Par Bonds
Par Bonds
A par bond trades at exactly 100% of its face value. This occurs when the bond's coupon rate equals the market's required yield for that bond. A par bond delivers neither a capital gain nor a capital loss at maturity—all return comes from the coupon.
Key takeaways
- A bond trades at par when its coupon rate equals the yield to maturity
- A par bond offers no capital gain or loss; all return is coupon income
- Par bonds are the baseline for bond valuation; discount and premium bonds are measured relative to par
- Newly issued bonds often trade at or very close to par, especially if the coupon was set competitively
- Par bonds are simpler to analyze than premium or discount bonds because the coupon and yield are aligned
What par means
Par is the face value of a bond, usually expressed as 100 (meaning 100% of the nominal value). A $1,000 par bond trading at par is priced at $1,000. A £100 par UK gilt trading at par is priced at £100.
When a bond trades at par, the coupon rate and the yield to maturity (YTM) are equal. A bond with a 4% coupon trading at par has a YTM of 4%.
The par bond condition
For a bond to trade at par, the coupon must equal the market's required yield. When a bond is newly issued, the coupon is usually set to equal or approximate the market yield at issue. If the coupon is set correctly, the bond trades at par (or very close to par) on the first day of trading.
Over time, as market yields change, the bond will trade at a discount (if yields rise) or a premium (if yields fall). A bond that was issued at par may no longer be at par if rates change.
Par bonds in practice: the new issue scenario
When a company or government issues a new bond, the underwriters set a coupon they think will be competitive. If the coupon is set accurately, the bond trades at par (or 99 to 101, a narrow range). Investors buy the bond at or near par, knowing the coupon was competitive at the time of issue.
A Treasury new issue might be auctioned at par. The Treasury sets a coupon (based on similar-maturity Treasuries), and auction participants bid on yield. If the coupon is set right, many bids come in at par (meaning buyers are willing to pay exactly face value for that coupon).
Once a bond is issued, secondary market trading can move it away from par if yields change.
Par bonds and secondary market trading
In the secondary market, a bond might trade at par even after issue. This occurs if:
- The coupon was set correctly at issuance and yields have not changed much, or
- The bond's credit quality is stable, and the required yield has remained constant.
A well-known bond from a strong issuer might trade at or near par if the coupon is still competitive.
For example, a high-quality corporate bond with a 4% coupon might trade at par if the market's required yield for that issuer and maturity is still 4%. If the company's credit improves and the required yield falls to 3.5%, the bond will trade above par (a premium). If credit deteriorates and the required yield rises to 4.5%, the bond will trade below par (a discount).
Par as a reference point
Par is the reference point for all bond analysis. Analysts ask:
- Is the bond trading at par, above par (premium), or below par (discount)?
- How much of a discount or premium?
- Is the discount or premium justified by the coupon-yield difference?
Par is the null hypothesis. If a bond is trading at par, the coupon is fairly priced relative to the yield. Departures from par signal opportunity or risk.
Coupons and yields at par
At par:
Current yield = Coupon rate = YTM
A bond with a 4% coupon trading at par has:
- Current yield: 4% (coupon ÷ price = 4% of par ÷ par = 4%)
- YTM: 4%
All three measures align. This is the simplest case for bond analysis.
When a bond is not at par, the three measures diverge:
- Discount bond (3% coupon, 4% market yield, trading below par): Current yield ≠ 3%, YTM = 4%
- Premium bond (5% coupon, 4% market yield, trading above par): Current yield ≠ 5%, YTM = 4%
Par is where simplicity reigns.
No capital gain or loss at par
The key attraction of a par bond: you know there will be no capital gain or loss. You pay face value, you collect the coupon, you receive face value at maturity. The only variability is the coupon rate.
This certainty appeals to some investors. But it comes at a cost: a par bond offers no potential for capital appreciation if rates fall.
Par and duration
The duration of a par bond (the price sensitivity to interest rate changes) depends on the coupon and maturity. All else being equal, a low-coupon bond has higher duration than a high-coupon bond, even if both are at par.
A 2% coupon 10-year bond at par has higher duration (more price sensitivity) than a 4% coupon 10-year bond at par. The duration might be 8.5 years versus 7.5 years. This is because the low-coupon bond has more of its cash flow back-loaded to maturity, making it more sensitive to yield changes.
Par bonds and callable bonds
For a callable bond, par is a significant price level. The call price is often par (100). A callable bond trading at par is at the call price. If rates fall and the bond's value rises above par, the issuer's incentive to call increases.
A callable bond trading well above par (say, at 105 or 110) is likely to be called if the coupon is high relative to current rates. A callable bond at par offers some cushion; rates must fall enough to make it profitable to call.
Par bonds and accrued interest
The clean price of a bond (quoted price) is the price excluding accrued interest. A bond might be quoted at par (100) but your actual cash payment includes accrued interest.
If a bond's clean price is par but it has accrued interest of 1% (because you are buying mid-coupon period), you pay 101% total. The dirty price (clean plus accrued) is 101; the clean price is 100 (par).
Par bonds across markets
In the U.S., par is 100 (equivalent to $1,000 for a bond with $1,000 face value).
In the UK, par is often quoted as 100 (equivalent to £100 of face value).
In some markets, par is quoted as 100 (a percentage), while in others it is quoted in absolute terms ($1,000, €1,000).
Conversions are straightforward, but you must understand the market convention.
Par bonds and perpetuals
Most bonds have maturity. A par bond pays coupons until maturity, then returns par. Some bonds are perpetual (no maturity date, like UK consols or some preference shares). A perpetual bond trading at par yields the coupon rate, and there is no maturity cash flow. The bond is valued purely on the coupon stream.
For perpetuals, par is the expected long-term value if the coupon is competitive. Perpetuals can trade above or below par depending on whether the coupon is above or below the required yield.
Par bonds in different interest rate regimes
In a high interest rate regime (e.g., 2023 with 5% Treasury yields), new bonds are issued with high coupons (5%, 6%) and trade at par. Existing bonds with low coupons (1%, 2%, issued in 2020) trade at deep discounts.
In a low interest rate regime (e.g., 2019 with 1.5% Treasury yields), new bonds are issued with low coupons (1%, 1.5%) and trade at par. Existing bonds with high coupons (3%, 4%, issued a few years earlier) trade at premiums.
The par bond is the newly issued bond, set to yield the current rate. Time and rate changes push old bonds away from par.
Par bonds and zero-coupon bonds
A zero-coupon bond (no coupons, all return at maturity) can never trade at par (except right at issuance if issued at par, which is rare). A zero-coupon bond issued at $50 (a $50 discount to the $100 face value) will converge to par as maturity approaches.
A zero-coupon bond is the opposite of a par coupon bond: all return is capital appreciation, no return is coupon income.
Par bonds and bond funds
A bond fund holding bonds at various prices (some at par, some at discount, some at premium) reports the fund's market value as the weighted average of all holdings. If the fund's average maturity is 5 years and rates have not moved, the fund's bonds might be a mix of par, discount, and premium, depending on the coupons.
A fund's net asset value (NAV) is the sum of all holdings' market values divided by the number of fund shares. Par is the benchmark; the NAV might be above or below the par value of the underlying bonds depending on rate and credit changes.
Par as a leveling event
When a bond matures, its price is par. All bonds, regardless of discount or premium, converge to par at maturity. This convergence is economically certain (barring default). You can predict the price at maturity: par.
This is why par is the foundation of bond math. Everything else is time value and risk premiums around the convergence to par.
Conclusion: par bonds are the baseline
Par bonds are conceptually simple: coupon equals yield, current price equals face value, return is coupon income alone. They are the baseline against which all other bonds are measured. When a bond moves to a discount or premium, it is because the coupon is out of line with the market yield. Understanding par bonds helps you understand why discounts and premiums exist and what they imply about value and risk.
Flowchart
Related concepts
Next
We have now covered the full spectrum of bond valuation: par bonds (coupon equals yield), discount bonds (coupon below yield), and premium bonds (coupon above yield). These concepts—face value, coupon, maturity, and yield—form the foundation of fixed income analysis. The next chapter builds on this foundation, exploring how bonds are priced, how different bonds interact in portfolios, and how to manage interest rate and credit risks.