Zero-Coupon Bonds

How a zero-coupon bond works

A conventional coupon bond sends interest payments on scheduled dates and returns principal at maturity. A zero-coupon bond sends no periodic coupon. Instead, the investor buys it for less than the amount due at maturity. If the issuer makes the promised payment and the investor holds to maturity, the gap between purchase price and redemption value is the basic source of return.

The discount is not a coupon paid every year. It reflects the present value of a future payment. A security due to pay $1,000 in ten years is worth less than $1,000 today because investors can earn a return during the waiting period. The required yield, time to payment, credit quality and marketability all affect the price a buyer will accept.

Some zero-coupon instruments are originally issued without coupons. Others are created when a financial institution separates the interest and principal payments of an eligible bond into individual claims. Treasury STRIPS are examples of separately traded interest and principal components of eligible Treasury securities. Each component has its own payment date and amount; the holder does not receive the original bond's regular coupon stream.

The term zero-coupon describes the cash-flow pattern, not the issuer's credit quality. A zero issued by a government, corporation or other entity still carries the relevant issuer risk and legal terms. A low market price does not mean the security is safe, and a large difference between purchase price and maturity amount does not mean the difference is guaranteed profit.

Price a single future payment

For a single payment, present value equals the future amount divided by one plus the yield raised to the number of periods: Price = F ÷ (1 + y)^n. F is the maturity amount, y is the yield per period, and n is the number of periods. Match the yield convention and period count. Annual compounding for ten years is different from semiannual compounding over twenty periods.

Suppose an investor considers a $1,000 zero due in ten years, and the required annual yield is 5% with annual compounding. Its estimated price is $1,000 ÷ (1.05)^10, or about $613.91. The discount to face is about $386.09. That arithmetic assumes the payment is made and the stated yield convention applies; it is not a forecast of what the investor can sell it for next year.

If comparable yields fall to 4%, the same payment has a present value of about $675.56. If yields rise to 6%, it is about $558.39. The security did not change its $1,000 maturity promise in this simplified example. The market's required discount rate changed, which altered today's value.

The calculation can be reversed. If a $1,000 payment due in ten years costs $613.91, the annual compound yield implied by the assumptions is approximately 5%, since $613.91 × (1.05)^10 is about $1,000. In a real quote, accrued discount, transaction costs, taxes and the exact day-count or compounding convention may affect the stated yield.

Why zeros can move sharply when rates change

A zero's entire promised payment arrives at maturity, so none of its value comes from near-term coupons. When market yields rise, that distant payment is discounted more heavily. When yields fall, it is discounted less heavily. A longer time to maturity generally makes the present value more sensitive to a given yield change, all else equal.

Compare two zero-coupon securities with the same issuer, yield convention and face amount. One pays in two years; the other pays in twenty. A change in required yield has more periods over which to affect the twenty-year payment. This is why long zeros can have substantial market-price volatility even when their contractual maturity amount is fixed.

The relationship between price and yield is curved rather than perfectly linear. A duration approximation can estimate a small price change, but it is only an estimate and becomes less accurate for larger yield moves. Zeros may have long duration relative to coupon bonds with similar maturity because their cash flows are concentrated at the end. Embedded features, credit spread changes and liquidity can alter the comparison.

Holding a zero to maturity does not eliminate economic risk. The investor may need to sell early, in which case the market price can be below the purchase price. Inflation can reduce the purchasing power of the fixed maturity amount. The issuer could fail to pay. If the maturity date does not match the investor's actual cash need, the security may leave a gap or force a sale.

Match a zero to a future liability

A zero can be useful when an investor has a defined future payment and wants a single maturity cash flow. For example, a family expects a $20,000 tuition bill in eight years. If a suitable bond with adequate credit quality matures on the needed date, the family can compare its current price with other ways to fund that liability. The match reduces dependence on selling a bond on a particular day, assuming the issuer pays.

The required purchase amount can be estimated by discounting the target cash need. At a hypothetical 4% annual yield, $20,000 due in eight years has a present value of about $14,612, because $20,000 ÷ (1.04)^8 is approximately that amount. This is a valuation illustration, not a quoted available security. Actual maturities, prices, taxes, issuer risk and the exact date must be checked.

A single maturity date may not match bills that are due in installments. An investor with three annual tuition payments might use separate maturity dates or another portfolio of cash flows rather than assume one bond solves the entire need. If a payment date shifts, a maturity slightly before the obligation may preserve time to settle and transfer funds, though it also creates a period in which proceeds must be managed.

A zero's cash-flow match is only as dependable as the issuer's promise and the investor's ability to hold it. A Treasury STRIP and a corporate zero are not interchangeable simply because both mature at the same time. Evaluate credit, tax, liquidity, concentration and the consequences if the liability amount changes.

Treasury STRIPS and separated payments

STRIPS are Treasury securities whose separate principal and interest payments are traded as individual zero-coupon securities. A Treasury note might otherwise pay coupons over time and return principal at maturity. When eligible payments are separated, a purchaser can buy a specific future payment rather than the full coupon-bearing instrument. TreasuryDirect explains the program and its terms.

The scheduled payment date differs across STRIPS. A principal component pays at the original security's maturity; an interest component pays on one of the coupon dates. This lets investors choose among available dates, but it does not create a periodic income stream if they hold just one component. The holder receives the one payment associated with that STRIP.

A STRIP's Treasury backing addresses issuer credit differently from a corporate zero, but it does not prevent market-price changes before maturity. An investor who sells early can receive less than the purchase price if rates rise or market conditions change. A security with a distant payment can be more rate-sensitive than a short-dated one.

Do not assume every zero-coupon security is a STRIP or that every payment can be separated under the same program. Identify the issuer and exact instrument. The product's prospectus or official terms explain payment amount, date, ownership and any operational details that matter to settlement.

Tax on discount accrual

For many taxable debt instruments issued at a discount, federal tax rules require holders to include original issue discount as it accrues, even though the bond pays no cash coupon during that period. The investor can therefore face taxable income without receiving cash from the security. This is often called phantom income in informal discussion, but the exact tax calculation depends on the instrument and the holder's circumstances.

Do not calculate a client's tax solely as the total discount divided evenly by years. Original issue discount is generally accrued under prescribed rules, and market discount, acquisition premium, tax-exempt instruments, retirement accounts and other circumstances can change the treatment. Treasury and other instruments can have specific rules. Use current IRS guidance and tax advice for the actual security and account.

This timing matters for cash planning. An investor may need money outside the bond to pay taxes before maturity. Buying a zero in a tax-deferred account can change when tax is recognized, but the account's distribution rules still matter. The exam may test the general distinction between no coupon cash and taxable discount accrual; it will not justify inventing a universal tax outcome for all zeros.

Tax treatment should be considered alongside yield rather than after the purchase decision. A quoted yield is typically before the investor's personal tax effects unless specified. Compare securities on a consistent basis, account for state or local rules where relevant, and confirm whether the quoted return assumes a particular holding period.

Zero-coupon bonds compared with coupon bonds

A coupon bond returns some cash before maturity, which the investor can spend or reinvest. A zero concentrates the payment at maturity. For the same maturity and issuer risk, the zero's price usually changes more when yields move because the investor waits longer for all the cash. The investor avoids coupon reinvestment decisions during the term but accepts a larger dependence on one distant payment.

A coupon bond's yield to maturity usually assumes interim coupons are reinvested at the calculated yield to express a compound return. A zero has no coupon stream to reinvest, so that particular assumption is less central before maturity. The investor still faces reinvestment risk when the maturity proceeds arrive: if the money is needed later, future rates may be lower than expected.

A zero also has no coupon to help meet ongoing expenses. A retiree who needs monthly income cannot spend the bond's gradual economic accretion as cash unless they sell pieces or pair the zero with other liquid assets. A maturity match can solve a lump-sum need, while an income plan requires attention to payment timing and liquidity.

The right comparison depends on the liability and risk tolerance. A coupon bond may suit a client seeking regular payments but require reinvestment choices. A zero may match a fixed future date but expose the client to larger interim price swings. Neither pattern is inherently better for every investor.

Worked case: evaluating a price decline

An investor buys a ten-year $1,000 zero for about $613.91 using a 5% annual yield assumption. Two years later, eight years remain. If the required yield is still 5%, the value is approximately $1,000 ÷ (1.05)^8, or $676.84. The increase reflects the passage of time under a constant yield model, not a cash coupon payment.

If required yield at that point rises to 7%, the eight-year payment has an estimated present value of about $582.01. The market value is below the original purchase price even though two years have passed and the maturity payment is unchanged. The investor has an unrealized loss at that price and a realized loss only if the security is sold below the relevant cost basis, subject to transaction and tax details.

The comparison isolates yield movement for teaching purposes. In real markets, the required yield may include a changing credit spread and liquidity premium as well as benchmark rates. A corporate zero could fall because the market reassesses the issuer even if Treasury rates do not move. Separate the risk sources before explaining a price change.

Questions to ask before choosing a zero

Start with the future cash need: amount, date, flexibility and whether it is a lump sum or a series. Identify the issuer, maturity payment, market price, yield convention, credit quality and available trading liquidity. Then test how the price could change if rates or spreads move before maturity.

Ask whether the investor can hold through the payment date and fund any taxes along the way. Review whether a sale might be needed for emergencies. A long zero can have pronounced price movement, so money needed on short notice should not be assumed available at face value.

Finally, compare the bond's payment date with the obligation and account for any tax or transfer lag. If the dates do not line up, a different maturity or a short-term cash reserve may be needed. State which assumptions are guaranteed by the contract, which depend on issuer payment, and which depend on future market prices.

How to answer Series 65 questions

A zero-coupon bond pays no periodic interest. It is generally sold below face value and pays the maturity amount if the issuer performs. Its return comes from the price discount and final payment, not from coupon checks.

With no interim coupons, a zero's value is concentrated in its maturity payment. A longer zero is generally more sensitive to a yield change than a shorter comparable security. The investor may need to sell at a loss before maturity if market yields rise.

Remember that a zero's no-coupon feature does not automatically mean no tax is due before maturity. Original issue discount may accrue for tax purposes. Identify the issuer and account, and avoid assuming that all zero-coupon instruments share identical tax treatment.

Sources

SEC Investor.gov, Zero-Coupon Bond; TreasuryDirect, STRIPS; IRS Publication 550 (2025), Original Issue Discount; NASAA Series 65 Test Specifications, Section I. Prices and yields are hypothetical.