Zero-Coupon Bond Economics

A zero-coupon bond makes no periodic interest payments. Instead, it is issued at a deep discount to par value and repays face value at maturity. The bondholder’s return consists entirely of the price appreciation from purchase to par. Zero-coupon bonds have unique properties: high duration risk, extreme convexity, and specific tax treatment that makes them valuable in certain portfolio contexts.

Basic structure and cash flows

A traditional bond pays coupon interest twice yearly (typically) and returns principal at maturity. A zero-coupon bond skips all coupon payments and returns only par value at a single future date. For example, a 10-year zero-coupon bond might be issued at $38.55 per $100 face value and mature at $100.

The initial discount reflects the time value of money. The investor purchasing the zero at $38.55 receives $100 in 10 years, locking in an internal rate of return (the bond’s yield to maturity) determined by the discount and maturity.

Duration and interest rate sensitivity

Zero-coupon bonds have the highest duration for a given maturity because all cash flows are received at the end, not spread over time. The duration of a zero-coupon bond equals its years to maturity. A 10-year zero has 10-year duration.

This high duration makes zeros extremely sensitive to interest rate changes. A 100 basis point decline in yields might increase a traditional 10-year bond’s price by 7–8%. The same move increases a 10-year zero’s price by 9–10% due to the concentrated cash flow. This leverage amplifies gains in falling-rate environments but magnifies losses in rising-rate environments.

Convexity and price acceleration

Zero-coupon bonds exhibit extreme positive convexity. Convexity measures how the duration-price relationship changes with yields. A bond with high positive convexity experiences accelerating price gains as yields fall and decelerating price losses as yields rise (compared to the linear prediction of duration alone).

A 10-year zero falling in price from $40 to $35 (yields rising) loses less in percentage terms than the duration model predicts. But if prices rise from $40 to $45 (yields falling), the gain is larger than duration alone would suggest. This asymmetry (more upside, less downside than duration-based models predict) is valuable in certain hedging and portfolio structures.

Tax treatment: Original Issue Discount (OID)

Zeros have a specific tax treatment in most jurisdictions. The bondholder must accrue and pay income tax on the implied interest (the difference between par value and issue price) each year, even though no cash is received until maturity. This is called original issue discount (OID) accrual.

For example, a $100 zero issued at $70 with 5-year maturity has total discount of $30. The annual OID is $30 ÷ 5 = $6 (using straight-line accrual; some use constant-yield methods). The investor must report $6 annual taxable income even though no cash is received. This creates negative cash flow in early years: the investor pays income tax on imputed interest while holding a security that has not yet paid.

This tax treatment makes zeros disadvantageous for taxable investors. They are more suitable for tax-deferred accounts (IRAs, 401(k)s) where the OID accrual is not immediately taxable. Some jurisdictions offer tax-exempt zeros (municipal zero-coupon bonds) where the OID accrual is tax-free, making them attractive even in taxable accounts.

Applications in portfolios and liability matching

Zeros are useful for matching specific future liabilities. A parent saving for a child’s college tuition 15 years hence can buy a 15-year zero, lock in the required return, and know the exact amount available at maturity. This eliminates reinvestment risk—the risk that coupon payments must be reinvested at lower rates in the future. A zero has no coupons to reinvest, so the return is fully determined at purchase.

Pension funds use zeros to match long-dated liabilities (pensions owed 20+ years hence). The precise cash flow timing of zeros aligns with predictable future obligations, reducing hedging complexity.

Comparison to coupon-bearing bonds

A coupon-bearing bond and a zero-coupon bond with the same maturity and yield have the same price and yield to maturity. But they behave differently as yields change due to duration differences. The zero has higher duration, so its price moves more.

From a reinvestment perspective, the coupon bond’s investor faces reinvestment risk: coupons received must be reinvested, and future interest rates are unknown. The zero investor faces no reinvestment risk because there are no intermediate cash flows. This trade-off explains why zeros are preferred for liability matching but coupon bonds are preferred for portfolios where cash flow flexibility is valued.

Zero-coupon strategies and STRIPS

In 1985, the U.S. Treasury introduced STRIPS (Separate Trading of Registered Interest and Principal Securities), allowing investors to strip Treasury bonds into their individual coupon and principal components and trade them separately. This created a liquid market for synthetic zero-coupon-like instruments. A Treasury STRIP maturing in 10 years functions like a zero-coupon bond.

Corporate and municipal zero-coupon bonds are typically issued directly by issuers. Treasury STRIPS and inflation-protected securities can be stripped into zero components. The availability of STRIPS has reduced the need for explicitly issued zeros because investors can synthetically create them.

Risks and considerations

Zeros carry high interest rate risk due to high duration. If an investor buys a 20-year zero and interest rates rise sharply, the mark-to-market loss can be substantial. Holding to maturity eliminates this risk, but selling before maturity locks in losses.

Also, zeros carry the credit risk of the issuer. If a corporation issues a 10-year zero and defaults after 7 years, the investor receives nothing despite being near maturity. The issuer’s obligation is no different because no coupons were paid; the entire obligation matures at the end.

Alternatives and evolution

Modern investors often achieve zero-coupon-bond-like structures through ETFs, barbell strategies (combining short and long bonds), or zero-coupon-swap positions. These alternatives offer liquidity and flexibility that explicit zeros may lack in certain markets.