Zero-Coupon Bond Price
Present value of a zero-coupon bond — a single discounted cash flow equal to the face value at maturity, with no intermediate coupons. The simplest case of bond pricing and the building block for spot-rate analysis.
When to use: Use to price Treasury STRIPS, zero-coupon Treasuries, or to back out a zero-coupon-equivalent rate from a non-coupon-paying instrument. The semi-annual convention (m = 2) is standard for US Treasury zeros.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| ZeroPrice | Zero-Coupon Price | Theoretical price of the zero-coupon bond | $ |
| F | Face Value | Par value paid at maturity | $ |
| y | Yield | Annual yield as a decimal; periodic yield is y/m | % |
| N | Years to Maturity | Years remaining until the bond matures | years |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: 10-Year Zero at 5% (Semi-Annual)
$1,000-face zero-coupon Treasury, 10 years to maturity, 5% yield, semi-annual compounding.
Given
Step-by-Step
You pay $610.27 today for $1,000 in 10 years — a 38.97% discount that reflects the time value of money over the holding period.
Example 2: 5-Year Zero at 4% (Annual)
$1,000-face zero, 5 years to maturity, 4% yield, annual compounding.
Given
Step-by-Step
A 5-year zero at 4% prices to about 82% of face. Zeros experience pure duration risk — no coupons cushion price moves when yields shift.
Frequently Asked Questions
Because all the cash flow is at maturity, the duration equals the time to maturity (Macaulay duration of a zero = N years). A coupon bond of the same maturity has a shorter duration because intermediate coupons effectively "pull forward" some of the cash flow.
Convention. US Treasury yields are quoted on a semi-annual bond-equivalent basis, so zero prices use m = 2 to stay consistent with coupon-Treasury yield quotes. International zero markets vary.
Conceptually yes (no coupon, redeemed at par), but T-bills use a different quote convention (discount rate, ACT/360 day count) rather than semi-annual yield. Use this formula for STRIPS and longer zeros; use the discount-rate formula for T-bills.