A fixed-rate bond can keep paying exactly the same coupon while its market price falls sharply. The reason is not mysterious. The coupon belongs to the old contract. The market yield belongs to today’s required return. When today’s required return changes, the price of the existing cash-flow stream must adjust.
This is one of the cleanest examples of discounting in finance. A bond promises future cash flows. Investors compare those cash flows with the returns now available elsewhere, adjusted for risk. If comparable new claims become more attractive, the old bond must become cheaper to compete. If comparable new claims become less attractive, the old bond can become more valuable.
This article owns the bond-specific price–yield mechanism inside How Finance Works. The broader How Interest Rates Work article remains the general rate owner. Here we hold the bond cash flows in our hands and watch the price move.
Educational scope: simplified fixed-income mechanics. Real bonds can contain credit spread changes, embedded options, liquidity effects, tax effects and other features that move price independently of a benchmark interest rate.
The inverse relationship in one sentence
When the yield required by the market rises, the present value of a fixed future cash-flow stream falls; when the required yield falls, the present value rises.
Investor.gov describes the relationship directly: bond prices generally move opposite market interest rates, and bond yield moves inversely with price. See Investor.gov’s corporate-bond bulletin.
The important word is fixed. If the contractual cash flows do not change but the market’s required return changes, price is the variable available to reconcile the two.
Coupon is not yield
Take a fictional S$1,000 bond with a 4% annual coupon. It pays S$40 a year. If it trades at par—S$1,000—and the cash-flow timing fits the simplified assumptions, its coupon rate and current market return can line up closely.
Now suppose newly issued bonds of similar risk and maturity offer around 6%. A new investor comparing S$40 a year on S$1,000 with roughly S$60 a year on S$1,000 will not normally pay the same price for both. The old 4% bond must fall in price until its total expected return becomes competitive with the new market environment.
Reverse the situation. If new comparable bonds offer 2%, an old bond paying S$40 on S$1,000 becomes attractive. Investors can bid its price above S$1,000, which reduces the yield available to the new buyer.
The present-value engine
At a high level, a bond’s price is the present value of its expected future cash flows under a chosen discount rate or yield assumption. For a simple annual fixed-coupon bond:
Price = coupon₁/(1+y) + coupon₂/(1+y)² + … + (final coupon + principal)/(1+y)ⁿ
where y is the market yield used for the calculation and n is the number of remaining periods under the simplified setup.
If y rises, every denominator gets larger. The present value falls. If y falls, the denominators get smaller. The present value rises.
This is the same logic developed more broadly in Present Value and Future Value. Bonds make the mechanism unusually visible because their promised cash flows are often clearly scheduled.
Worked example: the same bond at three yields
Take a fictional three-year bond with S$1,000 face value and a 4% annual coupon. It pays S$40 at the end of Years 1 and 2, then S$1,040 at the end of Year 3. Ignore default and every other complication.
| Required yield | Approximate present value | Relationship to par |
|---|---|---|
| 2% | About S$1,057.66 | Premium |
| 4% | S$1,000.00 | Par |
| 6% | About S$946.54 | Discount |
The bond’s contractual S$40 coupon did not change. The S$1,000 principal did not change. The price changed because the market return used to value those fixed cash flows changed.
This is why premium and discount are not moral judgements. They describe the relationship between a bond’s market price and its par value.
Why a premium bond can still be rational
Suppose market yields are 2% and an existing bond pays a 4% coupon. Paying more than S$1,000 can still be rational because the buyer receives the higher coupon stream. The premium gradually compensates for those larger coupon payments, while only S$1,000 principal is returned at maturity in the simple example.
The buyer does not receive the premium amount back as principal. That is part of why the yield is lower than the coupon rate.
Investor.gov’s corporate-bond examples show this same structure: bonds with coupon rates above current market rates can trade at a premium, while bonds with coupons below market rates can trade at a discount.
Why a discount bond can offer a yield above its coupon
Suppose the S$1,000 bond trades at S$946.54 in the 6% example. The buyer still receives S$40 coupons and, if the issuer pays as promised, S$1,000 principal at maturity. The difference between the purchase price and the maturity payment contributes to the total return.
This is why reading coupon alone can understate the return on a discount bond and overstate it on a premium bond. The price paid matters.
Current yield is useful but incomplete
Current yield = annual coupon ÷ current market price.
If the S$40 coupon bond trades at S$800, current yield is 5%. But current yield ignores the additional gain or loss between the market price and the principal repaid at maturity. It also ignores the time value of the intervening cash flows.
Yield to maturity attempts to incorporate the full schedule under a set of assumptions. It is more comprehensive, but still a model quantity rather than a guaranteed realised return.
Yield to maturity is a conditional return measure
Yield to maturity is the discount rate that equates a bond’s current price with the present value of its promised cash flows under the conventional assumptions used. Investor.gov describes it as a widely used comparison measure. See the bond bulletin.
But the phrase “yield to maturity” can sound more certain than it is. The issuer must pay as promised. The bond must remain outstanding to maturity rather than be called. Interim coupons may need to be reinvested at an assumed rate for the conventional yield interpretation to translate into a realised compound return.
A quoted yield is therefore a powerful comparison tool, not a prophecy.
Maturity changes price sensitivity
Consider two fixed-coupon bonds with the same issuer and coupon rate, one maturing in two years and another in twenty years. When yields rise, both prices can fall, but the longer bond generally moves more because more of its value depends on cash flows far into the future.
Discounting compounds through time. A one-percentage-point change applied to a payment twenty years away has a much larger present-value effect than the same change applied to a payment due next year.
This is the beginning of duration: a measure of how a bond’s price responds to changes in yield, shaped by the timing of its cash flows.
Coupon level also changes sensitivity
A high-coupon bond returns more of its economic value earlier through coupon payments. A low-coupon or zero-coupon bond leaves more of its value concentrated in the distant principal payment. All else equal, that usually makes the lower-coupon bond more sensitive to yield changes.
Take two ten-year bonds with the same face value and yield. One pays 8% annually. The other pays no coupons and returns principal at maturity. The zero-coupon bond’s entire contractual payment sits at Year 10, so its present value is more exposed to changes in the discount rate applied over that full horizon.
This is why “same maturity” does not mean “same interest-rate risk.” The cash-flow timing within the maturity matters.
Duration as an approximate price-sensitivity map
Modified duration is commonly used to approximate the percentage price change for a small change in yield:
Approximate % price change ≈ − modified duration × change in yield.
If a bond has modified duration of 7 and yield rises by 0.50 percentage points, or 0.005 in decimal form, the first-order estimate is approximately −3.5%.
This is an approximation. For larger yield changes, the curvature of the price–yield relationship matters, which leads to convexity. The negative sign encodes the inverse relationship: yield up, price down.
Convexity: the relationship is curved, not perfectly linear
Bond prices do not move along a straight line as yields change. For a conventional option-free bond, the price increase from a large fall in yields is generally larger than the price decrease predicted by a straight-line duration estimate of the same size in the opposite direction.
That curvature is called convexity. It matters when rates move significantly or when comparing bonds with similar duration but different cash-flow structures.
Embedded options can alter the shape. A callable bond may not rise as much when yields fall because the issuer becomes more likely to redeem it early. The option changes the effective cash-flow path.
Benchmark yields and credit spreads can move independently
A corporate bond’s yield is not driven only by a government benchmark. It can also include compensation for credit risk, liquidity and other factors. Suppose the benchmark yield falls by 1 percentage point while the company’s credit spread widens by 2 percentage points. The corporate bond’s total required yield can still rise.
In that case, saying “interest rates fell, so the bond price should rise” is incomplete. Which rate fell? What happened to the issuer’s credit spread?
The earlier Interest-Rate Spreads article explains the wider spread mechanism. Bond pricing combines the layers.
The market can reprice credit without any coupon change
Suppose a corporate bond pays a fixed 5% coupon. The issuer later reports weaker cash flow and takes on substantially more debt. Investors may require a higher yield because the probability or severity of future non-payment appears greater.
The coupon is still 5%. The price can fall because the required return for carrying the credit risk has increased.
This is why the inverse price–yield relationship should not be taught as merely a central-bank-rate story. Any component of required yield can move.
A bond held to maturity still has economic price risk before maturity
A common statement says, “Price changes do not matter if I hold to maturity.” That can be true in a narrow cash-flow sense for a non-defaulting plain bond held all the way to its contractual repayment date. But the statement can hide real constraints.
The holder might need to sell early. The issuer might default. Inflation might change the real value of the payments. A call provision might end the bond early. Opportunity cost matters because higher-yielding alternatives may become available while capital remains locked into the old bond.
Price therefore remains economically meaningful even if no sale is planned. It tells us what the existing claim is worth relative to current alternatives and risks.
Reinvestment risk moves in the opposite direction
When market yields fall, the price of an existing high-coupon bond can rise. But coupons received along the way may have to be reinvested at lower rates. That is reinvestment risk.
Longer-duration, lower-coupon bonds are generally more price-sensitive but less dependent on reinvesting large interim coupons. Higher-coupon bonds return more cash earlier and therefore expose more of the realised return to reinvestment conditions.
One risk can improve while another worsens. This is why “rates down is good for bonds” is too compressed to be a complete explanation.
Singapore Government Securities make the price–yield relationship visible
The Monetary Authority of Singapore publishes closing bid prices and yields for Singapore Government Securities. The tables show coupon, maturity, price and yield side by side, making the relationship observable rather than merely theoretical. See MAS SGS Bond Prices and Yields.
For example, two SGS issues can have different coupons and remaining maturities, so comparing their prices without the yield and cash-flow schedule would be incomplete. The market converts each bond’s unique contract into a price consistent with the prevailing yield required for that issue.
The table is therefore not a list of “better” and “worse” prices. It is a live map of different claims.
The reverse test: if price moved, which required return changed?
When a bond price falls, do not stop at “rates went up.” Ask which part of yield changed: benchmark interest rates, inflation expectations, credit spread, liquidity premium, embedded-option value or some other factor?
Then ask whether the contractual cash flows changed. A credit event may alter expected recovery or future payments. A pure rate move may leave the contract untouched while changing only its present value.
This two-step test separates cash-flow news from discount-rate news. Many financial price movements become easier to understand once those are kept apart.
An observable mastery test
Bond A and Bond B each have S$1,000 face value and five years remaining. Bond A pays a 2% coupon. Bond B pays an 8% coupon. Both have the same issuer and yield. Which one is usually more price-sensitive to a small rise in yield?
All else equal, Bond A is generally more sensitive because a larger share of its value sits in the distant principal payment rather than arriving earlier through coupons. It tends to have longer duration.
Now suppose Bond B is callable while Bond A is not. The comparison becomes more complex because the issuer’s call option can alter Bond B’s effective cash-flow timing when rates fall. Understanding the mechanism means knowing when the simple rule stops being enough.
The World Return of bond pricing
New information → changed required return → repriced bond → changed financing conditions → issuer behaviour → future cash flows → repayment or loss.
Bond prices do more than mark investors’ wealth. They feed back into the real financing environment. If yields rise sharply, refinancing becomes more expensive. Projects that were viable at a lower cost of capital may no longer clear the hurdle. Governments and companies may change borrowing, spending, investment or maturity choices.
The market price therefore sits between financial claims and real-world decisions. It is both a valuation result and an input into future financing.
Sources and further reading
The core inverse relationship is supported by Investor.gov’s corporate-bond bulletin and the MAS SGS price and yield database. The worked present-value cases and diagnostic examples are original teaching material.
Continue through the bond series
Return to What a Bond Represents for the contract. Continue to Government Bonds vs Corporate Bonds for issuer-risk structure and Bond Default for priority and recovery. Return to How Finance Works for the whole Finance system.