Refundable income annuities: Feasibility of money-back guarantees

TL;DR

This paper examines the feasibility and pricing of refundable income annuities, highlighting their market growth, complex valuation challenges, and counterintuitive pricing behaviors, with implications for insurance economics.

Contribution

It provides a tractable model for pricing refundable IAs, revealing counterintuitive age-price relationships and identifying valuation thresholds affecting market viability.

Findings

Refundable IAs now dominate U.S. sales.

Pricing is not always decreasing with age, contrary to intuition.

A valuation rate threshold determines market viability.

Abstract

Refundable income annuities (IA), such as cash-refund and instalment-refund, differ in material ways from the life-only version beloved by economists. In addition to lifetime income they 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 insurance and pension economists. And, although their pricing, duration, and money's-worth-ratio is complicated by recursivity which will be explained, we offer a path forward to make refundable IAs tractable. A key 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. Moreover, there exists a threshold valuation rate below which no price is viable. This may also explain why inflation-adjusted IAs have all but disappeared.