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There is confusion here.

The key of the question is how to mimic the plan benefits if it is not inflation-indexed. Pls be noticed that you are in the perspective of a plan manager not the beneficiary.

For a plan manager, you have to control the risk from deviating from the benchmark. The plan benefit for retired people is fixed in amount. The future annuity payment is fixed. This is similar to the coupon payment of a nominal bond. Thus, nominal bond best mimic the liability

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