Duration and Convexity of Bonds: A Treasury Management Exam Guide (2026)
Ask any candidate who has sat the Treasury Management paper what trips them up most in the fixed income section, and nine times out of ten the answer is duration and convexity of bonds. It sounds like pure mathematics, but examiners love it precisely because it separates candidates who memorised formulas from those who understand what a bond's price actually does when yields move. This guide breaks the concept down the way you need it for the exam hall — and the way you will actually use it on a real dealing desk.
📐 What Duration Actually Measures
Duration is not simply "how long until the bond matures." That is a common first-year mix-up, and IIBF examiners exploit it in tricky MCQs. Macaulay duration is the weighted average time to receive a bond's cash flows, where each cash flow is weighted by its present value as a share of the bond's total price. A 10-year bond paying a high coupon has a duration well short of 10 years, because a large chunk of value arrives earlier through coupon payments. A zero-coupon bond, by contrast, has duration exactly equal to its maturity, since the entire cash flow lands on a single date.
What treasury desks actually use day to day is modified duration, which converts Macaulay duration into a direct measure of price sensitivity: the approximate percentage change in a bond's price for a 1% (100 basis point) change in yield. If a bond has a modified duration of 6, a 1% rise in yield produces roughly a 6% fall in price. This single number is why duration sits at the heart of every interest-rate-risk conversation in a bank's treasury, and why the topic under Fixed Income Securities, Duration and Convexity carries disproportionate exam weight. Banks' own investment portfolios are governed by the Reserve Bank of India's classification and valuation norms, published on the RBI's official website, which is where treasury desks track any change to how duration-sensitive holdings must be marked.
💡 Exam Tip: If a question gives you modified duration and asks for the price change from a yield move, the formula is simply: % price change ≈ −(Modified Duration × Δyield). Watch the negative sign — bond prices and yields move inversely.
📊 Modified Duration vs Macaulay Duration vs Convexity
Candidates frequently confuse the three related measures because they all describe the same underlying price-yield relationship from different angles. The table below is the fastest way to keep them straight before the exam.
| Measure | What it tells you | Linear approximation only? | Used for large yield moves |
|---|---|---|---|
| Macaulay Duration | Weighted average time to cash flows (in years) | ✅ Yes | ❌ No |
| Modified Duration | % price change per 1% yield change | ✅ Yes | ❌ No |
| Convexity | Rate of change of duration itself as yields move | ❌ No — it's the correction term | ✅ Yes |
Notice the pattern: duration alone gives you a straight-line estimate, but the actual price-yield curve is curved, not straight. That curvature is exactly what convexity captures, and it is why relying on duration alone under-predicts price gains and over-predicts price losses for anything beyond a small yield shift.
🔄 Why Convexity Corrects Duration's Blind Spot
Duration assumes the price-yield relationship is a straight line, but bond prices actually trace a convex curve — bowed the same way for almost every plain-vanilla bond. For a given fall in yield, the price gain predicted purely by duration understates the real gain; for a given rise in yield, the price loss predicted by duration overstates the real loss. Convexity is the second-order term that fixes this. The fuller price-change formula candidates should carry into the exam is:
% price change ≈ −(Modified Duration × Δyield) + ½ × Convexity × (Δyield)²
For small yield movements — say 10-25 basis points — the convexity term is negligible and duration alone is a fine estimate. But once the Reserve Bank moves policy rates by 50-75 basis points in a single cycle, ignoring convexity can meaningfully misstate the P&L impact on a bank's investment portfolio. This is precisely why treasury desks that manage large SLR/HTM books watch convexity closely, and why the topic connects directly into the exam's coverage of Risk Analysis and Control.
⚠️ Common Mistake: Students often assume convexity is always a bad thing to manage. In fact, positive convexity is desirable — it means gains from falling yields exceed losses from rising yields of the same size. Only certain instruments (like callable bonds) can show negative convexity, which examiners specifically test.
🏦 Applying Duration-Convexity in a Bank's Treasury Book
On a real desk, duration and convexity are not academic exercises — they drive daily hedging and portfolio decisions. A bank's treasury holds a mix of government securities, corporate bonds and other capital market instruments largely to meet statutory SLR requirements while also generating trading gains. The portfolio's aggregate duration determines how much its market value will swing with each RBI monetary policy announcement, which is why treasury heads track "portfolio duration" as closely as they track yield levels themselves.
When a desk expects yields to rise, it typically shortens portfolio duration — selling longer-dated paper and rotating into shorter-tenor instruments discussed under Fixed Income Securities — to limit mark-to-market losses. When yields are expected to fall, extending duration captures larger price gains. Because these decisions interact with a bank's asset-liability position, duration analysis also feeds into the broader framework covered in our guide on ALM interface in treasury, and desks that use swaps or futures to adjust duration synthetically should also revisit treasury derivatives hedging for the instruments involved.
📌 Remember: Portfolio duration is simply the market-value-weighted average of the durations of every bond held — a concept that also underlies the broader discipline covered in bond portfolio management.
📈 How the Exam Frames Duration and Convexity Questions
IIBF numerical questions on this topic usually take one of three shapes: (1) calculate Macaulay or modified duration from a set of cash flows, (2) apply the modified-duration formula to estimate a price change for a given yield shift, or (3) test conceptual understanding — for example, asking which bond among several has the highest duration (hint: the one with the lowest coupon and the longest maturity generally wins), or why convexity matters more for long-tenor bonds than short-tenor ones. Case-study questions sometimes embed this inside a broader treasury scenario, so it pays to be comfortable moving between the pure formula and the practical "what would the desk do" framing. Candidates preparing across the full syllabus, not just this chapter, should also revisit integrated treasury management, since duration decisions rarely sit in isolation from a bank's overall treasury strategy. For the complete chapter list and structured revision, the Treasury Management tag hub is the fastest way to navigate every related article.
🧠 Practice MCQs: Duration and Convexity
Q1. A bond has a modified duration of 5. If yields rise by 0.5%, the approximate price change is: (a) +2.5% (b) −2.5% (c) −5% (d) +5%
Answer: (b) — % price change ≈ −(5 × 0.5%) = −2.5%; price falls when yields rise.
Q2. Which bond, all else equal, has the highest duration? (a) High coupon, short maturity (b) Zero coupon, long maturity (c) High coupon, long maturity (d) Zero coupon, short maturity
Answer: (b) — Zero-coupon bonds have duration equal to maturity, and longer maturity further raises duration since there are no early cash flows to pull the weighted average down.
Q3. Convexity is best described as: (a) The average maturity of a bond (b) The coupon reinvestment rate (c) The rate of change of duration as yields move (d) The credit spread over G-secs
Answer: (c) — Convexity captures the curvature in the price-yield relationship that duration, a linear measure, misses.
Q4. A treasury desk expecting a rate hike cycle would typically: (a) Extend portfolio duration (b) Shorten portfolio duration (c) Ignore duration entirely (d) Convert all holdings to equity
Answer: (b) — Shortening duration reduces the portfolio's sensitivity to rising yields, limiting mark-to-market losses.
Q5. Positive convexity means: (a) Losses from rising yields exceed gains from falling yields (b) Gains from falling yields exceed losses from rising yields of equal size (c) The bond has no interest rate risk (d) Duration equals zero
Answer: (b) — Positive convexity is favourable: for equal-sized yield moves, the price gain on a fall in yields exceeds the price loss on a rise.
Want chapter-wise mock tests with 100+ MCQs? Start practising free →
What is the difference between Macaulay duration and modified duration?
Macaulay duration is the weighted average time (in years) to receive a bond's cash flows. Modified duration adjusts this figure to directly estimate the percentage price change for a 1% change in yield, making it the measure actually used for price-risk calculations.
Why does convexity matter more for long-tenor bonds?
Long-tenor bonds have a more pronounced curve in their price-yield relationship, so the linear duration estimate diverges further from the actual price change as yields move. Convexity corrects this gap, and the correction grows with maturity.
Can a bond have negative convexity?
Yes. Callable bonds and certain mortgage-backed securities can exhibit negative convexity, where price gains from falling yields are smaller than price losses from rising yields, because the issuer's call option caps the upside.
How is duration and convexity tested in the IIBF Treasury Management exam?
Expect a mix of direct numerical questions (calculating duration or estimating price change from a yield shift) and conceptual questions comparing bonds with different coupons and maturities, often embedded in a treasury case-study scenario.
Duration and convexity together give you the full picture of a bond's interest-rate risk — one as the first-order estimate, the other as the correction that keeps it honest. Lock in both formulas, work through a few numerical variations, and test yourself with a full CAIIB Treasury Management mock before exam day.
Practice this topic
Take a free mock test, download chapter PDFs, or watch a video class — all included on iibf.store.
