Pull to Par: How a Bond Price Converges at Maturity

A pull-to-par bond—one trading above or below its par value—will see its price drift toward face value ($100 for a $100 bond) as the maturity date approaches. A premium bond bought at $105 will fall in price; a discount bond bought at $95 will rise. This is a mechanical reality, not a market forecast: the bond must be worth exactly par at maturity. Understanding pull-to-par is essential for fixed-income investors, especially those holding non-index securities or managing portfolios with frequent rebalancing.

Why Bonds Converge to Par

A bond obligates the issuer to pay a fixed coupon rate and return the principal (par value) at maturity. No matter what the bond trades for today, on the maturity date it pays exactly $100 (or whatever par is). If you hold a bond to maturity, you receive par.

This certainty creates the pull-to-par effect. Suppose you buy a bond with 10 years to maturity for $105. You’ve overpaid; you are losing $5 relative to par. But you will hold it to maturity and receive $100. The loss must happen somewhere; it shows up as a gradual price decline toward par over the 10 years. If the bond trades for $104 after 1 year, then $103 after 2 years, and so on, that’s pull-to-par in action.

Conversely, a discount bond bought at $95 will gradually appreciate toward $100 because the buyer is owed par at maturity. A gain of $5 accrues over time as the maturity date approaches.

A Worked Example: Premium Bond

Consider a 5-year bond with a 5% coupon, face value of $100, currently trading at $110.

• Coupon per year: $5
• Current market yield (implied by the $110 price): ~3.4%
• Price today: $110
• Par value at maturity: $100
• Price drift: From $110 toward $100

Year 1: The bond pays its $5 coupon. The investor earns $5 in income. But the bond’s market value has shifted. If the market yield stays at 3.4%, the bond now has 4 years to maturity. A 4-year bond with a 5% coupon yielding 3.4% has a price of approximately $107.50. The bond has depreciated from $110 to $107.50 even though the investor received the coupon payment.

Year 2: Another $5 coupon. Now the bond has 3 years left. At a 3.4% yield, a 3-year, 5% coupon bond trades at approximately $105. Price has fallen further.

Year 3: Another $5 coupon. 2 years left. Price: ~$102.50.

Year 4: Another $5 coupon. 1 year left. Price: ~$101.

Year 5: Final coupon ($5) + principal ($100) paid. Price = $100 (par).

The investor received five $5 coupons ($25 total) and got back $100 principal. Total cash: $125. The initial $110 investment plus the subsequent cash inflows average to a yield of 3.4%, consistent with the market yield at purchase. But each year, the investor watched the bond’s price fall from $110 toward $100. That decline is pull-to-par.

A Worked Example: Discount Bond

Now consider a 5-year bond with a 2% coupon, face value of $100, trading at $91.

• Coupon per year: $2
• Current market yield: ~4.5%
• Price today: $91
• Par value at maturity: $100
• Price drift: From $91 toward $100

Year 1: The bond pays $2 coupon. If the market yield stays at 4.5%, a 4-year, 2% coupon bond trades at approximately $93. The bond has appreciated from $91 to $93 even though only $2 was paid in coupon.

Year 2: Another $2 coupon. 3 years left at 4.5% yield: price ≈ $95.50.

Year 3: Another $2 coupon. 2 years left: price ≈ $97.50.

Year 4: Another $2 coupon. 1 year left: price ≈ $99.

Year 5: Final coupon ($2) + principal ($100). Price = $100.

Over five years, the investor received five $2 coupons ($10) and received $100 principal, for a total of $110. The $91 investment grew to $110; the annualized return is approximately 4.5%, consistent with the yield at purchase. The investor benefited from price appreciation of $9 ($91 → $100) in addition to the meager coupon income. That appreciation is pull-to-par.

The Mechanics: Why Does It Happen?

Pull-to-par occurs because of the inverse relationship between coupon rate and yield to maturity. A bond’s price is the present value of all future cash flows, discounted at the current market yield.

• Premium bond (coupon > yield): The coupon is high relative to current yields. The bond’s PV is above par. As maturity approaches, the number of high-coupon payments remaining shrinks. Eventually only one coupon + par remains. When there is only 1 day left, the bond is worth almost exactly par + the final coupon. As time elapses, the PV of remaining cash falls, pulling the bond price down toward par.

• Discount bond (coupon < yield): The coupon is low relative to current yields. The bond’s PV is below par. But par is guaranteed at maturity. As maturity approaches, the certain $100 repayment grows larger in relative importance (it’s the only cash left). Eventually, the bond’s value approaches par because $100 is coming imminently. The promise of par in the near future pushes the PV up toward par.

In both cases, it’s the mechanical certainty of receiving par at maturity that drives the convergence.

Speed of Pull-to-Par

Pull-to-par is not linear. Early in the bond’s life, drift is slow. A 20-year bond’s price changes slowly per year. A 1-year bond’s price converges to par rapidly. In the final 6 months, a bond’s price change per day may be noticeable.

The speed also depends on the coupon rate relative to the market yield. A deeply discounted bond (coupon 2%, yield 6%) converges faster than a slightly discounted bond (coupon 4.5%, yield 5%), because the pull from par’s certainty is stronger when the coupon is far below yield.

For a rough intuition: in a 10-year bond, pull-to-par contributes ~0.3–0.5% per year to return if the bond is moderately premium or discount. In a 1-year bond, pull-to-par can contribute 2–5% per year, especially for deeply discounted or deeply premium bonds.

Implications for Portfolio Management

Holding to Maturity: If you buy a bond and hold it to maturity, pull-to-par is irrelevant to your return. You receive exactly par plus the coupons, yielding your YTM. Pull-to-par is a phenomenon for mark-to-market accounting and interim sales.

Selling Before Maturity: If you sell a bond before maturity, pull-to-par affects your realized price. A premium bond you bought at $110 and sold 3 years later at $103 has pulled closer to par, reducing your capital return (but you still earned coupons). Understanding pull-to-par helps you forecast intermediate prices and decide when to trim positions.

Duration and Convexity: Pull-to-par is captured in duration models. A bond’s duration measures its interest-rate sensitivity and also implicitly includes pull-to-par drift. As a bond matures, its duration falls (less time-weighted cash flows remain). Pull-to-par is the mechanism through which duration declines.

Floating-Rate Bonds: A floating-rate bond pays a coupon tied to a benchmark (e.g., 3-month LIBOR + 2%). As the benchmark shifts, the coupon adjusts. Floating-rate bonds pull to par more slowly because the coupon moves with the market yield, maintaining near-par pricing. Most floating-rate bonds trade very close to par.

Bond ETF Returns: In a bond ETF, pull-to-par is a steady source of return for discount bonds and a steady drag for premium bonds. A bond ETF holding 5-year discount bonds benefits from 1–2% annual price appreciation (from pull-to-par) even if yields don’t move. An ETF of premium bonds faces a 1–2% annual depreciation headwind from pull-to-par.

Tax Considerations

In the United States, if you buy a bond at a discount to par, the annual accretion toward par is taxable income (market discount) even though you haven’t sold the bond. The IRS assumes you’re earning a return from pull-to-par and taxes it annually.

Conversely, if you buy a bond at a premium, you can elect to amortize the premium, reducing your taxable coupon income each year. If you don’t elect amortization, the full coupon is income, and the capital loss from pull-to-par shows up only when you sell.

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