Bond Duration
Why Duration Matters
Interest rate risk is the single biggest source of price volatility for high-quality bonds. When the Federal Reserve raises or lowers rates, bond prices move — and duration tells you how much they’ll move.
Without understanding duration, you’re flying blind. Two bonds can have the same maturity but very different durations depending on their coupon rates. A zero-coupon bond maturing in 10 years has a duration of exactly 10 years. A 10-year bond paying a 6% coupon has a duration closer to 7.5 years — because you’re getting cash flows sooner, reducing your effective exposure to distant rate changes.
Types of Duration
There are several duration measures. The two you need to know are Macaulay duration and modified duration.
Macaulay Duration
Macaulay duration is the weighted average time until you receive a bond’s cash flows, where each cash flow is weighted by its present value. It’s measured in years and gives you the economic “center of gravity” of the bond’s payments.
Where t is the time period, PV(CFt) is the present value of the cash flow at time t, and the sum runs across all coupon payments and the final principal repayment.
Interpretation: A Macaulay duration of 6.5 years means the present-value-weighted average timing of all cash flows is 6.5 years from now. It’s a time measure, not a direct price sensitivity measure — that’s what modified duration handles.
Modified Duration
Modified duration converts Macaulay duration into a direct measure of price sensitivity. It tells you the percentage price change for a 1% change in yield.
Where YTM is the bond’s yield to maturity and n is the number of coupon payments per year (typically 2 for semiannual bonds).
Interpretation: A modified duration of 6.2 means the bond’s price will change approximately 6.2% for every 1 percentage point (100 basis points) move in yield. Rates up 1% → price down ~6.2%. Rates down 1% → price up ~6.2%.
Effective Duration
For bonds with embedded options — like callable bonds or convertible bonds — modified duration doesn’t work well because cash flows change as rates move. Effective duration accounts for this by measuring actual price changes under different rate scenarios rather than using a formula based on fixed cash flows.
Where P− is the price if yield falls by ΔY, P+ is the price if yield rises by ΔY, P0 is the current price, and ΔY is the yield change used in the scenario.
What Affects Duration
| Factor | Effect on Duration | Why |
|---|---|---|
| Longer maturity | Increases duration | Cash flows are spread further into the future, increasing sensitivity to rate changes. |
| Higher coupon rate | Decreases duration | Larger early cash flows pull the weighted average forward, reducing exposure to distant rate changes. |
| Higher yield to maturity | Decreases duration | Higher discount rates reduce the present value of distant cash flows more than near-term ones. |
| Zero coupon | Maximum duration | No interim cash flows — duration equals maturity. All rate sensitivity is concentrated at one point. |
| Call feature | Decreases effective duration | When rates fall, the bond is likely called, capping price appreciation and shortening the expected life. |
Duration in Practice — A Quick Example
Suppose you own a bond portfolio with a modified duration of 5.5 years and a market value of $1,000,000. If interest rates rise by 0.50% (50 basis points):
Your portfolio would lose approximately $27,500 in market value. If rates fell by 0.50%, you’d gain roughly the same amount — though the actual gain would be slightly larger due to convexity (the curvature of the price-yield relationship).
Duration vs. Maturity
Duration and maturity are related but not the same thing.
| Feature | Duration | Maturity |
|---|---|---|
| What it measures | Price sensitivity to interest rate changes | Time until the bond’s final payment |
| Accounts for coupons? | Yes — higher coupons reduce duration | No — maturity is the same regardless of coupon |
| For a zero-coupon bond | Duration = maturity | Same |
| For a coupon-paying bond | Duration < maturity (always) | Fixed at the stated date |
| Use in portfolio management | Used to manage interest rate risk | Indicates timeline but not risk exposure |
Two bonds with the same 10-year maturity can have very different durations. A 10-year Treasury bond paying a 2% coupon will have a higher duration (and more rate sensitivity) than a 10-year corporate bond paying a 6% coupon.
How Investors Use Duration
Portfolio risk management: Portfolio managers target a specific duration to control interest rate exposure. If you expect rates to rise, you shorten duration (shift to shorter maturities or higher coupons). If you expect rates to fall, you extend duration to magnify price gains.
Immunization: Pension funds and insurance companies match the duration of their bond portfolios to the duration of their liabilities. This “duration matching” ensures that changes in interest rates affect assets and liabilities equally, insulating the funded status from rate movements.
Comparing bonds: Duration lets you compare the rate sensitivity of different bonds on equal footing — regardless of their maturities, coupons, or structures.
Hedging: Duration is the foundation of bond hedging strategies. If you’re long a portfolio with duration of 7, you can short Treasury futures with equivalent duration to neutralize your interest rate exposure.
Key Takeaways
- Duration measures a bond’s price sensitivity to interest rate changes — higher duration means more price volatility when rates move.
- Modified duration tells you the approximate percentage price change for a 1% change in yield.
- Longer maturity increases duration; higher coupons and higher yields decrease it.
- Zero-coupon bonds have the highest duration for a given maturity (duration = maturity).
- Use effective duration for bonds with embedded options (callable, convertible) where cash flows aren’t fixed.
- Duration is a linear approximation — for large rate moves, pair it with convexity for accuracy.
Frequently Asked Questions
Is higher or lower duration better?
Neither is inherently better — it depends on your view and goals. Higher duration amplifies gains when rates fall but amplifies losses when rates rise. Lower duration provides more price stability. Conservative investors and those expecting rate hikes prefer shorter duration; those betting on rate cuts prefer longer duration.
What is a typical duration for a bond portfolio?
The Bloomberg U.S. Aggregate Bond Index — a common benchmark — has a duration of roughly 6-7 years. Short-term bond funds might have a duration of 1-3 years. Long-term Treasury funds can have durations of 15-20+ years. Your target depends on your risk tolerance and interest rate outlook.
Why does a zero-coupon bond have the highest duration?
Because there are no interim cash flows. All of the bond’s value is concentrated in the single payment at maturity, so 100% of the present value is exposed to rate changes at that distant date. A coupon-paying bond distributes cash flows over time, pulling duration lower than maturity.
How is duration different from convexity?
Duration is the first-order (linear) measure of price sensitivity. Convexity is the second-order (curvature) measure. Duration tells you the slope of the price-yield curve; convexity tells you how that slope changes. For small rate moves, duration alone is sufficient. For larger moves, convexity becomes significant and improves the accuracy of price estimates.
Does duration apply to bond funds and ETFs?
Yes. Bond funds report an “effective duration” or “average duration” that represents the weighted average duration of all holdings. A fund with an effective duration of 5 years will behave roughly like an individual bond with the same duration — losing about 5% if rates rise 1%.