Bond Duration Explained: How Rate Changes Affect Bond Prices

The number behind the rule of thumb

The basic relationship is not controversial: when market interest rates rise, the prices of fixed-rate bonds fall. The SEC’s investor bulletin on interest rate risk states it directly and notes that the relationship applies to all bonds, including US Treasuries.

Duration turns that relationship into an estimate. Modified duration is the approximate percentage change in price for a one-percentage-point change in yield:

percentage price change ≈ -modified duration × change in yield

A bond with a modified duration of 5 is expected to fall about 5% if its yield rises from 4% to 5%, and rise about 5% if the yield falls to 3%. FINRA’s investor alert uses the same shorthand: a bond fund with a 10-year duration could drop about 10% if rates rise one percentage point, while a two-year duration fund could drop about 2%.

The estimate is a first-order approximation. It is useful because it is simple and comparable across bonds, and it is dangerous when treated as exact.

Macaulay, modified and effective

Three duration measures are common, and they answer different questions:

For a plain fixed-rate bond, modified duration is Macaulay duration divided by (1 + yield per period). For a zero-coupon bond, Macaulay duration equals maturity, because there is only one cash flow and it arrives at the end.

The distinction matters for the label. A 10-year zero-coupon bond has a Macaulay duration of 10 years and a modified duration close to 9.5 at a 5% yield. A 10-year coupon bond has a lower duration because coupons arrive along the way.

A worked example

Take a five-year bond with a 4% annual coupon, priced at par (100) when the yield is 4%. Its cash flows are 4, 4, 4, 4 and 104.

Discounting at 4% gives a price of 100. The present-value-weighted average time of the cash flows is a Macaulay duration of about 4.63 years. Dividing by 1.04 gives a modified duration of about 4.45.

Now raise the yield to 5%:

• Modified duration predicts a price change of -4.45%, or a price of about 95.55.
• The actual price, discounting the same cash flows at 5%, is about 95.67, a change of -4.33%.

The difference is convexity. The bond’s price-yield curve is not a straight line; duration is the tangent at 4%, and the curve bends away from the tangent as the yield moves. For a yield fall to 3%, the same logic produces an actual price of about 104.58, a gain of 4.58% against a duration estimate of 4.45%.

What moves duration

Duration is not fixed. It changes with the bond’s features and with the market:

• Maturity. Longer maturities generally mean higher duration, because more of the value is distant.
• Coupon. Higher coupons mean more cash arrives sooner, which lowers duration.
• Yield level. Higher yields discount distant cash flows more heavily, which lowers duration.
• Embedded options. Callable and mortgage-backed bonds can have cash flows that change with rates, so effective duration is used instead of modified duration. In some rate environments, these bonds can exhibit negative convexity.
• Floating rates. A floating-rate note resets its coupon, so its duration is typically very short, often close to the time to the next reset.

A portfolio’s duration is the market-value-weighted average of its holdings’ durations, which is why a fund with a 10-year duration behaves like a single 10-year-duration bond for small rate moves.

Where the shorthand fails

Duration is a local, linear measure. Three limits matter:

1. Large rate moves. The approximation error grows with the size of the yield change. Convexity is the correction term.
2. Credit and liquidity. A spread widening changes the discount rate for reasons unrelated to the policy rate. Duration tells you the price sensitivity, not the cause.
3. Cash-flow changes. For callable and mortgage-backed bonds, the cash flows themselves respond to rates. Modified duration assumes they do not; effective duration is the appropriate measure.

The SEC bulletin’s framing is useful: interest-rate risk is common to all bonds, and it is distinct from credit risk, inflation risk and liquidity risk. Duration isolates one of those risks and quantifies it approximately.

How to use it

For a quick comparison, duration is the right first number: a 2-year duration bond and a 10-year duration bond have very different exposure to a rate move, and the difference is visible without a pricing model.

For a decision, pair it with the yield, the credit quality, the maturity and the liquidity of the instrument. A high duration is not automatically bad; it is a larger exposure to a particular risk, and it may be intentional. What is rarely useful is treating a duration number as a prediction of total return. It is a sensitivity, not a forecast.