Why Bonds Trade at a Premium, Discount, or Par

A bond trades at a premium when its coupon rate exceeds the prevailing market yield, at a discount when its coupon rate falls below the market yield, or at par when the two are identical. This relationship is mechanical: higher market rates punish existing bonds paying lower coupons, while lower rates reward bonds paying higher coupons.

The Core Mechanism

When a bond is issued, its coupon rate is set to match the market’s required yield at that moment—it trades at par. But the moment market yields shift, the bond’s fixed coupon payment becomes misaligned with what new investors demand.

If market yields rise, existing bonds paying the old, lower coupon become less attractive. Investors will only buy them at a discount—a lower price that boosts the effective yield to match current market conditions. Conversely, if yields fall, older bonds paying higher coupons become more valuable, and they command a premium.

This inversion—bond price moves opposite to yield—is one of the most critical facts in fixed income. A 1% rise in market yields doesn’t move all bonds equally; longer-duration bonds see steeper price declines than shorter ones.

Worked Example: Premium and Discount

Imagine a 10-year corporate bond issued three years ago with a 5% annual coupon, paying $50 per year on a $1,000 face value. Seven years remain until maturity.

Scenario 1: Yields Rise to 6%

New investors can now buy similar bonds paying 6%. The old bond, paying only 5%, is less attractive. To make its total return competitive, its price must fall. Using bond valuation, that price is approximately $935. The bondholder buys at $935, receives $50 annually, and redeems $1,000 at maturity—achieving a 6% yield. The bond trades at a discount of $65 (or 6.5% of par).

Scenario 2: Yields Fall to 4%

New bonds now pay only 4%. The old bond’s 5% coupon is more generous. Investors will pay a premium for it. Its price rises to roughly $1,070. The bondholder pays $1,070, receives $50 annually, and redeems $1,000 at maturity—achieving a 4% yield. The bond trades at a premium of $70 (or 7% of par).

Why the Inverse Relationship Holds

The reason is pure mathematics. A bond’s value is the present value of all future cash flows: the annual coupons and the principal repayment at maturity. The discount rate used is the current market yield.

When market yields rise, future payments are discounted more heavily, lowering the bond’s value. When yields fall, payments are discounted less, raising the value. The coupon payment itself doesn’t change—only how investors value those future dollars.

Longer-maturity bonds are more sensitive to yield changes because they have more distant cash flows, which fluctuate more dramatically when the discount rate moves. A 30-year Treasury bond will swing far more in price than a 2-year bill when yields shift by the same amount.

Par as a Convergence Point

As a bond approaches maturity, its price always converges to par, regardless of how far it drifted into premium or discount territory. This is because the principal repayment—worth exactly $1,000 at maturity—becomes the dominant cash flow. The remaining coupons matter less and less.

A bond trading at $900 with one month left will recover toward $1,000. A bond trading at $1,100 will similarly decline. This convergence is predictable and creates a form of interest rate risk for traders holding bonds to maturity—they’re exposed to price swings in the interim but guaranteed to collect par at the end.

Accrued Interest and Market Conventions

One subtlety: bonds are quoted “clean” (without accrued interest), but buyers pay the “dirty” price (clean price plus accrued coupons earned since the last payment date). A premium or discount appears in both the clean and dirty prices, though the dirty price is what actually changes hands.

Over time, the dirty price of a premium bond drifts down toward par as the bond approaches maturity and accrued interest resets. The same is true for discount bonds drifting up. This “pull to par” is another manifestation of the same economic principle: at maturity, you get exactly par.

Premium and Discount Bond Tax Treatment

For U.S. investors, premiums and discounts have tax consequences. If you buy a bond at a premium, the IRS may require you to amortize that premium over the remaining life, reducing your annual taxable interest income. Conversely, discount accrual on original-issue discounts creates taxable imputed income each year, even if you don’t receive it until maturity. These rules affect whether owning a premium or discounted bond is tax-efficient.

Yield to Maturity vs. Current Yield

A bond’s yield to maturity accounts for capital gain or loss at redemption. A discount bond has a YTM higher than its current yield, because the price appreciation at maturity contributes extra return. A premium bond has a YTM lower than its current yield, because the price depreciation at maturity reduces total return. Par bonds have YTM equal to current yield.

This distinction matters for investors evaluating total return. Two bonds with the same coupon can have vastly different YTMs depending on their purchase price.

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