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NISM-Series-XXI-A: Portfolio Management Services (PMS) Distributors · Investing in Fixed Income Securities (NISM XXI-A)

Yield Curve and Term Structure of Interest Rates Explained

Updated 11 October 2026 · Fact-checked

A yield curve plots yields of similar-quality bonds against their time to maturity. The term structure explains why yields differ by maturity. To solve questions, identify the curve shape, match it to a theory (expectations, liquidity preference, market segmentation), and use spot rates to compute forward rates.

Understand Yield Curve and Term Structure of Interest Rates

A yield curve is a graph. The x-axis shows time to maturity. The y-axis shows yield. It compares bonds of similar credit quality, such as government securities (G-Secs) of different maturities. The relationship between yield and maturity is called the term structure of interest rates.

The curve has four common shapes. A normal (upward sloping) curve has longer maturities giving higher yields. An inverted (downward sloping) curve has short-term yields above long-term yields. A flat curve has similar yields across maturities. A humped curve rises, peaks at medium maturities, then falls. An upward curve is the usual shape. An inverted curve is often read as a sign that the market expects interest rates to fall and growth to slow.

Three classic theories explain the shape. The pure (unbiased) expectations theory says long-term yields reflect the average of expected future short-term rates. An upward curve means the market expects rates to rise. The liquidity preference theory says investors want extra yield, a liquidity or term premium, for holding longer bonds because they carry more price risk. So the curve slopes up more than expectations alone would suggest. The market segmentation theory says investors and borrowers stick to preferred maturities, so each segment's supply and demand set its own yield. A related idea is the preferred habitat theory, where investors may leave their habitat if compensated.

A spot rate is the yield today on a zero-coupon bond for a given maturity. A forward rate is the rate implied today for borrowing or lending over a future period. It is derived from spot rates. If you can lock in a 2-year spot rate, you can ask what 1-year rate, starting one year from now, gives the same final wealth. That rate is the forward rate.

For a PMS distributor, this matters because a client's fixed income exposure changes value as the curve moves. A parallel shift moves all yields equally. A steepening or flattening changes the gap between short and long yields.

Key formulas to remember

Forward rate from spot rates
(1 + S₂)² = (1 + S₁) × (1 + f₁,₂)
S₁ and S₂ are 1-year and 2-year spot rates. f₁,₂ is the 1-year rate starting one year from now. Use annual compounding unless told otherwise.
General forward rate
(1 + Sₙ)ⁿ = (1 + Sₘ)ᵐ × (1 + f)ⁿ⁻ᵐ
f is the annual forward rate from year m to year n.
Curve shapes
Normal: long yield > short yield | Inverted: long < short | Flat: equal
A humped curve peaks at medium maturities.
Spread (slope)
Slope = Long-term yield − Short-term yield
Positive for normal, negative for inverted, near zero for flat.

How to solve Yield Curve and Term Structure of Interest Rates questions

Questions on this topic are either conceptual (shape or theory) or numerical (forward rate). Use this method.

  1. 1Read what is asked: a shape, a theory, a definition, or a number.
  2. 2For shape questions, compare long-term yield with short-term yield. Higher long means normal, lower long means inverted, equal means flat.
  3. 3For theory questions, find the key phrase: average of expected future rates means expectations; extra premium for longer maturity means liquidity preference; separate maturity markets means segmentation.
  4. 4For forward rate questions, write the equation (1 + longer spot)^n = (1 + shorter spot)^m × (1 + forward)^(n−m).
  5. 5Convert percentages to decimals, solve for (1 + forward), then subtract 1.
  6. 6Convert back to a percentage and check it is sensible: if the curve is upward, the forward rate should exceed the longer spot rate.
  7. 7Eliminate options that mix up spot and forward definitions.

Quickest way: Forward rate shortcut for one-year gaps

When to use it: Use when the question asks for the 1-year forward rate between year 1 and year 2, and options are close in value.

  1. Compute (1 + S₂)² ÷ (1 + S₁) and subtract 1.
  2. Estimate first: forward ≈ 2 × S₂ − S₁. This gives a close approximation.
  3. Pick the option nearest the estimate, then check the exact figure if two options are close.
  4. Sanity check: with an upward curve the forward rate must be above S₂.

Common mistakes in Yield Curve and Term Structure of Interest Rates

  • Averaging spot rates to get the forward rate.

    Averaging feels natural and is quick.

    Fix: Always use the compounding equation. The forward rate is the rate that links the two spot rates, not their average.

  • Calling an inverted curve one where yields rise with maturity.

    The word inverted is confused with increasing.

    Fix: Inverted means short-term yields are higher than long-term yields, so the curve slopes down.

  • Mixing up expectations theory and liquidity preference theory.

    Both can explain an upward curve.

    Fix: Expectations has no premium; yields only reflect expected future short rates. Liquidity preference adds a premium for longer maturity.

  • Treating a spot rate as the yield on any coupon bond.

    Both are called yields.

    Fix: A spot rate belongs to a zero-coupon investment for a given maturity, with a single cash flow at the end.

  • Forgetting to subtract 1 after taking the root or dividing.

    The result looks like a rate such as 1.0850.

    Fix: The calculation gives 1 + f. Subtract 1 before writing the percentage.

  • Reading an inverted curve as a certain forecast of recession.

    It is often presented as a warning sign.

    Fix: Say it is commonly read as a signal of expected falling rates or slower growth, not a guarantee.

Worked examples

Example 1

The 1-year spot rate is 6% and the 2-year spot rate is 7%. What is the 1-year forward rate one year from now, to the nearest 0.01%?

Show the solution
  1. Write (1.07)² = (1.06) × (1 + f).
  2. Compute 1.07² = 1.1449.
  3. Divide: 1.1449 ÷ 1.06 = 1.08009.
  4. Subtract 1: f = 0.08009, or about 8.01%.
  5. Check: the curve is upward, and 8.01% is above 7%, which is sensible.

Answer: About 8.01%

Example 2

A market's 1-year yield is 7.5%, 5-year yield is 7.0% and 10-year yield is 6.5%. Which shape is this, and which theory would explain it by expected future rates?

Show the solution
  1. Compare yields: short 7.5% is above long 6.5%.
  2. The curve slopes downward, so it is inverted.
  3. The theory linking the curve to expected future short rates is the pure expectations theory.
  4. Under that theory, a falling curve means the market expects short-term rates to fall.

Answer: Inverted curve; pure expectations theory explains it by expected falling short-term rates.

Exam tips

  • Learn the four shapes with one line each. Many questions ask only for the shape from given yields.
  • Match the theory by its key phrase: expected future rates, liquidity or term premium, or separate maturity segments.
  • Remember the forward rate is built from spot rates by compounding, never by simple averaging.
  • Check whether options include both the spot and forward rate figures. The spot rate is a given, not the answer.
  • PMS distributor questions are usually conceptual here, so know the definitions well before practising numbers.

Practice questions from Investing in Fixed Income Securities (NISM XXI-A)

Yield Curve and Term Structure of Interest Rates in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Yield Curve and Term Structure of Interest Rates: frequently asked questions

What does an inverted yield curve mean?

Short-term yields are higher than long-term yields. It is often read as the market expecting interest rates to fall or growth to slow. It is a signal, not a certain forecast.

What is the difference between spot rate and forward rate?

A spot rate is today's yield on a zero-coupon bond for a given maturity. A forward rate is the rate implied today for a future period, calculated from spot rates.

Which theory says investors need a premium for longer bonds?

The liquidity preference theory. Longer bonds carry more price risk, so investors ask for a term or liquidity premium, which makes the curve slope up more.

How is the term structure different from the yield curve?

The yield curve is the graph of yields against maturity. The term structure is the relationship itself, along with the theories that explain why yields differ across maturities.