IIBF TIRM: yield curve and term structure of interest rates

For IIBF TIRM candidates, the yield curve and term structure of interest rates is the one topic that connects every other chapter in the paper: pricing a G-Sec, valuing a swap, setting funds transfer pricing, and measuring interest rate risk in the banking book all begin with a curve. Examiners rarely ask for a definition alone. They ask you to read a curve, derive a rate from it, name the theory that explains its shape, or say which risk survives after you have hedged duration.

This guide builds the topic the way a dealing room uses it — spot, par and forward curves, bootstrapping, shapes and signals, the three classical theories, and finally the Indian G-Sec curve in live treasury work.

📈 Spot, Par and Forward: Three Views of One Curve

The yield curve and term structure of interest rates describes the relationship between yield and residual maturity for instruments of identical credit quality. In India the reference set is Government of India dated securities, because they carry sovereign credit and the deepest secondary market. Three curves describe the same underlying data.

• Spot (zero-coupon) curve — the rate for a single cash flow received at time t, with no intermediate coupons. This is the only curve you may legitimately use to discount individual cash flows.
• Par curve — the coupon that would make a bond of that maturity price exactly at par (Rs 100). Traded G-Sec yields and the FBIL published curve are par-type quotes.
• Forward curve — rates for a future period implied today, such as the 1-year rate starting one year from now (the "1y1y" forward).

The three are arithmetically linked, not independent opinions. When the curve slopes upward, the ordering is always forward > spot > par; when it is inverted, the ordering reverses. If a question hands you a par yield and asks for a discount factor, the intended step is a conversion, not a shortcut.

Understanding this trio is what separates a rote answer from an applied one. A revision of the basics of instrument classes and market structure in the financial markets chapter makes the curve work far easier, because the curve is only as good as the instruments feeding it.

💡 Exam Tip: If a numerical gives you coupon-bearing bond yields and asks you to value a cash flow, you are being tested on whether you know that coupon yields must first be converted to zero rates.

🧮 Bootstrapping Zero Rates from the Indian G-Sec Curve

Everything quantitative in the yield curve and term structure of interest rates begins here. Bootstrapping is the sequential process of extracting zero-coupon rates from observed par or coupon yields, working outward from the shortest maturity. Because a coupon bond is a bundle of zero-coupon claims, each new maturity can be solved once every earlier one is known.

Take an illustrative set of numbers (not live market levels). Suppose the 1-year zero rate is 6.20% and a 2-year bond trades at par with a 6.80% coupon. Price it:

100 = 6.80 / (1.0620) + 106.80 / (1 + z₂)²

The first term is Rs 6.403, leaving Rs 93.597 as the present value of the final flow. Solving gives a 2-year zero rate of about 6.82%, slightly above the 6.80% par yield — exactly what theory predicts on an upward-sloping curve. The implied 1y1y forward then works out to roughly 7.44%, well above both.

Where does the raw input come from? The short end is anchored by money market rates — call, TREPS, T-Bills and CDs — while the belly and long end come from actively traded G-Sec benchmarks. Primary issuance therefore matters: the way a security is allotted feeds directly into the observed curve, which is why the government securities auction process is examined alongside this topic. Where liquid coupon bonds are scarce, stripped cash flows help, and the mechanics of STRIPS in government securities give you observable zero prices directly.

In practice, banks in India do not bootstrap privately for regulatory valuation. FBIL publishes the benchmark G-Sec par yield curve and valuation prices, and bank investment portfolios are marked using that published curve rather than an in-house construction.

🔍 Curve Shapes and What Each One Signals

Shape questions are the highest-frequency multiple-choice format on this topic, because each shape carries an economic story. Four canonical shapes of the yield curve and term structure of interest rates appear in the syllabus.

An inverted curve is the one to understand properly. It does not mean markets expect low rates forever; it means the market expects future short rates to fall below today's. For a bank funding long assets with short liabilities, inversion compresses the net interest margin immediately, which is why asset-liability committees track slope, not just level.

Shape reading is inseparable from the short end. Policy operations, liquidity conditions and the pricing of money market instruments in treasury management pin down the first year of the curve, and everything beyond is built on that anchor. Revising the money market chapter alongside curve theory is the efficient route. For policy rate context while you practise, keep the current RBI policy rates page open.

⚠️ Common Mistake: Treating "inverted curve" as a synonym for recession in an exam answer. State it as a market expectation of falling future short rates — that is what the term structure actually encodes.

🏛️ Three Theories Behind the Term Structure

The syllabus expects you to distinguish three explanations of why the yield curve and term structure of interest rates takes the shape it does, and to know the weakness of each.

Pure expectations theory

Long rates are simply the geometric average of expected future short rates. A 2-year rate of 6.82% with a 1-year rate of 6.20% implies the market expects roughly 7.44% one year out. The theory's weakness: it predicts a flat curve on average, which observed data contradicts.

Liquidity preference theory

Investors demand extra compensation — a term or liquidity premium — for locking money away and bearing greater price volatility. Forward rates therefore overstate expected future spot rates by that premium, and the curve slopes upward even when rates are expected to stay flat. This is the standard explanation for a normally upward-sloping curve.

Market segmentation and preferred habitat

Different investors are structurally confined to different maturity buckets: banks to the short and medium segments for SLR and liquidity purposes, insurers and pension funds to the long end for liability matching. Supply and demand clear separately in each bucket, so a large long-dated auction can lift the long end without any change in rate expectations. Preferred habitat softens this — participants will leave their habitat, but only for a sufficient yield pick-up.

📌 Remember: Expectations explains movement, liquidity preference explains the upward tilt, and segmentation explains local kinks and humps. Most real curves need all three.

💹 Using the Curve: Valuation, FTP, Curve Trades and Curve Risk

In an Indian bank treasury the yield curve and term structure of interest rates does four jobs, and TIRM tests all four.

Valuation. Investment portfolios classified as AFS and FVTPL under the RBI investment classification framework are marked to market using FBIL prices and the published curve; HTM holdings are carried at amortised cost. A curve shift therefore hits the revaluation reserve or the profit and loss account depending on the bucket a security sits in.

Funds transfer pricing. FTP assigns each asset and liability an internal rate drawn from the curve at its repricing tenor. This strips interest rate risk out of business units and parks it centrally in treasury, where it can be managed. Products whose coupons reset periodically, such as floating rate and inflation indexed bonds, are priced off the forward curve rather than a single spot rate.

Curve trades. Riding (rolling down) the curve means buying a 3-year bond on an upward-sloping curve and selling it a year later as a 2-year bond at a lower yield, capturing roll-down gain on top of accrual — profitable only if the curve does not shift up meaningfully. A steepener is long the short end and short the long end, expressing a view on slope. A butterfly is long the wings and short the belly (or the reverse), expressing a view on curvature alone. All three depend on the day-to-day funding position, so the liquidity management chapter is a necessary companion.

Curve risk versus parallel-shift duration

Modified duration and PV01 assume the entire curve moves by the same amount. Real curves twist. A steepener can be constructed with a net modified duration close to zero and still lose heavily when the curve flattens, because the exposure is to slope, not level. The fix is to measure key rate durations (or bucketed PV01) at 1, 2, 5 and 10 years and to limit each bucket separately — the approach set out in the risk analysis and control chapter.

🧠 Practice MCQs: Yield Curve and Term Structure

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❓ Frequently Asked Questions

🎯 Conclusion

Master three things and the yield curve and term structure of interest rates is secured for the exam: the arithmetic linking par, spot and forward rates; the four shapes and what each implies for a bank's margin; and the fact that duration alone will not protect a portfolio against a twist. Everything else in TIRM — valuation, FTP, hedging, limits — sits on top of that base.

Work through more chapters on the Treasury Investment and Risk Management topic hub, then test yourself with the full CAIIB and certificate course material before your attempt.