Understanding markets · Rates & bonds
Bond Prices and Interest Rates: Why Bonds Fall When Rates Rise
A bond that has already been issued pays a fixed coupon. When market interest rates rise, new bonds pay more, so the old bond can only be sold at a lower price – low enough that its yield matches the new rate level. That is why bond prices and yields always move in opposite directions.
How far the price falls depends mainly on the time to maturity: the longer a bond runs, the more sensitive it is. That sensitivity is called duration.
By Sofia ·
The mechanism: fixed coupon, moving price
A bond is a loan you make to a government or company. In return you receive a fixed interest payment each year, the coupon, and get the face value back at maturity. Coupon and repayment are fixed at issue. What changes every day is the price at which the bond trades in the market.
Say you hold a bond with a 2% coupon. Rates then rise, and comparable new bonds pay 4%. No buyer will pay full face value for your 2% bond when the same money can earn 4%. It only sells at a discount – precisely large enough that the buyer also earns about 4% a year over its remaining life, from the low coupon plus the price gain as it is repaid at face value.
Coupon
The fixed interest, based on face value. It does not change over the life of a conventional fixed-rate bond.
Yield
The return a buyer earns to maturity at today’s price. It moves with the market and is the number quoted in the news as a government bond’s “rate”.
Price
Quoted as a percentage of face value. It is the dial through which an old bond’s yield adjusts to the new rate level.
The relationship works both ways. When rates fall, an old bond’s fixed coupon becomes more attractive and its price rises above face value. That is why bonds gain when rates come down.
Worked example: what a rise from 2% to 4% costs
A bond’s fair price is the sum of all its future payments, discounted at the current market yield. When the yield rises, every future payment is discounted more heavily and the price falls.
Worked example · illustrative, not market data
- Annual coupon
- $20
- Price at a 2% market yield
- $1,000
- Present value of the ten coupons at 4%
- about $162
- Present value of the repayment at 4% ($1,000 ÷ 1.04¹⁰)
- about $676
- New price at a 4% market yield
- about $838
- Price change
- about −16%
A buyer now pays about $838 and still receives $20 a year plus $1,000 at the end. The low coupon plus the roughly $162 price gain to maturity add up to about 4% a year – exactly the new market level.
| Time to maturity | Yield 2% → 3% | Yield 2% → 4% |
|---|---|---|
| 2 years | about −2% | about −4% |
| 10 years | about −9% | about −16% |
| 30 years | about −20% | about −35% |
The table shows the key point: the same rate rise hits a 30-year bond almost ten times as hard as a two-year one. Short-dated bonds are therefore much less volatile – but often pay a lower yield.
Duration: the measure of interest rate risk
Duration sums up in one number how sensitive a bond is to changes in rates. Modified duration tells you approximately how many percent the price changes when the yield rises or falls by one percentage point.
- Rule of thumb: price change in % ≈ −modified duration × change in yield in percentage points.
- Our 10-year 2% bond has a modified duration of just under 9, so one percentage point more yield costs about 9% in price.
- The longer the maturity and the lower the coupon, the higher the duration. A zero-coupon bond has the highest duration for a given maturity.
- The rule is a linear approximation. For large rate moves, the price falls a little less and rises a little more than calculated. That curvature is called convexity.
Funds and ETFs have a duration too
Bond funds and bond ETFs report their average duration in the factsheet. A long-dated government bond ETF with a duration of about 17 loses roughly 17% on a one-point rise in yields by the rule of thumb – a risk many underestimate when they hear “safe bonds”.
Holding to maturity: does the loss go away?
If you hold an individual bond to the end, you get face value back – provided the issuer pays. The interim price loss then disappears, because the price converges to face value at maturity. Economically it is still real: you earned 2% for years while the market offered 4%. The price drop simply makes those forgone returns visible straight away.
If you have to sell before maturity, you lock in the loss. Bond funds and ETFs have no fixed maturity date, because they keep replacing maturing bonds with new ones. In exchange, they reinvest coupons and repayments at the now higher yields. As a rough rule of thumb, the higher income offsets a one-off rise in rates over a period of about the fund’s duration – further rate moves shift that calculation.
Why bonds can fall even though rates are “already high”
What drives the price is not the level of rates but the change in yield since you bought. If you bought a long bond when rates were low, you keep losing as long as yields keep rising – even if they are already higher than before. On top of that, central banks mainly steer short-term rates. Long-term yields are set in the market and can rise even while the central bank holds or cuts its policy rate – for example because investors expect higher inflation, more government bonds are being issued or buyers demand a bigger premium for lending long.
The yield curve: short and long rates
The yield curve plots the yields of bonds from the same issuer, usually a government, across maturities. Its shape shows what the market expects for policy rates, growth and inflation.
Normal (upward sloping)
Longer maturities yield more than shorter ones. Investors want extra return for tying up money longer. This is the usual state.
Flat
Short and long yields are close together. Often a transition, when central banks are raising rates or the market expects cuts.
Inverted
Short maturities yield more than long ones. The market expects policy rates to fall, often because of a weaker economy. In the US an inverted curve has often preceded recessions, but it is an unreliable timing signal.
Besides maturity, the issuer’s creditworthiness drives the yield. Corporate bonds pay a risk premium over government bonds. That spread can widen in a crisis and push their prices down further – a separate risk on top of interest rate risk.
What rising yields mean for stocks and options
Bond yields are the yardstick every other investment is measured against. When they rise, they affect stocks in two ways: safe alternatives become more attractive, and future profits are discounted at a higher rate and are worth less today. More in our guide what moves stock prices.
Growth stocks, whose expected profits lie far in the future, are especially sensitive. They behave much like long bonds with high duration: a large part of their value today depends on the discount rate. Companies with high current profits and payouts are usually less affected, although dividend stocks compete directly with higher bond yields.
Rho: the rate sensitivity of options
For options, rho measures how much the price changes when the risk-free rate rises by one percentage point. Calls have positive rho, puts negative rho: higher rates make calls slightly more expensive and puts slightly cheaper, because holding cash instead of stock earns more interest. Our guide the Greeks explained shows where rho sits next to delta, gamma, theta and vega.
Worked example · illustrative, not market data
- 1-month call, assumed rho
- about 0.04
- Price effect per contract (100 shares)
- about +$4
- 1-year call, assumed rho
- about 0.45
- Price effect per contract (100 shares)
- about +$45
For short-dated options, rho is usually negligible; price moves and volatility dominate. For long-dated options such as LEAPS it becomes noticeable. In practice a rate rise also works indirectly through the stock price and implied volatility – often far more strongly than through rho itself.
Central bank decisions and inflation data are therefore high-volatility dates for options traders too. Our implied volatility guide explains how expected swings show up in option prices, and what drives exchange rates covers how rates move currencies.
Three myths about bonds and interest rates
“Bonds are risk-free.”
High-quality government bonds carry little default risk but real interest rate risk. Long maturities can lose double digits within months.
“Higher rates are good for my bonds.”
For bonds you already own, a rate rise is first of all a price loss. It is good for new money and for coupons that get reinvested at higher yields.
“When the central bank cuts, all bonds rise.”
Policy rate cuts mainly affect short maturities. Long yields can still rise if the market expects higher inflation or more government borrowing.
Frequently asked questions
Why do bond prices fall when interest rates rise?
Because an existing bond’s coupon is fixed. When new bonds offer higher rates, nobody buys the old bond at full price. Its price falls until its yield to maturity matches the new rate level.
How much does a bond fall when rates rise?
Modified duration tells you. As a rule of thumb, the percentage price change is roughly minus duration times the change in yield in percentage points. A bond with a duration of 9 loses about 9% when yields rise one percentage point.
Do I lose money if I hold the bond to maturity?
If the issuer pays, you get face value back at the end and the interim price loss disappears. Economically you still earned less than a new, higher-yielding bond would have paid. If you have to sell earlier, you realise the price loss.
Does this apply to bond ETFs as well?
Yes. Bond ETFs fall when yields rise in line with their average duration, shown in the factsheet. Because they have no fixed maturity date, they recover the loss over time only through the higher income from newly purchased bonds.
Which bonds are less sensitive to interest rates?
Bonds with a short time to maturity and a high coupon have a low duration and fluctuate less. Floating-rate bonds reset their coupon regularly and are barely rate-sensitive. In return, short maturities often offer a lower yield.
Why do growth stocks fall when yields rise?
Their value rests heavily on profits expected far in the future. When those are discounted at a higher rate, their value today drops sharply. Growth stocks therefore behave much like long-duration bonds.
How do interest rates affect option prices?
Directly through rho: rising rates make calls slightly more expensive and puts slightly cheaper. The effect is small for short-dated options and more noticeable for long-dated ones. Indirectly, rate changes usually matter more through the stock price and implied volatility.
Sources and context
The worked examples use round, fictional values and simplified assumptions (annual coupons, no costs, no default); they show the mechanism, not market data. This guide is educational and is not investment advice.