Refundable Income Annuities: Feasibility of Money-Back Guarantees

Abstract

[Refundable income annuities (IA), such as cash-refund and instalment-refund, differ in material ways from the life-only version beloved by pension and financial economists. In addition to lifetime income they also guarantee the annuitant or beneficiary will receive their money back albeit slowly over time. We document that refundable IAs now represent the majority of sales in the U.S., yet they are mostly ignored by the literature. And, although their pricing, duration, and money's-worth-ratio is complicated by internal recursivity -- which is carefully explained in the paper -- we offer a path forward to make refundable IAs tractable. A key -- and perhaps even the primary and quotable -- result concerns the market price of cash-refund IAs, when the actuarial present value is grossed-up by an insurance loading. We prove that price is counterintuitively no longer a declining function of age and older buyers might pay more than younger ones for this type of pension annuity. Moreover, there exists a threshold valuation rate below which no market price is viable. The product can't exist. This may also explain why inflation-adjusted IAs have all but disappeared.