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Estimating Portfolio Duration from Bond ETF Weights

Article Quant Q&A · Author: the_brass_bottle
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Summary

The document asks whether a portfolio’s duration can be estimated as the market-value-weighted average of the durations of its bond ETFs. It gives an example portfolio containing several funds with different stated durations and sketches the weighted-average calculation using each holding’s share of total value.

For small parallel changes in yields, this is a reasonable first-order estimate when the fund durations are comparable measures of modified duration and the weights reflect current market values. The estimate summarizes approximate portfolio price sensitivity; it is not an exact measure for every rate move. Accuracy can depend on duration definitions, yield-curve shifts, convexity, and changes in ETF holdings or market values. The document poses the calculation but includes no answer, validation, or discussion of these caveats, so it does not establish that the numerical result is correct for the portfolio as specified.

Key ideas

  • A portfolio’s first-order duration estimate can be formed by weighting constituent durations by their shares of portfolio market value.
  • The weights should use a consistent valuation basis and sum to the portfolio total.
  • A weighted duration approximates sensitivity to small, parallel interest-rate changes.
  • Convexity, nonparallel yield shifts, and inconsistent duration definitions can limit the estimate.

Tags

Fixed incomePortfolio constructionRisk management
Full text
# Calculate the duration of group of Bond ETFs


# Calculate the duration of group of Bond ETFs












Is it correct to get the weighted average of a bunch of bond ETFs to get the duration? Is it theoretical correct to say that.

I have 6M AGG (duration 8.39), 30M BND (duration 8.7), 60M SHY (duration 1.98), 10 VTIP (duration 2.7), 5M BIV (duration 7.3). So my duration for this portfolio is (6/111 * 8.39) + (30/111 * 8.7) + ... + (5/111 * 7.3) = 4.439

Is that the correct way to calculate the duration for the portfolio?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.