Refundable Immediate Annuities (IAs): Feasibility of Money-Back Guarantees

We investigate the market for refundable immediate annuities (IA), where in contrast to basic life only IAs, the annuitant or their beneficiary is guaranteed to receive no less than their premium money back, albeit slowly over time. Refundable IAs are complicated by recursivity (to be explained) which is likely one of the reasons most insurance and pension economists have ignored them in the portfolio choice literature. Yet, the data show refundable IAs now form the majority of sales in the U.S.

We offer some basic - albeit perhaps long forgotten - theorems and observations related to: (i) cash-refund and (ii.) instalment-refund IAs. We distinguish between the (loaded) insurance price paid by annuitants and the (unloaded) actuarial premium, abbreviated as value. We start by proving that annuity values are a declining function of issue age $x$ and valuation rates $r$, neither of which are trivial when dealing with refundable products. We also compute measures of duration and show how they differ from traditional interest rate sensitivity, again due to the refund feature.

Our main (novel) result relates to loaded cash-refund IAs, that is once the value is grossed-up by $(1+pi)$ and converted to a market price paid by or charged to retiring annuitants. It seems the price of a cash-refund IA is no longer a declining function of age and older annuitants might have to pay more than younger ones for the same dollar of lifetime income. More importantly, there exists a threshold valuation rate $r_{pi}$, at which the pricing function of a cash-refund IA is no longer viable. Practically speaking, if-and-when the insurance company or pension fund assumed investment return (i.e. portfolio yield) is projected to fall under $r_{pi}$, they are unable to offer refundable IAs at any price. Indeed, with long-term interest rates being in the range of zero around the globe - and negative in some areas of Europe - this theoretical result has a clear testable implication.