CFA Level I · CFA Level I Exam

Interest Rate Risk and Return for CFA Level I

Interest rate risk is the change in a bond's price when yields change. You measure it with duration (first-order effect) and convexity (second-order effect). Price change ≈ −ModDur × ΔYield + ½ × Convexity × (ΔYield)². Returns over a holding period combine coupons, reinvestment and the sale price.

What this chapter covers

This chapter in Fixed Income explains why bond prices move when yields move, and how to measure and manage that movement. It starts with the inverse price-yield relationship, then builds tools: horizon yield, the duration family, money duration, price value of a basis point, and convexity. It ends with portfolio-level duration, yield curve risk and matching duration to an investment horizon.

The maths is mostly short formulas and a few calculator steps. Most items ask you to apply a formula, or to judge direction: which bond is more sensitive, what happens to price if yield rises, what happens to reinvestment income. Each topic feeds the next, so a gap early shows up later.

The chapter connects to bond valuation and yield measures earlier in Fixed Income, to credit analysis and structured products, and to Portfolio Construction and Derivatives, where duration is used to hedge and to set risk. Quantitative Methods also helps, since duration is a derivative-style approximation and convexity is the curvature correction.

Fixed Income carries 11-14% of the 2027 Level I exam, and duration and convexity are among its most testable ideas. Questions are multiple-choice items with a stem and three options, and there is no penalty for wrong answers, so a clean grasp of the formulas lets you earn quick marks. The same concepts return in portfolio and risk questions, so effort here pays off in several topics.

Interest Rate Risk and Return: topics in the order to study them

1Bond Price-Yield RelationshipEverything else describes this curve: price falls as yield rises, and the curve is convex.
2Bond Returns and Horizon YieldIt shows how coupons, reinvestment and sale price drive return, and sets up why duration matching works.
3Macaulay, Modified and Effective DurationDuration is the core measure of price sensitivity; you need all three versions and when each applies.
4Money Duration and Price Value of a Basis PointThese convert percentage duration into currency amounts, using the duration you just learned.
5Bond Convexity and Price Change EstimationConvexity corrects duration's error, so you must know duration first.
6Portfolio Duration and Yield Curve RiskIt extends duration to portfolios and shows where the one-yield-change assumption breaks down.
7Investment Horizon and Macaulay Duration MatchingIt pulls together price risk and reinvestment risk, so it comes last.

How to prepare Interest Rate Risk and Return

Work from the concept to the formula, then to the calculator, then to timed questions. Keep a one-page formula sheet and refine it as you go.

Sketch the price-yield curve and mark where price rises, falls and curves. Explain in words why a lower coupon or longer maturity makes the bond more sensitive.
Practise horizon return questions by splitting the total into coupons, reinvestment income and sale price. Use the calculator for the sale price: set N, I/Y, PMT and FV, then compute PV (BA II Plus: N, I/Y, PMT, FV, CPT PV).
Learn the duration family as a ladder: Macaulay is a weighted time, modified converts it to price sensitivity, effective is used when cash flows change with yield. Write when each is used.
Do ten price-change estimates in a row using duration only, then add the convexity term. Compare each to the exact price so you see how large the error gets.
Compute portfolio duration as a weighted average, then answer direction questions on parallel shifts versus steepening and flattening.
Finish with horizon matching: state the conditions, and decide what happens to price risk and reinvestment risk when yields move.
Finish with timed sets of about 90 seconds per question. For each wrong answer, note whether the cause was a formula, a sign or a concept.

Common mistakes in Interest Rate Risk and Return

Using Macaulay duration directly to estimate price change.
Fix: Always convert to modified duration first: divide by (1 + y/m). Use the modified figure in the price-change formula.
Getting the sign wrong in the price-change estimate.
Fix: Decide the direction first: yield up means price down. Then check your answer's sign against that.
Forgetting to square the yield change, or to halve it, in the convexity term.
Fix: Write ½ × Convexity × (ΔYield)² each time. Check that the term is always positive when convexity is positive. It is small for small yield changes, but it grows with the square of the yield change.
Treating money duration or PVBP as a percentage.
Fix: Money duration and PVBP are currency amounts. Multiply annual modified duration by the full price of the position (its market value, including accrued interest). Then PVBP ≈ money duration × 0.0001.
Assuming a portfolio's duration captures all rate risk.
Fix: Remember it assumes a parallel shift. Non-parallel moves need yield curve analysis, such as key rate exposures.
Ignoring reinvestment risk in horizon questions.
Fix: Split the total return into coupons, reinvestment income and sale price, and ask how a rate change affects each.

Last-day revision: Interest Rate Risk and Return

Bond price and yield move in opposite directions.
For equal yield changes, a fall in yield raises price by more than a rise in yield lowers it, because of convexity.
Lower coupon and longer maturity generally mean higher price sensitivity.
Modified duration = Macaulay duration ÷ (1 + y/m), where m is the number of periods per year.
Price change ≈ −ModDur × ΔYield, then add ½ × Convexity × (ΔYield)².
Effective duration is used when cash flows depend on yield, such as callable bonds.
Money duration = annual modified duration × full price of the position (its market value), expressed in currency units. Always use the full price, including accrued interest.
PVBP is the price change for a one basis point yield change. PVBP ≈ money duration × 0.0001.
Portfolio duration is the market-value weighted average of bond durations, and it assumes a parallel shift in yields.
Yield curve risk arises when rates do not shift in parallel; duration alone misses it.
Price risk and reinvestment risk approximately offset when the bond's Macaulay duration (not modified duration) equals the investment horizon. This holds for a single instantaneous parallel yield shift right after purchase, and for a bond with fixed cash flows (no default or embedded options). Non-parallel shifts or later yield changes break the offset, so the match needs rebalancing over time.
Positive convexity helps the investor: it adds to price gains and cushions losses.

Interest Rate Risk and Return practice questions

Interest Rate Risk and Return in other exams

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

Interest Rate Risk and Return: frequently asked questions

Which duration formulas must I memorise for Level I?

Know modified duration from Macaulay duration, the price-change approximation with and without convexity, money duration and PVBP. Know the portfolio duration weighted average. Questions are mostly application, so practise each formula until the steps are automatic.

When is effective duration used instead of modified duration?

Use effective duration when expected cash flows change as yields change, as with callable bonds or bonds with embedded options. Modified duration assumes fixed cash flows. Effective duration is estimated from prices when the benchmark curve shifts up and down.

Why does convexity matter if duration already estimates price change?

Duration is a straight-line estimate, but the price-yield curve bends. For large yield changes, duration alone misses the curvature. Adding the convexity term gives a closer estimate.

Can I use the BA II Plus for these questions?

Yes. Use the time value keys to find a bond's price at a new yield: enter N, I/Y, PMT and FV, then compute PV. Compare that with your duration estimate to see the error.