NakedPuts2011

The first statement applies to immunizing a single liability. In your 2nd paragraph, they may be referring to multiple liability immunization, although I'm not sure.

Using a barbell approach results in greater dispersion around the liability, creating greater immunization risk. The more clustered the hedging instruments are relative to your liability reduces immunization risk.

But in multiple liability immunization, the range of your assets have to be wider than your liabilities, so this may be where the barbell approach comes into play.

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