Extreme Barbell vs. Laddered Portfolio

Reading 24. 6.3 Extreme Barbell vs. Laddered Portfolio

First paragraph compares these 2 portfolios and says in the end: “The barbell portfolio gives up nearly 30 bps in yield. Although we are using an instantaneous yield curve shift for this analysis, note that over a longer horizon, the barbell portfolio would be penalized for the give-up in yield.”

Could someone elaborate how the barbell portfolio would be penalized for the give-up in the yield over a longer horizon? How will this penalty occur?

Barbells have the highest convexity and that causes a yield drag, if yield change unfolds over too long a period the yield sacrifice will be larger than the price effect.