portfolio convexity

CFA Level III
#1

is it possible for a portfolio to have different convexities after certain points?

e.g., portfolio 1 has greater convexity than portfolio 2 from 0% to 10%, but after 10%, portfolio 2 has greater convexity than portfolio 1

#2

Absolutely.

But I think that you’re not asking the full question you want answered.

For example, can portfolios 1 and 2 have markedly different prices for different yields?

#3

here;s my situation…from, say, 0% to 4%… A > L…after that A < L …let’s say 4% is the breakeven point

graphically,

i was thinking of if assets were simply MORE convex than liabilities - -> after 4% …A should still > L …correct?

But since it’s the opposite situation…different convexity after certain yields

another question…so i suppose even if durations of A and L match, you’re not completely hedged due to convexity. how would one hedge convexity?