Portfolio Management Pathway · Yield Curve Strategies

Bond Return Decomposition and Yield Curve Scenario Analysis

Updated 8 October 2026 · Fact-checked

Bond return decomposition splits expected portfolio return into yield income, rolldown, price change from yield shifts (duration plus convexity), credit losses, and currency effects if relevant. For each yield curve scenario, estimate each piece separately, then add them. Writing each line helps accuracy and checking.

Understand Yield Curve Scenario Analysis and Return Decomposition

A bond's return over a holding period does not come from one source. It comes from several, and each one reacts to a different view you hold. Splitting the return into parts lets you see which part of a yield curve strategy is a sure thing and which is a bet.

The first part is yield income, also called carry. It is the coupon income earned over the horizon, usually expressed as a percentage of the starting price. If nothing else changed, you would earn this. The second part is rolldown return. If the yield curve slopes upward, a bond that ages becomes shorter and is valued at a lower yield. The lower yield lifts its price. If the curve is flat, rolldown is zero. If the curve is inverted, rolldown is negative.

The third part is the price change from a yield shift. This is where your scenario comes in. You assume the curve moves, for example up 50 bps in parallel, or steepens. Duration gives the first-order price effect. Convexity adds a second-order correction. Because convexity is positive for option-free bonds, it adds to return whether yields rise or fall, and the effect grows with the square of the move.

The last parts are credit effects and currency. A change in credit spread moves price through spread duration. Expected default losses reduce return. In a multi-currency portfolio, expected currency gains or losses are added as well. The exam usually gives you the inputs. Your job is to use the right duration, the right yield change, the correct units and the correct signs, and to add the lines.

For non-parallel shifts, use key rate durations. Each key rate duration measures sensitivity to a change at one maturity point. Multiply each by its own yield change and sum. This is how you compare a bullet, a barbell and a ladder under a steepening or flattening scenario.

Key rules to remember

Expected return decomposition: E(R) ≈ Yield income + Rolldown return + E(price change from yield and spread changes) − E(credit losses) + E(currency gains or losses); Add only the lines the question gives. Keep each in the same period, usually the horizon return.
Price change from yield shift: %ΔP ≈ −Duration × ΔY + ½ × Convexity × (ΔY)²; ΔY in decimals, so 50 bps = 0.0050. Use modified or effective duration, not Macaulay duration. Convexity must match the units of the one given.
Convexity effect alone: Convexity effect = ½ × Convexity × (ΔY)²; Positive when convexity is positive, whether yields rise or fall.
Key rate duration approximation: %ΔP ≈ −Σ (KRD_i × ΔY_i) + ½ × Convexity × (ΔY)²; Use for non-parallel shifts. Each ΔY_i is the yield change at that maturity point.
Credit spread effect: %ΔP from spread ≈ −Spread duration × ΔSpread; Widening spreads reduce price. Do not also count the spread change as part of the benchmark yield change.
Rolldown return: Rolldown return ≈ (Price at horizon with unchanged curve − Price today) ÷ Price today, excluding coupon; Positive for an upward-sloping curve, zero for a flat curve, negative for an inverted curve.

How to solve Yield Curve Scenario Analysis and Return Decomposition questions

Use this order for any scenario or return decomposition question. It keeps the lines separate and makes errors easy to spot.

1Read the horizon and the scenario. Note whether the shift is parallel or non-parallel, and whether spreads or currencies also change.
2List the inputs given: yield income, rolldown, duration, key rate durations, convexity, spread duration, credit loss and currency view.
3Convert every basis point change to a decimal. For example 25 bps = 0.0025.
4Compute the duration effect: −Duration × ΔY. For non-parallel shifts, sum −KRD × ΔY over each maturity point.
5Compute the convexity effect: ½ × Convexity × (ΔY)². Keep its sign positive for positive convexity.
6Compute the spread effect if spreads change: −Spread duration × ΔSpread. Subtract expected credit losses.
7Add yield income, rolldown, duration effect, convexity effect, spread effect, credit loss and currency effect. Write each line so you can check it.
8State the total as a percentage with the units asked, then answer any follow-up such as which strategy performs better.

Quickest way: Five-line return stack

When to use it: Use for any question that asks for expected return under a given yield scenario when inputs are provided. In item sets, you can check your result against the options.

Write five lines: Income, Rolldown, Duration effect, Convexity effect, Credit or other.
Fill the income and rolldown lines directly from the vignette.
Compute duration effect as −D × ΔY in percent. A 50 bps rise with duration 6 gives −3.00%.
Compute convexity effect: ½ × C × ΔY² with ΔY in decimals, then convert to percent.
Add the lines with correct signs and check against the options. If a result looks far off, check bps conversion first.

Common mistakes in Yield Curve Scenario Analysis and Return Decomposition

Entering ΔY as 0.5 or 50 instead of 0.0050 in the convexity term
Duration is easy to compute with percentages, so students keep the same units for the squared term.
Fix: Convert bps to decimals before using either formula. Squaring 0.0050 gives 0.000025.
Forgetting the ½ in the convexity term
Students remember convexity as a second-order term but not its coefficient.
Fix: Write the formula as ½ × C × (ΔY)² at the top of your working every time.
Using Macaulay duration for the price estimate
Macaulay duration is introduced first and sounds like the main duration.
Fix: Use modified duration, or effective duration for bonds with options, unless the question gives only the one you must adjust.
Treating convexity as a cost when yields rise
Students think the convexity sign follows the direction of the yield move.
Fix: For positive convexity, the term is positive for both rising and falling yields because (ΔY)² is always positive.
Counting rolldown on a flat or inverted curve as positive
Students memorize that rolldown adds return without checking the curve shape.
Fix: Check the slope. Rolldown is positive for an upward-sloping curve, zero for a flat one, and negative for an inverted one.
Applying one portfolio duration to a non-parallel shift
It is faster, and parallel shifts are the usual case.
Fix: If the question gives key rate durations and different yield changes by maturity, multiply each pair and sum.

Worked examples

Example 1

A bond portfolio has a one-year horizon. Yield income is 4.00% and rolldown return is 0.60%. At the start of the horizon, modified duration is 6.0 and convexity is 50. You expect a parallel upward shift of 50 bps. Expected credit losses are 0.20%. Estimate the expected return.

Show the solution

Convert the shift: ΔY = 50 bps = 0.0050.
Duration effect = −6.0 × 0.0050 = −0.0300 = −3.00%.
Convexity effect = ½ × 50 × (0.0050)² = ½ × 50 × 0.000025 = 0.000625 = +0.0625%.
Credit loss = −0.20%.
Total = 4.00% + 0.60% − 3.00% + 0.0625% − 0.20% = 1.4625%.

Answer: Expected return ≈ 1.46%.

Example 2

A portfolio has key rate durations of 1.0 at 2 years, 2.0 at 5 years and 3.0 at 10 years. Yield income is 3.50% and rolldown return is 0.40% over the horizon. The scenario is a steepening shift in benchmark (government) yields: 2-year yields up 10 bps, 5-year up 30 bps, 10-year up 50 bps. Separately from these benchmark yield changes, credit spreads widen by 10 bps, and spread duration is 5.0. For this non-parallel shift, the convexity effect is given as an estimate of +0.05%. Ignore credit losses. Estimate the expected return.

Show the solution

The key rate yield changes are benchmark yield changes only. The spread widening is a separate change, so it is not counted twice.
Duration effect from benchmark yields = −(1.0 × 0.10% + 2.0 × 0.30% + 3.0 × 0.50%).
= −(0.10% + 0.60% + 1.50%) = −2.20%.
Spread effect = −5.0 × 0.10% = −0.50%. This applies only to the spread change.
Convexity effect = +0.05%. It is given as an estimate for this non-parallel shift, so use it as stated.
Total = 3.50% + 0.40% − 2.20% + 0.05% − 0.50% = 1.25%.

Answer: Expected return ≈ 1.25%.

Exam tips

Write out every line of the decomposition. A correct number typed on its own earns full credit for a calculation, and showing your working is good practice in essays because it helps you check your own arithmetic.
Watch command words. If the question says calculate, give a number. If it says justify or explain, add one sentence tied to the scenario, such as positive convexity adds return in both directions.
Check units before computing. Convert bps to decimals, and confirm whether the vignette gives duration at the start or at the horizon.
For multi-scenario questions, keep income and rolldown fixed when the curve view does not change them, and recompute only the duration, convexity and spread lines.

Yield Curve Scenario Analysis and Return Decomposition in other exams

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

CFA Level IIFactor Model Return Attribution and Risk Decomposition

Yield Curve Scenario Analysis and Return Decomposition: frequently asked questions

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

Split it into yield income, rolldown, price change from the yield shift, credit losses and any currency effect. Compute each line from the inputs given, using duration and convexity for the price change. Add the lines to get the total.

How does convexity affect bond returns numerically?

The convexity effect is ½ × convexity × (ΔY)². With convexity of 50 and a 50 bps move, it is 0.0625%. It is positive for option-free bonds whether yields go up or down, and it grows quickly as the yield change gets larger.

What is the difference between carry and rolldown?

Carry is the income earned from coupons over the horizon. Rolldown is the price gain from the bond aging into a lower yield on an upward-sloping curve. Rolldown needs the curve to stay unchanged and sloping upward. A flat curve gives no rolldown.

When do I use key rate durations instead of portfolio duration?

Use key rate durations when the yield change differs by maturity, such as a steepening or flattening move. Multiply each key rate duration by its own yield change and add them. A single portfolio duration only fits a parallel shift.