A Funding-Ratio-Based Framework for the Consolidation of Military Shareholder Mutual Benefit Funds (MTS–MTN–MTA)

This paper develops a funding-ratio-based analytical framework for evaluating the consolidation of military shareholder mutual benefit funds (MTS, MTN, MTA). When participating funds enter a merger with heterogeneous pre-merger funding ratios, naïve pooling of assets and actuarial liabilities can embed implicit value transfers, raising fairness and legitimacy concerns. We formalize each fund’s position using assets, actuarial liabilities, and the funding ratio FRi=Ai/Li , and introduce budget-balanced side payments as an explicit compensation instrument. This yields an adjusted funding ratio AFRi(s)=(Ai+si)/Li that makes redistribution transparent and testable. Two widely invoked safeguards, FR-based “no gain–no loss” and “non-dilution”, are then stated as axioms under budget balance, and we derive an impossibility result showing that these strong adequacy-preservation requirements collapse to the trivial zero-transfer outcome. Building on this boundary, we propose an implementable rule that equalizes adjusted funding ratios to the pooled benchmark FRtot=A/L, producing a closed-form, budget-balanced sidepayment vector. The framework offers both a diagnostic tool to detect implicit transfers and a constructive mechanism for designing transparent consolidation policies.