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CFA Level I · CFA Level I Exam

Yield-Based Bond Duration Measures and Properties for CFA Level 1

Duration measures a bond's sensitivity to changes in its yield to maturity. Macaulay duration is the weighted average time to cash flows. Annual modified duration = Macaulay duration (years) ÷ (1 + y/m), where y is the annual yield and m is periods per year. For an option-free bond, %ΔPrice ≈ −ModDur × ΔYield + ½ × Convexity × (ΔYield)². Add convexity for large moves.

What this chapter covers

This chapter teaches you to measure interest rate risk on a bond using its yield to maturity. You start with Macaulay duration, the weighted average time until the bond's cash flows arrive. You then convert it to modified duration, which gives the approximate percentage price change for a 1% (100 bps) yield change. Money duration restates the same risk in currency terms.

The chapter then explains what makes duration larger or smaller: coupon, yield, maturity and the effect of coupon dates. It extends duration to portfolios and shows where the portfolio average breaks down. Convexity corrects the straight-line duration estimate, which is too crude for large yield changes. The last topic links Macaulay duration to the investment horizon, which is how a bond manager can immunise a liability.

This chapter sits inside Fixed Income, which has a 11-14% topic weight in the 2027 curriculum. It builds on bond pricing and yield measures, and it leads into credit analysis, structured products and the liability-driven strategies in Portfolio Construction. Duration ideas also return in Derivatives and Risk Management when you hedge interest rate exposure.

Fixed Income carries 11-14% of the Level I exam, and duration is one of its most tested ideas. The questions are short and often numerical, so each one is quick marks if you know the formulas. Every question is a three-option MCQ with no penalty for wrong answers, so you can often eliminate options just by checking direction: a yield rise means a price fall, and for an option-free bond the convexity adjustment is positive, so it adds to the estimated percentage price change (it reduces a fall or increases a rise). Bonds with embedded options can have negative convexity, so do not assume this for them. The concepts also help in later fixed income chapters, so the effort pays back more than once.

Yield-Based Bond Duration Measures and Properties: topics in the order to study them

  1. 1Macaulay, Modified and Money DurationThese are the core definitions and formulas; every other topic builds on them.
  2. 2Duration Properties and DeterminantsOnce you can compute duration, learn how coupon, yield and maturity move it, which most conceptual questions test.
  3. 3Portfolio Duration and Its LimitationsThis applies the single-bond measure to a group of bonds and shows why the average assumes a parallel yield shift.
  4. 4Convexity and Price Change EstimationThis refines the duration estimate and needs modified duration to be solid first.
  5. 5Investment Horizon and Macaulay DurationThis is the capstone use of Macaulay duration and ties price risk to reinvestment risk, so it comes last.

How to prepare Yield-Based Bond Duration Measures and Properties

Duration is a formula topic with a lot of direction-of-change logic. Practise both the arithmetic and the reasoning, in short sessions that fit a phone and a working day.

  1. Write the key formulas from memory: annual modified duration = MacDur ÷ (1 + y/m), with MacDur in years, y the annual yield and m the number of periods per year. Money duration = annual modified duration × full price.
  2. Compute Macaulay duration once by hand for a small two- or three-year bond, so you see it as a weighted average of times with present values as weights.
  3. Practise approximate price change: %ΔPrice ≈ −ModDur × ΔYield. Check the sign each time before choosing an answer.
  4. Build a one-page table of how coupon, yield and maturity affect duration, and note the exceptions for long-maturity low-coupon bonds.
  5. Add convexity: %ΔPrice ≈ −ModDur × ΔYield + ½ × Convexity × (ΔYield)². Practise with both small and large yield changes and compare the two estimates.
  6. Work through portfolio duration and horizon questions, stating the assumptions (parallel shift, matching duration to horizon) in your own words.
  7. Finish with timed sets of MCQs at about 90 seconds each, and review every miss by sorting it into a formula slip, a sign slip or a concept gap.

Common mistakes in Yield-Based Bond Duration Measures and Properties

  • Forgetting the minus sign and choosing a price rise when yields rise.

    Fix: Decide the direction first from the yield move, then compute the size. Eliminate any option with the wrong direction.

  • Dividing by (1 + annual yield) when the bond pays semiannually.

    Fix: Divide by (1 + y/m), where y is the annual yield and m is the number of periods per year. Keep Macaulay duration in years so modified duration is annual.

  • Using the bond's par value instead of its full price for money duration.

    Fix: Multiply annual modified duration by the full price, or by the market value of the position, not the face value.

  • Treating duration alone as accurate for large yield changes.

    Fix: For large changes, add the convexity term. For an option-free bond, the convexity term is positive and is added to the duration estimate, so the actual price is higher than the duration-only estimate.

  • Applying portfolio duration as if it handles any yield curve move.

    Fix: State the assumption of a parallel shift. Non-parallel shifts need other measures, and the average gives only an approximation.

  • Mixing up what 'horizon equals Macaulay duration' protects against.

    Fix: Remember: a rate rise lowers price but raises reinvestment income. When the horizon matches Macaulay duration, the two effects roughly offset for a parallel shift.

Last-day revision: Yield-Based Bond Duration Measures and Properties

  • Macaulay duration is the present-value-weighted average time to receipt of a bond's cash flows.
  • Annual modified duration = Macaulay duration (in years) ÷ (1 + y/m), where y is the annual yield and m the periods per year.
  • %ΔPrice ≈ −ModDur × ΔYield; prices and yields move in opposite directions.
  • Money duration = annual modified duration × the bond's full price; it gives the currency change per unit yield change.
  • Duration generally rises with longer maturity, but for a long-maturity bond trading at a discount to par this relationship can fail. Duration falls with a higher coupon rate, other things equal.
  • Higher yield to maturity means lower duration, other things equal.
  • Portfolio duration as a weighted average of bond durations assumes a parallel shift in yields.
  • For an option-free bond, convexity adds a positive correction: ½ × Convexity × (ΔYield)².
  • For a given duration, higher convexity is favourable for a bond holder, whether yields rise or fall.
  • Duration plus convexity is a better estimate than duration alone, especially for large yield changes.
  • When the investment horizon equals the Macaulay duration, price risk and reinvestment risk roughly offset for a parallel shift.
  • Check units: yield changes in decimals (50 bps = 0.005). In the modified duration formula, divide by (1 + y/m) using the annual yield y divided by m, not the annual yield alone.

Yield-Based Bond Duration Measures and Properties practice questions

Yield-Based Bond Duration Measures and Properties in other exams

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

Yield-Based Bond Duration Measures and Properties: frequently asked questions

What is the difference between Macaulay duration and modified duration?

Macaulay duration is a time measure in years: the weighted average time to the bond's cash flows. Modified duration converts it into price sensitivity by dividing by (1 + y/m), where y is the annual yield and m is the periods per year. Use modified duration to estimate the percentage price change.

Do I need to memorise the convexity formula for Level I?

Focus on using convexity in the price change estimate and on knowing what it means. Be ready to apply the approximation with a given convexity figure, and to explain why higher convexity helps a bond holder. Check the current curriculum text for any formula you are expected to recall.

Which calculator keys help with duration questions?

Duration is mostly arithmetic, so a basic sequence works. On the TI BA II Plus, you can find the bond price with the time value keys (N, I/Y, PMT, FV, CPT PV) and then apply the duration formula by hand. Practise this flow so you stay inside the 90-second guide.

Why does a higher coupon give lower duration?

A higher coupon returns more of the bond's value early, which pulls the weighted average time toward the present. A zero-coupon bond pays everything at maturity, so its Macaulay duration equals its maturity.