CAIIB BFM: duration and convexity explained for the 2026 exam

Every CAIIB BFM paper carries at least one question where candidates lose marks not because they don't know bond math, but because they mix up two closely related ideas. This article is built around duration and convexity, the pair of tools every treasury desk and every BFM examiner leans on to answer one question: if interest rates move by 1%, how much does my bond portfolio's value move? Get the mechanics right and this becomes one of the easiest scoring areas in the paper.

We build the concept from the ground up — bond price and yield, Macaulay duration, modified duration, and the convexity correction that duration alone misses — then tie it back to how Indian bank treasuries actually use it for interest rate risk management.

📉 Why Bond Prices Move When Yields Move

A bond's price is the present value of its future coupons and redemption value, discounted at the market yield. When the yield goes up, the discount rate applied to those future cash flows goes up too, so the present value — the price — comes down. This inverse price-yield relationship is the starting point for everything else in this topic.

But the relationship is not a straight line. A bond doesn't lose the same rupee amount for every 1% rise in yield; the price-yield curve is convex, bowed toward the origin. For small yield changes, a straight line is a good enough approximation. For larger changes, the curve bends away from that line, and that bend is exactly what the second measure in this topic captures.

Banks care about this because a large chunk of the investment book — SLR holdings, AFS and HFT securities — is priced to market. A treasury that cannot estimate how much its book will swing on a 25 or 50 basis point rate move is flying blind, which is why this pair of measures sits at the core of every BFM treasury chapter.

For a bank's SLR portfolio this is far from academic. A single 100 basis point parallel shift in the yield curve can move the mark-to-market value of a large bond book by several hundred crore rupees, hitting the available-for-sale reserve directly and, past the trigger levels a bank sets internally, spilling into the profit and loss account as well.

🧮 Macaulay Duration and Modified Duration Explained

Macaulay duration is the weighted average time (in years) it takes to recover a bond's price through its cash flows, where each cash flow is weighted by its present value share of the total price. A zero-coupon bond's Macaulay duration equals its maturity; a coupon-paying bond's duration is always shorter than its maturity because some cash comes back earlier through coupons.

Modified duration converts this time measure into a price-sensitivity measure: Modified Duration = Macaulay Duration / (1 + y/n), where y is the yield and n is the number of compounding periods a year. The approximate percentage price change for a given yield change is then:

% change in price ≈ − Modified Duration × Change in yield

A bond with modified duration of 6 will fall by roughly 6% in price for a 1% (100 bps) rise in yield, and rise by roughly 6% for a 1% fall. Longer maturity, lower coupon, and lower yield all push duration higher — a fact examiners like to test with "which bond has higher duration" comparison questions.

Take a 10-year bond carrying an 8% annual coupon and priced to yield 8%. Its Macaulay duration works out close to 7.25 years, well short of the 10-year maturity, because a sizeable share of its total present value comes back through coupons long before redemption. Dealing-room bond calculators compute this instantly, but examiners still expect candidates to trace the weighted-average logic by hand.

🔎 Convexity: The Correction Duration Misses

Because the price-yield curve bends, modified duration alone under-predicts the price gain when yields fall and over-predicts the price loss when yields rise. Convexity captures this curvature and is added as a second-order correction:

% change in price ≈ − (Modified Duration × Change in yield) + (½ × Convexity × (Change in yield)²)

Positive convexity is good news for a bondholder: it means gains on a yield fall are larger than losses on an equivalent yield rise. Plain-vanilla government and corporate bonds are positively convex. Bonds with embedded call options behave differently — a callable bond can show negative convexity near the call price because the issuer's option to redeem early caps the price upside.

Convexity is typically expressed in units of years-squared and, much like duration, rises with maturity and falls with a higher coupon rate or yield. Two bonds can share an identical modified duration yet carry different convexity — the one whose cash flows are more spread out across early and late years usually shows higher convexity than one whose payments cluster evenly around the average maturity.

💡 Exam Tip: If a question gives both figures and asks for the price change on a large yield move (say 2% or more), always add the convexity term — questions testing "small move" scenarios can be solved with duration alone, but large-move questions are convexity questions in disguise.

🏦 Duration and Convexity in Bank Treasury and ALM

In a bank's Asset-Liability Management setup, this analysis is used well beyond a single bond. Treasury desks compute the weighted average duration of the entire investment portfolio, and separately the duration of rate-sensitive liabilities, to understand how the bank's net worth reacts to a rate shock. This portfolio-level view is what allows the ALCO to decide whether to shorten or lengthen the book ahead of an expected rate cycle turn.

This also drives the choice of hedging instruments. A treasury expecting yields to rise on a long-duration SLR book may sell bond futures or enter an interest rate swap to bring the effective duration down without an outright sale of securities — avoiding a hit to available-for-sale reserves. The related chapters on External Commercial Borrowings And Foreign Investments In India and Exchange Rates and Forex Business show the same duration logic applied to foreign-currency borrowings and forex-linked treasury positions.

Because assets and liabilities rarely share the same duration, banks routinely track the duration gap between the two sides of the balance sheet as one input into their broader interest rate risk monitoring, alongside the periodic rate-sensitivity returns that the Reserve Bank of India prescribes. A positive duration gap means assets are more rate-sensitive than liabilities, so a sharp rate rise erodes net worth by more than an equivalent fall would add to it.

⚠️ Common Mistake: Candidates often assume higher coupon means higher duration. It is the opposite — a higher coupon returns more cash sooner, pulling the weighted-average recovery time down, not up.

📊 Duration and Convexity: Price Sensitivity at a Glance

The table below summarises how the two measures behave and where each is reliable, a comparison that comes up directly in CAIIB BFM objective questions.

📌 Remember: Duration alone is a straight-line estimate; convexity is what bends that line back onto the real, curved price-yield relationship — always report both when a question asks you to justify a price forecast.

Duration and convexity rarely appear in isolation in the CAIIB BFM paper. Understanding trading book vs banking book classification makes it easier to see why a bank marks some duration-sensitive holdings to market daily while others sit at amortised cost. The hedges used to manage this risk also feed into accounting treatment — candidates who have studied hedge accounting for banks will recognise a fair value hedge on a bond position as a duration-management trade wrapped in Ind AS 109 documentation. Since much of a bank's rate-sensitive book originates from its deposit franchise, it is worth revisiting cost of deposits and deposit pricing for the liability side of the same mismatch story.

The way these treasury decisions show up in shareholder value is explained through economic value added EVA, covered in the CAIIB ABFM paper. For the regulatory backdrop, see the Reserve Bank of India's official website. For a worked example, see Correspondent Banking and NRI Accounts, and browse every article tagged under Bank Financial Management for the rest of the syllabus.

🧠 Practice MCQs: Duration and Convexity

Want chapter-wise mock tests with 100+ MCQs? Start practising free

🎯 Conclusion: Make Duration and Convexity Your Easy Marks

Duration and convexity are formula-driven, which makes them some of the most predictable marks available in the CAIIB BFM paper once the underlying logic clicks — price falls when yield rises, duration gives the linear estimate, convexity corrects the curve. Revisit the worked example, work through the practice MCQs above a second time, and you will be able to answer both numerical and conceptual variants confidently. Put this to the test with a full timed set on the CAIIB course page or jump straight into chapter-wise mock tests to see how these numbers show up under real exam pressure.