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What duration risk measures
Duration expresses interest-rate sensitivity through the timing and discounting of expected cash flows. The farther in the future an investment’s cash flows arrive, the more their present value depends on the discount rate used today. A small change in that rate can therefore have a larger effect on a distant payment than on a payment due soon.
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The SEC’s Investor.gov summarizes the basic bond relationship: “market interest rates and bond prices move in opposite directions.” When market yields rise, the fixed coupons on an existing bond become less attractive relative to newly issued bonds, so the existing bond’s price generally falls. When yields decline, the existing fixed coupons become more valuable and its price generally rises.
Duration risk concerns market value, not necessarily the amount of cash a bond will pay at maturity. If an investor holds an option-free bond to maturity and the issuer pays as promised, the scheduled principal and coupons do not change merely because market yields moved. A bond fund, however, continually marks holdings to market and usually has no maturity date for the investor, so duration is central to its short- and medium-term results.
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Macaulay duration
Macaulay duration is the present-value-weighted average time at which a bond’s cash flows are received. Each coupon and the principal repayment receives a weight based on its present value; large, distant payments receive more weight than small, near-term payments. It is measured in years and is a timing measure rather than a direct percentage-price forecast.
Modified duration
Modified duration converts Macaulay duration into approximate price sensitivity to a change in yield. For a small, parallel shift in yields, the estimate is:
percentage price change ≈ −modified duration × change in yield
The change in yield must be expressed as a decimal. A 0.50-percentage-point increase is 0.005, not 0.50. A modified duration of 4 implies an approximate 2% decline for a 0.50-point rise (−4 × 0.005 = −0.020), assuming the bond’s cash flows do not change and the yield curve moves in parallel.
Convexity improves larger-move estimates
Duration is a first-order, straight-line approximation. Bond prices generally have convex relationships with yields, so the actual result for a large rate move will differ from the duration-only estimate. Convexity adds a second-order curvature term; it becomes more important as the yield change grows. A useful conceptual expansion is price change ≈ −duration × yield change + ½ × convexity × (yield change)2. The exact convexity convention and units vary by provider, so an investor should use the figures reported for the specific security or fund.
Effective and key-rate duration
Modified duration assumes known, fixed cash flows. Callable bonds, putable bonds, mortgage securities and some convertibles can change their expected cash flows when rates move. Effective duration revalues the security under small upward and downward rate shocks while allowing those cash flows to change, making it more appropriate for securities with embedded options.
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A single duration number also assumes a particular yield-curve move. Key-rate duration separates sensitivity at specific maturities, such as the two-, five- or 10-year point. A portfolio can have little net parallel-shift duration while remaining highly exposed to a twist or a move concentrated at one maturity.
Why some bonds have more duration risk than others
Maturity and cash-flow timing
All else equal, a longer-maturity bond has more duration because more of its value is tied to distant cash flows. A short-term note that returns principal soon has less time for discounting to change. “Long-term” and “long-duration” are related but not identical: a high-coupon long-maturity bond can have less duration than a very low-coupon bond that matures sooner.
Coupon size
Lower coupons push more of a bond’s present value into the final principal payment, increasing duration. Higher coupons return more cash earlier and generally reduce duration. A zero-coupon bond has a particularly transparent case: its duration is approximately its maturity because there are no interim coupons.
Yield level
For otherwise comparable bonds, a lower yield generally produces higher duration. The discounting pattern changes the relative weight of each cash flow. This is why duration can change even when the maturity and coupon remain unchanged.
Duration changes as a bond ages
Duration is not static. As a bond approaches maturity, the time remaining to its cash flows shortens and its duration generally declines. A fund’s reported duration can therefore change as holdings age, mature, are replaced, or experience changes in yields and option exercise assumptions.
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One free scan finds every outdated or missing driver and matches the right update for your exact hardware.Free scan · exact hardware matchCredit, liquidity and inflation are separate risks
Duration isolates sensitivity to a rate measure; it does not capture every reason a bond price can move. Credit-spread widening can lower a corporate bond’s price even if government yields are unchanged. Liquidity conditions can widen trading discounts, and unexpected inflation can reduce the purchasing power of fixed payments. These effects can add to or offset the pure interest-rate move.
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How to estimate a bond fund’s loss when rates rise
Start with the fund’s published effective or modified duration, identify which rate move you are testing, and apply the small-move approximation. The result is an estimate, not a guarantee, because a fund holds many securities, receives coupon income, trades during the period, and may experience curve, spread and option effects.
- Find the relevant duration. Use effective duration for a fund containing callable, mortgage or other option-sensitive holdings. Use modified duration only when its fixed-cash-flow assumptions fit the portfolio.
- Convert the rate change to decimal form. A 1-percentage-point increase is 0.01; a 25-basis-point increase is 0.0025.
- Multiply and apply the sign. A rate increase produces an approximate negative price change; a rate decline produces a positive one.
- Add income and other effects for a holding-period estimate. Coupon accrual, reinvestment, credit-spread changes, fees and convexity mean the fund’s total return will not equal the instantaneous duration estimate.
The following examples use the linear formula only. They illustrate sensitivity for a parallel yield shift and are not forecasts for any particular fund.
| Modified duration | Rates rise 0.5 percentage point | Rates rise 1 percentage point | Rates rise 2 percentage points |
|---|---|---|---|
| 2 years | −1.0% | −2.0% | −4.0% |
| 5 years | −2.5% | −5.0% | −10.0% |
| 8 years | −4.0% | −8.0% | −16.0% |
| 12 years | −6.0% | −12.0% | −24.0% |
For example, a fund with duration 8 would have an estimated 8% immediate price decline after a parallel 1-point rise, before convexity, income and all non-rate effects. A fund does not necessarily remain at duration 8 after that move, and the actual loss can be smaller or larger.
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Fixed-rate bond return has three sources, as described by CFA Institute: coupon and principal payments, reinvestment of coupons, and a gain or loss on sale before maturity. Rate changes affect these sources in different directions.
- Price risk: rising rates generally reduce the market price of an existing bond.
- Reinvestment risk: falling rates reduce the rate available when coupons or returned principal are reinvested; rising rates improve future reinvestment opportunities.
- Sale or mark-to-market risk: an investor who sells before maturity, or owns a fund that must report daily net asset value, realizes the prevailing market price rather than simply waiting for principal repayment.
If an investor’s horizon equals the bond’s Macaulay duration, price risk and coupon-reinvestment risk can approximately offset under the assumptions used to calculate duration. The offset is not a promise of a fixed return: nonparallel yield-curve moves, credit changes, taxes, defaults, trading costs and changes in reinvestment rates can prevent it. A fund investor also faces ongoing purchases and sales, so there is no single maturity-date payoff to lock in.
Why growth stocks can act like long-duration assets
A stock is valued as the present value of expected future cash flows, including dividends, buybacks or the cash that the business may eventually generate for shareholders. Raising the discount rate lowers the present value of distant cash flows, just as it lowers the present value of a bond’s distant payments.
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Growth companies often have a larger share of expected value tied to profits many years ahead. Their cash-flow duration can therefore be higher than that of value companies whose expected cash flows arrive sooner. A CFA Institute digest describing work by Clifford S. Ang (2018) reported that low-cash-flow-duration stocks earned 1.10% per month more than high-cash-flow-duration stocks in that study sample. That historical result is sample-specific evidence, not a forecast or a permanent premium.
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There is no single, market-standard equity duration published in the way bond funds publish modified or effective duration. Analysts may calculate dividend-discount duration, cash-flow duration or a model’s total interest-rate sensitivity. Each depends on assumptions about growth, payout policy, terminal value, discount rates and the forecast horizon.
CFA Institute research notes that a stock’s total rate sensitivity includes both discount-rate changes and the way inflation or real-rate changes affect earnings growth. Those interactions can make total equity sensitivity substantially shorter than a traditional dividend-discount duration. As the institute puts it, “For equities, however, duration is only one of several factors describing risk.”
Several channels can move stocks during a rate shock
- Discount-rate channel: a higher risk-free rate reduces the present value of future earnings and can compress valuation multiples.
- Growth channel: inflation, real rates and economic conditions can change expected revenue, margins and long-run earnings growth.
- Equity-risk-premium channel: investors may demand more or less compensation for owning stocks, independently of government yields.
- Financing channel: leveraged companies face higher refinancing costs when rates rise, while banks and cash-rich firms can experience different effects.
- Risk-appetite channel: a rate move can coincide with shifts toward or away from riskier assets, overwhelming the mechanical discounting effect.
Consequently, “long-duration equity” describes cash-flow timing and valuation exposure; it does not guarantee that a stock will fall by a fixed percentage whenever Treasury yields rise. Earnings surprises, competitive changes and business-specific news can dominate the rate effect.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.Bonds and stocks: the risks are comparable only up to a point
| Comparison | Fixed-rate bonds | Stocks |
|---|---|---|
| Cash-flow certainty | Contractual coupons and principal, subject to default and issuer terms | Dividends, buybacks and earnings are uncertain |
| Common sensitivity measure | Modified, effective and key-rate duration | Model-based cash-flow, dividend-discount or total rate sensitivity |
| Convexity and optionality | Convexity is important; calls, puts and mortgage prepayments can change cash flows | Operating, financing and strategic options alter future cash flows and valuation |
| Investment horizon | Holding to maturity can reduce price concern for an individual bond; funds remain marked to market | No contractual maturity payoff; value depends on an ongoing business and market expectations |
| Other major risks | Credit spread, default, liquidity and inflation risk | Earnings, leverage, valuation-multiple, business and equity-risk-premium risk |
The comparison explains why a portfolio’s apparent duration can differ materially from the duration of its bond sleeve. Equities, liabilities and other assets may add or offset rate sensitivity even when the bond allocation itself is unchanged.
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A practical way to use duration in portfolio decisions
Match the measure to the exposure
For an option-free bond, modified duration can be a useful first estimate. For securities whose cash flows respond to rates, use effective duration and convexity. For a portfolio exposed to a nonparallel curve move, inspect key-rate durations rather than relying on one aggregate number.
Match duration to the spending horizon
Money needed soon is more vulnerable to a forced sale after a rate shock than money that can remain invested through a full interest-rate cycle. Investors with a known liability date can compare that horizon with Macaulay duration, while recognizing that the comparison works best for a specific bond with stable cash flows, not a constantly changing fund.
Stress more than one scenario
- Test a parallel rise and fall in yields.
- Test a steepening or flattening curve by changing short- and long-term rates separately.
- For credit funds, add a spread-widening scenario.
- For callable or mortgage holdings, test changes in prepayment and call assumptions.
- For equity holdings, vary discount rates, earnings growth, risk premiums and leverage rather than applying a bond-duration formula.
Read the disclosure date
Duration is a snapshot based on a portfolio’s holdings and assumptions at a stated date. Check whether the number is modified or effective, whether it includes derivatives, and whether the fund reports a separate option-adjusted or key-rate measure. A later rate move, portfolio turnover or changing option exercise can make the published figure different from today’s exposure.
Common mistakes and how to avoid them
Confusing maturity with duration
Maturity tells you when the final contractual payment is due. Duration weights every payment and can be much shorter than maturity for a high-coupon bond. Use duration for rate sensitivity and maturity for the contractual endpoint.
Treating the estimate as an exact loss
The duration formula is linear and local. Convexity, income, curve shape, spreads and changing cash flows affect the realized result, particularly for large moves.
Assuming a stock has a fixed duration
Equity duration changes as prices, earnings forecasts, payout policies, inflation expectations and discount rates change. Always identify whether a quoted number is cash-flow duration, dividend-discount duration or total modeled rate sensitivity.
Ignoring the fund structure
An individual bond can mature and repay principal; an open-end bond fund continuously replaces holdings and reports a market-based net asset value. The same duration number can therefore imply different practical risks for an investor who must withdraw money on a specific date.
Looking only at rates
Credit, liquidity, inflation, earnings and leverage can dominate a portfolio’s return. Duration is a valuable lens for one risk factor, not a complete risk rating.
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