Sebastian Hallstein is a doctoral student at Goethe University Frankfurt. Daniel Liebler is a postdoctoral researcher at Goethe University Frankfurt. Raimond Maurer is a Professor of Finance at Goethe University Frankfurt.
As the new year begins, many people feel renewed motivation to pursue fitness goals, yet some still hesitate to sign up for a gym membership. A common concern is that initial enthusiasm may fade, turning the up-front fee into a regretted expense if the gym is used infrequently. In our latest research, we show that a similar form of loss aversion helps explain the annuity puzzle, the empirical observation that households make little voluntary use of life annuities despite standard economic models predicting widespread annuitization because annuities efficiently insure against longevity risk.
The Annuity Puzzle at a Glance
An extensive literature argues that individuals should optimally purchase annuities to insure against the risk of outliving their savings. By converting a lump-sum premium into guaranteed lifelong payouts, annuities provide effective protection against longevity risk. Standard life cycle models therefore predict high levels of annuitization.
In reality, few households voluntarily purchase private annuities, a discrepancy widely known as the annuity puzzle. Numerous explanations have been proposed, including bequest motives and concerns about large out-of-pocket medical expenses, both of which can reduce the willingness to transfer liquid wealth to an insurer.
A Missing Piece: The Role of Money-Back Guarantees
An important feature of modern annuity markets has received relatively little attention in the literature. A 2022 study by Moshe Milevsky and Thomas Salisbury documents that only about 10% of price quotes in the U.S. annuity market refer to contracts without guarantee features, even though this is the annuity type commonly studied in the literature.
Today, more than 60 percent of the U.S. annuity market consists of refundable annuities. These products make payments to heirs that cover the difference between the initial annuity investment and the total payouts received by the policyholder. As a result, the annuitant and heirs together are guaranteed to at least recoup the initial premium, effectively eliminating the possibility that the annuity generates a financial loss. Because this refund feature is valuable, refundable annuities are typically 15 to 25 percent more expensive than comparable life-only annuities and therefore provide lower lifelong payouts (see the Figure, below).
Figure: Prices of life-only and refundable annuities
Note: This Figure shows the prices (in €) of life-only and refundable annuities purchased at ages 20–66 per euro of lifelong payout from age 67 onward. We use German unisex mortality rates of 2018, a gross real interest rate of 1.01% and a price loading of 12.5% added to the fair annuity prices.
What a Life Cycle Model Predicts under Loss Aversion
Motivated by the contrast between low empirical demand for life-only annuities and the high annuitization predicted by standard models, we modify preferences to incorporate loss aversion with respect to annuity-related losses arising from early death. We solve life cycle models calibrated to the German market in which individuals optimally choose consumption and allocate wealth across stocks, bonds, and annuities.
When individuals can choose between life-only annuities and annuities with money-back guarantees, several clear patterns emerge. First, in the absence of concerns about leaving money to heirs, people strictly favor life-only annuities. These products offer higher monthly payments, and without a desire to leave a bequest, a refund feature provides no additional value. Second, even when leaving money to heirs is important, life-only annuities remain attractive. Their higher payouts help stabilize consumption throughout retirement, while the potential refunds offered by guaranteed annuities typically do not justify their higher prices and lower monthly income.
This picture changes once fear of losses is taken into account. When people focus on the possibility of dying early and “losing” their annuity investment, interest in life-only annuities drops sharply. At the same time, annuities with money-back guarantees become more appealing because they provide lifelong income while ensuring that the initial investment is not lost.
With moderate concern about potential losses, individuals choose a balanced mix of both types of annuities. This pattern closely matches what we observe in actual annuity markets. Concern about leaving money to heirs alone cannot explain this outcome. Aversion to losses is needed to reduce reliance on life-only annuities and increase demand for products with guarantees.
Why This Matters and How Our Insights Could Be Leveraged
Avoiding annuities because of loss aversion can be costly. Much like skipping a gym membership can undermine long-term fitness goals, refraining from cheaper life-only annuities may jeopardize living standards at advanced ages. Annuities with money-back guarantees are more expensive and therefore deliver lower lifelong payouts.
Greater familiarity with annuity products and clearer communication about how they work could reduce the tendency to overemphasize potential losses at the time of purchase. Transparent explanations of the trade-off between guarantees and payout levels are essential for informed decision making. Financial institutions and advisors can use these insights to design and communicate pension solutions more effectively, helping individuals make choices that better reflect how guarantees shape long-term retirement income.
Views of our Guest Bloggers are theirs alone, and not of the Pension Research Council, the Wharton School, or the University of Pennsylvania.
