CFA Level I Exam · Yield-Based Bond Duration Measures and Properties

Portfolio Duration and Its Limitations Explained

Updated 7 October 2026 · Fact-checked

Portfolio duration is the market-value-weighted average of the durations of the bonds in the portfolio. It estimates the percentage price change for a small, parallel shift in all yields. It is weak when the yield curve twists or bonds have different yield volatility, because it assumes one common yield change.

Understand Portfolio Duration and Its Limitations

A bond's duration tells you the approximate percentage price change for a 1% change in its yield. A portfolio holds many bonds. The simplest way to get one number for the whole portfolio is to take each bond's duration and weight it by its share of the portfolio's market value.

This is the weighted average method. If a portfolio is 60% in a bond with duration 4 and 40% in a bond with duration 9, portfolio duration is 0.60 × 4 + 0.40 × 9 = 6.0. Weights use market values (including accrued interest, i.e. full price), not par values. The weighted average is the common practical approach. Effective duration is the appropriate measure for bonds with embedded options. For option-free bonds, modified and effective durations are approximately equal, so the weighted average is meaningful when durations are measured consistently.

The method has a hidden assumption. It works only if every bond's yield changes by the same amount, which is a parallel shift of the yield curve. In reality, short rates can rise while long rates fall (a twist), or the curve can steepen or flatten. Then two portfolios with the same duration can behave very differently.

There is another approach: the cash flow yield method. You pool all the portfolio's cash flows, find the single yield (a portfolio IRR) that discounts them to the portfolio's market value, and compute duration from that. It is theoretically sound because it treats the portfolio as one set of cash flows. But it is more complex to compute, and it is less commonly used. The yield is a portfolio IRR, not a market yield for any one bond.

The weighted average approach is the one you will calculate. Know the cash flow yield approach for comparison questions. Both assume a parallel shift in yields. For non-parallel shifts, you need measures such as key rate duration.

Key formulas to remember

Portfolio duration (weighted average): D_p = w₁D₁ + w₂D₂ + … + wₙDₙ = Σ wᵢDᵢ; wᵢ = market value of bond i ÷ total portfolio market value. Weights sum to 1. Effective duration is the appropriate measure for bonds with embedded options. For option-free bonds, modified and effective durations are approximately equal. Measure durations consistently across the portfolio.
Portfolio price change estimate: %ΔPortfolio value ≈ −D_p × ΔYield; Use modified or effective duration as appropriate. Valid for small, parallel yield changes only.
Portfolio money duration: Portfolio money duration = Σ (money duration of each bond); Money durations add up directly in currency terms, since they are not percentages.
Cash flow yield method: Find y such that PV of all portfolio cash flows at y = portfolio market value; then compute duration at y; Treats the portfolio as one bond. More complex and less commonly used. Also assumes a parallel shift in yields.

How to solve Portfolio Duration and Its Limitations questions

Use this method for any portfolio duration question, numerical or conceptual.

1Read what is asked: portfolio duration, price change, or a limitation of the measure.
2List each bond's market value and duration. Note the duration type for each bond. Effective duration suits bonds with embedded options, and the durations should be measured consistently.
3Compute the total market value and each weight = bond value ÷ total value.
4Multiply each weight by its duration and sum the results to get portfolio duration.
5For a price change, multiply by the yield change: %Δ ≈ −D_p × Δy. Check the sign: yields up means value down.
6For a money value change, multiply the percentage change by the portfolio value, or use money duration.
7For conceptual questions, ask: is the yield shift parallel? If not, flag the weighted average as unreliable.

Quickest way: Weights-first mental shortcut

When to use it: Use for two- or three-bond portfolios in the 90-second exam window.

Convert market values to weights using simple fractions (e.g. 30 of 100 is 0.30).
Estimate the answer's range: it must lie between the lowest and highest bond duration.
Eliminate any option outside that range.
Do the exact sum only if two options remain.
With a calculator, key each product and add: 0.6 × 4 = 2.4, then + 0.4 × 9 = 3.6, giving 6.0.

Common mistakes in Portfolio Duration and Its Limitations

Weighting by par value or number of bonds instead of market value
The question lists par amounts and they look convenient.
Fix: Always use market value (full price). Convert par amounts to prices first when prices are given.
Averaging durations with equal weights
It feels like a simple average.
Fix: The portfolio duration is weighted. A large holding of a low-duration bond pulls the answer toward that bond.
Treating portfolio duration as valid for any yield curve move
The formula looks general.
Fix: State that it assumes a parallel shift. For twists or steepening, use key rate duration.
Using modified duration for a bond with an embedded option
Data are given for different bonds in different forms, and modified duration is the more familiar measure.
Fix: Effective duration is the appropriate measure for bonds with embedded options. For option-free bonds, modified and effective durations are approximately equal, so the weighted average is meaningful when durations are measured consistently.
Forgetting the negative sign in the price change
Focus is on getting the duration number.
Fix: Rising yields mean falling prices. Write −D × Δy and check the direction.
Thinking the cash flow yield method removes the parallel shift assumption
It sounds more rigorous.
Fix: It is more theoretically sound but still assumes a parallel shift in yields, so it does not handle non-parallel shifts.

Worked examples

Example 1

A portfolio has three bonds: Bond X, market value EUR 20 million, modified duration 3.0; Bond Y, EUR 50 million, modified duration 6.0; Bond Z, EUR 30 million, modified duration 10.0. What is the portfolio modified duration? Options: A) 5.4, B) 6.6, C) 7.2.

Show the solution

Total value = 20 + 50 + 30 = EUR 100 million.
Weights: X = 0.20, Y = 0.50, Z = 0.30.
Weighted durations: 0.20 × 3.0 = 0.6; 0.50 × 6.0 = 3.0; 0.30 × 10.0 = 3.0.
Sum = 0.6 + 3.0 + 3.0 = 6.6.
Check: 6.6 lies between 3.0 and 10.0, as it must.

Answer: B) 6.6

Example 2

A USD 80 million portfolio has a portfolio modified duration of 5.0. All yields rise by 40 basis points in a parallel shift. What is the approximate change in portfolio value? Options: A) −USD 16.0 million, B) −USD 1.6 million, C) +USD 1.6 million.

Show the solution

Yield change = +0.40% = 0.0040.
Percentage change ≈ −5.0 × 0.0040 = −0.020, i.e. −2.0%.
Value change ≈ −0.020 × USD 80 million = −USD 1.6 million.
Option C has the wrong sign. Option A is out by a factor of ten.

Answer: B) −USD 1.6 million. This holds only because the shift is parallel and small.

Exam tips

Expect the weighted average calculation to use market values. Check whether the stem gives prices and par amounts, and use value.
Conceptual items often ask for the main limitation. The answer is the assumption of a parallel yield curve shift.
If a stem describes a steepening or twist, do not trust portfolio duration. Look for key rate duration as the better tool.
Use range elimination: the answer cannot lie outside the lowest and highest bond durations.
For cash flow yield versus weighted average, remember: cash flow yield is more theoretically sound but more complex and less commonly used, and both assume a parallel shift in yields.

Practice questions from Yield-Based Bond Duration Measures and Properties

Portfolio Duration and Its Limitations in other exams

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

FRM Part ILimitations of Duration and Key Rate Measures

Portfolio Duration and Its Limitations: frequently asked questions

How do you calculate portfolio modified duration?

Find each bond's share of total market value, multiply that weight by the bond's modified duration, and add the results. The weights must sum to one. Use market values, not par amounts.

Why does portfolio duration assume a parallel shift?

The formula applies one yield change to every bond. That is only true if all yields move by the same amount. If short and long yields move differently, the weighted average gives a poor estimate.

What is the difference between cash flow yield duration and weighted average duration?

The weighted average method averages individual bond durations. The cash flow yield method pools all cash flows, finds one IRR for the portfolio and computes duration from it. The second is more theoretically sound but more complex and less commonly used, and both assume a parallel shift in yields.

Can I use effective duration in the weighted average?

Yes. Effective duration is the appropriate measure for bonds with embedded options. For option-free bonds, modified and effective durations are approximately equal. The weighted average is meaningful when durations are measured consistently.