Duration, Modified Duration & Convexity: Practical Bond Risk Answers for Interviews
The biggest misconception about bonds is that βsafe issuerβ means βsafe price.β A government security can have almost no default risk and still fall sharply when yields rise - because duration is not about whether you get paid, it is about how far in the future your money is locked into todayβs rates.
- Bond prices and yields move inversely: when required yield rises, the present value of fixed cash flows falls.
- Macaulay duration is the weighted average time to receive a bondβs cash flows.
- Modified duration estimates percentage price change for a 1 percentage point change in yield.
- Convexity corrects duration because the price-yield relationship is curved, not a straight line.
- Higher coupon means lower duration, all else equal: more cash comes back earlier.
- Higher maturity usually means higher duration: more value is exposed to far-future discounting.
- Interview one-liner: Duration gives first-order interest-rate risk; convexity improves the estimate for larger yield moves.
Big Picture: Duration Is the Bond Investorβs Speedometer
A bond is a sequence of future cash flows. When the market yield changes, each future cash flow is discounted at a new rate. Duration and convexity are the tools that translate that yield move into an estimated price move.
The Core Explanation: From Cash Flows to Price Risk
Start with the clean intuition: a bond is a loan with promised coupons and principal repayment. The price of the bond is the present value of those future payments. If investors now demand a higher yield, the same fixed payments are discounted more heavily, so the price falls.
Duration answers: βOn average, when do I receive the bondβs money?β The later the cash flows arrive, the more the price suffers when yields rise.
Modified duration answers the more practical trading question: βIf yield changes by 1 percentage point, roughly how much will price change?β A modified duration of 5 means the bond price will move about 5% in the opposite direction for a 1 percentage point yield move.
Convexity answers: βHow wrong is the straight-line duration estimate because the true price-yield curve is curved?β For plain vanilla bonds, positive convexity is helpful: prices rise more when yields fall than they fall when yields rise, for the same size move.
Definitions and Formulas You Must Know
- Macaulay duration: Weighted average time to receive a bondβs cash flows, using present-value weights.
- Modified duration: Percentage price sensitivity of a bond to a 1 percentage point change in yield.
- Convexity: Curvature of the bond price-yield relationship, improving duration-based price estimates.
- DV01: Rupee price change for a one basis point change in yield.
The three main formulas are:
- Price: P = Ξ£ CFt / (1 + y)t
- Macaulay duration: DMac = Ξ£ [t Γ PV(CFt)] / Price
- Modified duration: DMod = DMac / (1 + y), for annual compounding
- Approximate price change: ΞP / P β -DMod Γ Ξy + 0.5 Γ Convexity Γ (Ξy)2
Measures to Track: Not Just One Duration Number
In real bond portfolios, one duration number is not enough. A fund manager, treasury analyst or risk team tracks a small dashboard of interest-rate sensitivity measures.
Worked Example: Calculate Duration and Price Impact
Take a 2-year bond with face value βΉ100, annual coupon 8%, and yield to maturity 10%. Cash flows are βΉ8 at the end of year 1 and βΉ108 at the end of year 2.
If yield rises from 10% to 11%, modified duration predicts:
- Approximate percentage price change = -1.750 Γ 1% = -1.75%
- Approximate rupee price fall = 1.75% of βΉ96.529 = about βΉ1.69
- New estimated price = βΉ96.529 - βΉ1.69 = about βΉ94.84
Actual price at 11% yield is βΉ8 / 1.11 + βΉ108 / 1.11Β² = about βΉ94.86. The estimate is close because the yield move is small. For larger moves, convexity becomes more important.
The Duration Management Loop
Portfolio duration is not a βset and forgetβ number. Coupons are received, time passes, new bonds are bought, credit spreads move, the yield curve changes, and the portfolioβs interest-rate risk drifts. Good bond managers keep duration inside a disciplined loop.
Real Example: SVB Showed Duration Risk Without Default Risk
Silicon Valley Bank held a large portfolio of long-duration securities, including US government-backed bonds and mortgage-backed securities. The primary problem was not borrower default; it was asset-liability duration mismatch when interest rates rose sharply. Supporting drivers included concentrated deposits, liquidity pressure and unrealised losses becoming economically important during a run. The so what: high-quality bonds can still create balance-sheet risk if duration is mismanaged.
Case Study: Bharat Bond ETF and the Power of Roll-Down Duration
Edelweiss Mutual Fundβs Bharat Bond ETF uses a target-maturity structure to make duration risk more intuitive for Indian debt investors.
Situation: Indian retail debt investors often understood fixed deposits better than bond funds because bond fund NAVs fluctuate daily. The challenge was to offer access to high-quality public sector bond exposure while making maturity and interest-rate risk easier to understand.
The move: Bharat Bond ETF, managed by Edelweiss Mutual Fund, follows a target-maturity design. The portfolio invests in bonds of eligible public sector entities and matures around a stated target year. As time passes, the portfolio naturally βrolls downβ the yield curve - its remaining maturity and duration reduce, assuming the manager holds bonds close to maturity and maintains the defined structure.
Outcome and lesson: The product does not remove interest-rate risk from interim NAVs. If yields rise, the ETF price can still fall. But the target-maturity structure makes the risk path clearer: duration is higher at the beginning and falls as maturity approaches. The primary driver is the defined maturity design; supporting drivers are high-quality PSU exposure, passive structure, exchange tradability and portfolio transparency.
The strategic takeaway: duration is most useful when linked to an investorβs time horizon. A target-maturity fund makes that link visible.
How AI Changes Duration, Modified Duration & Convexity
AI does not change the formulas. It changes the speed and quality of analysis around them.
- Faster portfolio risk engines: AI-assisted analytics can read a bond portfolio, classify cash flows, estimate duration, DV01, convexity and key-rate duration, then run yield-curve shocks across scenarios.
- Better rate narrative extraction: LLMs can summarise RBI MPC statements, inflation commentary, corporate bond outlooks and treasury reports to identify what the market is watching. The caveat: they support judgement; they do not predict rates with certainty.
- Smarter constraint-based portfolio construction: AI tools can help optimise portfolios across duration, credit quality, liquidity, maturity buckets and mandate limits, especially when a fund manager needs to test many combinations quickly.
Use NotebookLM or Claude: upload a debt fund factsheet, the latest RBI monetary policy statement and this lesson. Ask: βIdentify the fundβs duration risk, likely NAV impact if yields rise by 50 bps, and three interview questions an AMC recruiter may ask.β Then verify all calculations in Excel.
Interview Relevance
βA 10-year bond and a 10-year zero-coupon bond have the same maturity. Will they have the same duration? Explain with modified duration and convexity.β
If you get a numerical bond question, write the cash-flow timeline first. Most errors disappear once the timeline is visible.
Common Mistake
The costliest mistake is saying βduration means maturity.β It costs candidates because it ignores coupons, present-value weights and actual price sensitivity. One-line fix: say βmaturity is the final date; duration is the weighted average cash-flow timing, and modified duration is the price-risk estimate.β
What to Revise Next
Now that you can measure a bondβs sensitivity to yield moves, revise the curve that drives those moves and the instruments where they appear.