Insights
How Interest Rates Affect Bond Prices
Alphanume Team · May 29, 2026
The inverse relationship, quantified.
The relationship between interest rates and bond prices is one of the most consequential mechanics in fixed income — and one of the most frequently misunderstood. When market yields rise, the price of an existing bond falls. When yields fall, prices rise. The direction is always opposite, and the magnitude is not random: it is governed by the bond's maturity, coupon, and yield level in ways that are precisely calculable. Use the bond pricing calculator to see the numbers move in real time as you adjust the inputs. This post explains why the inverse relationship exists, how large the moves are, and where the relationship breaks down.
Why interest rates and bond prices move in opposite directions
A bond promises a fixed stream of cash flows: coupon payments at regular intervals and the return of face value at maturity. Those coupon payments are set at issuance and do not change. What changes is the rate at which the market discounts future cash flows — and that rate is driven by prevailing yields.
Suppose you hold a bond paying a 5% annual coupon on a $1,000 face value — $50 per year. If new bonds of similar credit quality are issued today at 7%, your bond's fixed $50 coupon looks unattractive by comparison. Buyers will only purchase your bond at a discount steep enough to bring its effective yield up to the market rate of 7%. The coupon has not changed; the price has to fall to make the math work. Conversely, if new bonds now yield only 3%, your 5% coupon is generous, and buyers will bid the price above par until the effective yield compresses to match the market.
This is not a quirk or a sentiment effect. It is arithmetic. A bond's price is the present value of its cash flows, and the discount rate is the market yield.
The discounting mechanism
For a bond paying coupon C annually for n years with face value F, the price at yield y is:
P = C / (1+y) + C / (1+y)2 + … + C / (1+y)n + F / (1+y)n
Every term in that sum is divided by a power of (1 + y). Raise y and every term shrinks — the price falls. Lower y and every term grows — the price rises. There is no scenario in which raising the discount rate increases the present value of a fixed cash flow stream. The inverse relationship is baked into the formula itself.
What makes fixed income interesting is that the sensitivity of that price to a change in y is not uniform. It depends on how long the cash flows extend into the future and how large the early coupons are relative to the final payment.
Duration and convexity: the size of the move
Duration and convexity are the tools that quantify how much a bond's price moves for a given change in yield. Modified duration gives the first-order (linear) approximation:
ΔP / P ≈ −Dmod × Δy
where Dmod is the modified duration in years and Δy is the change in yield. A bond with a modified duration of 7 loses approximately 7% of its value for a 100 basis-point rise in yield. Convexity adds a second-order correction — a positive adjustment that means the actual price decline is slightly less than the linear estimate for large moves, and the actual price gain is slightly more.
Two structural features drive duration higher and therefore amplify price sensitivity:
- Longer maturity. Cash flows further in the future are discounted through more compounding periods, making them more sensitive to the discount rate. A 30-year bond has far more duration than a 2-year note.
- Lower coupon. A larger share of the bond's value comes from the terminal face-value payment, which sits at the far end of the maturity. A zero-coupon bond has duration equal to its maturity — the most extreme case.
A worked example at multiple yield levels
Consider a 10-year bond, $1,000 face value, 5% annual coupon ($50/year). Its price at a range of yields:
| Yield | Price | Change from par |
|---|---|---|
| 3% | $1,170.60 | +17.1% |
| 4% | $1,081.11 | +8.1% |
| 5% | $1,000.00 | 0.0% |
| 6% | $926.40 | −7.4% |
| 7% | $859.53 | −14.0% |
Notice the asymmetry: the price gain from a 200 bp yield drop (+17.1%) exceeds the price loss from a 200 bp yield rise (−14.0%). That is convexity at work — a desirable property that investors pay for in the form of accepting a slightly lower yield on high-convexity bonds.
A zero-coupon bond with the same 10-year maturity would move far more dramatically. Its modified duration equals 10 / (1 + y), roughly 9.5 at a 5% yield, versus approximately 7.7 for the coupon bond. Every basis point of yield change hits harder.
Reinvestment risk versus price risk
Rising rates are not uniformly bad for bondholders. A buy-and-hold investor who plans to reinvest the coupons benefits from higher rates: each coupon can be reinvested at a better rate, compounding wealth faster over the holding period. This is reinvestment risk — the uncertainty about the rate at which intermediate cash flows will be reinvested.
Price risk and reinvestment risk pull in opposite directions. When rates rise, price falls but reinvestment income rises; when rates fall, price rises but reinvestment income falls. Duration measures the point in time at which these two effects exactly offset — the horizon at which the investor is immunized against a parallel shift in yields. Pension funds and insurers exploit this directly, matching asset duration to liability duration so that rate changes do not change their net funded position.
Market rates versus credit spreads
Not every yield change has the same source, and the source matters. The yield on a corporate bond is the sum of the risk-free rate (read from the yield curve) and a credit spread that compensates for default risk. A 50 bp rise in a bond's yield could reflect a 50 bp rise in the underlying risk-free rate, a 50 bp widening of its credit spread, or some combination.
The price impact on the bond is the same either way — both a rate move and a spread move enter through the discount rate in the pricing formula. But the implications for a portfolio differ sharply. A rate-driven move tends to affect all investment-grade bonds simultaneously; a spread-driven move is idiosyncratic to the issuer or its sector. Duration hedges rate risk; it does not hedge credit spread risk. Managing the two requires separate tools and separate analyses, and conflating them is one of the more common errors in fixed-income portfolio management.