Guide

Bond duration and interest rate risk explained

A portfolio manager holds $10 million of investment-grade corporates with an average maturity of eight years. Overnight, the five-year Treasury yield rises 75 basis points on hotter-than-expected inflation data. By afternoon the bond sleeve is down roughly 5% on paper — about $500,000 — even though no issuer defaulted and every coupon still pays on schedule. That gap between coupon income and mark-to-market price is interest rate risk, and duration is the standard yardstick for measuring it. Duration estimates how much a bond’s price changes when yields move, weighted by the timing of its cash flows. Fund fact sheets, risk dashboards, and liability-driven investors all lean on duration — but the headline number hides assumptions about parallel yield shifts, reinvestment, and embedded options. This guide defines Macaulay and modified duration, explains the price-yield approximation and convexity, covers effective duration for callable bonds and bond funds, walks through portfolio duration and immunization, presents a Harbor Capital bond-sleeve worked example, offers a metric decision table, common pitfalls, and an investor checklist alongside our yield to maturity guide, bond fundamentals primer, and yield curve explainer.

Why bond prices move opposite to yields

A bond is a stream of future cash flows discounted at market yields. When required yields rise, those future payments are worth less today, so price falls. The relationship is nonlinear — a curved price-yield graph — but for small yield changes duration provides a useful linear shortcut.

Interest rate risk is the risk that changes in benchmark Treasury yields (and, for corporates, credit spreads) reduce market value before maturity. It is distinct from credit risk (issuer default) and reinvestment risk (coupons reinvested at lower rates). Longer cash-flow horizons and lower coupons amplify rate sensitivity: a zero-coupon 30-year Treasury has far more duration than a 2-year T-bill trading near par.

Macaulay duration: weighted average time to cash flows

Macaulay duration (in years) is the present-value-weighted average time until you receive the bond’s cash flows. Intuitively, it answers: “When do I get my money back, on average?” A 10-year zero-coupon bond has Macaulay duration of 10 years because the only payment arrives at maturity. A 10-year bond with a 5% coupon has Macaulay duration below 10 years because coupons return principal earlier.

Macaulay duration is foundational but investors more often quote modified duration, which converts the time measure into a price-sensitivity percentage.

Modified duration: the price-sensitivity workhorse

Modified duration approximates the percentage change in bond price for a 1% (100 basis point) change in yield, holding everything else constant:

Modified duration ≈ −%ΔPrice / %ΔYield

The negative sign reflects the inverse price-yield relationship. A bond with modified duration of 6 loses roughly 6% in price if yields rise 1% (100 bps), and gains roughly 6% if yields fall 1%. For a 50 bp rise, halve the estimate: about −3%.

Quick approximation rule

For small parallel shifts in yield:

%ΔPrice ≈ −Modified duration × ΔYield (in decimal)

Example: duration 7.5, yields up 40 bps (0.0040) → price change ≈ −7.5 × 0.0040 = −3.0%. Add back coupon income over the holding period for total return, not price return alone.

Modified duration is derived from Macaulay duration divided by (1 + yield per period). For semiannual U.S. bonds, use the semiannual yield in the denominator. Bloomberg and fund fact sheets typically display modified duration directly.

Convexity: why duration underestimates gains when yields fall

Duration is a tangent-line estimate on a curved function. When yields move sharply, the curve matters. Convexity measures the curvature of the price-yield relationship. Positive convexity means:

When yields fall, prices rise more than duration alone predicts.
When yields rise, prices fall less than duration alone predicts.

Option-free Treasury and corporate bonds exhibit positive convexity — a desirable asymmetry for buy-and-hold investors. Callable bonds can show negative convexity when rates fall: the issuer calls the bond, capping price upside. Mortgage-backed securities often display negative convexity when prepayments accelerate as rates drop.

A second-order adjustment: %ΔPrice ≈ −D_mod × Δy + ½ × Convexity × (Δy)². For 25–50 bp moves, duration alone is usually sufficient for retail sizing; for 100+ bp shocks or long portfolios, convexity matters.

What drives duration higher or lower

Factor	Effect on duration	Intuition
Longer maturity	Higher	Cash flows further out are more discounted
Lower coupon	Higher	More value tied to distant principal repayment
Lower current yield	Higher	Same cash flows discounted at a lower rate
Callable feature	Lower effective duration when rates fall	Call caps price appreciation
Zero-coupon structure	Equals maturity	Single payment at the end

Do not confuse maturity with duration. A 30-year bond with a high coupon may have duration under 15 years; a 10-year zero can have duration of 10. When comparing funds, always use duration (or effective duration), not average maturity alone.

Effective duration and bond funds

For bonds with embedded options — calls, puts, prepayment schedules — modified duration from a static formula misstates risk. Effective duration estimates price sensitivity by shocking the entire yield curve up and down and observing the price change. It captures how call likelihood shifts as rates move.

Mutual funds and ETFs publish average effective duration in the fact sheet. An intermediate-term bond fund might show 5.2 years; a short-term fund 2.5 years; a long-government fund 15+ years. Aggregate bond indices typically sit in the 6–7 year range — meaningful rate exposure even for “conservative” allocations.

Spread duration (covered in our credit spreads guide) measures sensitivity to credit spread changes, separate from Treasury rate moves. Corporate total return blends both.

Portfolio duration and immunization

Portfolio duration is the market-value-weighted average of constituent durations. A 60/40 stock-bond portfolio’s rate risk is driven almost entirely by the bond sleeve’s duration times its weight. Pension funds and insurers practice immunization: matching portfolio duration to liability duration so that asset and obligation values move together when rates shift.

Retail investors use duration more simply: pick a bond fund whose effective duration matches their rate outlook and drawdown tolerance. If you cannot stomach a 6% mark-to-market loss on the bond allocation from a 1% rate spike, avoid funds with duration near 6 unless you have a long horizon and rebalance discipline.

Worked example: Harbor Capital bond sleeve stress test

Harbor Capital’s fixed-income sleeve holds $50 million split evenly across three vehicles:

Short Treasury ETF — effective duration 2.0 years, $16.7M
Intermediate IG corporate fund — effective duration 6.5 years, $16.7M
Long government bond fund — effective duration 14.0 years, $16.7M

Weighted average duration: (2.0 + 6.5 + 14.0) / 3 = 7.5 years. The CIO models a parallel +50 bp shift in Treasury yields (spreads unchanged for simplicity).

Estimated price impact: −7.5 × 0.005 = −3.75% on the bond sleeve, or roughly −$1.875 million before coupons. Over a six-month window, coupon income (~2.5% annualized blended yield on half a year) adds back ~$625,000, netting about −$1.25 million or −2.5% on the full $50 million — still painful if the equity leg also sells off.

Response options: trim the long fund (cut tail duration), add T-bills as a cash buffer, or accept the drawdown if liabilities are 10+ years out. The stress test does not predict the next Fed meeting; it sizes worst-case mark-to-market for governance and client communication.

Metric decision table

Question you are asking	Use this measure	Why not duration alone
How much will price move if Treasury yields shift 25–50 bps?	Modified or effective duration	—
Total return if I hold to maturity?	Yield to maturity	Duration is instantaneous sensitivity, not hold-to-maturity return
Impact of credit sentiment, not rates?	Spread duration	Rate duration ignores OAS moves
Large yield shock (100+ bps) on long bonds?	Duration + convexity	Linear estimate drifts on big moves
Callable corporate near current market rates?	Effective duration	Modified duration overstates upside
Match pension payments in 15 years?	Portfolio immunization (duration matching)	Single-bond duration is insufficient
Steepening vs flattening yield curve?	Key-rate durations	Single duration assumes parallel shift
Equity-like upside with bond label?	Inspect convexity and credit quality	High yield can behave like equities in stress

Common pitfalls

Confusing maturity and duration — a 20-year bond with a 6% coupon has far less rate risk than a 20-year zero.
Assuming parallel yield curves — real shocks often steepen or flatten the curve; long and short durations move differently.
Ignoring spread risk on corporates — IG funds can lose from both higher rates and wider spreads simultaneously.
Using stale duration — as yields and prices change, duration drifts; refresh before stress tests.
Forgetting coupon income — duration estimates price change, not six-month total return.
Callable bonds near par — modified duration can imply unrealistic upside; use effective duration.
Leveraged bond funds — duration is multiplied by leverage; a 2x long Treasury ETF doubles rate sensitivity.
International bonds unhedged — duration is local-currency rate risk; FX adds another layer.

Investor checklist

Read effective duration on every bond fund fact sheet before allocating.
Multiply duration by plausible yield shock (e.g., 50–100 bps) to estimate mark-to-market drawdown.
Add convexity adjustment for long portfolios or shocks above 75 bps.
Separate Treasury rate duration from spread duration for corporate holdings.
Align bond sleeve duration with investment horizon and liquidity needs.
Stress-test the full 60/40 portfolio, not bonds in isolation.
Rebalance after large rate moves rather than chasing last year’s winners.
Compare duration across peer funds — “intermediate” labels vary by 2+ years.
For individual bonds, verify whether quoted duration is modified or effective.
Document assumptions when communicating rate-risk exposure to stakeholders.

Key takeaways

Duration measures interest rate sensitivity — roughly the percent price change per 1% yield move.
Modified duration is the practical quote for option-free bonds; effective duration handles calls and funds.
Convexity improves large-move estimates and explains asymmetry in price-yield curves.
Portfolio duration is weighted average — size your bond allocation with eyes open.
Pair duration with YTM and spread risk for a complete fixed-income picture.