Convexity and Structural Risk

Hi all,

It is said that when immunizing a single liability asset, we alway aim for lower convexity to minimize structural risk and higher return.

However, when we have multiple assets in the portfolio, are we looking for higher convexity, because it offers portfolio with more CF dispersions that can potentially minimize CF mismatches and possibly lower duration - beneficial during non-parallel large shifts in yield curve, and twists?

Please correct me if my understanding is wrong, thanks.

In both cases you want to match the duration of the liability(ies), and match or slightly exceed the convexity of the liability(ies). You rarely want to exceed the convexity significantly, simply because convexity is expensive.

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