Bond Duration: The Math Behind Your Rate Risk

Two bond funds, both labeled "bonds", both holding investment-grade paper. Interest rates rise by one percentage point. One fund loses about 1%, the other loses about 6%. Nothing about the credit quality explains the difference; the entire gap is captured by one number printed in every fund's fact sheet: duration. It is the single most useful number in fixed-income investing and the least understood outside the bond desk, because it quietly does double duty - it is both a measure of time and a measure of sensitivity.

This guide builds duration from first principles with a fully worked example on a five-year bond, shows the approximation every investor should memorize, and then covers how to actually use it: matching duration to your spending horizon and reading fund fact sheets the right way.

Definition one: a weighted average of when you get paid

A bond is a schedule of cash flows: coupons every year and the principal at maturity. Macaulay duration is the weighted average time until those cash flows arrive, where each cash flow is weighted by its present value. That is the whole definition. It answers: "in how many years, on average, does this bond pay me?"

The intuition for why this number governs price sensitivity: if a bond pays you everything tomorrow, a change in interest rates barely compounds against it. If it pays you in fifteen years, every year of higher rates compounds against the wait. The longer the average wait, the more the price must move when the discount rate changes.

The worked example: a five-year, 4% annual-coupon bond

Assumptions: face value $1,000, a $40 coupon each year for five years, and the market interest rate (yield to maturity) is also 4%, so the bond trades at par - exactly $1,000. Here is the full calculation, reproducible with any calculator:

Each present value is the cash flow divided by 1.04 raised to the year: for example, year 5 is $1,040 / 1.04^5 = $855.03. The final column multiplies each present value by its year. Duration is the sum of that column divided by the price:

Macaulay duration = $4,631.01 / $1,000.22 = 4.63 years.

Notice what the table reveals: even though this is a "five-year" bond, 85.5% of its present value arrives in the final year. Coupons barely matter to the average; the principal dominates. That is why two five-year bonds can have different durations - the one with bigger coupons pays more of its value early, so its duration is shorter.

Definition two: the price-sensitivity approximation

For practical use, duration converts directly into a price change estimate. The version used in the industry is modified duration, which is Macaulay duration divided by (1 + yield):

Modified duration = 4.63 / 1.04 = 4.45.

The rule: for each 1 percentage point change in yield, the bond's price moves approximately modified-duration percent, in the opposite direction. Test it against the exact answer. If the yield rises from 4% to 5%, repricing our bond exactly: price = $40 x (1 - 1.05^-5)/0.05 + $1,000/1.05^5 = $173.18 + $783.53 = $956.71.

Actual change: ($956.71 - $1,000) / $1,000 = -4.33%.
Duration estimate: -4.45% per 1% move x 1 = -4.45%.

The estimate overshoots by 0.12 percentage points. That gap is convexity - the curvature the approximation misses - and it always works in the bondholder's favor for ordinary rate moves: prices fall slightly less than duration predicts when rates rise and rise slightly more when rates fall. For a first approximation, duration alone gets you within a few tenths of a percent for moves of one point or so; for moves of 3-4 points, convexity stops being a footnote and the linear estimate degrades visibly.

What pushes duration up and down

• Longer maturity → longer duration. A ten-year zero-coupon bond has a duration of exactly 10 (all cash arrives at once); a ten-year 4% coupon bond has a duration around 8.2, because coupons pull some value forward.
• Higher coupons → shorter duration. More of the value arrives early. This is why a 20-year high-coupon bond can carry less rate risk than a 10-year zero-coupon bond.
• Lower yields → longer duration. Duration itself lengthens when rates fall (each future cash flow is discounted less aggressively, increasing the weight of distant payments). This is one reason bond risk felt higher in 2020-2021 than in 2010: the same funds were running longer durations at lower absolute yields.

Using duration in practice

Match duration to when you need the money

The cleanest use of duration is horizon matching. If you need the money in about three years, a fund with duration 3 has a specific, useful property: the price loss from a rate rise is approximately offset by the higher reinvestment rates you earn in the years before you sell. You have immunized (approximately) the three-year return. Hold an 8-year-duration fund for a three-year goal and you are exposed to rate levels at an arbitrary future date - the mistake that turned "safe" bond funds into -15% positions in the 2022 rate repricing. The allocation framework in choosing a stock-bond mix becomes far more precise once you read "bonds" as "bonds of a given duration".

Read the fact sheet number, not the fund name

Fund names are marketing; duration is measurement. Intermediate-term index funds typically run 5 to 7 years of duration, short-term funds 1 to 3, long-term funds 10 to 20+. The number to look for is usually labeled "effective duration" or "average duration" in the fund's statistics table, and it is computed across the whole portfolio - including whatever the managers hold beyond the name of the category. Two funds in the same category can differ by several years of duration, which is several times the rate risk.

Know what duration does not measure

Duration prices interest-rate risk for bonds whose credit is stable. Corporate bond funds can lose far more than duration implies if credit spreads widen, because widening spreads are a second discount-rate shock on top of the rate move. Long-term Treasury funds are the purest duration plays; high-yield funds are partly credit vehicles whose duration number understates their real-world volatility. Duration also says nothing about inflation risk beyond what nominal yields already embed - the distinction developed in the inflation and real-return math.

The rule in reverse: what 2022 actually did

The 2022 rate repricing is the largest live demonstration of duration math in a generation, and it paid out almost exactly as the formula predicted. US Treasury yields rose by roughly 2.5 to 3 percentage points across the year as the Federal Reserve tightened. Apply the rule to a plain intermediate-term Treasury index fund running a duration of about 6:

Estimated price impact: -6 x 2.75 ≈ -16.5%.

The actual 2022 total return for that fund category landed in the -14% to -17% range, with the difference from the linear estimate explained by convexity, the curve not shifting in parallel, and the partial offset from yield earned during the year (a fund earning 1.5% in coupons softens a 16.5% price hit to roughly a 15% total loss). The arithmetic was public information in advance: anyone who knew their fund's duration could have estimated the damage before it happened. What the episode taught - and what the horizon-matching section above is really about - is that "low risk" is a statement about duration and credit, not about the word "bond" on the fund's label.

A sobering counterpoint for balance: the same math runs forward, not just backward. A fund with duration 6 gains roughly 6% for each percentage point rates fall, which is why the sharp 2024-2025 rate cuts turned bond funds into double-digit gainers for holders who had sat through 2022. Duration cuts both ways; it is risk, not punishment.

The limits, stated plainly

Duration is a linear approximation of a curved relationship, valid for small yield moves around the current level; convexity corrections matter for large moves. It assumes a single parallel shift in the yield curve, while real curves steepen and flatten. And for individual callable bonds, the effective duration can change as rates move because the issuer's option to call changes expected cash flows - fund-level "effective duration" accounts for this, Macaulay duration does not. None of these limits change the working rule; they just mean the rule is an estimate, which is exactly how the fund industry uses it.

If this clarifies why bond funds fell in 2022, the mechanics are expanded in why bond prices fall when rates rise, and the fund-level fee angle is covered in what an expense ratio actually costs you. For how bond funds slot into retirement vehicles, see how target-date funds work.

This article is general financial education, not investment advice or a recommendation of any security. Bond funds involve risk of loss; duration is an approximation. Consider consulting a qualified financial professional about your own situation.

By The Long View editorial team · How we check our guides