Work out the duration of a portfolio and explain where the measure falls short
The idea
Portfolio duration is commonly computed as the market-value-weighted average of the constituent bonds' durations, which is simple and is what managers use. It rests on an assumption worth stating: that all yields move by the same amount, a parallel shift. Curves do not shift in parallel — they steepen, flatten and twist — so two portfolios with identical duration can perform quite differently. The theoretically correct alternative computes the cash flow yield of the whole portfolio and its duration directly, but it is rarely used because the inputs move constantly.
Formulas
Portfolio duration
portfolio duration = Σ wᵢ × Dᵢ
- wᵢ
- the share of the portfolio's market value held in bond i
- Dᵢ
- the duration of bond i
The weights are market values, not par amounts or holdings. It assumes every yield in the portfolio moves by the same amount on the same day, which is its limitation: one number says nothing about a curve that steepens.
A practice question
How is portfolio duration usually calculated?
- As the market-value-weighted average of the constituent bonds' durations — correct
- As the simple average of the bonds' maturitiesWhy not: Two errors at once — maturity is not duration, and equal weighting ignores how much is invested in each holding.
- As the duration of the longest bond heldWhy not: That would describe a portfolio holding only that bond. A small position in a long bond contributes only a small part of the total sensitivity.
Weighting by market value reflects how much of the portfolio's value each bond's sensitivity applies to.
A harder one
A portfolio holds 60% in a bond of duration 3 and 40% in a bond of duration 8. What is its duration?
- 4.60Why not: Corresponds to weights of roughly 68% and 32%, not the ones given. With 60% at duration 3 and 40% at duration 8 the contributions are 1.8 and 3.2.
- 5.50Why not: (3 + 8) ÷ 2 — the simple average, which ignores that 60% of the money sits in the shorter bond.
- 5.00 — correct
0.6 × 3 = 1.8 and 0.4 × 8 = 3.2, and the two weighted contributions add to 5.00.
The hardest tier
Two portfolios have identical duration but one is concentrated at five years and the other split between two and thirty. How do they behave when long yields rise and short yields hold?
- Identically, since duration is the sameWhy not: Equal duration means equal response to a *parallel* shift. A rise confined to long yields is not one.
- The concentrated portfolio loses more, because it is exposed to the middle of the curveWhy not: The rise falls on long yields, so the damage lands on the thirty-year leg rather than on the five-year point.
- The barbell loses more, because its long leg bears the rise — correct
Equal duration hides very different curve exposure. Duration measures the response to a parallel shift only, so managing to that single number leaves a portfolio unprotected against a change in the curve's shape, which is why key rate durations exist. Note that the direction has to be stated: a steepening driven by short yields falling instead would favour the barbell's two-year leg and could reverse the comparison.
In the app: 9 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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