Barbell portfolios

Why would a barbell portfolio outperform a benchmark (on the run US Treasuries) in :

  1. increased curvature where the short and long term rates rise? (I read it for “more curvature” and considering a scenario of curvature on the downside of the curve by myself) )

  2. for parallel changes, shouldn’t the difference in upward and lower changes be almost the same? (6 bp difference in extreme barbell vs less extreme)

  3. Why would a barbell outperform a bullet portfolio in a parallel upward shift?

Outperform what, exactly?

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updated the post

increased curvature = short and long end rates decrease, mid-rate increases.

Barbell with its greater convexity benefits from it vs bullet.

Increased curvature leads to decrease in short and long rates, so investing in short term security and long term security will outperform a bullet security invested in the middle (with high rates)