Actuarial Mathematics for Modelling · Allowing for inflation

Index-Linked Bonds and Implied Inflation Explained

Updated 11 October 2026 · Fact-checked

An index-linked bond pays coupons and redemption that rise with a price index, so its yield is a real yield. Compare it with a conventional bond of the same term: implied inflation e = (1 + i) ÷ (1 + r) − 1, where i is the money yield and r the real yield. It is a market-implied rate, not a forecast.

Understand Index-Linked Bonds and Implied Inflation

A conventional bond pays fixed rupee amounts. Its yield is a money (nominal) yield, because the cash flows are not protected against rising prices. If inflation turns out higher than expected, the real value of those payments falls.

An index-linked bond pays coupons and a redemption amount that are scaled up by a price index, such as a consumer price index. If prices rise 5%, the payments rise 5%. So the bond fixes the real return. Its yield, worked out on the real (uninflated) cash flows, is the real yield r.

Now put the two bonds side by side. Assume they have the same term, the same credit quality and similar coupon patterns. The conventional bond gives money yield i. The index-linked bond gives real yield r plus whatever inflation turns out to be. Investors will only hold both if the money yield compensates for expected inflation. This gives the link 1 + i = (1 + r)(1 + e). Solving for e gives the implied inflation rate, also called break-even inflation. If actual inflation beats e, the index-linked bond does better. If it is lower, the conventional bond does better.

The word implied matters. e is what the market prices in. It is not a forecast. In practice it also contains an inflation risk premium and liquidity effects, and it is only clean when the bonds really are comparable. Different coupon sizes, tax treatment and an indexation lag all blur the comparison. In CM1 questions you normally ignore these unless the question tells you to include them.

You use the same idea in reverse. If you are given the money yield and an inflation assumption, you can find the real yield. If you are given the real yield and a money yield, you can find the inflation rate. The relationship is always multiplicative, never a simple subtraction.

Key rules to remember

Link between money, real and inflation rates: 1 + i = (1 + r)(1 + e); i = money (nominal) effective annual yield, r = real yield, e = inflation rate, all per year on the same basis.
Implied inflation (break-even inflation): e = (1 + i) ÷ (1 + r) − 1; Use the conventional yield for i and the index-linked real yield for r, both for the same term.
Real yield from money yield: r = (1 + i) ÷ (1 + e) − 1; Use when inflation is assumed or given.
Rough approximation: e ≈ i − r; Only a quick check when rates are small. Exam answers should use the exact formula.
Continuous-time version: δ(money) = ρ(real) + δ(inflation); With force of interest, the relationship is additive: e^δ(money) = e^ρ × e^δ(inflation).
Price of an index-linked bond (no lag): Price = Σ real cash flow(t) × v^t at real yield r; Real cash flows are the amounts before indexation, as if the index stayed at its base level.

How to solve Index-Linked Bonds and Implied Inflation questions

Use this method for any question that links an index-linked bond, a conventional bond and inflation.

1Write down what is given: the term, coupon rates, price or yield for each bond, and any stated lag or assumption about the index.
2Identify the yield type. A conventional bond gives a money yield i. An index-linked bond gives a real yield r. Convert the quoted rate to an effective annual rate if needed.
3If the real yield is not given, find it. Write the price equation using real cash flows (coupon and redemption before indexation), discounted at r, and solve for r.
4Check that the two bonds are comparable: same term, similar coupon. If not, say so and state the assumption you are making.
5Apply 1 + i = (1 + r)(1 + e). Rearrange for the unknown, usually e = (1 + i) ÷ (1 + r) − 1.
6Calculate with enough decimal places, then give the answer as a percentage, usually to two decimals.
7State the meaning in one line: the implied inflation is the average annual rate the market prices in over that term, and it may include a risk premium.

Quickest way: Divide the yield factors

When to use it: Use this when both yields are given and the question asks for implied inflation or real yield, especially in multiple-choice questions.

Turn both yields into factors: 1 + i and 1 + r.
Divide money factor by real factor to get 1 + e.
Subtract 1. Do not subtract the yields directly.
Sense check: the exact answer is slightly below i − r when both are positive, so if your answer is far from i − r, recheck.
If the question gives e and r and wants i, multiply the factors instead: i = (1 + r)(1 + e) − 1.

Common mistakes in Index-Linked Bonds and Implied Inflation

Finding implied inflation as i − r and quoting that as the exact answer.
The subtraction is easy and is a good approximation when rates are small, so it feels right.
Fix: Use e = (1 + i) ÷ (1 + r) − 1. Keep i − r only as a sense check.
Discounting the indexed cash flows at the real yield, or the real cash flows at the money yield.
Real and money amounts look alike, and students lose track of which basis they are on.
Fix: Real cash flows go with real rates. Money cash flows (after indexation) go with money rates. Never mix them in one calculation.
Comparing bonds of different terms and calling the result the implied inflation.
Students take the first two yields they see without checking maturity.
Fix: Check the terms match. If they do not, say so, or use yields for the same term or spot rates.
Treating implied inflation as the market's forecast of inflation.
The textbook name 'expected inflation' makes it sound like a prediction.
Fix: Call it market-implied or break-even inflation. Note that it can include an inflation risk premium and liquidity effects.
Indexing the coupon at the wrong time or from the wrong base date.
The index value used for each payment is not clearly written down.
Fix: Write the index ratio for each payment date next to the cash flow. Follow any lag stated in the question. If none is stated, assume payments are indexed to the date of payment.
Solving for the real yield and then forgetting to convert back to the percentage rate asked for, or using v instead of 1 + r.
Quadratic solutions give v, not the rate, and this step is rushed.
Fix: After finding v, calculate r = 1 ÷ v − 1 and check by substituting back into the price equation.

Worked examples

Example 1

A 10-year conventional government bond has a gross redemption yield of 8% per year. A 10-year index-linked government bond has a real yield of 3% per year. Assume the bonds are comparable. Find the implied annual rate of inflation.

Show the solution

Money yield i = 0.08 and real yield r = 0.03.
Use 1 + i = (1 + r)(1 + e), so 1 + e = 1.08 ÷ 1.03.
1.08 ÷ 1.03 = 1.048544 (to six decimals).
e = 1.048544 − 1 = 0.048544, or 4.85% to two decimals.
Check: i − r = 5%, and the exact answer is slightly lower, as expected.

Answer: The implied inflation rate is about 4.85% per year.

Example 2

A 2-year index-linked bond pays an annual coupon of 4 per 100 nominal in real terms and is redeemed at 100 in real terms, with both amounts indexed to a price index with no lag. Its price is 98.1405 per 100 nominal. A 2-year conventional bond has a gross redemption yield of 7.25% per year. Find the real yield on the index-linked bond and the implied inflation rate.

Show the solution

Write the price equation on a real basis with v = 1 ÷ (1 + r): 98.1405 = 4v + 104v².
Rearrange: 104v² + 4v − 98.1405 = 0.
Use the quadratic formula: v = [−4 + √(16 + 4 × 104 × 98.1405)] ÷ (2 × 104).
4 × 104 × 98.1405 = 40,826.448, so the discriminant is 40,842.448 and its square root is 202.0951.
v = (202.0951 − 4) ÷ 208 = 0.952381.
r = 1 ÷ 0.952381 − 1 = 0.05, so the real yield is 5%.
Check: 4 ÷ 1.05 + 104 ÷ 1.05² = 3.8095 + 94.3310 = 98.1405, which matches the price.
Now take i = 0.0725. Then 1 + e = 1.0725 ÷ 1.05 = 1.021429.
e = 0.021429, or 2.14% to two decimals.

Answer: The real yield is 5% per year and the implied inflation rate is about 2.14% per year.

Exam tips

Show the formula 1 + i = (1 + r)(1 + e) before you substitute. Method marks in written answers depend on seeing it.
In multiple-choice questions, work out the exact answer and compare it to i − r. The wrong options often include the simple subtraction.
Write 'real' or 'money' beside every rate and cash flow in your working. It prevents mixing the two bases.
If a question asks you to comment, say that implied inflation depends on the bonds being comparable and can include a risk premium. Do not call it a forecast.
In computer-based Paper B questions, keep full precision in the spreadsheet or R code and round only the final answer. State your assumption about indexation lag.

Practice questions from Allowing for inflation

Index-Linked Bonds and Implied Inflation: frequently asked questions

How do I find implied inflation from bond yields?

Take a conventional bond and an index-linked bond of the same term. Divide one plus the conventional (money) yield by one plus the index-linked (real) yield, then subtract one. This gives the market-implied annual inflation rate.

What is the real yield on an index-linked bond?

It is the yield found by discounting the real cash flows, which are the coupons and redemption before indexation, so that the present value equals the price. It shows the return above inflation.

What is break-even inflation?

It is the inflation rate at which a conventional bond and an index-linked bond of the same term give the same return. If actual inflation is higher, the index-linked bond wins. If lower, the conventional bond wins.

Is implied inflation the same as expected inflation?

Not exactly. Implied inflation is what bond prices suggest. It can include an inflation risk premium, liquidity effects and tax differences, so it may differ from what investors actually expect.