Bond Pricing and the Price-Yield Relationship
Now that you understand how yields are calculated, you can see what drives them: the bond's market price. This section covers the most fundamental principle in fixed income (the inverse relationship between price and yield) and the factors that determine how sensitive a bond's price is to rate changes.
The Inverse Relationship Between Price and Yield
This is the single most important concept in bond investing:
- Bond prices and interest rates (yields) move in opposite directions
- When market interest rates rise, existing bond prices fall (their fixed coupon becomes less attractive compared to new bonds)
- When market interest rates fall, existing bond prices rise (their fixed coupon becomes more attractive compared to new bonds)
Think of it this way: A bond's coupon is locked in at issuance. If new bonds offer 7% and yours pays 5%, no buyer will pay full price for yours. Your bond's price has to drop until its effective yield matches the market. When rates fall, the opposite happens; your 5% coupon looks generous, so buyers bid the price up.
Discount, Premium, and Par Bonds
The relationship between a bond's coupon rate and prevailing market rates determines whether it trades at a discount, premium, or par.
| Bond Type | Price vs. Par | Coupon Rate vs. Market Rate | Capital Effect at Maturity |
|---|---|---|---|
| Discount | Below $1,000 | Coupon lower than market | Capital gain (price rises to par) |
| Premium | Above $1,000 | Coupon higher than market | Capital loss (price falls to par) |
| Par | Equals $1,000 | Coupon equals market | No gain or loss |
- Discount bonds: The discount represents additional return (capital gain) earned at maturity. As the bond approaches maturity, the price pulls toward par
- Premium bonds: The premium represents a capital loss absorbed at maturity (only par is returned). As maturity nears, the price pulls toward par
- Par bonds: All yields (nominal yield, current yield, and yield to maturity) are equal when a bond trades at par
Exam Tip: Gotchas
- A bond's price always converges toward par as maturity approaches, whether it is trading at a discount or premium. At maturity, every bond is worth exactly $1,000 (par).
Factors Affecting Bond Price Sensitivity
Two characteristics determine how much a bond's price moves when interest rates change:
Coupon Rate
- Lower coupon bonds are more volatile (more sensitive to rate changes) than higher coupon bonds
- A zero-coupon bond has the greatest sensitivity because the investor receives no cash flow until maturity; all return depends on the final payment
Maturity
- Longer maturity bonds are more volatile than shorter maturity bonds
- A longer time horizon means more future cash flows are affected by the rate change
Combined Effect
| Characteristic | Most Volatile | Least Volatile |
|---|---|---|
| Coupon rate | Low (or zero) | High |
| Maturity | Long | Short |
| Combined | Long-term, zero-coupon | Short-term, high-coupon |
Exam Tip: Gotchas
- The exam frequently asks "which bond is most sensitive to interest rate changes?" Always pick the one with the longest maturity AND lowest coupon. A 30-year zero-coupon bond is the most volatile fixed-income instrument.
Basis Points
- A basis point (bp) is 1/100th of 1% (0.01%)
- 100 basis points = 1%
- Used to express small changes in yields and interest rates
Example: If a bond's yield moves from 4.50% to 4.75%, it has increased by 25 basis points
Value of a basis point: The dollar price change in a bond for a 1-basis-point change in yield. For a bond priced at par, 1 basis point is approximately $0.10 per $1,000 bond (varies with maturity and coupon).
Dollar Price vs. Basis (Yield) Price
Bonds can be quoted two different ways depending on the type of security:
| Quoting Method | What It Means | Used For |
|---|---|---|
| Dollar price | Percentage of par (e.g., 98.50 = $985 per $1,000) | Corporate bonds, government bonds |
| Basis price (yield price) | Quoted by yield to maturity (YTM) (e.g., 5.25 means YTM is 5.25%) | Municipal bonds |
Quoting conventions by security type:
- Corporate bonds: Dollar price (percentage of par in decimals or eighths)
- Municipal bonds: Often quoted on a yield basis (YTM or yield to call (YTC))
- Government bonds: Dollar price (percentage of par in 32nds)
- Example: A Treasury quoted at 99-16 means 99 and 16/32 = 99.50% of par = $995.00
Exam Tip: Gotchas
- Government bonds are quoted in 32nds, not decimals. A quote of 99-16 is $995.00, not $99.16.
- Municipal bonds are typically quoted on a yield basis (YTM or YTC), not a dollar price. If you see a muni quoted at "5.25," that is the yield, not the price.