Reading the spread of duration across a portfolio's holdings

Portfolio and risk · 5 min read · GiltIQ

A portfolio's weighted duration is an average, and an average hides how the holdings are spread around it — two portfolios with the same weighted duration can respond very differently when the yield curve changes shape rather than shifting in parallel.

An average hides the spread

The portfolio view reduces a portfolio's interest-rate sensitivity to one weighted modified duration: each holding's duration weighted by the share of market value it makes up. That single figure is useful, and it is also an average, so it says nothing on its own about whether the holdings cluster around it or sit far apart. Two portfolios can share a weighted duration of nine years while one holds only gilts of about nine years and the other holds short and long gilts whose durations average to nine. The average is the same; the spread is not.

This is why the weighted duration and the spread answer different questions. The weighted figure answers what happens if every yield moves by the same amount; the spread answers what happens if the curve moves unevenly, or if only one end of it moves. A reader who wants only the first can stop at the average; a reader who wants to understand a portfolio's behaviour across market conditions needs the spread as well.

Where the spread shows

The spread is visible in two places on the portfolio view. The positions table carries a modified duration for every holding, so reading down that column shows whether the durations are bunched or ranged. The yield-against-duration chart plots each holding by its modified duration and its yield, with the bubble area set to the holding's allocation, so the shape of the spread — clustered, or spread across the axis — is drawn rather than tabulated.

A barbell against a bullet

The table below makes the difference concrete with two illustrative portfolios that have the same weighted duration and different spreads. The figures are round numbers and not from any portfolio or report: each portfolio is £100,000, and the spread is built from modified durations of 4.0 and 14.0 years against a uniform 9.0.

PortfolioHoldingMarket valueModified durationWeighted contribution
UniformU1£50,0009.0 years4.5
UniformU2£50,0009.0 years4.5
UniformWeighted duration£100,000—9.0 years
BarbellB1£50,0004.0 years2.0
BarbellB2£50,00014.0 years7.0
BarbellWeighted duration£100,000—9.0 years

Under a parallel one per cent move in yields, both portfolios would move by roughly nine per cent of their value, because their weighted durations are equal. Under a move that changes the shape of the curve — the short end falling while the long end rises, say — they part company. The uniform portfolio's two holdings respond much alike; the barbell's long holding, at fourteen years, carries most of its sensitivity, so a rise at the long end costs it far more than it costs the uniform portfolio. The same average, two different exposures.

The spread of gross yield too

Duration is not the only figure that spreads across the holdings. Each gilt's gross yield — the return it offers if held to maturity, with coupons reinvested at the same rate — is shown beside its duration, and those yields spread too. A portfolio of gilts at different maturities usually draws its yield from across the curve, and the gilt yield curve is where that shape is visible: which parts of the curve the holdings sit on, and how their yields compare with the fitted line through them. Reading duration and gross yield together, per holding, describes both the sensitivity and the return the portfolio carries across its spread.

What spreading duration does and does not do

Spreading durations across a portfolio changes how it responds to a curve that moves unevenly, and it changes when its redemptions land. It does not remove interest-rate risk: a parallel move still hits both portfolios by their weighted duration, and a spread of holdings does not make the value fall any less when every yield rises together. The spread describes the exposure; it does not protect against it. A reader who wants to know how a given reshaping would affect a particular portfolio is asking a question the per-holding durations, weighted by allocation, can answer — but the answer is a shape of exposure, not a recommendation to hold one shape over another.

The timing of redemptions is the companion point. Two holdings of the same duration can return their principal in different years, and a portfolio's cash-flow analysis is where that timing shows. Duration describes how the holdings respond to yield; the years their redemptions land describe when the principal comes back and has to be reinvested. Neither substitutes for the other, and both are visible on the portfolio view.

Background, not advice

This explains how the spread of modified duration across a portfolio's holdings can differ from its weighted average, and what that difference does and does not change; it is general background, not investment, tax or legal advice for any reader's circumstances. The figures above are illustrative, and the durations and yields for a real portfolio are those the site computes from its trades at the day's report. A spread of durations is a description of exposure, not a guarantee of any outcome.

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