Bond Price vs. Yield: Why Prices and Yields Move in Opposite Directions

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Yes: when a bond’s price goes up, its yield goes down, and when the price falls, the yield rises. The reason is that a standard bond’s cash payments are fixed when it is issued. The coupon amount and the face value repaid at maturity never change. The only thing that can adjust to new market conditions is the price someone pays for those payments. Paying more for the same fixed cash flows means earning a lower return on your money. Paying less means earning a higher one. Yield is that return expressed as a rate, so it has to move opposite to price.

Why a fixed coupon forces the price to move

Buy a newly issued bond at its face value, and your yield equals its coupon rate. A $1,000 bond paying 4% a year for three years pays $40 annually and returns $1,000 at the end. If you never sell, what the bond is “worth” in between has no practical effect on you.

Now suppose that six months later, comparable new bonds are issued with a 5% coupon. Your bond still pays $40 a year, while a new one pays $50 on the same $1,000. No buyer will pay you $1,000 for $40 a year when $50 is available for the same price. To sell, you would have to cut your price to the point where a buyer’s total return on your bond roughly matches the 5% available elsewhere. That lower price is what pushes the yield up to market levels.

The reverse happens when rates fall. If new comparable bonds pay only 3%, your 4% coupon becomes more valuable, and buyers will pay more than $1,000 for it. They bid the price up until the yield they would earn drops to about 3%.

How bond prices are quoted

Bond prices are usually quoted as a percentage of par value (the face amount the issuer repays at maturity). Par is expressed as 100, so a quote of 100 means the bond trades at exactly its face value, 98.90 means 98.90% of face value, and 102 means 102%.

To convert a quote into dollars, multiply it by the face amount you are buying. A quote of 98.90 on $100,000 of face value means a price of about $98,900. The same quote on a single $1,000 bond means $989.

Three conventions affect how you read quotes:

• Premium, par and discount. Above 100 is a premium, exactly 100 is par, below 100 is a discount. A discount usually reflects higher market yields since issuance, or changes in the issuer’s credit standing.
• Treasury notes and bonds use 32nds. They have traditionally been quoted in 32nds of a point rather than decimals.
• Yield changes are measured in basis points. One basis point is one hundredth of a percentage point (0.01%). A yield that moves from 4.20% to 4.53% has risen 33 basis points.

Clean price, dirty price and accrued interest

Coupons are usually paid semiannually, but bonds trade on any day. A buyer between coupon dates receives the entire next coupon, so they pay the seller the interest earned since the last coupon date. This is called accrued interest. The quoted price usually excludes it. That figure is the clean (or flat) price. What you actually pay at settlement is the clean price plus accrued interest, sometimes called the dirty or full price. The difference is interest owed to the seller, not a change in the bond’s value.

Yield is the discount rate that matches price to cash flows

A bond’s cash flows are its coupon payments plus the return of principal at maturity. Its yield to maturity (YTM) is the single discount rate that makes the present value of all those cash flows equal its current price:

Price = C / (1 + y) + C / (1 + y)² + … + (C + F) / (1 + y)ⁿ

Here C is the coupon per period, F is face value, n is the number of periods and y is the yield per period. For a semiannual bond, C is half the annual coupon, n is the number of half-years, and y is half the annual yield.

The formula shows the inverse relationship mechanically. C and F are fixed, and y sits in the denominator of every term. Raise y, and every term shrinks, so the price falls. Lower y, and every term grows, so the price rises. In practice, the price is observed in the market and the yield is solved backward from it. Either way, the two are locked together.

It also explains why premium and discount pricing make sense. If two bonds with the same maturity and credit quality are discounted at the same market yield, the one with smaller coupons has smaller cash flows. It therefore has a lower present value, so its price is lower.

Yield measures differ

“Yield” can refer to several calculations, and they answer different questions:

• Coupon rate: the annual coupon as a percentage of face value. Fixed at issuance; it does not change with price.
• Current yield: annual coupon divided by current price. It reflects price but ignores the gain or loss you lock in by buying below or above par.
• Yield to maturity: the full discount-rate calculation above. It includes all coupons and the pull toward par at maturity.
• Yield to call: for callable bonds, the same calculation run to a possible call date and call price instead of maturity.

Yield to maturity has a built-in assumption: every coupon is reinvested at the same yield until maturity. Future rates are unknown, so the return you actually realize can differ from the YTM you bought at, even if you hold to maturity.

For callable bonds, the issuer decides whether to redeem early, so a single YTM figure can overstate what you will earn if a call is likely. For non-callable bonds such as most U.S. Treasury notes and bonds, the maturity date is fixed. That makes YTM a clean measure of the return implied by today’s price.

Worked example: one bond, three market yields

Hypothetical bond, for illustration only: $1,000 face value, 4% annual coupon ($40 per year, paid annually to keep the arithmetic simple), three years to maturity, no default risk assumed.

At a 5% market yield, the price is $40/1.05 + $40/1.05² + $1,040/1.05³ = $38.10 + $36.28 + $898.39 = $972.77.

This answers a question that often seems backward: why does paying less for a bond raise its yield? A buyer who pays $972.77 still collects $40 a year. At maturity, they also receive $1,000, which is $27.23 more than they paid. That built-in gain, spread over three years and added to the coupons, lifts the total return to 5%. The current yield (4.11%) captures only the coupon part, which is why it sits below the 5% YTM.

A buyer paying the premium price of $1,028.29 gets the same $40 coupons. However, they receive only $1,000 at maturity, a $28.29 shortfall that drags their total return down to 3%. That is why someone who pays up for a high-coupon bond when rates have fallen does not really earn the coupon rate. They earn roughly the lower market yield.

The price-yield curve is not a straight line

Look at the dollar changes from par. A one-point drop in yield (4% to 3%) raised the price by $28.29. A one-point rise (4% to 5%) lowered it by $27.23. The gain from falling yields is larger than the loss from rising yields of the same size. This property is called convexity. Plotted on a chart with yield on the horizontal axis and price on the vertical, the line slopes downward and bows outward toward the origin rather than running straight. The effect is small for short bonds and small yield moves, and grows with maturity and with larger yield changes.

How far the price moves: maturity and coupon

The direction of the relationship holds for any standard fixed-rate bond. The size of the move does not. Keep the same 4% coupon but extend the maturity to ten years. At a 5% market yield, the price falls to about $922.78, a decline of roughly 7.7% from par. The three-year bond lost about 2.7%.

Longer bonds move more because more of their cash flows sit far in the future, and distant cash flows are discounted more heavily by a change in yield. A one-point yield change applied over ten years compounds into a much larger present-value effect than the same change over three years.

Coupon size matters too. A bond with a low coupon receives a larger share of its total value from the final principal payment, which is the most distant cash flow. That makes it more rate-sensitive than a high-coupon bond of the same maturity. Zero-coupon bonds, which pay everything at maturity, are the most sensitive for a given maturity. The standard measure of this sensitivity is duration. Approximately, a bond’s price changes by its duration (in years) times the change in yield, in the opposite direction.

What moves yields in the first place

Price and yield move together by definition, so the real question is what pushes the market yield on a bond up or down. Four broad factors drive it.

Prevailing interest rates. When the Federal Reserve raises or lowers its policy rate, yields across the economy tend to follow. That changes the return investors require from existing bonds, which is why bond prices fall when interest rates rise.

Inflation expectations. Fixed coupons lose purchasing power when inflation rises, so investors demand higher yields to compensate. Inflation concerns also raise the chance of Fed rate increases. Both effects push yields up and existing bond prices down. When inflation expectations ease, the process runs in reverse.

Credit quality. The greater the perceived chance that an issuer misses payments, the higher the yield investors require and the lower the price. A bond whose issuer is downgraded can fall in price even if general interest rates do not move at all.

Time to maturity. Longer-term bonds often carry higher yields than shorter-term bonds, because lenders tie up money longer and face more uncertainty about inflation and rates. Plotting yields against maturity for one issuer produces the yield curve. It inverts when shorter maturities yield more than longer ones, a sign the market expects different near-term rates than over the longer horizon.

Supply and demand also play a role. Heavy new issuance can push yields up as sellers compete for buyers. A rush toward safe assets can push yields on government debt down.

Exceptions and limits that change the answer

The inverse relationship is exact for a fixed-rate bond at a given moment. Several situations change what it means for an investor.

Holding to maturity. If you keep a bond until it matures and the issuer pays as promised, you receive exactly the coupons and face value set at purchase. A drop in market price in the meantime is a loss only if you sell. The real cost is opportunity cost: your money is earning the old, lower rate while new bonds pay more.

Floating-rate bonds. Their coupons reset periodically to a reference rate. Because the cash flows adjust as rates change, the price tends to stay much closer to par than a fixed-rate bond’s price would. The inverse relationship is weak because the coupon is not fixed.

Inflation-protected bonds. Treasury Inflation-Protected Securities (TIPS) adjust their principal with the Consumer Price Index. Their quoted yield is a real (after-inflation) yield. The inverse price-yield relationship still applies, but to that real yield, so their prices react to changes in real rates rather than to inflation surprises in the same way as ordinary Treasuries.

Callable bonds. When rates fall, an issuer may redeem a callable bond early and refinance more cheaply. Buyers know this, so the price of a callable bond tends to rise less than a comparable non-callable bond when yields drop. The upside is capped near the call price.

Credit-driven moves. A yield rise caused by worsening credit is not the same as one caused by higher market rates. In the second case, the bond’s cash flows are as secure as before. In the first, the chance of receiving them has fallen, and the higher yield is compensation for risk that may not be paid out.

Bond funds. A bond fund holds many bonds and keeps replacing them as they mature, so the fund itself never matures and never pulls back to a par value. When yields rise, the fund’s share price generally falls, and there is no maturity date at which the loss is guaranteed to reverse. The benefit is that maturing holdings are reinvested at the higher yields, which raises the fund’s income over time.

Are high yields good for bonds?

It depends on your position.

For a new buyer, higher yields mean bonds are cheaper relative to their cash flows. You lock in a higher return from the price you pay.

For an existing holder, rising yields mean the market value of your bonds has fallen. You still collect the coupons you bought, but selling now would mean taking a loss.

A high yield on one particular bond compared with others usually signals higher risk rather than a better deal. High-yield (junk) bonds pay more because their issuers are more likely to default. For investors whose priority is preserving capital, a lower yield on a higher-quality issuer may be the more suitable choice.

FAQs

The Bottom Line

Anyone who owns or plans to buy bonds should expect prices and yields to move in opposite directions, with longer and lower-coupon bonds moving the most. New buyers gain from higher yields, while existing holders see market value fall but still collect promised payments if they hold to maturity. Bond funds offer no such maturity date, and an unusually high yield on one bond usually signals higher risk.