Bonds course · Lesson 1 of 7
When rates go up, bond prices go down.
A bond pays fixed interest. When the market pays more for new bonds, the price of an old bond must fall. This lesson shows how far, and why.
The example bond
The example bond has a face value of $1,000, a coupon of 4% and 10 years to maturity. It pays two coupons a year, of $20 each. At maturity, it repays the $1,000.
The coupons and the repayment never change. Only the price changes.
The price at each yield
| Market yield | Price | Change from face value | Current yield |
|---|---|---|---|
| 2% | $1,180.46 | +18.0% | 3.39% |
| 3% | $1,085.84 | +8.6% | 3.68% |
| 4% | $1,000.00 | -0.0% | 4.00% |
| 5% | $922.05 | -7.8% | 4.34% |
| 6% | $851.23 | -14.9% | 4.70% |
When the market yield equals the coupon, the bond sells at its face value. When new bonds pay 5%, nobody pays $1,000 for a bond that pays 4%. The price falls to $922.05, and at that price the bond gives 5% a year.
Two yields
Current yield is the yearly coupon divided by the price. At a price of $922.05, it is 4.34%.
Yield to maturity also counts the gain at maturity. A buyer at $922.05 gets back $1,000, which is $77.95 more. Coupons plus that gain give 5% a year. When the price is below face value, current yield is lower than yield to maturity.
The curve is not a straight line
A fall of 1 point in the yield adds $85.84 to the price. A rise of 1 point takes away $77.95. The gain is larger than the loss. Lesson 2 shows why.
Key points
- A bond pays fixed coupons and repays its face value. Only the price changes.
- When market yields go up, bond prices go down, until the yield matches the market.
- Yield to maturity counts the coupons and the gain or loss at maturity.
Sources
- Investor.gov, Municipal Bonds, for the tax treatment of municipal bond interest, and for prices that fall when rates rise.