Bond Yield and the Price-Yield Relationship
Bond prices and yields move in opposite directions. As the required yield rises, the present value of fixed future cash flows falls, so the price drops, and vice versa. The yield to maturity, or YTM, is the single discount rate that equates the present value of all the bond’s cash flows to its current price, the internal rate of return on holding the bond to maturity. It differs from the current yield, which is only the annual coupon divided by price and ignores any gain or loss as the price converges to face value. YTM is the standard summary of a bond’s return because it captures both coupon income and price change.
Try it yourself
A bond's price is the present value of its coupons plus face, discounted at the market yield. Move the yield and watch price trace the downward-sloping, convex curve — price moves inversely to yield.
Face value fixed at 100, so price reads as a percent of face.
Why it matters
Price and yield are two sides of the same coin. Fix the cash flows, and a higher price can only mean a lower return, while a lower price means a higher return. Yield to maturity is the honest, all-in return. It is the rate that makes the discounted cash flows exactly equal what you pay, so it folds in both the coupons you collect and the pull of the price toward face value at maturity. Current yield is a quick snapshot of coupon income alone, which is why it misleads for premium and discount bonds.
Formulas
Worked examples
A bond with A$1,000 face value and an annual coupon of A$80 currently trades at A$950. Compare its current yield with the direction of its yield to maturity.
Current yield is , about 8.42 percent. Because the bond trades at a discount, it will also gain value as the price climbs toward A$1,000 at maturity, so the YTM exceeds the current yield. The YTM here is roughly ten percent once that price gain is included.
Common mistakes
- ✗When interest rates rise, bond prices rise too. The relationship is inverse. Higher required yields shrink the present value of fixed cash flows, so prices fall when rates rise.
- ✗Current yield and yield to maturity are the same thing. Current yield counts only coupon income over price. YTM also includes the gain or loss as the price moves to face value, so the two differ for any non-par bond.
- ✗Yield to maturity is guaranteed if you hold to maturity. YTM assumes coupons are reinvested at the same yield. If reinvestment rates differ, the realized return will not exactly equal the quoted YTM.
- ✗A higher coupon always means a higher yield. Yield depends on price relative to all cash flows. A high-coupon bond bought at a steep premium can have a lower yield than a low-coupon bond bought at a discount.
Revision bullets
- •Bond price and yield move in opposite directions
- •YTM is the discount rate equating present value of cash flows to price
- •YTM is the bond’s internal rate of return if held to maturity
- •Current yield is annual coupon over price and ignores price change
- •For discount bonds YTM exceeds current yield; for premium bonds it is lower
- •Quoted YTM assumes coupons are reinvested at that same rate
Quick check
If the market yield required on a bond increases, the bond’s price will
For a bond trading at a discount to face value, the yield to maturity is
Connected topics
Sources
- Brailsford, Heaney & Bilson (2015), Ch. on bond valuationBrailsford, T., Heaney, R., & Bilson, C. Investments: Concepts and Applications. 5th ed. Cengage Learning Australia, 2015.Explains the inverse price-yield relationship and distinguishes yield to maturity from current yield.
- Bodie, Kane & Marcus (2021), Ch. 14Bodie, Z., Kane, A., & Marcus, A. J. Investments. 12th ed. McGraw-Hill Education, 2021.Defines yield to maturity as the internal rate of return and contrasts it with current yield.