Zero-Coupon Bond

A zero-coupon bond is a debt security that makes no interest payments during its life. Instead, the investor buys it for less than its face value and receives the full face value when it matures. The gap between the purchase price and the redemption amount is the investor's return. Governments, companies and banks issue zero-coupon debt, and investors use it to lock in a known sum on a known future date.

Ordinary bonds pay a coupon, usually every six or twelve months, set by a fixed interest rate or a floating one. A zero-coupon bond strips that feature away, leaving a single cash flow. Short-term Treasury bills are zero-coupon instruments by design, while longer zeros are often created by separating the coupons and principal of existing government bonds. Because there is only one payment, zeros are also the building block analysts use to value every other fixed-income instrument.

Imagine buying a gift voucher for 80 that a shop promises to honour for 100 in five years. You get nothing in between, but when the date arrives you collect the full 100. Your reward for waiting is the extra 20. A zero-coupon bond works the same way: pay less now, collect a fixed larger amount later.

The longer you have to wait, the cheaper the voucher must be to make waiting worthwhile. That is why a zero-coupon bond due in 30 years can cost a small fraction of its face value, while one due in three months costs almost the full amount.

The price of a zero-coupon bond is the present value of its single payment, discounted at the market yield. With annual compounding the formula is:

• $P$ is the price paid today.
• $F$ is the face value repaid at maturity.
• $y$ is the annual yield, written as a decimal.
• $n$ is the number of years to maturity.

Take a zero with a face value of 1,000 maturing in 10 years when the market yield is 5%. Then $(1.05)^{10} \approx 1.6289$, so the price is $1{,}000 \div 1.6289 \approx 613.91$. The investor pays about 613.91 today and receives 1,000 in ten years, earning 5% a year compounded. This is a direct application of the time value of money and the same discounting used in net present value analysis. Because a zero has no coupons to reinvest, its yield to maturity is exactly the return an investor earns by holding it to the end.

Some zeros are issued directly as discount securities, including Treasury bills, commercial paper and some corporate and municipal issues. Others are manufactured. Since 1985 the US Treasury has allowed eligible notes and bonds to be split into separate components under its STRIPS programme (Separate Trading of Registered Interest and Principal of Securities). Each coupon payment and the final principal become individual zero-coupon securities that trade on their own. Several other governments, including the UK for gilts, run similar stripping facilities.

Prices of these separated pieces reveal the market's discount rate for each future date. Fitting them together produces the zero-coupon or spot yield curve, which banks use to value swaps, forward rate agreements and other derivatives.

• Liability matching. Pension funds and insurers buy long zeros to meet payments due on known future dates, since a zero delivers a fixed sum with no reinvestment uncertainty.
• Saving for a goal. Households and trusts use them to fund fixed future costs such as education fees.
• Structured products. A bank can combine a zero with an option so that the zero guarantees the return of capital and the option provides market upside.
• Rate views. Because zeros are highly sensitive to rate changes, traders use long ones to take positions on falling interest rates.

A zero's whole value rests on one distant payment, so its price is more sensitive to rate changes than a coupon bond of the same maturity; its duration equals its maturity. Using the formula, a 30-year zero with a face value of 1,000 costs about 231 at a 5% yield but about 174 at 6%, a fall of roughly a quarter from a one-point rise in yields. This makes interest rate risk the dominant concern. Inflation matters too, since the fixed payment arrives far in the future.

Credit risk is also concentrated. If a corporate issuer has a default before maturity, the holder has received nothing along the way, unlike a coupon-bond holder who has collected some interest. Zeros issued by stable governments carry little of this credit risk, which is why STRIPS are widely held.

Tax can be a surprise. In the United States the annual growth in a zero's value, known as original issue discount, is generally taxed each year as interest even though no cash is paid, often called phantom income. Investors therefore often hold zeros in tax-deferred accounts. Rules differ by country, and in some jurisdictions the gain at redemption is treated as a capital gain rather than income.

• TreasuryDirect: STRIPS
• Investor.gov (US SEC): Zero-coupon bond