Why Bond Prices Fall When Interest Rates Rise
The most counterintuitive line in finance, explained with a bond you can price on a calculator. Includes the full discounting arithmetic, a duration shortcut, and why bond funds behave differently from bonds held to maturity.
"Bond prices fall when interest rates rise" is repeated so often that it stops being explained. The result is a rule people recite and cannot use, because the rule only makes sense once you can see a bond's price being computed. This guide does that computation twice, from first principles, with numbers you can check yourself.
What a bond actually is
A bond is a loan with three defining features:
- Face value (also called par) — the amount repaid at maturity. In the standard example that is $1,000.
- Coupon — the fixed interest payment, expressed as an annual percentage of face value. A 5% coupon on $1,000 pays $50 every year, without exception.
- Maturity — the date the $1,000 comes back.
The coupon is the crux of everything that follows. It is written into the contract and does not change for the life of the bond. Prices are quoted as a percentage of face value, so a bond trading at "93.20" costs $932 for each $1,000 of face value.
Why the price has to move
Suppose you own the 5% bond described above and you are happy with $50 a year. Now suppose new bonds with identical credit quality and nine years to run are being issued with a 6% coupon, paying $60 a year. Nobody will buy your bond at $1,000 while a better contract is available at the same price.
The only way your bond can compete is on price. Its cash flows are fixed, so the price is the single variable that can adjust. It falls until the total return from buying your bond matches the 6% available elsewhere. The reverse happens when rates fall: your above-market coupon becomes desirable and the price rises above $1,000.
The one-sentence version. A bond's price is whatever makes its fixed stream of payments produce the yield currently available on comparable bonds. Rates up, price down. It is arithmetic, not sentiment.
Worked example: pricing the same bond twice
Take a bond with a $1,000 face value, a 5% annual coupon ($50), and nine years remaining. To find its price at any market yield, discount every future payment back to today at that yield and add the results:
Price = Σ [ $50 ÷ (1 + y)t ] for t = 1 to 9 + $1,000 ÷ (1 + y)9
Case A — market yield rises to 6%. The discount factors are 1.061 through 1.069. Discounting the nine $50 coupons gives $340.089, and the $1,000 principal returned in year nine is worth $1,000 ÷ 1.689479 = $591.898. Total price = $931.99.
Case B — market yield falls to 4%. The same two sums with 1.04t: the coupons are worth $371.767 and the principal $1,000 ÷ 1.423312 = $702.587. Total price = $1,074.35.
| Scenario | Market yield | Coupons (PV) | Principal (PV) | Price | Change |
|---|---|---|---|---|---|
| Rates fall 1 point | 4% | $371.767 | $702.587 | $1,074.35 | +7.4% |
| Baseline (par) | 5% | $355.391 | $644.609 | $1,000.00 | — |
| Rates rise 1 point | 6% | $340.089 | $591.898 | $931.99 | −6.8% |
Three things are worth noticing. First, the loss on the 6% case is not a default: the borrower paid every coupon on time and will still repay $1,000 at maturity. The price changed because the market's rate changed. Second, the asymmetry: a one-point fall in rates produced a 7.4% gain while a one-point rise produced a 6.8% loss, which is the mild "positive convexity" that bond mathematics always carries. Third, at maturity the bond converges to $1,000 regardless of the path in between, provided you can hold it there.
Duration: the shortcut worth memorising
Repricing a bond cash flow by cash flow is tedious, so the market uses duration, which is the weighted average time until the bond's cash flows arrive. For the nine-year 5% bond at a 6% yield, that weighted average is 7.40 years (Macaulay duration), and dividing by 1 + y gives the modified duration of 6.98.
Modified duration converts directly into an approximate price change:
% price change ≈ − modified duration × change in yield
For a one-point rise: −6.98 × 0.01 = −6.98%. The exact answer computed above was −6.80%. The shortcut overshoots slightly because it is a linear approximation of a curved relationship, but it is close enough to size a risk in your head — and it explains why a 30-year bond, with a modified duration near 15, can lose roughly 15% of its value when yields rise one percentage point, while a two-year bond loses about 2%.
Why bond funds feel different from individual bonds
This is the source of most of the confusion. An individual bond has a maturity date, a known repayment date, and a known face value — the price you see in the meantime is bookkeeping unless you sell. A bond fund never matures. It holds a rolling portfolio and maintains a roughly constant duration by construction. There is no date on which it hands you a defined sum.
What follows from that is concrete and often unstated: a fund's price decline when rates rise is permanent in the sense that the fund does not converge back to a former price. What recovers your position is the higher yield on the newly purchased bonds inside the fund. Over a holding period roughly equal to the fund's duration, the extra income from higher rates has historically offset the price decline — but that is a statement about income over time, not about the price chart, and it requires staying invested for the period.
Two risks the headlines merge
| Risk | Cause | What it does to price |
|---|---|---|
| Interest rate risk | Market yields change | Moves the price up or down, scaled by duration |
| Credit risk | Doubts about repayment | Moves the price down, and can be permanent |
These are unrelated. A US Treasury bond has essentially no credit risk and plenty of rate risk; a short-dated bond from a shaky issuer can have little rate risk and severe credit risk. News about "bonds falling" rarely distinguishes them, and the distinction is the whole question of whether the loss is recoverable.
What this means for a portfolio
Bonds occupy the defensive slot in most portfolios because they usually move differently from stocks and because the income is contractual. The rate arithmetic above is the price of that steadiness: the same fixed coupons that make bonds predictable make their prices sensitive to a variable nobody controls. That trade-off — lower expected return, lower expected volatility, real sensitivity to rates — is exactly what the asset allocation guide works through numerically.
The takeaway
Bond prices fall when rates rise because the coupon is fixed and the price is not. A one-point increase in yield costs roughly 7% on a nine-year bond and roughly 15% on a thirty-year bond, and that loss is a change in the market's discount rate, not a failure of the borrower. The number that tells you how much is duration; the number that tells you whether it matters is your holding period. For how these prices produce the long-run returns you plan around, the compound growth calculator will run your own scenarios, and the full set of guides is on the articles page.
This guide is general educational information, not financial advice, and it recommends no specific security. The bond priced above is a simplified illustration with annual coupons, a single flat yield curve, and no transaction costs, taxes, or default; real bonds pay semi-annually and trade with credit spreads, so figures will differ. Duration is an approximation that becomes less accurate for large yield changes and for bonds with embedded options. Bond investing involves risk, including the risk of loss. Consider your full circumstances and consult a licensed professional before making investment decisions.
