Immunization of coupon-paying bonds does not imply that the portfolio manager is inactive because:
I. The portfolio must be rebalanced every time interest rates change.
II. The portfolio must be rebalanced over time even if interest rates don't change.
III. Convexity implies duration-based immunization strategies don't work.

A) I only
B) I and II only
C) II only
D) I, II, and III

Immunization of coupon-paying bonds requires ongoing portfolio management to maintain the desired duration and convexity targets, which may need adjustment due to changing interest rates and market conditions. Therefore, option I is correct. Additionally, even in the absence of interest rate changes, the portfolio must be rebalanced over time to account for the cash flows from the coupons paid by the bonds, making option II also correct. Option III is incorrect because duration-based immunization strategies can still be effective, although convexity can provide additional protection against interest rate risk.