Key takeaways
- Price and yield move inversely by construction. Duration says how much.
- YTM assumes reinvestment at the YTM itself, which is why realized return usually differs.
- Duration is linear and convexity corrects it. The error grows with the size of the yield move.
- Long maturity and low coupon both lengthen duration and raise rate sensitivity.
- Callable bonds have truncated upside, so yield to call is usually the more relevant figure.
Price is discounted cash flow
A plain bond’s value is the present value of coupons and principal discounted at the market yield for comparable cash flows. When required yield rises above the coupon rate, price generally falls below face value. When yield falls below the coupon, price generally rises.
Yield measures answer different questions
Coupon rate is coupon divided by face value. Current yield is annual coupon divided by market price. Yield to maturity is the single discount rate that equates scheduled cash flows with price, assuming the bond is held and payments occur as modeled.
Duration converts time into rate sensitivity
Macaulay duration is the present-value-weighted timing of cash flows. Modified duration approximates the percentage price change for a small yield move. DV01 translates that sensitivity into dollars for a one-basis-point move.
Know what the simple model omits
Credit spreads, default, embedded calls, accrued interest, taxes, liquidity and large nonlinear yield moves can dominate a real bond result. Convexity improves the approximation for larger moves. But it does not remove credit or call risk.
Price and yield move in opposite directions by construction
A bond's coupon is fixed at issue. If market yields rise, an existing bond paying the old coupon is less attractive. So its price falls until its yield to maturity matches what is newly available. The inverse relationship is not a market behaviour that might change. It is arithmetic. What varies is how much the price moves for a given yield change, and that is what duration measures.
Yield to maturity assumes things that rarely all hold
YTM is the single discount rate that equates the bond's price with its remaining cash flows. It assumes the bond is held to maturity, every payment is made, and every coupon is reinvested at the YTM itself. The last assumption is the least realistic, because reinvestment happens at whatever rates prevail. YTM is therefore an excellent comparison tool between bonds and an imperfect prediction of realized return.
Duration is a sensitivity, and convexity corrects it
Modified duration approximates the percentage price change for a one-percentage-point change in yield. Because the price-yield relationship is curved instead of straight, that linear approximation is accurate for small moves and increasingly wrong for large ones. Convexity measures the curvature and improves the estimate. For a typical bond convexity is positive, which means duration overstates the loss when yields rise and understates the gain when they fall.
What lengthens and shortens duration
Longer maturity increases duration. A higher coupon shortens it, because more of the value is returned sooner. A lower yield lengthens it. So a long-dated low-coupon bond is the most rate-sensitive instrument in a conventional portfolio, and why a short-dated high-coupon bond barely moves. Duration, not maturity, is the variable to manage when the concern is interest-rate risk.
Current yield, yield to maturity and yield to call differ
Current yield divides the annual coupon by the price and ignores any gain or loss to maturity. So it overstates return on a premium bond and understates it on a discount. Yield to call assumes redemption at the first call date and price. For a callable bond trading above par, yield to call is usually the more conservative and more relevant figure, which is why the lower of the two is often quoted.
Call features cap the upside
An issuer will call when it is advantageous to refinance, which is precisely when yields have fallen and the bondholder would otherwise have a gain. This truncates the price appreciation of a callable bond and gives it negative convexity in the region near the call price. The compensation is a higher yield. Whether that compensation is adequate is the judgement a buyer makes.
Credit risk is separate from rate risk and behaves differently
Duration describes sensitivity to the general level of rates. Credit spread describes compensation for the possibility of default. The two can move in opposite directions: in a flight to quality, government yields fall while credit spreads widen. So a corporate bond may lose value even as rates decline. Treating a corporate bond's yield as if it were a government yield plus a constant misses this entirely.
Accrued interest, day counts and quoting conventions
Bonds are typically quoted clean, without accrued interest, and settled dirty, with it added. Different markets use different day-count conventions, which changes the accrued figure and slightly changes yield calculations. These conventions are not academic details: they determine the amount that actually changes hands and are a common source of disagreement between a modeled and a quoted price.
Worked with real numbers
What this looks like in the bond price calculator
The guidance above is easier to judge against figures. Using the bond price calculator worked example, moving yield to maturity from 4.0% to 8.0% changes the estimated bond price from $796 to $1,082.
| Yield to maturity | Estimated bond price | Current yield |
|---|---|---|
| 4.0% | $1,082 | 4.6% |
| 5.0% | $1,000 | 5.0% |
| 6.0% | $926 | 5.4% |
| 7.0% | $858 | 5.8% |
| 8.0% | $796 | 6.3% |
Open the Bond Price Calculator to use your own numbers →
The inputs behind those figures
| Input | Value | Definition |
|---|---|---|
| Face value | $1,000 | Enter the face value for this scenario. |
| Annual coupon rate | 5.0% | Enter the annual coupon rate for this scenario. |
| Yield to maturity | 6.0% | Enter the yield to maturity for this scenario. |
| Years to maturity | 10.0 years | Enter the years to maturity for this scenario. |
| Payments per year | 2 | Enter the payments per year for this scenario. |
What goes wrong
Common mistakes
Each of these produces an answer that looks reasonable, which is why they survive review. To catch them in bond price, yield and duration explained, rerun the bond price calculator with a different assumption and check whether the result moves in the direction the guidance predicts, since an error that survives that test is usually in one of the inputs and not in the arithmetic.
| The mistake | Why it misleads | Do this instead |
|---|---|---|
| Comparing bonds on current yield | It ignores the pull to par, overstating return on premium bonds and understating it on discounts. | Compare on yield to maturity, and on yield to call as well for callable bonds. |
| Using maturity as a proxy for interest-rate risk | Coupon and yield also affect sensitivity. Two bonds of equal maturity can have quite different durations. | Compare modified duration, and use convexity for large yield moves. |
| Assuming a callable bond will run to maturity | Issuers call when refinancing is favourable, which caps the price gain exactly when you would have had one. | Evaluate on the lower of yield to maturity and yield to call. |
| Treating a corporate yield as a government yield plus a fixed spread | Spreads widen in stress, so credit and rate risk can move in opposite directions. | Model rate sensitivity and credit spread separately. |
People also ask
Frequently asked questions
Why do bond prices fall when yields rise?
Existing fixed cash flows become less valuable when new market yields are higher.
Is YTM guaranteed?
No. It depends on scheduled payments, reinvestment assumptions, holding to maturity and no default or call disruption.
If I hold to maturity, does price movement matter?
Not for the cash you receive, assuming no default: you get the coupons and the par value regardless. It matters if you might sell early, if the position is marked to market for reporting or collateral, or if you want to compare against reinvesting at current rates. Opportunity cost is real even when realized loss is not.
What does a duration of 7 mean?
Roughly a 7% price fall for a one-percentage-point rise in yield, and a similar rise for a fall. It is an approximation that is good for small moves and increasingly optimistic about losses for large ones, because positive convexity means the actual loss is smaller than the linear estimate.
Why did my bond fund lose money when rates rose?
A fund holds bonds and marks them at market. When yields rise, existing bonds fall in price. So the fund's value falls. Unlike an individual bond, a fund has no fixed maturity date at which it returns par, though it does gradually reinvest at the new higher yields, which is what eventually recovers the loss over a period related to the fund's duration.
Should I buy individual bonds or a bond fund?
Individual bonds give a known maturity and a known cash flow if held, plus control over credit selection, at the cost of concentration and the work of laddering. Funds give diversification and liquidity with no maturity date. The choice depends on whether you need a specific amount on a specific date, which favours individual bonds or a ladder.
How does inflation affect a bond?
It erodes the real value of fixed coupons and principal, and rising inflation expectations usually raise nominal yields, which lowers prices. Inflation-linked bonds adjust principal or coupon with an index and so behave very differently, trading primarily on real , not nominal yields.
Which input moves the estimated bond price most in the bond price calculator?
Ranked by how far each moves the estimated bond price across the range tested: face value ($185, 20%), annual coupon rate ($149, 16%), yield to maturity ($142, 15%) and years to maturity ($33, 3.6%).
If I double face value in the bond price calculator, does the estimated bond price double?
Doubling it from $1,000 to $2,000 takes the estimated bond price from $926 to $1,851, which is 2.00 times the worked-example figure. So the result scales almost exactly in proportion. Halving it to $500 gives $463.