Why do bond portfolios cease to be immunized if interest rates fluctuate more than once?

Let’s say we have a single asset and a single liability with an effective duration of 5 years.

If interest rates go up 100bps, then the value of the portfolio goes down by 5% in both positions, leaving their duration still matching (we are assuming all changes are instantaneous and parallel).

If this is true, then how would a second change in interest rates (let’s say rates go down 100bps), break the equality of duration?

The classical single-period immunization strategy does not take convexity into account either (as I understand it).

title of thread “immunized”. content of thread “duration matched”.

these things are different. if you immunize a 5yr bond with a 10yr future, then you see the reason…

I’m not really following you.

The idea behind classical immunization is ALM through matching their effective duration. However this only works if interest rates move only once.

My question was, why would this not work if interest rates moved more than once simultaneously.

Because the bonds in the portfolio have various individual durations that move. So maybe your dollar duration was matched but as rates move, the bonds’ durations could change in a way that if you keep the allocation unchanged, the dollar duration of the liabilities will no longer be matched. So you need to rebalance every time