How Bond Pricing Works: Price, Yield, Duration, and Risk

A bond’s price is the present value of every future payment it will make, discounted back to today at the return the market currently demands. That required return is the bond’s yield, and understanding how bond pricing works comes down to a single rule: when yield rises, price falls; when yield drops, price climbs. Everything else in fixed income builds on that inverse relationship.¹

The Fixed Terms That Anchor the Math

Three things about a bond are locked in the day it’s issued, and they don’t change. That’s exactly why the price has to move when market conditions do.

Face value, also called par value, is the amount the issuer promises to repay at maturity. Most bonds carry a $1,000 face value, though $100 denominations exist. Face value is also the base for calculating interest.

The coupon rate is the annual interest rate the bond pays, expressed as a percentage of face value. A $1,000 bond with a 5% coupon generates $50 a year, usually paid in two semiannual installments of $25.² Once set, the coupon rate never changes.

The maturity date is when the issuer must return the face value and stop paying interest. Treasury notes mature in 2 to 10 years; Treasury bonds mature in 20 or 30 years.² The number of periods remaining determines how many future cash flows an investor is buying.

Why Price and Yield Move in Opposite Directions

The SEC states the rule directly: when market interest rates rise, prices of fixed-rate bonds fall.¹ This isn’t a tendency. It’s a mathematical certainty built into how present value works.

Yield to maturity (YTM) is the total annualized return an investor earns by buying a bond at its current price and holding it to maturity. Mathematically, YTM is the discount rate that makes the present value of all future cash flows equal to the bond’s current market price.³ Push YTM up, and those future cash flows get discounted more heavily; the price drops. Pull YTM down, and the discounting eases; the price rises.

The interaction between the fixed coupon and the moving YTM produces three pricing states:

A par bond trades at face value because the coupon rate equals the required YTM. A 5% coupon bond in a 5% yield environment sits at $1,000.
A discount bond trades below face value because the required YTM exceeds the coupon rate. The capital gain at maturity (buying at $950 and receiving $1,000) makes up for the below-market coupon.
A premium bond trades above face value because the required YTM is below the coupon rate. The capital loss at maturity (buying at $1,050 and receiving $1,000) offsets the above-market coupons.

TreasuryDirect puts it in a single line: if the yield to maturity is greater than the interest rate, the price will be less than par; if the two are equal, the price is par; and if the yield is less than the interest rate, the price exceeds par.²

Current Yield vs. Yield to Maturity

These two numbers measure different things, and mixing them up trips up plenty of investors. Current yield is the annual coupon divided by the current market price.³ A $1,000 par bond with a 6% coupon trading at $950 has a current yield of $60 ÷ $950, or 6.32%.

Current yield tells you what the bond throws off as income relative to what you paid. It ignores the capital gain or loss you’ll realize at maturity and the effect of compounding on reinvested coupons. YTM captures the full picture: coupon income, the difference between purchase price and face value, and the time value of money over the remaining term. If you plan to hold to maturity, YTM is the number to use.

How the Price Calculation Actually Works

A bond’s fair price equals the present value of two cash streams: the periodic coupons and the lump-sum face value returned at maturity. Both are discounted using the required YTM.

Take a 10-year, $1,000 bond with a 6% coupon paid semiannually. It produces 20 coupon payments of $30 each plus a single $1,000 payment at the end. To price it, you discount each of those 20 coupons and the $1,000 back to today using half the annual YTM, because payments are semiannual.

The coupon payments form an annuity. Each $30 payment is worth slightly less today than the one before it because it arrives further in the future. Summed together, they represent what the income stream alone is worth right now. The higher the YTM, the smaller that sum.

The face value is a single future payment discounted over the bond’s full remaining term. On a 10-year semiannual bond, you’re discounting $1,000 over 20 periods. Because this cash flow sits at the very end of the timeline, it’s especially sensitive to the discount rate.

If the YTM matches the 6% coupon rate, the two present values sum to exactly $1,000. If the required YTM rises to 7%, both components shrink and the bond prices below par. If the required YTM falls to 5%, both grow and the bond trades at a premium. The math enforces the inverse relationship with no exceptions.

What Actually Moves Bond Prices

The biggest force is the general level of interest rates. When the Federal Reserve raises its benchmark rate, yields on new issues climb. Existing bonds with lower coupons look less attractive, so their prices fall until their effective yields match the new market.¹ When rates fall, an older bond paying 5% in a 3% world suddenly looks generous, and buyers bid it up until its YTM settles near the prevailing rate. Price is the balancing mechanism.

Not every bond reacts the same. Two features determine how much the price swings when rates move:

Lower coupons increase sensitivity. When a bond pays little periodic interest, more of its total value is tied up in the distant face-value repayment, which gets hit harder by discounting.¹
Longer maturities increase sensitivity. A 30-year bond’s cash flows stretch far into the future, so its price moves far more than a 2-year note’s price for the same rate change.¹

Duration

Duration collapses those two features into one number. FINRA describes it as a measure of how sensitive a bond investment will be to interest rate changes, where a higher number means more sensitivity. The rule of thumb: for every 1 percentage-point change in rates, a bond’s price moves in the opposite direction by roughly its duration.⁴ A bond with a duration of 7 loses about 7% if rates jump a full point, and gains about 7% if rates fall the same amount. Longer maturities and lower coupons both push duration higher. Zero-coupon bonds have the highest duration for their maturity because every dollar of return arrives at the end.

Credit Risk and Ratings

Credit risk is the chance the issuer can’t make its scheduled payments. Higher risk means higher demanded yield, which means a lower price. S&P Global’s scale runs from AAA down to D, with the line between investment grade and speculative grade at BBB-. Anything below that is commonly called junk or high yield. Default rates climb steeply as ratings fall, which is why the yield spread between investment-grade and speculative-grade bonds can be several percentage points wide.⁵ A downgrade alone can drop a bond’s price, even if the issuer never misses a payment, because the market reprices the risk.

Inflation, Reinvestment, and Liquidity

A bond’s coupons are fixed in dollar terms, so inflation eats their purchasing power. Earning 4% while inflation runs 5% delivers a negative real return, and investors who expect higher inflation demand higher yields, which drives prices down. Treasury Inflation-Protected Securities adjust their principal up or down with the Consumer Price Index, and the fixed coupon rate is applied to that adjusted principal.⁶ At maturity, a TIPS pays the inflation-adjusted principal or the original principal, whichever is greater.⁷

Reinvestment risk works in the other direction. YTM assumes you can reinvest each coupon at the same rate for the bond’s remaining life. If rates fall, you’ll reinvest at lower rates, and your actual return will trail the YTM you calculated at purchase. Rising rates hurt your bond’s price but improve reinvestment returns; falling rates do the opposite. Hold-to-maturity investors care more about reinvestment; investors who might sell care more about price.

Liquidity matters, too. Small municipal issues and obscure corporate bonds can be hard to sell without accepting a lower price, so investors demand extra yield as compensation. The less liquid the bond, the higher the yield and the lower the price, all else equal.

Clean Price vs. Dirty Price

The price you see quoted in financial news is almost always the clean price, which excludes any interest that has built up since the last coupon date. What you actually pay at settlement is the dirty price, which includes that accrued interest.

Bonds pay coupons on a fixed schedule but trade every business day. If you buy halfway between coupon dates, the seller has earned half the period’s interest, and you compensate them for it. The formula is simple: dirty price equals clean price plus accrued interest. On a coupon payment date the two prices are identical; between dates the dirty price climbs above the clean price and then resets on the next payment. Two bonds with the same clean price can have different dirty prices depending on where each sits in its coupon cycle, so the dirty price is what to look at when comparing actual purchase cost.

Zero-Coupon Bonds

Zero-coupon bonds pay no periodic interest. You buy them at a steep discount and receive the face amount at maturity. FINRA gives the example of paying $3,500 for a 20-year zero with a $10,000 face value.⁸ The full return comes from that price appreciation.

Because there are no coupons cushioning the blow, zeros are extremely sensitive to rate changes. All of the value sits in one distant payment, so even small rate moves produce large price swings. Long-term zeros carry particularly high duration risk.⁸

There’s also a tax wrinkle. The IRS treats the difference between purchase price and face value as imputed interest and requires you to pay tax on a portion each year, even though no cash arrives until maturity.⁸ This phantom income creates a tax bill without matching cash flow, which is why zeros often fit better inside tax-advantaged accounts like IRAs.

Callable Bonds and Yield to Call

A callable bond gives the issuer the right to buy the bond back before maturity at a preset price. Issuers typically call bonds when rates drop, for the same reason a homeowner refinances: they can reissue debt at a lower rate.⁹

Call risk is real for anyone buying a bond for its income stream. If the bond is called, you lose the future coupons and have to reinvest the returned principal at lower prevailing rates, which FINRA warns can significantly affect expected return.⁹

YTM alone can mislead you on a callable bond. Yield to call calculates your return assuming the issuer redeems at the earliest possible call date rather than letting the bond run to maturity. For a premium callable bond, yield to call is often the more realistic measure. The conservative move is to look at both numbers and plan around the lower one. To offset call risk, callable bonds sometimes offer higher coupons than comparable noncallable bonds, and some issuers set the call price slightly above face value as an additional cushion.⁹

How Taxes Change What a Bond Is Worth

What matters for real returns is after-tax yield, and taxes shape what investors will pay.

Interest from most bonds is taxed as ordinary income at your federal rate. Interest on bonds issued by state and local governments is generally excluded from federal income tax.¹⁰ That exemption lets municipal issuers offer lower coupons while still delivering competitive after-tax returns, and for investors in higher brackets, a muni’s tax-equivalent yield can beat a higher-coupon corporate bond.

Not every municipal bond qualifies. Private activity bonds that don’t meet federal public-use requirements can be fully taxable, and some municipal bonds are subject to the alternative minimum tax.¹¹ AMT bonds usually carry slightly higher yields to reflect that.

Selling a bond before maturity for more than your adjusted cost basis produces a capital gain; selling for less produces a loss. Adjusted basis isn’t always what you paid. For bonds bought at an original issue discount, the basis climbs each year as you accrue the discount as ordinary income, and only the difference between the sale price and that adjusted basis counts as a capital gain or loss.

Prices Converge to Par as Maturity Approaches

As a bond nears maturity, its price gravitates toward face value regardless of what’s happening with rates, credit spreads, or anything else. A bond trading at $1,050 with five years left will drift toward $1,000 as the years tick down, assuming no default. A bond at $940 will drift upward.

Interest rate risk, credit risk, and liquidity risk all matter less in a bond’s final months because the price simply has less room to deviate from par. For investors holding to maturity, the day-to-day swings along the way are temporary, and the terminal value is contractually fixed.¹

1
SEC. Interest Rate Risk – When Interest Rates Go Up, Prices of Fixed-Rate Bonds Fall
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TreasuryDirect. Understanding Pricing
3
FINRA. Bond Yield and Return
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FINRA. Duration – What an Interest Rate Hike Could Do to Your Bond Portfolio
5
S&P Global. Understanding Credit Ratings
6
TreasuryDirect. TIPS/CPI Data
7
SEC. SEC Yield for Funds That Invest Significantly in TIPS
8
FINRA. Zero Coupon Bonds
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FINRA. Callable Bonds: Your Issuer May Come Calling
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Office of the Law Revision Counsel. 26 USC 103 – Interest on State and Local Bonds
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MSRB. Municipal Bond Basics