Bond prices and yields move in opposite directions because a bond’s coupon payments are fixed at the time it’s issued. When market interest rates change, the only way a bond can adjust to stay competitive is through its price. If new bonds offer higher rates, existing bonds must drop in price to attract buyers. If new bonds offer lower rates, existing bonds become more valuable and their prices rise. This inverse relationship is baked into the math of how bonds work.
Fixed Coupons Are the Core Reason
When you buy a bond, the issuer promises to pay you a set amount of interest (called the coupon) at regular intervals, plus your principal back at maturity. A £1,000 bond with a 5% coupon pays £50 per year, no matter what happens in the broader market. That number never changes.
The problem arises when market interest rates shift after the bond is issued. Suppose rates rise to 6%. New bonds now pay £60 per year on the same £1,000 investment. Your bond, still paying £50, looks less attractive by comparison. No rational buyer would pay full price for it. So its market price has to fall until the £50 annual payment, relative to the lower purchase price, effectively offers a competitive return. The reverse works the same way: if rates drop to 4%, your 5% coupon is now better than what’s available, and buyers will bid the price above £1,000 to get it.
A Simple Example With Real Numbers
Consider a bond with a face value of £1,000 and a 5% coupon, paying £50 per year. If the market interest rate is also 5%, the bond trades right at £1,000, its par value. Now watch what happens when rates move.
If the market rate falls to 4%, the bond’s price rises to roughly £1,250. That’s because £50 divided by 0.04 equals £1,250. The bond now trades at a premium to par. Investors are willing to pay more because that 5% coupon is better than the 4% they’d get elsewhere.
If the market rate rises to 6%, the bond’s price drops below £1,000, trading at a discount. New bonds pay more, so yours has to cheapen to compete. The price adjusts until the yield a buyer would earn matches what’s available in the current market.
What “Yield” Actually Means Here
Yield is not the same thing as the coupon rate, even though people sometimes use the terms loosely. The coupon rate is the fixed interest payment expressed as a percentage of the bond’s face value. Yield to maturity is the total return you’d earn if you bought the bond at its current market price and held it until it matures, accounting for all coupon payments plus the difference between what you paid and the face value you’ll receive at the end.
A Wharton School finance textbook illustrates this with a two-year bond carrying a 5% coupon. If that bond sells for $914.06 instead of its $1,000 face value, the yield to maturity works out to about 9.95%. The buyer gets the same $50 annual coupons, but because they paid less upfront, their effective return is much higher than the stated 5% coupon. This is the inverse relationship in action: the price dropped, so the yield climbed.
When a bond trades at par, the coupon rate and yield to maturity are identical. The moment the price moves away from par, they diverge.
Why This Matters When Interest Rates Change
Central bank decisions directly affect this dynamic. When a central bank raises its benchmark rate, newly issued bonds come with higher coupons to reflect the new rate environment. Existing bonds with lower coupons lose value on the secondary market. When rates are cut, the opposite happens, and older bonds with higher coupons become prized.
This is why bond portfolios can lose money even though bonds are considered “safe” investments. You’re guaranteed your principal back if you hold to maturity, but if you need to sell before then, the market price might be lower than what you paid. The longer you have until maturity, the more sensitive your bond’s price is to rate changes, because there are more years of below-market (or above-market) coupon payments baked into the valuation.
How Duration Measures Price Sensitivity
Not all bonds react equally to rate changes. A bond maturing in 2 years barely flinches when rates shift, while a 30-year bond can swing dramatically. Duration is the standard measure of this sensitivity. It estimates the percentage change in a bond’s price for each 1% change in interest rates.
A bond with a duration of 7 years, for example, would lose roughly 7% of its value if interest rates rose by 1 percentage point, and gain roughly 7% if rates fell by the same amount. Longer maturities and lower coupon rates both increase duration, making a bond more reactive to rate changes. This is why long-term government bonds are sometimes more volatile than people expect from a “safe” investment.
The Relationship Is Not Perfectly Straight
Duration treats the price-yield relationship as a straight line, which works well for small rate changes. In reality, the relationship is curved. This curvature is called convexity, and it means that price gains from falling yields are slightly larger than price losses from rising yields of the same magnitude.
Think of it this way: as yields drop lower and lower, each additional decline pushes the price up by a slightly bigger amount. And as yields rise higher, each additional increase pushes the price down by a slightly smaller amount. For everyday investors holding typical bonds, convexity is a minor detail. It becomes more important for large portfolios or bonds with very long maturities, where even small curvature effects can translate into meaningful dollar amounts.
What This Means for Bond Investors
Understanding the inverse relationship helps you anticipate what happens to your bonds in different rate environments. If you expect rates to fall, longer-duration bonds will benefit the most because their prices are the most sensitive to declining yields. If you expect rates to rise, shorter-duration bonds offer some protection because their prices won’t drop as sharply, and they’ll mature sooner, letting you reinvest at the new higher rates.
The key takeaway is mechanical, not speculative: a bond’s price is simply the present value of its future cash flows, discounted at the current market rate. When that discount rate goes up, the present value goes down. When it goes down, the present value goes up. Every bond in every market, from U.S. Treasuries to corporate debt, follows this same fundamental math.