How Does a Zero-Coupon Bond Earn a Return?
Without interim coupons, return can still come from the difference between purchase price and face value received at maturity.
Try it and see the difference
The same ten-year maturity, without interim coupons
Both bonds share face value, maturity and market YTM with semiannual compounding. The difference is whether a 5% coupon is paid.
- Purchase today
- −610.27
- Interim coupons
- None
- Year-ten principal
- +1,000.00
Zero-coupon bond
- Price
- 610.27
- Macaulay duration
- 10.00 years
- Estimated price effect of +50 bps
- -4.88%
5% coupon bond
- Price
- 1,000.00
- Macaulay duration
- 7.99 years
- Estimated price effect of +50 bps
- -3.90%
Today's price 610.27 is 389.73 below the maturity payment of 1,000. At this positive YTM, that difference is the source of accumulation when held to maturity, with no interim coupons to reinvest.
The price estimate uses modified duration for small changes; actual price versus yield is curved. Credit risk and options are excluded.
Why does this happen?
Place today's payment and the 1,000 received in ten years on one timeline to see the source of growth. A coupon bond returns some value earlier; a zero waits for the final payment. At the same maturity and yield, the zero has longer duration.
Greater sensitivity needs a controlled comparison
The comparison below holds face value, ten-year maturity and semiannual yield convention constant for a zero and a 5% coupon bond. The +50 bps effect is a modified-duration linear estimate, not exact repricing; zero-coupon does not automatically mean more sensitive than every bond.
Show formal definition and formula
A zero-coupon bond pays no coupons before maturity; all scheduled payment is the maturity face value. At positive yield, price is below face, and in this fixed-payment model Macaulay duration equals time to maturity.
Discount only the final principal payment
One final payment means weighted time equals maturity
Linear estimate for a small yield change
- P₀ / F
- Zero-coupon price / maturity face value
- y / m
- Nominal annual yield, decimal / compounding frequency
- T
- Years to maturity
- DMac / DMod
- Macaulay / modified duration
- Δy
- Decimal yield change; 50 bps = 0.005
Fixed scheduled payments, valued on a coupon date with decimal rates. Default, taxes, fees and calls not defined in the example are excluded.
A common misconception
No coupons does not mean no return or no risk. Selling before maturity exposes the price to market-yield changes; at negative yield, price can also exceed face value.