Matching Macaulay duration is treated as making two bond portfolios behave alike when rates move. The guarantee holds for one specific kind of rate move, and curves do not restrict themselves to it.
What follows constructs two portfolios with identical duration and shows them diverging by 3.5 percentage points on a single realistic curve move.
Two Portfolios, Duration Five by Construction
- Bullet: 100% in a single 5-year zero-coupon bond. All cash flow sits at year 5, so duration is 5 by construction.
- Barbell: 50% in a 2-year zero and 50% in an 8-year zero. Weighted average maturity 0.5×2 + 0.5×8 = 5 - identical duration.
Under a parallel shift, every maturity up by 1%, both behave exactly as duration predicts:
- Bullet: -5.00%
- Barbell: -5.00%
A Twist Breaks the Equivalence
Now apply a flattening move of the kind real curves produce: the 2-year yield up 2%, the 8-year down 1%, and the 5-year point between them up a much smaller 0.3%.
- Bullet: -1.50% - it feels only the small move at its own single maturity point.
- Barbell: +2.00% - the loss on the short leg is more than offset by the gain on the long, because the long end rallied while the short end sold off.
Same starting duration, same average size of yield move. One portfolio loses, the other gains, and the gap is 3.5 percentage points on a risk measure both were supposed to share.
Twists Are the Normal Case, Not the Exception
This is not a contrived shock. Litterman and Scheinkman’s 1991 decomposition of yield curve movements established that curve changes resolve into roughly three factors - level, slope and curvature - of which only the first is the parallel shift duration assumes.
Slope and curvature account for a material share of realised curve variation. A risk measure blind to two of the three factors is not a rare-event problem; it is a routine one that happens to be invisible whenever the level factor dominates.
Immunisation Needs Cash Flows, Not Averages
This is why fixed-income theory treats Macaulay duration as a first-order approximation rather than a complete description of rate risk. It works well for the move it was built to describe.
A genuinely immunised portfolio needs its cash flows concentrated near the horizon date, not merely averaging to the right number - which is exactly what a bullet does and a barbell does not, even when the duration figures agree to two decimal places.
What This Means for Allocators
Pair duration with a dispersion or convexity measure. Duration alone cannot distinguish a bullet from a barbell, and that distinction is where twist risk lives.
Stress-test against slope and curvature moves, not only parallel ones. The parallel case is the one scenario in which the two portfolios are genuinely equivalent.
And match cash flows to the horizon where immunisation is the actual objective. An average that lands on the right number is not the same thing as money arriving when it is needed.
Back to Writing