Odds are 100%. Indeed pensions, insurance companies, banks, retirees are structually long bonds. Their are regulated into this.

Banks and insurance companies get special accounting rules to prevent margin calls or get bailed out when bonds are marked down.

Pensions and retirees do not enjoy these benefits. Not only that, the fiduciaries advising these plans HAVE to recommend bonds for "risk management". Sadly, the clients are paying 1%+ to be forced to pay for wall street and DCs excess.

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Do you know the rule (term/acronym) for what % that (state) pensions funds have to allocate to treasuries?

Hm not exactly sure. Let me say some words and see if any hit.

Pensions generally use a combo of asset/liability and modern portfolio theory to determine their asset allocation. Managers of pensions have a fiduciary duty to the beneficiaries of the pension.