Why do zero-coupon bonds always trade at a deep discount, and how do you price them?

Zero-coupon bonds are simpler to price than coupon bonds because there's only one cash flow — the face value at maturity. The entire return comes from buying at a discount and receiving par at maturity.

Pricing Formula:

P = FV / (1 + r)^n

Where:

• FV = Face value (e.g., $1,000)
• r = YTM per period
• n = Number of periods

Example:

A 10-year zero-coupon bond with a YTM of 4.5% and face value of $1,000:

P = $1,000 / (1.045)^10 = $1,000 / 1.5530 = $643.93

You pay $643.93 today and receive $1,000 in 10 years. Your return of $356.07 is all capital appreciation.

Why buy zeros?

1. Duration matching: Zeros have duration equal to maturity (no reinvestment risk), making them perfect for liability matching.
2. Known terminal value: If you need exactly $1,000 in 10 years, a zero guarantees it.
3. Tax advantages in certain accounts: In tax-deferred accounts, you avoid annual phantom income taxation.

Key characteristics:

• Highest interest rate risk: Zeros have the longest duration for any given maturity, making them the most price-sensitive to rate changes.
• No reinvestment risk: Since there are no interim cash flows, you don't face the risk of reinvesting coupons at lower rates.
• Phantom income: In taxable accounts, the IRS taxes the annual accretion (price increase toward par) even though you receive no cash.

Zero-coupon bonds are foundational for understanding the spot rate curve and bootstrapping, which you'll encounter later in Fixed Income. Master this pricing first.

Check out our CFA Level I Fixed Income module for more on zero-coupon bond applications.