A bond’s payments are fixed, so when new bonds pay more, an existing one is worth less. A 1,000 bond paying 5% a year with 10 years left is priced at 857.88 when similar bonds yield 7%, 14.2% below its face value. With 2 years left, the same yield prices it at 963.27, 3.7% below.
The price is what the remaining payments are worth when discounted at the market’s yield. A higher yield lowers the value of every payment, and lowers payments further away by more, which is why the bond with longer to run moves further. When yields fall below 5%, the price rises above 1,000.
Prices at five market yields
The same bond, with two different times left to run:
| Market yield | 2 years left | 10 years left |
|---|---|---|
| 3% | 1,038.54 | 1,171.69 |
| 4% | 1,019.04 | 1,081.76 |
| 5% | 1,000.00 | 1,000.00 |
| 6% | 981.41 | 925.61 |
| 7% | 963.27 | 857.88 |
What the example leaves out
Real prices also reflect the risk that the issuer does not pay, how easily the bond can be sold, and the cost of trading. Held to the end, the bond still repays 1,000 if the issuer pays.