I keep reading that "a step-up bond provides more protection to an investor in the face of market interest rate fluctuations", that "a step-up bond typically performs better than any other fixed-rate investment in a rising rate market", etc.
To me, this appears completely wrong. Compared to a fixed rate bond (of the same issue price and face value, maturity, seniority etc.) a step-up bond should have a higher duration, i.e. a higher sensitivity to market interest rate fluctuations. In particular, if market rates go up, the market price of the step-up should decrease more, not less. In this sense the "ultimate" step-up is the zero-coupon, that can be seen as paying 0% coupons for most of its lifetime, and a single stepped-up coupon equal to the difference between the face value and issue price at the very end; and indeed as I understand it zero-coupons are, roughly speaking, the "vanilla" bond type with the longest duration for a given maturity.
Am I mistaken? Am I missing some unspoken assumption often made in such cases?