The Annuity Puzzle and an Outline of Its Solution

Abstract

In his seminal 1965 paper, Yaari showed that, assuming actuarially fair annuity prices, uncertain lifetimes, and no bequest motives, utility-maximizing retirees should annuitize all of their wealth on retirement. Nevertheless, the markets for individual immediate life annuities in the United States, the United Kingdom, and several other developed countries have been small relative to other financial investment outlets competing for retirement savings. Researchers have found this situation puzzling, hence the so-called “annuity puzzle.” There are many possible explanations for the annuity puzzle, including “rational” explanations such as adverse selection, bequest motives, and incomplete markets; and “behaviorial” explanations, such as mental accounting, cumulative prospect theory, and mortality salience. We review the literature on the various plausible explanations given for the existence of the annuity puzzle, suggest ways of stimulating the demand for annuities, and suggest a few of the ingredients needed for further development of hybrid annuity products that may provide a solution to the puzzle.

Acknowledgements

This research was supported in part by a 2015 Society of Actuaries CAE grant awarded to University of Nebraska-Lincoln.

Notes

¹Of course, an important missing element here is when to retire. This article is not concerned with the timing and/or motivation of the retirement decision. For an excellent discussion of the behavioral and psychological aspects of the retirement timing decision see, for example, Knoll (2011).

²Under a defined benefit plan, the employer is responsible for paying its retired employees a monthly pension for life. However, this type of pension plan is becoming less common among U.S. employers.

³Under a defined benefit pension plan, retirees’ benefits are paid by the employer for the rest of their lives. Under a defined contribution plan (also commonly called a 401(k) plan in the United States), however, the employer periodically contributes a specific amount or fraction of an employee’s salary into an account. The account is invested and the proceeds made available to the employee on retirement. Thus the employee is responsible for funding her or his own retirement benefits. According to the December 2012 American Benefits Council 401(k) Fast Facts (https://www.americanbenefitscouncil.org/pub/?id=e6124993-b0e1-904c-6e54-31411c76727d, defined contribution plans are the most popular employer-sponsored retirement plan in the United States, and they have become America’s predominant retirement plan. Hurd and Panis (2006) provide a detailed analysis of the optimal choices available to individuals who desire to liquidate their retirement assets. workplace savings vehicle.

⁴Hurd and Panis (2006) provide a detailed analysis of the optimal choices available to individuals who desire to liquidate their retirement assets.

⁵https://www.willistowerswatson.com/en/insights/2017/01/global-pensions-asset-study-2017.

⁶A complete annuity market permits an individual to hedge the uncertainty of the date of death by exchanging his or her initial resources for a stream of payments that continue as long as the she survives (e.g., Kotlikoff and Spivak 1981).

⁷SoA (2016) found that the two most frequently mentioned financial shocks and unexpected expenses among U.S. retirees are home repairs and dental expenses.

⁸The U.K. annuity market has also been negatively impacted by the March 2011 Court of Justice of the European Union (EC 2001a, b, and 2012) ruling that declared as null and void legislation that allowed the European Union to maintain differentiations between men and women in insurance and annuity premiums and benefits (Sass and Seifried 2014; Slettvold 2015; Oxera 2010).

⁹https://www.ftadviser.com/pension-freedom/2017/03/09/what-has-happened-to-the-annuity-market-post-pension-freedoms/.

¹⁰Based on OECD 2017 data: https://data.oecd.org/healthstat/life-expectancy-at-65.htm.

¹¹According to Purcal and Piggott (2008), the Japanese life annuity market produces only a few thousand life annuity contracts each year.

¹²Following Hurd (1987), an individual is said to have a bequest motive if he or she cares about the welfare of the recipients of his or her estate.

¹³For a detailed discussion of adverse selection in insurance markets in general, see Cohen and Siegelman (2010). Although the authors have found evidence of asymmetric information in annuity markets, it is often not clear whether the asymmetry is due to adverse selection or moral hazard. In the context of annuity markets, moral hazard refers to actions taken by annuitants to increase their own longevity.

¹⁴It should be pointed out that actuaries would term the observed behavior of healthy individuals purchasing annuities as self-selection rather than adverse selection because the behavior is entirely anticipated and priced accordingly. Thus insurers are not actually “adversely” affected because they understand the market situation they face and the (high) risk type of their potential customers.

¹⁵According to the U.K. government report: “At present, individuals with tax-relieved pension savings are required to secure an income by age 75. Alternatively Secured Pensions (ASPs) exist for people reaching age 75 with principled objections to mortality pooling, but these are subject to strict income withdrawal limits and tax charges of up to 82%. In practice, annuitisation by age 75 is effectively compulsory for almost all pension savers” (HM Treasury 2010, p. 3).

¹⁶Following Finkelstein and Poterba (2004), a back-loaded annuity is one with a payment profile that provides a greater share of payments in later years. This contrasts with most annuities, which pay out a constant nominal amount each period.

¹⁷It should be reiterated that insurers typically use annuitant mortality tables rather than a general or population average mortality tables.

¹⁸Although they noted that this finding could be due to overconfidence issues or distrust towards banks and insurers, they found that the evidence about respondents’ use of information sources concerning retirement savings supported distrust toward banks and insurers.

¹⁹For an overview of the various ways of drawing down of a retiree’s assets, see MacDonald et al. (2013).

²⁰Suppose an individual aged x has a random curtate future lifetime denoted by K(x). In modern actuarial science, the present value of a future lifetime annuity due with payments of b per annum is defined to be $Y={bä}_{\overline{K(x)+1|}}$, which is a random variable. The actuarial present value is not a random variable and is defined as $\mathbb{E}[Y]=b{\ddot{a}}_x$. For more on the present value random variable, see, for example, Bowers et al. (1997, chapter 5.3, p. 143) or Dickson et al. (2013, chapter 5.4.1, p. 111).

²¹Gardner and Pittman (2013) provide some practical means to estimate the probability of running out of money during retirement.

²²Cox and Lin (2007) provide a method for deriving a “natural hedge” that utilizes the interaction of life insurance and annuities to changes in mortality to stabilize the insurer’s aggregate cash outflows. Cox and Lin show how to design a mortality swap between a life insurer and an annuity writer to create a natural hedge.

²³Suppose an individual aged x has a survival probability function _tp_x for t ≥ 0. Under an exogenous mortality model we assume the individual cannot change _tp_x for any t > 0. However, under an endogenous mortality model we assume the individual can take (non-random) actions that change _tp_x for some t > 0.

²⁴Moral hazard means annuitants using their annuity payments to extend their life time by making lifestyle changes such as purchasing better food and/or clothing, moving to a better neighborhood, accessing better medical care, etc.

²⁵In the accumulation phase, variable annuities offer tremendous flexibility. For example, Horneff, et al. (2015) has found that it is optimal to buy a variable annuity with living benefits using a guaranteed minimum withdrawal benefit rider. This means that the annuity provider guarantees the policyholder the right to take back his or her entire premium in small portions over a certain time frame, irrespective of the actual investment performance of the underlying portfolio.

²⁶A complementary theory to mortality salience is the terror management theory. Terror management theory states that awareness of one’s own mortality creates the potential for paralyzing terror, which could undermine an individual’s functioning. Therefore, applying terror management theory to mortality salience implies that mortality salience engenders potential overwhelming existential anxiety, which in turn triggers defensive responses that help people avoid or minimize emotional distress such as annuity decisions (DeWall and Baumeister 2007).

²⁷An installment option involves an annuity certain lasting for a specified period of not longer than the joint life expectancy of the employee and spouse.

²⁸A market is ripe for close regulation if certain conditions exist. These conditions include market power, externalities, asymmetric information, and if consumers are not fully rational (Cannon and Tonks 2011). These factors are present in the annuities market and make it necessary for government to intervene or regulate the industry.

²⁹See table 1 of https://www.bls.gov/ncs/ebs/benefits/2016/ownership/private/table01a.pdf.

³⁰Record keepers are hired to keep track of plan cash flows and employee loans from the plan. They also keep the plan participants’ accounting records for their investment in the plan and are responsible for sending the participants periodic reports of their 401(k) assets (Golly 1996).

³¹https://www.cdc.gov/aging/pdf/cognitive_impairment/cogimp_poilicy_final.pdf.

³²Belbase et al. (2017) classifies any individuals as having mild cognitive impairment if they (1) cannot remember the correct date, (2) failed in two attempts counting backwards from 86, (3) failed in two attempts counting backwards from 20, or (4) remembered at most one word from a list of 10 words.

³³A default payout option is the form of payment that results if the retiree makes no specific choice on the type of payout he or she wants. Rappaport (2008) provides a discussion of the various default options available in defined contribution plans.

³⁴Alternatively, instead of establishing pooling annuity funds, equitable income tontines could be established; see, for example, Bräutigam et al. (2017).

³⁵Episodic memory refers to the memory for specific personal experiences (Allen and Fortin 2013).

³⁶According to the U.S. Department of Health and Human Services, deferred long-term care annuity plans are available to people up to age 85 and are purchased via a single premium payment. In return, the annuitant receives monthly income for a specified period of time in the event of a medical condition that requires long-term care. The annuity creates two funds: one for long-term care expenses and another separate fund that can be used for any purpose (https://longtermcare.acl.gov/costs-how-to-pay/paying-privately/annuities.html).

³⁷https://www.fidelity.com/about-fidelity/employer-services/health-care-costs-for-couples-in-retirement-rise.

³⁸A cash refund annuity is a special whole life annuity with a decreasing term insurance component that pays, on the insured’s death, the excess of the purchase price over the total annuity payments made, excluding interest, with the excess being paid in a single-lump sum payment (e.g., Reid 1960).

³⁹An installment refund annuity is a special whole life annuity that guarantees payments to the insured (or the insured’s beneficiaries) will continue until the total payments made, excluding interest, reaches the purchase price after which point payments will continue thereafter only if the insured is alive (e.g., Reid 1960).

⁴⁰As defined by the U.S. Securities and Exchange Commission (https://www.sec.gov/reportspubs/investor-publications/investorpubsvaranntyhtm.html), a variable annuity is an annuity contract where the value of the annuity depends on the performance of the investment options the individual choose. Variable annuities can make periodic payments for the rest of the life of any person or persons designated as beneficiaries. Variable annuities also have a death benefit if death occurs during the accumulation phase. In addition, variable annuities are tax-deferred, that is, no taxes are paid on the income and investment gains from annuity accumulations until liquidation starts.

⁴¹As Horneff et al. (2015) noted, under a guaranteed minimum withdrawal benefit rider, the annuity provider guarantees the policyholder the right to take back her entire premium (or another guarantee base) in small portions (i.e., a “money-back” guarantee) over a certain time frame, regardless of the actual investment performance of his or her underlying portfolio.