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Constructing a Duration-Neutral Bond Portfolio with Positive Convexity

Article Quant Q&A · Author: ensabahnur
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Summary

The document gives two ways to form a bond portfolio with matched dollar BPV, making the portfolio duration-neutral while retaining positive convexity. One example pairs a lower-coupon Treasury with a higher-coupon Treasury of a nearby maturity. The stated positions are sized to offset BPV, and the example reports positive convexity. It also notes that a larger coupon difference can increase the convexity exposure.

A second example pairs a longer-maturity bond with a shorter-maturity bond, both with the same coupon, and sets their principal amounts so their dollar BPVs match. This illustrates that duration neutrality does not require matching maturities. The examples are illustrative rather than a full construction guide: the document gives no discussion of yield-curve shifts, rebalancing, financing, or other risks that can affect the portfolio in practice.

Key ideas

  • Matching dollar BPVs can create a duration-neutral bond position.
  • A lower-coupon bond paired against a higher-coupon bond can produce positive convexity when the BPVs are matched.
  • A longer-maturity bond can be paired with a shorter-maturity bond to create a duration-neutral portfolio.
  • Duration neutrality does not require the bonds to have the same maturity.
  • A wider coupon difference is described as a way to increase convexity exposure.

Tags

Fixed incomePortfolio constructionRisk management
Full text
# Bond Duration hedging with long convexity


# Bond Duration hedging with long convexity












How do you build a duration-neutral bond portfolio which is long convexity? can you give me an example?

## Answer by Lliane (score 1)

https://quant.stackexchange.com/a/31112

I would say you can go

- Long a bond with a low coupon

- Short a bond with a higher coupon

For instance current for US Treasury circa 10Y

- 2% 15NOV26, BPV 8.7265, Convx 89.9624

- 1.5% 15AUG26, BPV 8.3071, Convx 87.9649

Buy 1,000,000 of the 1.5% and Sell 951,939 of the 2% would give you positive convexity and 0 duration. Of course more extreme coupon differential will give you a much better convexity exposure.

## Answer by dm63 (score 0)

https://quant.stackexchange.com/a/31137

More typically this refers to a portfolio like:

Long 100MM 10yr bond with coupon 3% Short 180MM 5yr bond with coupon 3%

with the principal amounts chosen such that the BPVs in dollars are equal. This portfolio is long convexity.

The term "duration neutral" does not imply matched maturity.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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