Annuity Puzzle Research Articles

Examining the impact of mortality improvements on the attractiveness of annuity products: A focus on the mortality drag

Improvements in life expectancy have led to an increase in longevity risk, yet the phenomenon of the annuity puzzle persists. This study examines the attractiveness of annuity products by considering the impact of mortality improvements from the perspective of mortality drag. Our analysis shows that improvements in mortality rates reduce mortality drag, which in turn reduces the mortality-adjusted return on annuities. This reduction in mortality drag is observed across countries. Mortality drag is generally higher in Western countries, excluding Australia and the United Kingdom, than in Asian countries. In terms of gender, women have a relatively lower mortality drag and a slower declining mortality drag than men. The overall analysis suggests that increasing life expectancy is exacerbating the annuity puzzle by reducing the attractiveness of annuity products.

Optimal strategies for the decumulation of retirement savings under differing appetites for liquidity and investment risks

AbstractA retiree’s appetite for risk is a common input into the lifetime utility models that are traditionally used to find optimal strategies for the decumulation of retirement savings. In this work, we consider a retiree with potentially differing appetites for the key financial risks of decumulation: liquidity risk and investment risk. We set out to determine whether these differing risk appetites have a significant impact on the retiree’s optimal choice of decumulation strategy. To do so, we design and implement a framework which selects the optimal decumulation strategy from a general set of admissible strategies in line with a retiree’s goals, and under differing appetites for the key risks of decumulation. Overall, we find significant evidence to suggest that a retiree’s differing appetites for different decumulation risks will impact their optimal choice of strategy at retirement. Through an illustrative example calibrated to the Australian context, we find results which are consistent with actual behaviours in this jurisdiction (in particular, a shallow market for annuities), which lends support to our framework and may provide some new insight into the so-called annuity puzzle.

Annuity puzzle: Evidence from a Swiss pension fund

AbstractWe analyze individual annuitization decisions at retirement in an environment with mandatory participation in a funded pension pillar and low average annuity price. Using administrative data from a large Swiss insurance company over the period 2011–2015, we document that, even in this favorable environment, only 42.7% of the retirees fully annuitize, against 45% taking full lump sum. We show that individual annuitization decisions strongly respond to financial incentives, measured by the Money Worth Ratio, and to the tax rates on annuity and lump‐sum payments. Lump‐sum payments are more common among French‐ and Italian‐speaking individuals. Using Survey of Health, Ageing and Retirement in Europe data, we show that French‐ and Italian‐speaking Swiss are more likely to leave inheritance—thus suggesting that preferences for bequests may affect annuitization decisions. Finally, we provide evidence of asymmetric information, using the unused observable test, to show that individuals living in high mortality municipalities are less likely to annuitize and more likely to cash out their pension wealth.

Survival Pessimism and the Demand for Annuities

AbstractThe “annuity puzzle” refers to the fact that annuities are rarely purchased despite the longevity insurance they provide. Most explanations for this puzzle assume that individuals have accurate expectations about their future survival. We provide evidence that individuals misperceive their mortality risk and study the demand for annuities in a setting where annuities are priced by insurers on the basis of objectively-measured survival probabilities but in which individuals make purchasing decisions based on their own subjective survival probabilities. Subjective expectations have the capacity to explain significant rates of nonannuitization, yielding a quantitatively important explanation for the annuity puzzle.

Solving the Puzzle within the Annuity Puzzle: Incorporating Irrevocability Aversion into Annuity Choice

Solving the Puzzle within the Annuity Puzzle: Incorporating Irrevocability Aversion into Annuity Choice

Optimal lifetime income annuity without bequest: Single and annual premiums

This paper studies the optimal annuitization, risk-free investment, and consumption problem in a post-retirement lifecycle model without bequest motives. We characterize annuitization in scenarios where a retiree allocates wealth to a lifetime income annuity in exchange for single or annual premiums. We show that demand for an annuity is influenced by risk aversion in exchange for a single premium and by wealth for annual premiums. The effect of allocating wealth to purchase a lifetime income annuity increases with higher risk aversion for a single premium and decreases with residual wealth for annual premiums. We compare the certainty equivalence of investment yielding the same utility in an actuarially fair pricing framework and show that the product with annual premiums is more attractive. Finally, we show that partial annuitization can be optimal for different risk levels. Our findings thus reflect an explanation for the “annuity puzzle” in the literature on lifecycle consumption.

The nexus between investor sophistication and annuity insurance ownership: evidence from FINRA's National Financial Capability Study

PurposeAlthough annuitization provides insurance against longevity risk that can benefit households, researchers have uncovered an annuitization puzzle, which suggests households are reluctant to annuitize their wealth. This study contributes to the discussions on the annuitization puzzle by examining investor sophistication and owning annuities in non-retirement accounts.Design/methodology/approachThe study utilizes data from the 2018 U S National Financial Capability Study (NFCS). The empirical analyses are based on logistic regression estimates of annuity ownership on investor sophistication. Interpretations are based on odds ratios.FindingsThe findings indicate that investor sophistication contributes to the annuity puzzle. Investors with low objective and high subjective investment knowledge (overconfident investors) are more likely to own annuities compared to those with low objective and low subjective investment knowledge. However, investors with high objective and low subjective investment knowledge (under-confident investors) are less likely to choose annuity ownership compared to those with low objective and low subjective investment knowledge. The findings and ensuing discussion highlight the importance of annuitization when planning for retirement, with implications for financial service professionals.Research limitations/implicationsThe measure of investor sophistication does not assess the difficulty level of each financial knowledge question. The questions used to construct the investor sophistication variable are based on general investment knowledge. In addition, the annuity ownership variable used in this study pertains to investments outside retirement accounts. Despite these limitations, the findings highlight the importance of annuitization when planning for retirement.Originality/valueUnlike prior studies, the authors consider four mutually exclusive measures of investor sophistication constructed from measures of objective and subjective investment knowledge to understand the effect of investor sophistication on annuity ownership in the United States.

Value of life and annuity demand

AbstractHow does the value of life affect annuity demand? To address this question, we construct a portfolio choice problem with three key features: (i) agents have access to life‐contingent assets, (ii) they always prefer living to dying, (iii) agents have nonexpected utility preferences. We show that as utility from being alive increases, annuity demand decreases (increases) if agents are more (less) averse to risk rather than to intertemporal fluctuations. Put differently, if people prefer early resolution of uncertainty, they are less interested in annuities when the value of life is high. Our findings have two important implications. First, we get a better understanding of the well‐known annuity puzzle. Second, we argue that the observed low annuity demand provides evidence that people prefer early rather than late resolution of uncertainty.

Is the Annuity Puzzle Really So Puzzling? An Analysis of the Consumer Lifetime Annuitization Decision in a Low Interest Rate World

Is the Annuity Puzzle Really So Puzzling? An Analysis of the Consumer Lifetime Annuitization Decision in a Low Interest Rate World

Accounting for Social Security Claiming Behavior

Why do most individuals claim Social Security benefits before the full retirement age? Claiming benefits early results in a substantial reduction in pension income, yet many people claim as early as possible (age 62) or soon thereafter. We argue that by answering this question, we can make two additional contributions to the literature. First, early claiming is equivalent to low demand for Social Security annuity, thus it offers a unique context for studying the well-known annuity puzzle. Since participation in Social Security is nearly universal, the low demand for this annuity cannot be explained away by market failures. Second, we show that claiming decisions are closely linked to the subjective rate of time preferences and thus can provide a new angle for the identification of this parameter. We provide a quantitative analysis of claiming decisions using a rich structural life-cycle model that matches many important features of the data. We find that the claiming puzzle can be attributed to a combination of three factors: (i) the discrepancy between individuals' subjective valuation of Social Security annuity and its implicit price, (ii) strong bequest motives, (iii) pre-annuitized wealth. We show that if individuals were rewarded for delaying claiming not with additional annuity income but with equivalent (in present value terms) lump-sum payments, the fraction of early claimers would be significantly reduced.

주택연금퍼즐현상에 관한 분석적 연구 : 주택연금 가입의향을 중심으로

주택연금퍼즐현상에 관한 분석적 연구 : 주택연금 가입의향을 중심으로

The annuity puzzle and consumption hump under ambiguous life expectancy

We establish a continuous-time model to solve the optimal consumption-saving problem with life annuity. The decision-maker has ambiguous beliefs in the force of mortality and is averse to this model uncertainty. The ambiguity aversion is represented by the max-min principle under the framework of robust control. We show that the optimal annuity demand decreases with the extent of ambiguity aversion, bequest motives, and extent of relative risk aversion. For an individual with non-zero bequest motives, the optimal annuity demand becomes zero when the extent of ambiguity aversion exceeds a certain threshold. We also show that, even if the individual has access to actuarially fair annuities, the optimal consumption would have a hump-shaped path when the individual is ambiguity-averse.

The ‘Annuity Puzzle’ and Model Portfolios

The paper presents a model that demonstrates the advantages of partial annuitization in the most straightforward manner. The paper also briefly discusses “the annuity puzzle”, a decades old problem.

A Stydy of the Choice between Annuity or Lump sum in Annuity Puzzle

A Stydy of the Choice between Annuity or Lump sum in Annuity Puzzle

Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods

We operationalise the theoretical modelling of Marín-Solano and Jorge Navas (2010), seeking to understand the consequences for optimal consumption, life insurance and annuity demand in a time inconsistent world, by incorporating the insurance insights from Richard (1975). Richar, in particular, has an elegant treatment of optimal annuity demand, rarely harnessed in the literature. Central to Richard’s creation of demand for personal insurance is a bequest motive and, in addition to implementing time inconsistency through hyperbolic discounting, our analysis is further expanded to include naïve and sophisticated agents with a luxury bequest motive (Lockwood, 2012). Compared to a more simplistic ‘necessity’ bequest framework, luxury bequests (broadly) weaken optimal life insurance demand and strengthen optimal life annuity demand for the less wealthy. In contrast, time inconsistency offers a wide spectrum of outcomes, and our modelling, calibrated to Swiss data, contributes to understanding the annuity puzzle—observed low levels of (voluntary) purchases of life annuities.

Survival Pessimism and the Demand for Annuities

Abstract The “annuity puzzle” refers to the fact that annuities are rarely purchased despite the longevity insurance they provide. Most explanations for this puzzle assume that individuals have accurate expectations about their future survival. We provide evidence that individuals misperceive their mortality risk, and study the demand for annuities in a setting where annuities are priced by insurers on the basis of objectively-measured survival probabilities but in which individuals make purchasing decisions based on their own subjective survival probabilities. Subjective expectations have the capacity to explain significant rates of non-annuitization, yielding a quantitatively important explanation for the annuity puzzle.

Value of Life and Annuity Demand

How does the value of life affect annuity demand? To address this question, we construct a portfolio choice problem with three key features: i) agents have access to life-contingent assets, ii) they always prefer living to dying, iii) agents have non-expected utility preferences. We show that as utility from being alive increases, annuity demand decreases (increases) if agents are more (less) averse to risk rather than to intertemporal fluctuations. Put differently, if people prefer early resolution of uncertainty, they are less interested in annuities when the value of life is high. Our findings have two important implications. First, we get better understanding of the well-known annuity puzzle. Second, we argue that the observed low annuity demand provides evidence that people prefer early rather than late resolution of uncertainty.

Individual Tontine Accounts

An individual tontine account (ITA) is similar to a conventional investment brokerage account, but with the added feature of mortality pooling through participation in an open-ended fair tontine. In showing them to be fair to all participants, we envision ITAs as complementary to individual retirement accounts (IRAs), allowing retirees to derive extra income from savings without taking additional investment risk and to obtain lifetime income at a lower cost than with insurance products. ITAs represent an efficient new solution in addressing retirement needs and may help address the “annuity puzzle” by providing a more transparent, lower-cost alternative to insurance-based products.

Retirement Security, Finance Science, SeLFIES and The Flex MMM Plan

Prof. Merton’s attempts to improve retirement security over the last 40 years, when viewed through his preferred lens of using “finance science” to address societal challenges, results in the creation of SeLFIES (Standard-of-Living indexed, Forward-starting, Income-only Securities) to improve retirement outcomes. SeLFIES have been proposed in countries as diverse as Australia, Chile, Colombia, France, India, Japan, Portugal, Spain, South Africa, South Korea, Turkey, and the United States – all interested in funding infrastructure and improving retirement security. Merton (1984) introduced the idea of government-issued consumption-linked bonds as a way to allow a fully funded public pension fund to offer consumption-indexed annuities. Later, Merton (2007) would address the challenges of defined contribution (DC) plans and argue that the welfare of individuals should be expressed in units of retirement income, and not wealth. A key insight is that the traditional “risk-free” asset in Modern Portfolio Theory (MPT) was risky from a retirement income perspective. Muralidhar, Ohashi and Shin (2014), in developing the Relative Asset Pricing Model (RAPM), leveraged the Merton (2007) idea that in retirement planning (or in any goals-based portfolio), investors care about (the utility of) funded status, defined as wealth divided by stochastic liabilities, and not expected utility of wealth. In RAPM, an additional variable – the relative risk-free asset or the asset that replicates the stochastic goal – is critical to asset allocation and asset pricing (and CAPM is just a special case of RAPM; namely CAPM assumes a deterministic goal). Currently in DC plans, the goal replicating portfolio (an annuity) is illiquid, costly and complex and Modigliani (1986) highlights the “annuity puzzle”. Muralidhar (2015) and Muralidhar, Ohashi and Shin (2015) recommend the creation of a new bond that replicates the desired cash flow profile in DC plans – a bond (called BFFS) that pays a fixed currency coupon, in real-terms, that starts paying once an individual retires for a period equal to the life expectancy of the country. Merton and Muralidhar (2017b) recommend linking these bonds to per-capita consumption (leveraging Merton 1984) thereby creating SeLFIES and show why SeLFIES are a good deal for governments too. BFFS/SeLFIES help complete financial markets and this idea is easily extended to other goals. The paper concludes by demonstrating how finance science can be used to design effective DC pension plans for uncovered workers.

Doubly Enhanced Annuities (DEANs) and the Impact of Quality of Long-Term Care under a Multi-State Model of Activities of Daily Living (ADL)

The relatively small size of global voluntary immediate life annuity markets seemingly contradicts a well-known result that, under certain conditions, utility-maximizing retirees should annuitize all of their wealth upon retirement. This apparent contradiction contributes to what is called the “annuity puzzle.” The main explanations for the annuity puzzle include adverse selection, bequest motives, and retirees’ fear of health shocks that may require them to need long-term care. To explore a potential solution to this puzzle in the U.S. annuity market, we consider a cohort of retirees who are independent and identical except for a hidden immutable health parameter, , that identifies the retiree’s risk type. We assume that the “average” or “standard” retiree has θ = 1, with larger values of θ denoting less healthy individuals. Because private insurers fear that annuitants may live well beyond their life expectancy—that is, they fear adverse selection—voluntary immediate life annuities are generally priced in a manner that makes them attractive mainly to retirees who believe themselves to be healthier than average. These retirees, however, typically represent a small fraction of their cohort of retirees. To expand annuity markets, we are proposing a hybrid voluntary fixed immediate annuity product called a doubly enhanced annuity (DEAN), which we feel will be attractive to the larger retiree population; that is, retirees with . DEANs are medically underwritten to provide greater annual benefits to annuitants with shorter than average life expectancies, they provide long-term care benefits, and they satisfy a bequest motive through a death benefit. Our underlying model of retiree mortality and morbidity is based on a multi-state Markov process with states representing various levels of an insured retiree’s ability to perform activities of daily living (ADL). A major contribution of our research is to explicitly include in our multi-state Markov model a parameter, α, that reflects the level of quality of long-term care a retiree receives over her lifetime. Our main objectives are to develop a theoretical basis for pricing DEANs for the U.S. market, to determine a retiree’s expected discounted utility gained from these annuities, to determine the optimal choice of quality of care, and to explore some of the quality of life implications. A numerical example is provided.