Term structure of interest rates
Also written Term structure of interest rates (yield curve) · Yield curve · Zero coupon yield curve · Term structure
Interest rate plotted against term — one curve per credit quality, with the risk-free curve as the base and every other borrower quoted as a spread over it.
In plain language
"What is the interest rate today?" is an unanswerable question, and the workbook says so directly. It is incomplete in two respects.
First, the rate depends on the term. Overnight money and thirty-year money are different products at different prices. Markets quote only standard tenors — overnight, 1 week, 2 weeks, then monthly out to a year in the money market; 2, 5, 7, 10, 15, 20, 25, 30 and 40 years in the bond market.
Second, the rate depends on who is borrowing. For the sovereign the rate is quoted directly. For everybody else what is quoted is the credit spread over it, grouped by rating.
Plot rate against term and you have the term structure. Do it for each rating and you have a family of curves: a risk-free curve, an AAA curve, a BBB curve, and so on, stacked upward.
How it works
What sets the level. Demand and supply for money, assessed separately at each end. Short-term rates are driven by liquidity — seasonal credit demand, foreign portfolio flows, the bunching of tax and government payments. Long-term rates are driven mainly by the inflation outlook and by industry capital expenditure. Central banks control the short end through repo and reverse repo; in developing economies they reach the long end too, through the bank rate, the cash reserve ratio, the statutory liquidity ratio and open market operations.
The workbook notes a specific Indian distortion: the SLR compels banks to hold sovereign debt, so a slice of demand is regulatory rather than economic and the government has influence over the rate it finds acceptable.
The four shapes.
| Shape | What it looks like | What it is read as |
|---|---|---|
| Normal | upward sloping | growth expected, with inflation risk priced into longer tenors |
| Inverted | short rates above long | tight policy, or rates expected to fall; often read as a recession signal |
| Flat | little difference across tenors | late in the cycle, rates rising on inflation expectations |
| Humped | medium-term above both ends | — |
The three shifts, which matter more than the shape:
- Parallel — all rates move the same way by the same amount
- Steepening — the long-short spread widens, the curve rotating anti-clockwise
- Flattening — the spread narrows, rotating clockwise
Steepening and flattening arise three ways: the two rates move in opposite directions, which is a twist; they move the same way by different amounts; or one stays put while the other moves. The last two are a convexity change.
The formula
Rate for a borrower = Risk-free rate for that term + Credit spread for that rating
Curve shift : parallel → Δ(long rate) = Δ(short rate)
steepening → (LR − SR) widens
flattening → (LR − SR) narrows
A worked example
The workbook's rate grid. Risk-free rates by term, with credit spreads by rating:
| Term | Risk-free | AAA | A | BBB |
|---|---|---|---|---|
| 1M | 5.00% | +0.15% | +0.25% | +0.35% |
| 3M | 5.25% | +0.25% | +0.50% | +0.75% |
| 1Y | 5.75% | +0.40% | +0.75% | +1.10% |
| 5Y | 6.50% | +0.85% | +1.50% | +2.25% |
Read it as all-in rates and two patterns appear at once. A BBB borrower pays 5.35% for a month and 8.75% for five years. The spread widens with term as well as with credit, so a 5-year BBB is 225 bp over sovereign while a 1-month BBB is only 35 bp over.
What that costs. A BBB-rated NBFC raising Rs 500 crore for 5 years:
Sovereign cost : 6.50% × Rs 500 crore = Rs 32.50 crore a year
BBB cost : 8.75% × Rs 500 crore = Rs 43.75 crore a year
Credit spread : Rs 11.25 crore a year
Over five years the rating alone costs Rs 56.25 crore, undiscounted. An upgrade to A saves 75 bp, or Rs 3.75 crore a year.
Why a bond desk watches shifts, not shapes. A bank holds a barbell: Rs 200 crore of 1-year paper and Rs 200 crore of 10-year paper with a modified duration of 7.2. The curve steepens by way of a twist — the 1-year rate falls 25 bp while the 10-year rate rises 40 bp.
Short leg : +0.25% × 0.95 duration × Rs 200 cr = + Rs 0.48 crore
Long leg : −0.40% × 7.2 duration × Rs 200 cr = − Rs 11.52 crore
Net = − Rs 11.04 crore
The average level of rates barely moved. The shape moved, and it cost Rs 11 crore — which is why a hedge built for a parallel shift can leave a book badly exposed.
Why NISM asks about it
Chapter 1, section 1.6 (Term Structure of Interest Rates), is the reference: the standard tenors, the risk-free-plus-spread construction, the four shapes with charts, and the shift taxonomy with its twist-versus-convexity-change distinction. Section 1.11.4 then prices a bond off the term structure of zero rates, and Chapter 3 derives forward rates from it.
Questions are largely identification — name the shape from a description, say which shift is a twist, state what an inverted curve is read as — plus the compositional point that a corporate rate is the risk-free rate for that term plus a rating-based spread.
Common exam traps
- There is no single yield curve. There is one per credit quality; "the yield curve" without qualification means the risk-free curve.
- A twist is not any steepening. It is specifically the case where the two rates move in opposite directions; same-direction moves of different size are a convexity change.
- Duration protects against parallel shifts only. A steepening or flattening can hurt a duration-neutral book badly, as the barbell above shows.
- An inverted curve signals expectations, not arithmetic certainty. The workbook lists flight-to-quality and global currency conditions as alternative causes.
- Spreads widen with term as well as with rating. The same issuer is a narrower spread at one month than at five years.
- The Indian curve is not purely market-determined. SLR-driven demand for sovereign debt distorts it, and the workbook flags this explicitly.
Where this is taught
Free preparation for NISM Series V-DRelated terms
- Modified DurationMacaulay's duration divided by (1 + yield) — the percentage by which a bond's price moves for a one percentage point change in interest rates, and so the standard measure of interest rate risk.
- Yield to MaturityThe single discount rate at which a bond's future coupons and redemption amount add up to exactly its market price today — the return you actually earn if you hold it to maturity.
- Credit spreadThe extra yield a non-government borrower must pay over a government security of the same tenor — the market price of credit risk, quoted as an add-on over the risk-free rate.
- Forward rateThe interest rate for a period that starts in the future, implied today by two spot rates — because rolling a short investment must return the same as locking in a long one, or arbitrage follows.
- Risk-free rateThe rate on a sovereign borrowing in its own currency, where credit risk is absent because the government can print the money — the benchmark every other valuation is measured against.
- Spot rateThe true return on money invested today for one stated term with no interim cash flow — read straight off a zero-coupon instrument, and the only rate a cash flow should be discounted at.
- Real interest rateThe nominal rate adjusted for inflation — what the lender actually gains in purchasing power, and a number that turns negative whenever inflation runs above the coupon.
- Fisher effectThe proposition that, other things equal, a rise in expected inflation raises the nominal interest rate — which is why interest rate derivatives are the household sector's instrument for hedging inflation.