Level III Core · Overview of Fixed-Income Portfolio Management

Return Sources and Duration Management for CFA Level 3

Updated 8 October 2026 · Fact-checked

Expected bond return is the sum of yield income, rolldown return, expected credit losses and price change from yield moves. You approximate the price change with duration and convexity, and use key rate durations to see yield curve risk. Build the return piece by piece, then check the horizon.

Understand Return Sources and Duration Management

A bond earns money in a few separate ways. You collect coupons and accrue the yield. If the bond is still on an upward-sloping curve, it ages into a shorter maturity with a lower yield, and its price rises. That is rolldown return. Then you add the price effect of any change in the yield curve, and subtract losses from credit events or currency moves where they apply.

The building-block approach is the standard way to think about this. Start with the yield income (coupon income plus pull to par, or simply the yield for a quick estimate). Add rolldown return, which is the price gain if the curve does not move. Add the E(change in price from view on yields), which uses duration and convexity. Subtract E(credit losses). For foreign bonds, add E(currency gains or losses).

Duration measures how much price changes for a small, parallel yield shift. Convexity corrects for the fact that the price-yield relationship is curved. Positive convexity helps you in both directions: you gain more when yields fall and lose less when they rise. The pair gives a better estimate than duration alone, especially for large yield moves.

Real curves rarely move in parallel. Key rate duration measures sensitivity to a change in one point on the curve (for example the 2-year or 10-year), holding other points fixed. The key rate durations of a portfolio sum to (approximately) its effective duration. Comparing them with the benchmark shows where you are over- or underweight on the curve. That is yield curve risk, and it drives duration management: you can match the benchmark duration and still carry big curve bets.

In the exam, always tie the technique to the mandate. A manager with a tracking-error limit controls duration and key rate gaps against the benchmark. A liability-driven investor matches duration and cash flows to liabilities instead.

Key rules to remember

Building-block expected return: E(R) ≈ Yield income + Rolldown return + E(change in price from yield view) − E(credit losses) + E(currency gains/losses); Use only the pieces the question gives. Keep all terms on the same horizon, usually one year.
Rolldown return: Rolldown return ≈ (Price at the new, shorter maturity with the unchanged curve yield − Beginning price) ÷ Beginning price; Assumes the yield curve stays unchanged. It is zero on a flat curve and negative on an inverted curve.
Price change from duration and convexity: %ΔPV ≈ −(ModDur × ΔYield) + ½ × Convexity × (ΔYield)²; Enter ΔYield as a decimal, for example 0.0050 for 50 bps. Some questions use effective duration and effective convexity; apply them the same way.
Portfolio duration: Portfolio duration = Σ (market value weight × bond duration); Weights use market value. The weighted average is a good approximation only for a parallel shift in the yield curve. It is not exact when yields differ across bonds.
Key rate duration: KRD(i) = −(% change in portfolio value) ÷ (change in key rate i); Only the one key rate shifts. The key rate durations sum to (approximately) the portfolio's effective duration.
Money duration and PVBP: Money duration = ModDur × Market value; PVBP ≈ Money duration × 0.0001; PVBP is the value change for a 1 bp yield change.
Duration gap against benchmark: Active duration = Portfolio duration − Benchmark duration; Positive means the portfolio gains more than the benchmark when yields fall.

How to solve Return Sources and Duration Management questions

Use this order for any return-decomposition or duration-management question.

1Read the mandate or objective first: benchmark-relative, absolute return, or liability matching. It decides what the right answer targets.
2Fix the horizon, usually one year, and confirm that yields, durations and returns are on the same basis.
3Calculate yield income for the horizon (coupon plus pull to par, or the yield given).
4Calculate rolldown: find the yield for the shorter remaining maturity on the unchanged curve, reprice the bond, and divide the price gain by the starting price.
5Estimate the price effect of the yield view with duration, plus the convexity term. Convert bps to decimals and watch the signs.
6Subtract expected credit losses and add currency effects if the question gives them. Add all components.
7For curve risk, compare the key rate durations with the benchmark and state the exposure (for example overweight the 10-year point). Match your recommendation to the constraints.
8Show each step in an essay. A clearly labelled number earns credit even if a later step is wrong.

Quickest way: Component shortcut for expected return

When to use it: When the question gives yields and a yield change view and asks for a one-year expected return.

Write the lines: yield income, rolldown, price change, credit loss (and currency if given).
Fill yield from the question and take rolldown as a given or as a quick price difference.
Use −Duration × ΔY first; add ½ × Convexity × ΔY² only if convexity is supplied.
Sum the lines and sanity check: a falling-yield view should add return, a rising-yield view should subtract it.
For multiple-choice, eliminate options with the wrong sign before calculating.

Common mistakes in Return Sources and Duration Management

Treating rolldown as part of the price change from a yield view
Both change price, so they blur together.
Fix: Rolldown assumes an unchanged curve. Any move in the curve goes in the separate yield-view term.
Forgetting the minus sign in the duration term
Rushing and thinking only about size.
Fix: Write −Duration × ΔY every time. A yield rise means a price fall.
Using bps instead of decimals in the convexity term
Squaring 50 gives 2,500 instead of 0.000025.
Fix: Convert to decimals first: 50 bps = 0.0050.
Assuming matching the benchmark duration means no curve risk
Duration is a single number that assumes a parallel shift.
Fix: Compare key rate durations. Equal total duration can hide large overweights at some points and underweights at others.
Applying the one-year yield income to a different horizon
Horizon is stated in a vignette and missed.
Fix: Underline the horizon. Scale each component to that horizon, or use one year when asked for annual return.
Forgetting expected credit losses or currency effects
Students stop after yield and duration.
Fix: Scan the vignette for default probability, recovery rate and foreign currency. If given, include them.

Worked examples

Example 1

A bond portfolio has a yield income of 4.00% over one year and a rolldown return of 0.60%. The manager expects yields to rise by 50 bps. Modified duration is 6.0 and convexity is 50. Expected credit losses are 0.30%. Estimate the expected one-year return.

Show the solution

Yield income = 4.00%.
Rolldown = 0.60%.
Duration effect = −6.0 × 0.0050 = −0.0300 = −3.00%.
Convexity effect = ½ × 50 × (0.0050)² = 25 × 0.000025 = 0.000625 = 0.0625%.
Price change = −3.00% + 0.0625% = −2.9375%.
Credit loss = −0.30%.
Total = 4.00 + 0.60 − 2.9375 − 0.30 = 1.3625%.

Answer: Expected return ≈ 1.36%

Example 2

A manager must keep the portfolio's duration equal to the benchmark's at 5.0. Key rate durations (portfolio vs benchmark): 2-year 0.5 vs 1.0; 10-year 3.5 vs 2.5; 30-year 1.0 vs 1.5. (a) Check total duration. (b) Estimate the portfolio's value change relative to the benchmark if the 10-year rate rises 20 bps and others do not move. Explain the curve exposure.

Show the solution

Portfolio total = 0.5 + 3.5 + 1.0 = 5.0. Benchmark total = 1.0 + 2.5 + 1.5 = 5.0. Total durations match.
Portfolio change = −3.5 × 0.0020 = −0.70%.
Benchmark change = −2.5 × 0.0020 = −0.50%.
Relative = −0.70% − (−0.50%) = −0.20%.
The portfolio is overweight the 10-year point by 1.0 and underweight the 2-year and 30-year points by 0.5 each. This is a belly-heavy (bullet-type) curve position.
The underperformance occurs because the 10-year rate rises. If the 10-year rate fell by 20 bps instead, the same overweight would produce outperformance of about 0.20%.

Answer: (a) Both are 5.0. (b) The portfolio underperforms the benchmark by about 0.20% because it is overweight the 10-year key rate and the 10-year rate rises. A fall in the 10-year rate would produce outperformance. The match in total duration hides this yield curve risk.

Exam tips

Read command words in bold. 'Calculate' needs a number; 'justify' needs a reason tied to the client's objective.
Show every component on its own line. A correct number alone earns credit, but a labelled line protects partial credit when a later step fails.
Check units: percent versus decimals, and bps versus percent, before you type.
In curve questions, compare key rate durations to the benchmark, not to zero. State which point is over- or underweight and what curve move hurts.
Item sets often hide the horizon or the credit loss in the vignette. Re-read it before answering.

Return Sources and Duration Management: frequently asked questions

What is rolldown return in a bond portfolio?

It is the price gain a bond earns as it ages into a shorter maturity on an upward-sloping curve, if the curve stays unchanged. It is zero on a flat curve and negative on an inverted one. You add it to yield income when building expected return.

Why do I need convexity if I have duration?

Duration is a straight-line estimate, and the true price-yield relationship is curved. Convexity adds a correction that matters for larger yield changes. For positive convexity it makes the actual price rise bigger and the fall smaller than duration alone suggests.

What does key rate duration tell me that duration does not?

It shows sensitivity to a move at one maturity point only. That reveals curve exposure such as steepener or flattener positions and non-parallel shifts. Total duration assumes a parallel shift and can hide these bets.

How do I calculate the expected return of a bond portfolio?

Add yield income and rolldown return, add the price effect from your yield view using duration and convexity, then subtract expected credit losses. Include currency gains or losses if the bonds are foreign. Keep all pieces on the same horizon.