What Is Bond Duration? Duration in Fixed Income Explained

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Duration measures how sensitive a bond’s price is to a change in interest rates. It is expressed as a number that does two jobs. As Macaulay duration, it is the weighted average time, in years, until you receive a bond’s cash flows. As modified duration, it is the approximate percentage change in the bond’s price for a 1 percentage point change in its yield. A bond with a modified duration of 6 would lose roughly 6% of its market value if its yield rose from 4% to 5%, and gain roughly 6% if the yield fell from 4% to 3%.

That second meaning is what most investors use. A fund fact sheet’s “duration” figure, a portfolio manager “adding duration,” and a bond fund’s “duration risk” all refer to the same thing: how much the price moves when rates move.

What Is Duration in Fixed Income?

A bond is a schedule of promised payments: coupons at regular intervals and the face value at maturity. Its market price is the present value of those payments, discounted at the bond’s yield. When the yield changes, every payment is discounted at a new rate and the price changes. Duration summarizes how large that price change will be.

The time-based definition explains why. Payments far in the future are discounted over more periods, so a change in the discount rate affects their present value much more than it affects a payment due next month. A bond whose value is concentrated in distant payments is therefore more sensitive to yield changes. Macaulay duration measures where the bond’s value sits in time: it averages the dates of each payment, weighting each date by that payment’s share of the bond’s present value. The later the “center of gravity” of the cash flows, the higher the duration and the greater the price sensitivity.

Duration is not the same as maturity

Maturity is the date the issuer repays principal. It is fixed in the bond’s terms and does not change with market conditions. It counts down one year for every year that passes.

Duration depends on the size and timing of every payment and on the current yield. Two bonds maturing on the same day can have very different durations if one pays a large coupon and the other pays none. Duration also changes as market yields change, and it declines as the bond ages, though not at exactly one year per year. For a coupon-paying bond, duration is always shorter than maturity, because some of the bond’s value arrives before the final payment.

What “duration” means in a fund or portfolio

For a bond fund or portfolio, duration is a weighted average of the durations of the holdings. A fund reporting a duration of 5 years would be expected to lose about 5% of its value if the yields on its holdings rose by 1 percentage point across the board, and gain about 5% if they fell by the same amount. That rule of thumb is a common way regulators and fund companies explain interest rate risk to investors. It works as an approximation for parallel, moderate yield changes.

Why Bond Prices Fall When Rates Rise

Duration only makes sense once the inverse relationship between yields and prices is clear.

Suppose you own a bond that pays a $30 annual coupon on $1,000 face value, a 3% coupon. Market rates then rise, and newly issued bonds of similar quality and maturity pay 4%. No buyer will pay $1,000 for your 3% bond when $1,000 buys a 4% bond elsewhere. Your bond’s price has to fall until its yield to the new buyer, counting both the coupon and the gain from buying below face value, matches the 4% available in the market. If rates instead fall to 2%, your 3% coupon becomes attractive and buyers will pay more than $1,000 for it.

The coupon payments themselves never change on a fixed-rate bond. What changes is the price someone will pay for them. Duration answers the question that follows: by how much? The bond’s yield to maturity is the rate that links its price to its cash flows, and duration measures how responsive that price is to changes in the yield.

This matters mainly if you sell before maturity or mark your holdings to market, as bond funds do every day. If you hold an individual bond to maturity and the issuer pays as promised, you receive the scheduled coupons and face value regardless of what happened to the price in between. Price changes still have an economic meaning for a hold-to-maturity investor (a bond whose price has fallen is locking in a below-market yield), but they are not realized as losses unless the bond is sold.

What Determines a Bond’s Duration

Four features drive duration: time to maturity, coupon rate, yield, and whether the cash flows are fixed or can change.

Time to maturity

The longer the maturity, the higher the duration, all else equal. A longer bond has more of its value in distant payments, especially the face value.

The relationship is not proportional. Hypothetical bonds paying a 5% annual coupon and priced at a 5% yield (at par) have these Macaulay durations:

Going from 2 to 10 years more than quadruples duration. Going from 10 to 30 years only doubles it. Very distant payments are worth little in present-value terms, so adding years at the far end adds less and less duration. A coupon bond priced at par approaches a limit equal to (1 + y) / y, which is 21 years at a 5% annual yield. For bonds trading at a deep discount (coupon well below yield), duration can rise above that limit at very long maturities and then drift back down toward it, a quirk that mainly matters for long, low-coupon bonds.

Coupon rate

A higher coupon lowers duration. More of the bond’s value arrives early in the form of coupons, which pulls the weighted average time forward.

Here are three hypothetical 10-year bonds with annual coupons, all priced at a 5% yield:

The zero-coupon bond has a single payment at maturity, so its duration equals its maturity exactly. That makes zero-coupon bonds, such as Treasury STRIPS, the most rate-sensitive bonds for a given maturity. The 8% bond returns a larger share of its value through coupons over the 10 years, so its duration is about two and a half years shorter.

Yield level

A higher yield lowers duration. Discounting at a higher rate shrinks the present value of distant payments more than near ones, which shifts the weights toward the early cash flows. The same bond therefore has a somewhat lower duration when market yields are high than when they are low. This is also why duration is not a fixed attribute of a bond: it moves whenever the yield moves.

Payment frequency and embedded options

Bonds that pay coupons more often (semiannually rather than annually) have slightly lower durations, because some cash arrives sooner.

Embedded options have a much larger effect. A callable bond can be redeemed by the issuer early, which is most likely when rates fall. A mortgage-backed security’s principal is repaid faster when homeowners refinance at lower rates. A floating-rate note resets its coupon to market rates periodically, so its price sensitivity is tied to the time until the next reset rather than to final maturity. In each case the expected cash flows change with rates, and a duration figure calculated from a fixed payment schedule would misstate the risk. Effective duration, covered below, deals with this.

Types of Duration

The word “duration” covers several related measures. They differ in units and in what they assume about cash flows.

Macaulay duration

Macaulay duration is the weighted average time until a bond’s cash flows are received, measured in years. Each cash flow’s weight is its present value divided by the bond’s total present value (its price).

In formula form:

Macaulay duration = Σ [ t × PV(CFt) ] / Price

where:

• t = time in years until each cash flow is received
• CFt = the cash flow (coupon, or coupon plus principal) at time t
• PV(CFt) = CFt / (1 + y/k)^(number of periods until t)
• y = yield to maturity (annual)
• k = number of compounding periods per year (2 for semiannual bonds)
• Price = the sum of all PV(CFt)

The calculation has two parts. First, find the present value of each payment. Second, multiply each payment’s time by its share of the total present value and add the results. Because the weights add up to 1, the answer is an average of the payment dates, measured in years.

Macaulay duration has a useful interpretation beyond risk. It is the holding period over which a bond’s price risk and reinvestment risk approximately offset each other. If rates rise, the bond’s price falls, but coupons are reinvested at higher rates. If rates fall, the price rises, but coupons are reinvested at lower rates. For a single change in rates shortly after purchase, an investor who holds for a period equal to the Macaulay duration ends up with close to the originally promised yield either way. This is the basis of immunization strategies, described later.

Modified duration

Modified duration converts Macaulay duration into a price sensitivity:

Modified duration = Macaulay duration / (1 + y/k)

For a bond with semiannual coupons, that is Macaulay duration divided by (1 + YTM/2).

Modified duration is not measured in years in any practical sense. It is the percentage price change for a 1 percentage point change in yield:

Approximate % price change ≈ −Modified duration × Change in yield

With the yield change written as a decimal, a modified duration of 7 and a yield increase of 0.50 percentage points (0.005) gives −7 × 0.005 = −3.5%. The minus sign carries the inverse relationship: rising yields, falling prices.

Two points are easy to get wrong. Modified duration gives a percentage of the current price, not a dollar amount per bond. And the estimate assumes the bond’s cash flows stay fixed when the yield changes, which is true for an option-free bond but not for a callable one.

Effective duration

Effective duration measures price sensitivity directly, by revaluing the bond at a higher and a lower yield and seeing how the price responds. It is used when cash flows depend on rates, as with callable bonds, putable bonds and mortgage-backed securities, because the valuation model can change the expected cash flows in each scenario.

Effective duration = (P− − P+) / (2 × P0 × Δy)

where P0 is the current price, P− is the price if yields fall by Δy, P+ is the price if yields rise by Δy, and Δy is the yield shift as a decimal.

For an option-free bond, effective duration and modified duration come out nearly identical. For a callable bond, effective duration is lower than the duration of an otherwise identical noncallable bond, because the call caps how much the price can rise when rates fall. Bond funds that hold mortgage-backed or callable securities commonly report effective duration for this reason. Some securities can even have negative effective duration. Interest-only mortgage strips, for example, tend to lose value when rates fall because faster prepayments cut off the interest stream.

Dollar duration and DV01

Percentage changes are useful for comparing bonds; dollar changes are useful for managing positions.

Dollar duration = Modified duration × Price

Multiplying dollar duration by a yield change (as a decimal) gives the estimated dollar change in value. Conventions differ on scaling, so some systems quote dollar duration per 1 percentage point and others per 100% change in yield.

The most common dollar measure among traders is DV01 (dollar value of one basis point), also called PV01 or the price value of a basis point. A basis point is 0.01 percentage point.

DV01 = Modified duration × Price × 0.0001

DV01 tells you how much a position gains or loses for each basis point move in yield. Because it is in dollars, DV01s of different positions can be added together, which makes it the working tool for hedging. To hedge a bond with a DV01 of $500 per basis point, a trader sells enough of another bond or futures contract to create −$500 of DV01.

Key rate duration

Standard duration assumes every yield on the curve moves by the same amount, a parallel shift. In practice, short-term and long-term rates often move differently: the curve can steepen, flatten or twist. Key rate duration measures sensitivity to a change in the yield at one specific maturity (for example 2, 5, 10 or 30 years) while holding the others constant. The key rate durations across the curve add up approximately to the bond’s effective duration. A portfolio manager uses them to see where on the curve the exposure sits. Two portfolios with the same overall duration can respond very differently if one holds mainly 2-year and 30-year bonds and the other holds 10-year bonds.

Spread duration

A corporate bond’s yield is the yield on a comparable government bond plus a credit spread. Spread duration measures price sensitivity to a change in that spread alone. For a fixed-rate, option-free corporate bond, spread duration and interest rate duration are nearly the same number, because a yield change has the same effect on the price whether it comes from the Treasury curve or from the spread. For a floating-rate note, they diverge: the coupon resets with the base rate, so interest rate duration is short, but the spread is fixed at issue, so spread duration reflects the full remaining maturity.

How to Calculate Bond Duration: A Worked Example

Take a hypothetical bond:

• Face value: $100
• Coupon: 10% annual, paid semiannually ($5 every six months)
• Maturity: 3 years (six payments)
• Yield to maturity: 6% annual, which is 3% per six-month period

Step 1: Find the present value of each cash flow

Each payment is discounted at 3% per period for the number of periods until it arrives.

The present values add up to $110.834, which is the bond’s price at a 6% yield. It trades above face value because its 10% coupon exceeds the 6% market yield. If you already know a bond’s price and yield, you do not need to derive the price this way, but you still need each payment’s present value to build the weights.

Step 2: Compute Macaulay duration

Multiply each payment’s time by its weight and add: the result is 2.684 years. Equivalently, divide the sum of time × present value (297.48) by the price (110.834).

The final payment, which includes the $100 principal, carries about 79% of the bond’s value, so the duration sits close to the three-year maturity. It is still about four months shorter than maturity because the five earlier coupons pull the average forward.

Step 3: Convert to modified duration

Because coupons are semiannual, divide by 1 plus the periodic yield:

Modified duration = 2.684 / (1 + 0.06/2) = 2.684 / 1.03 = 2.606

The bond’s price should change by about 2.61% for each 1 percentage point change in its yield.

Step 4: Translate into dollars

Dollar change for a 1 percentage point move ≈ 2.606% × $110.834 ≈ $2.89 per $100 of face value

DV01 ≈ 2.606 × $110.834 × 0.0001 ≈ $0.029 per $100 of face value, or about $289 per basis point on $1 million of face value.

Note the difference between 2.61 and $2.89. Modified duration is a percentage of the current price. Here the price is above $100, so the dollar change per $100 of face value is larger than the duration number itself.

Step 5: Check the estimate against actual repricing

Repricing the same bond at 7% and 5% yields gives:

The duration estimate is close in both directions, but not exact. The actual price rises more than estimated when yields fall and falls less than estimated when they rise. That asymmetry is convexity.

Running the effective duration formula on these prices gives (113.770 − 107.993) / (2 × 110.834 × 0.01) = 2.606, matching the modified duration, as expected for an option-free bond.

A zero-coupon shortcut

For a zero-coupon bond, no calculation is needed for Macaulay duration: it equals the time to maturity, because there is only one cash flow. A hypothetical 10-year zero priced at a 4% yield compounded semiannually has a Macaulay duration of 10 years and a modified duration of 10 / 1.02 = 9.80. Its price would move about 9.8% for a 1 percentage point change in yield.

Calculating duration in practice

Most investors never compute duration by hand. Brokerage bond screens and fund fact sheets report it, and spreadsheet software has built-in functions (in Excel, DURATION returns Macaulay duration and MDURATION returns modified duration, given the settlement date, maturity, coupon, yield and payment frequency). The manual method is still worth knowing because it shows what the number depends on, and why the reported figure changes when yields change.

Convexity: Where Duration Falls Short

Duration treats the price-yield relationship as a straight line: each basis point of yield change produces the same price change. The real relationship is curved. For an option-free bond, the curve bends so that prices rise at an accelerating rate as yields fall and decline at a decelerating rate as yields rise. Convexity measures that curvature.

The worked example showed the effect. For a 1 percentage point move, duration estimated ±$2.888, while the actual changes were +$2.936 and −$2.841. In both directions the bond did about $0.047 better than the duration estimate.

Adding a convexity term corrects most of the gap:

% price change ≈ (−Modified duration × Δy) + (½ × Convexity × Δy²)

Convexity can be estimated from the same repriced values used for effective duration:

Convexity ≈ (P− + P+ − 2 × P0) / (P0 × Δy²)

For the example bond: (113.770 + 107.993 − 221.668) / (110.834 × 0.0001) ≈ 8.5. The convexity adjustment for a 1 percentage point move is ½ × 8.5 × 0.0001 ≈ 0.043%, or about $0.047 on a $110.83 price. Adding it to the duration estimate gives +$2.935 and −$2.841, matching the actual prices.

Three practical points follow:

• Convexity matters more for big moves. The adjustment grows with the square of the yield change, so for a 10 basis point move it is negligible, and for a 2 or 3 percentage point move it becomes significant.
• Longer, lower-coupon bonds have more convexity. A long zero-coupon bond has far more convexity than the short coupon bond in the example.
• Callable bonds and mortgage-backed securities can have negative convexity. When rates fall, the likelihood of a call or prepayment rises, which caps price gains. In that range, the price rises less than duration predicts as yields fall and still falls about as much when they rise.

All else equal, positive convexity is a desirable feature: it helps in both directions. Markets usually price it in, so a bond with more convexity typically offers a somewhat lower yield than a comparable bond with less.

Duration of a Bond Portfolio or Fund

A portfolio’s duration is approximately the market-value-weighted average of the durations of its holdings.

Hypothetical example: you hold $60,000 in a short-term bond fund with a duration of 2 years and $40,000 in a long-term bond fund with a duration of 10 years.

Portfolio duration ≈ (0.60 × 2) + (0.40 × 10) = 1.2 + 4.0 = 5.2 years

For a 1 percentage point parallel rise in yields, the portfolio would be expected to lose about 5.2%, or about $5,200 on $100,000. The weighted average works cleanly only under the assumption that all yields move together. If short-term rates rise while long-term rates stay put, the long-term fund barely moves and the short-term fund absorbs the change, so the actual result depends on the curve shift, not on the single 5.2 figure.

Reading a bond fund’s duration

A bond mutual fund or ETF differs from an individual bond in one important way: it never matures. The manager sells aging bonds and buys new ones to keep the fund’s duration roughly within a target range. That has two consequences.

First, the fund’s net asset value responds to yield changes according to its duration for as long as you own it. There is no maturity date at which you receive face value back.

Second, a fund’s duration is a useful guide to the time horizon over which a rate increase tends to be offset. When yields rise, the fund’s price falls immediately, but the fund reinvests coupons and maturing bonds at the higher yields. Over a holding period roughly equal to the fund’s duration, the higher income can recover the initial price loss, assuming yields stay at the new level. An investor with a two-year horizon who buys a fund with an eight-year duration is taking on price risk that the higher income will not have time to recover.

Fund documents may report effective duration, modified duration or both. For funds holding callable bonds or mortgage-backed securities, effective duration is the more meaningful figure.

How Duration Is Used in Investment Decisions

Comparing interest rate risk

The simplest use is comparison. Two bonds with similar credit quality and yield but different durations carry different amounts of rate risk. If one has a duration of 3 and the other 9, the second will move roughly three times as much for the same yield change. Duration lets you compare bonds with different maturities and coupons on one scale, which maturity alone cannot do.

Long-duration and short-duration positioning

In bond investing, “long duration” and “short duration” describe how much rate sensitivity a portfolio has, not whether the investor owns or has borrowed the asset.

• A long-duration stance favors bonds with high durations, typically long maturities and low coupons. It benefits most if yields fall, which has often been the case in recessions, when central banks cut rates and investors seek safety. It suffers most if yields rise.
• A short-duration stance favors bonds that mature soon or have high coupons. It is used by investors who expect rates to rise or who want to limit price swings. The cost is that short bonds lock in current yields for less time, so if rates fall, the investor must reinvest sooner at lower rates.

When managers talk about “adding duration” or “extending duration,” they mean increasing the portfolio’s sensitivity, usually by buying longer bonds or futures, because they expect yields to fall or want more protection against a decline in rates. “Shortening duration” is the reverse.

In factor-based investing, a “duration” or “term” factor is sometimes built as the return on long-duration bonds minus the return on short-duration bonds. It isolates the compensation investors earn, or lose, for bearing interest rate risk.

Matching a time horizon: immunization

Because Macaulay duration is the horizon at which price risk and reinvestment risk roughly offset, investors with a known future obligation can match the two. Pension funds and insurers do this with their liabilities, and the same logic applies to an individual saving for a known expense.

Hypothetical example: you need a sum of money in seven years. A portfolio with a Macaulay duration of seven years would, for a one-time parallel shift in yields, deliver close to the originally expected value on that date whether rates rise or fall. If rates rise, price losses are offset by higher reinvestment income; if they fall, price gains offset lower reinvestment income.

Immunization requires maintenance. Duration and the time horizon do not shrink at the same pace, and every yield change alters duration, so the portfolio has to be rebalanced periodically to keep the two aligned. It also protects against parallel shifts, not against the curve twisting.

Bullets, barbells and ladders

Duration lets investors compare portfolio structures on equal terms:

• A bullet concentrates holdings near one maturity, for example all bonds around 7 years.
• A barbell splits holdings between short and long maturities, for example 2-year and 20-year bonds, weighted to reach the same overall duration as the bullet.
• A ladder spreads holdings evenly across maturities, so some bonds mature every year and are reinvested.

A bullet and a barbell with the same duration respond similarly to a small parallel shift. They differ in convexity (the barbell typically has more) and in how they respond to curve changes. A steepening curve, in which long yields rise relative to short yields, tends to hurt the barbell’s long leg more, while a flattening tends to help it. Key rate durations show these differences where a single duration number hides them.

Hedging

Because DV01 is additive, duration is the basis for hedging rate risk. A manager holding corporate bonds who wants to remove rate exposure while keeping the credit exposure can sell Treasury futures with a matching DV01. Banks use duration gaps, the difference between the duration of their assets and their liabilities, to measure how a change in rates would affect their equity.

Real versus nominal rates

Duration measures sensitivity to changes in nominal yields for ordinary fixed-rate bonds. Inflation expectations are one of the drivers of those yields, so periods of rising inflation, such as those visible in U.S. inflation history, have tended to coincide with rising yields and losses on long-duration bonds. For inflation-protected securities such as TIPS, the relevant duration is sensitivity to real yields, because the principal adjusts with inflation.

Limitations of Duration

Duration is the most widely used measure of bond rate risk, but it rests on assumptions that do not always hold.

It is a linear approximation. Duration describes the slope of the price-yield curve at the current yield. For small changes the estimate is accurate; for large ones it ignores convexity. A portfolio’s risk in a sharp rate move can differ meaningfully from the duration estimate.

It assumes parallel yield curve shifts. A single duration figure assumes every maturity’s yield moves by the same amount. Real curve moves are rarely parallel, which is why key rate durations exist.

It changes over time and with yields. A bond’s duration falls as it approaches maturity and shifts whenever its yield changes. A figure from a fund fact sheet is a snapshot as of its reporting date, not a permanent property.

It ignores default risk as such. Duration measures how the price responds to a change in yield, whatever the cause: a move in government rates or a widening of the issuer’s credit spread. It does not measure the probability that the issuer will fail to pay. A short-duration high-yield bond can still lose most of its value in a default. Credit risk needs separate analysis, including credit ratings, the issuer’s finances and the credit spread.

Options make modified duration misleading. For callable bonds, putable bonds and mortgage-backed securities, modified duration computed from the stated schedule can be badly wrong. Effective duration is better but depends on the model’s assumptions about prepayment and call behavior.

It says nothing about expected return. Duration measures sensitivity, not direction. A high-duration bond is not a better or worse investment in itself; its outcome depends on what yields do and on the yield you earn in the meantime. Measures of risk-adjusted return, such as the Sharpe ratio, answer a different question.

Duration vs. Related Terms

Duration vs. maturity. Maturity is the date principal is repaid. Duration is the weighted average timing of all payments and the price sensitivity that follows from it. For a zero-coupon bond the two are equal; for any coupon bond, duration is shorter.

Duration vs. average maturity. Bond funds often report both. Weighted average maturity is the average time until the holdings mature, weighted by market value. It ignores coupons and yields, so it overstates rate sensitivity for funds holding higher-coupon bonds. Duration is the better gauge of how the fund’s price will react to rate changes.

Duration vs. weighted average life. Weighted average life, common for mortgage-backed and amortizing securities, is the average time until each dollar of principal is repaid. It ignores interest payments and discounting. It describes the repayment schedule, not price sensitivity.

Duration vs. yield. Yield measures what a bond pays relative to its price. Duration measures how much that price changes when yields change. Two bonds with the same yield can have very different durations, and a higher yield does not mean higher or lower rate sensitivity on its own.

Macaulay vs. modified duration. Macaulay duration is a time measure in years. Modified duration is a percentage price sensitivity. They are numerically close (modified is slightly smaller), which is why the terms get used loosely, but only modified (or effective) duration should be used to estimate price changes.

Duration in the everyday sense. Outside fixed income, “duration” simply means a length of time, as in the duration of a contract or loan. In bond analysis, it has the specific technical meaning described here.

Why Price Sensitivity Is Called “Duration”

The name comes from the measure’s origin as a time concept. The economist Frederick Macaulay introduced it in 1938, in a study of U.S. interest rates and bond yields. He was looking for a better way to describe how “long” a bond is than its maturity date, which ignores the fact that coupon bonds return much of their value before maturity. His answer was the weighted average time to receipt of the cash flows: a duration in the literal sense.

The link to price sensitivity follows mathematically. Because a change in yield affects each payment’s present value in proportion to how far away it is, a bond’s weighted average time to payment determines how strongly its price responds. Modified duration is the derivative of the bond’s price with respect to its yield, divided by the price, and it equals Macaulay duration divided by one plus the periodic yield. British actuary Frank Redington developed the related idea of immunization in 1952, showing how matching the durations of assets and liabilities could protect an insurer against rate changes. Over time, as practitioners focused on risk management, “duration” came to mean price sensitivity first and time second, even though the number started as a measure of time.

FAQs

The Bottom Line

Duration matters to anyone holding bonds or bond funds who might sell before maturity, since funds never mature and reprice daily. Matching a fund's duration to your time horizon helps higher reinvestment income offset price losses when rates rise. Treat the figure as a snapshot for moderate, parallel rate moves, and check effective duration, convexity and credit risk separately.