate the income stream from a $1000 10% coupon bond.
The handout shows detailed calculations for various bonds and discount rates. The basic result is that long-term bond prices are very sensitive to changes in the discount rate.
The bond yield is that discount rate that makes the bond worth the observed market price.
An excerpt from the WSJ table for Treasury securities illustrates the practical version of these calculations. Q: Which bond is the better investment?
Arbitrage Pricing
An arbitrage profit is (1) risk-free and (2) requires none of your own money. Thinking about potential arbitrage profits provides a basis for pricing bonds according to the discounted present values of their income streams.
If the bond price is below 909.09, there are arbitrage profits to be gained by borrowing money to buy the bond.
If the bond price is above 909.09, there are arbitrage profits to be gained by selling the bond and depositing the proceeds in the bank.
We can extend this analysis to a bond that matures in two years.
