ZERO-COUPON BOND

Definition

A Zero-Coupon Bond is a debt security that does not pay periodic interest (coupons). Instead, it is issued at a deep discount to its face (par) value and pays the full face value at maturity. The return to the investor is the difference between the purchase price and the par value.

It’s a “pure discount bond”—your gain is built into the price, not paid along the way.

Origins

Zero-coupon bonds emerged in their modern form in the 1970s and 1980s, particularly in the U.S. Treasury market, when financial institutions began stripping interest and principal payments from standard bonds and selling them as separate zero-coupon securities (e.g., Treasury STRIPS).

Usage

Industry Applications:

• Government Bonds – Commonly used by treasuries (e.g., U.S. STRIPS, Indian zero-coupon securities).

• Corporate Finance – Firms issue zeros for capital needs without interim cash outflows.

• Financial Engineering – Use in duration matching, liability immunization, and structured products.

• Tax Planning – In some jurisdictions, zero-coupon structures defer taxable income (though others tax imputed interest annually).

• Education/Retirement Saving – Useful for long-term goal-based investments due to fixed maturity values.

How Zero-Coupon Bond Works

• No coupon payments over the bond’s life.
• Issued at a discount to par (e.g., issued at $700, redeemed at $1,000).
• Interest income is implicitly earned through appreciation.
• Highly sensitive to interest rates (longer duration).
• Common maturities: 1 to 30 years.

Key Takeaway

• Zero-coupon bonds are simple and predictable—known cost, known return.

• Ideal for matching future liabilities (e.g., pension plans, tuition).

• Higher duration makes them more volatile in interest rate changes.

• Useful in bond laddering, ALM, or defeasance strategies.

Types of Zero-Coupon Bonds

Context in Financial Modeling

Zero-coupon bonds are modeled with:

• Single future cash flow (no interim interest).

• Compound interest math for pricing and valuation.

• Used in:

  • Yield curve construction

  • Bond portfolio optimization

  • Discount factor calibration in DCF models

Zero-coupon structure simplifies present value calculation, making them useful in theoretical models like Black-Scholes or binomial trees.

Nuances & Complexities

• Tax Treatment:

  • In some countries (e.g., U.S.), accrued interest is taxable annually as phantom income.

• Reinvestment Risk:

  • None—no interim cash to reinvest (unlike coupon bonds).

• Interest Rate Risk:

  • Higher duration makes zeros more sensitive to rate changes.

• Liquidity:

  • Some zeros (especially stripped securities) may have lower liquidity.

Mathematical Formulas

1. Present Value (Price) of a Zero-Coupon Bond:

$$P = \frac{F}{(1 + r)^n}$$

Where:

• $P$ = Present value (price)

• $F$ = Face value

• $r$ = Interest rate (yield to maturity)

• $n$ = Number of periods to maturity

2. Yield to Maturity (YTM):

$$r = \left( \frac{F}{P} \right)^{1/n} - 1$$

3. Imputed Interest (Annual Accretion):

$$\text{Interest} = P_t \times r$$

$$\text{Book Value}-\text{Tax Base})\times \text{Tax Rate}$$

Related Terms

• Coupon Bond

• Discount Bond

• Duration

• Yield to Maturity (YTM)

• Present Value

• Bond Laddering

• STRIPS (Separate Trading of Registered Interest and Principal Securities)

Real-World Applications

1. Treasury STRIPS Investment

An institutional investor buys $1M in 10-year STRIPS at $600,000, locking in a risk-free yield of ~5.2% annually.

2. Corporate Finance

A startup issues a 5-year zero-coupon bond at a steep discount to avoid near-term interest payments during ramp-up.

3. Pension Funding

A pension fund buys zeros maturing in 20 years to match long-term benefit payouts, minimizing reinvestment risk.

4. Education Savings Plan

A parent purchases a zero-coupon municipal bond to mature when their child enters college, ensuring fixed future funds.

References & Sources

• U.S. Treasury – STRIPS and Zero-Coupon Market Guides

• SEC.gov – Disclosure on Taxation of Zero-Coupon Bonds

• International Valuation Standards (IVS) – Discounted Cash Flow Valuation Methods

• Federal Reserve Board – Yield Curve Construction and Duration Models