Sep 28

Barbell vs. Bullet Bond Portfolio

by David Harper, CFA, FRM, CIPM

FRM |

actualBarbells400w

Learning Outcome

  • LO 23.12: Describe the construction of a barbell and a bullet portfolio, and compare and contrast the convexity of the two portfolios.

Barbells and bullets

The idea here is that portfolios with similar durations do not necessarily have similar convexities; and therefore, they are not necessarily responsive in the same way to interest rates changes. Let's define barbells and bullets:

  • A barbell bond portfolio combines short maturities (low duration) with long maturities (high duration) for a blended, moderate maturity (moderate duration)
  • A bullet bond portfolio concentrates in medium-term maturities (moderate duration)

Further, in a portfolio of bonds, both the portfolio duration and portfolio convexity are weighted averages of the individual bond durations and convexities. Therefore it is easy to match asset duration with liability duration: just match portfolio weighted averages. But convexities are not so easy.

  • The duration of bullet portfolio can match the duration of a barbell portfolio, but
  • The convexity of a barbell portfolio is generally going to be greater than the bullet portfolio. That's because convexity increases with the square of maturity.

 

An Example

Assume a simple two-bond portfolio, where each bond is 50% of the portfolio.

A two-asset barbell portfolio might combine a short-term bond (duration equals 1.0) with a long-term bond (duration equals 30). The portfolio duration is about 15.5 (31/2 = 15.2) but the portfolio convexity is about 450 (901/2 = 450.5) because the convexity of the 30-year bond is nearer to 900 (these are rough estimates):

actualBarbells400w

A two-asset bullet portfolio could invest entirely in two 16-year bonds (or one 15-year bond and one 16-year bond) with a duration of 15.5. The bullet portfolio could be constructed to match the duration of the barbell portfolio above. However, the convexity of the bullet portfolio will be lower:

barbells400w

Therefore, although the durations match, the barbell portfolio (and generally a portfolio that spreads out cash flows to longer maturities) will be still be more sensitive to interest rate changes.

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