Feb 2024 CFA Boston mock 2 session 1, set 2, question 1 - why choose barbell instead of bullet when instantaneous upward parallel shift?

Leonard Jennevin serves as a portfolio manager at Riviera Partners, a boutique investment firm. Jennevin is in charge of actively managing fixed-income portfolios, which consist primarily of investment-grade corporate bonds.
Over the past 12 months, the yield curve has been stable, concave, and upward sloping. The portfolio’s benchmark is a broad index with a duration of eight years. However, according to the investment mandate, Jennevin is not obligated to match the index’s duration. Jennevin outlines three potential approaches to constructing a client’s fixed-income portfolio: a barbell, a bullet, and a laddered portfolio. Jennevin assumes that both the barbell and bullet portfolios have the same duration. When determining the most suitable bond portfolio for a new client, he takes into account three potential scenarios regarding changes in the yield curve over the coming year:
Scenario 1: instantaneous upward parallel shift of 100 basis points

Under Scenario 1, which of the following portfolio construction strategies is most appropriate?
A. Selling convexity
B. Choosing a bullet portfolio
C. Choosing a barbell portfolio, with the bonds with durations of 1 year and 8 years

LOS: Volume 2, Learning Module 5, Section 3, Evaluate strategies for managing a single liability.
In order to benefit from the upward parallel shift, an investor should shift to a barbell-like portfolio to gain convexity (due to increased dispersion of cash flows compared to bullet-like portfolios).
Answer A is incorrect: selling convexity will not be beneficial in case of yield curve movements (it would rather make sense to sell convexity in case of a stable curve). Answer B is incorrect for the same reason: bullet-like portfolios have less convexity compared to barbell-like ones and therefore are less beneficial in case of parallel shifts of the curve.
Reference: 2024, Fixed Income, Volume 2, Learning Module 5, Section 3, Managing the Interest Rate Risk of a Single Liability, p. 299.

It is due to convexity. For a the same duration - assumption in question - the barbell will have greater convexity.
All else equaly when rates change you want higher convexity.

This is very crude but will illustrate the point :
Zero coupon bonds = Duration approx equal matuirity, Convexity can be thought of as maturity squared.
Portfolio convexity = weighted average of bonds.
Barbell with 1 and 8 say equally weighted = (1^2 + 8^2)/2 = 32.5
Assume bullet has same average duration = (1 + 9)/2 = 4.5
Convexity bullet 4.5^2 = 20.25

These slides illustrate the point much better than I can

Some time link does not work directly so search :
convexity debt instruments and markets professor carpenter

thank you for the great explanation