The Implied Longevity Yield: A Note on Developing an Index for Life Annuities

I develop an index for tracking the dynamic behavior of life (pension) annuity payouts over time, based on the concept of self‐annuitization. Our implied longevity yield (ILY) value is defined equal to the internal rate of return (IRR) over a fixed deferral period that an individual would have to earn on their investable wealth if they decided to self‐annuitize using a systematic withdrawal plan. A larger ILY number indicates a greater relative benefit from immediate annuitization. I use age 65—with a 10‐year period certain—compared against the same annuity at age 75 as the standard benchmark for the index, and calibrate to a comprehensive time series of weekly (Canadian) life annuity quotes from 2000 through 2004. I find that during this period the ILY varied from 5.45 percent to 6.90 percent for males and from 5.00 percent to 6.42 percent for females and was highly correlated with a duration‐weighted average yield of 10‐year and long‐term Government of Canada bonds. I believe our ILY metric can help promote and explain the benefits of acquiring lifetime payout annuities by translating the abstract‐sounding longevity insurance into more concrete and measurable financial rates of return.     

Dynamic portfolio choice with deferred annuities

We derive the optimal life-cycle portfolio choice and consumption pattern for households facing uncertain labor income, risky capital market, and mortality risk. In addition to stocks and bonds, the households have access to deferred annuities. Deferred payout life annuities are financial contracts providing life-long income to the annuitant after a specified period of time conditional on survival. We find that deferred annuities play an important role in household portfolios and generate significant welfare gains. Households with high benefits from state pensions, moderate risk aversion and moderate labor income risk purchase deferred annuities from age 40 and gradually increase their portfolio share. At retirement, deferred annuities account for 78% of total financial wealth. Households with low state pensions and high labor income risk purchase more annuities and earlier. Uncertainty with respect to future mortality rates has the same effect, i.e. household hedge against longevity risks using deferred annuities.     

What Do We Know About Annuitization Decisions?

Against the background of aging societies and increasing life expectancies, the protection of individuals from outliving their savings has become increasingly relevant. Annuities represent insurance against longevity risk and can prevent old‐age poverty. The aim of this article is to present the current state of theoretical, empirical and experimental evidence with regard to annuitization decisions. Toward this end, we conduct a systematic literature review that includes 89 articles. Based on this, we study welfare effects of mandatory annuitization, annuitization rates and the optimal fraction of wealth to be annuitized, as well as determinants of retirees’ choice to annuitize and their impact on annuity demand. Finally, we present possible solutions for overcoming the low uptake of annuities based on its causes. One main result is that behavioral biases in annuitization decisions particularly require considerably more theoretical research and empirical evidence, and that theoretical models already appear to well explain empirically observed annuitization rates.     

Maximum Withdrawal Rates: A Novel and Useful Tool

Even after accumulating a portfolio of investment assets, retirees still need to know how much of their wealth they can spend each year without risking running out of money before they die. Traditionally, financial advisers use extensive simulation to predict a “failure rate” (i.e. the probability of a retiree running out of money before they die). Unfortunately, the failure rate approach is flawed because strategies with the same failure rate may not be comparable overall. For example, different withdrawal strategies may have the same failure rate but wind up leaving significantly different amounts of wealth behind. Instead of failure rate, this author recommends using the maximum withdrawal rate, or MWR, approach that predetermines a desired bequest (which could be zero or some positive sum), thus enabling an apples‐to‐apples comparison of retirement strategies. In addition to permitting direct comparisons of retirement strategies, the MWR provides a way to assess how likely a retiree is to sustain a target sequence of inflation‐adjusted withdrawals. This is the main advantage of the MWR; it is a single tool that can be used to explore two of the most important issues in retirement analysis. The MWR as presented here is essentially a measure of the best a retiree could have done had he known the future returns of his portfolio. Obviously, one cannot be sure of future rates of return ahead of time, so the MWR does not eliminate all retirement risk. That said, its adoption would be an improvement upon current practice.     

Choosing the optimal annuitization time post-retirement

In the context of decision making for retirees of a defined contribution pension scheme in the de-cumulation phase, we formulate and solve a problem of finding the optimal time of annuitization for a retiree having the possibility of choosing her own investment and consumption strategy. We formulate the problem as a combined stochastic control and optimal stopping problem. As criterion for the optimization we select a loss function that penalizes both the deviance of the running consumption rate from a desired consumption rate and the deviance of the final wealth at the time of annuitization from a desired target. We find closed-form solutions for the problem and show the existence of three possible types of solutions depending on the free parameters of the problem. In numerical applications we find the optimal wealth that triggers annuitization, compare it with the desired target and investigate its dependence on both parameters of the financial market and parameters linked to the risk attitude of the retiree. Simulations of the behaviour of the risky asset seem to show that, under typical situations, optimal annuitization should occur a few years after retirement.     

Longevity Risk Management in Singapore's National Pension System

Although annuities are a theoretically appealing way to manage longevity risk, in the real world relatively few consumers purchase them at retirement. To counteract the possibility of retirees outliving their assets, Singapore's Central Provident Fund, a national defined contribution pension scheme, has recently mandated annuitization of workers’ retirement assets. More significantly, the government has entered the insurance market as a public‐sector provider for such annuities. This article evaluates the money's worth of life annuities and discusses the impact of the government mandate and its role as an annuity provider on the insurance market.     

Explaining Low Annuity Demand: An Optimal Portfolio Application to Japan

Using an optimizing financial planning model in the tradition of Merton and Richard we explore how individuals should determine their life insurance and annuity choices, given uncertainty about investment returns and mortality. Both consumption and bequests appear as arguments in the individual's preference function. The model explicitly recognizes the existence of social security in retirement, and of loadings on insurance premiums, due to administration costs in the life insurance and annuities markets. The model sheds light on the reasons for the thinness of voluntary life annuity markets worldwide. The relative importance of pre‐existing annuitization through social security, the role of bequests, and premium loadings are quantitatively assessed within a single optimizing framework. Results are presented for a model specification calibrated to Japan.     

Fixed and variable longevity income annuities in defined contribution plans: Optimal retirement portfolios taking social security into account

This paper investigates retirees' optimal purchases of fixed and variable longevity income annuities using their defined contribution (DC) plan assets and given their expected social security benefits. As an alternative, we also evaluate using plan assets to boost social security benefits through delayed claiming. Using a calibrated life-cycle model, we determine that including deferred income annuities in DC accounts is welfare-enhancing for all sex/education groups examined. We also show that providing access to well-designed variable deferred annuities with some equity exposure further enhances retiree well-being, compared to having access only to fixed annuities. Nevertheless, for those facing the highest mortality rates, delaying claiming social security is mostly preferred, whereas those anticipating living longer than average will benefit more from using accumulated DC plan assets to purchase deferred annuities.     

Optimal annuitization with imperfect information about insolvency risk

Even the highest‐rated life‐annuity providers have a nonzero probability of becoming insolvent during an annuitant's retirement, and many potential annuitants are unaware of the state guaranty associations (SGAs) which provide insurance against the associated financial consequences. We study the theoretical implications of insolvency risk—real and perceived—for annuitization. Then, using a disciplined calibration of annuitant misperceptions in a standard life cycle model, we show that even the modest perceived risk of default associated with highly‐rated providers can—absent awareness of the SGAs—reduce annuitization and significantly reduce welfare. We further consider the implications of information frictions which prevent retirees from discerning true insolvency risk and we find that these frictions have plausibly large additional quantitative implications for annuitization and welfare. Simulations of our model further suggest that the general lack of awareness of the SGA backstop by potential annuitants can erode a sizable fraction of the potential welfare benefits thereof.     

Human Survival at Older Ages and the Implications for Longevity Bond Pricing

Abstract

Governments are concerned about the future of pension plans, for which increasing longevity is judged to be an important risk to their future viability. We focus on human survival at age 65, the starting age point for many pension products. Using a simple model, we link basic measures of life expectancy to the shape of the human survival function and consider its various forms. The model is then used as the basis for investigating actual survival in England and Wales. We find that life expectancy is increasing at a faster rate than at any time in history, with no evidence of this trend slowing or any upper age limit. With interest growing in the use of longevity bonds as a way to transfer longevity risks from pension providers to the capital markets, we seek to understand how longevity drift affects pension liabilities based on mortality rates at the point of annuitization, versus what actually happens as a cohort ages. The main findings are that longevity bonds are an effective hedge against longevity risk; however, it is not only the oldest old that are driving risk, but also more 65-year-olds reaching less extreme ages such as 80. In addition, we find that the possibility of future inflation and interest rates could be as an important a risk to annuities as longevity itself.     

The asset allocation decision in retirement: lessons from dollar-cost averaging

How should a retiree allocate his wealth between stocks and bonds? We address this question by studying whether it would have been better to have consumed periodically from stocks than from bonds over the seven decades of U.S. financial markets beginning in 1926 and ending in 1995. We find that retirees would have consistently done better by investing in stocks as opposed to bonds. When we analyze dispersion in consumption around its mean we find that there are greater chances for low consumption from the bond portfolio and greater chances for high consumption from the stock portfolio. Thus, we challenge the conventional wisdom that one should move away from stocks and towards bonds as one ages.     

The Joy of Giving or Assisted Living? Using Strategic Surveys to Separate Public Care Aversion from Bequest Motives

The “annuity puzzle,” conveying the apparently low interest of retirees in longevity insurance, is central to household finance. Two possible explanations are “public care aversion” (PCA), retiree aversion to simultaneously running out of wealth and being in need of long‐term care, and an intentional bequest motive. To disentangle the relative importance of PCA and bequest motive, we estimate a structural model of the retirement phase using a novel survey instrument that includes hypothetical questions. We identify PCA as very significant and find bequest motives that spread deep into the middle class. Our results highlight potential interest in annuities that make allowance for long‐term care expenses.     

Annuities and lifetime income: the Anglo-Saxon experience

A number of western industrialized nations have found themselves in a similar position to the United States today: an aging population leading to increasing, and perhaps unsustainable, expenditures on a traditional social security system. This article examines the risks that individuals face in retirement, describes the role of annuities in addressing those risks and examines why annuitization rates are so low. It then reviews the pension structures in the United Kingdom, Australia and New Zealand--countries with similar governmental and economic structures to those of the United States--and describes how these have impacted those countries' annuitization rates.     

Portfolio management and retirement: what is the best arrangement for a family?

In comparing an immediate life annuity with a payout-equivalent investment fund payout plan (self-annuitization), research to date has focused mainly on shortfall probabilities of self-annuitization. As an exception, Schmeiser and Post (2005) propose a family strategy where the chances of self-annuitization (i.e., bequests) are taken into consideration as well. In such a family strategy, potential heirs must bear shortfall risks, but in return have a chance of receiving a bequest. This paper analyzes under which conditions heirs will be willing to agree to a family strategy. The idea of a family strategy is integrated into a realistically calibrated intertemporal expected utility framework, taking into account risks arising from stochastic life span, asset returns, and nontradable labor income. A family strategy is shown to be accepted for many parameter combinations, especially in families with low marginal tax rates, if the heirs are wealthy, or in a case where the retiree has an average population life expectancy. We also work out how family self-annuitization decisions interact with asset allocation, saving decisions, and labor income risk. Under realistic conditions our results support two explanations for the empirically observable low demand for annuities (the so-called annuity puzzle), namely intra-family risk sharing and high cost of market-annuitization.     

Mortality Heterogeneity and the Distributional Consequences of Mandatory Annuitization

This article investigates the distributional consequences of mandatory annuitization. Using Health and Retirement Study (HRS) data and accounting for longevity risk pooling within marriage and preannuitized wealth, we find substantial redistribution away from disadvantaged groups in expected utility terms. Using HRS data on subjective survival probabilities, we construct a subjective life table for each individual in the HRS. We calculate the value each household would place on annuitization, based on the husband and wife's subjective life tables, and the household's degree of risk aversion and proportion of preannuitized wealth. A significant minority would perceive themselves as suffering a loss from mandatory annuitization.     

Optimal Annuitization Policies

Abstract

At, or about, the age of retirement, most individuals must decide what additional fraction of their marketable wealth, if any, should be annuitized. Annuitization means purchasing a nonrefundable life annuity from an insurance company, which then guarantees a lifelong consumption stream that cannot be outlived. The decision of whether or not to annuitize additional liquid assets is a difficult one, since it is clearly irreversible and can prove costly in hindsight. Obviously, for a large group of people, the bulk of financial wealth is forcefully annuitized, for example, company pensions and social security. For others, especially as it pertains to personal pension plans, such as 401(k), 403(b), and IRA plans as well as variable annuity contracts, there is much discretion in the matter.

The purpose of this paper is to focus on the question of when and if to annuitize. Specifically, my objective is to provide practical advice aimed at individual retirees and their advisors. My main conclusions are as follows:

? Annuitization of assets provides unique and valuable longevity insurance and should be actively encouraged at higher ages. Standard microeconomic utility-based arguments indicate that consumers would be willing to pay a substantial “loading” in order to gain access to a life annuity.

? The large adverse selection costs associated with life annuities, which range from 10% to 20%, might serve as a strong deterrent to full annuitization.

? Retirees with a (strong) bequest motive might be inclined to self-annuitize during the early stages of retirement. Indeed, it appears that most individuals—faced with expensive annuity products—can effectively “beat” the rate of return from a fixed immediate annuity until age 75?80. I call this strategy consume term and invest the difference.

? Variable immediate annuities (VIAs) combine equity market participation together with longevity insurance. This financial product is currently underutilized (and not available in certain jurisdictions) and can only grow in popularity.     

Portfolio choice in retirement: Health risk and the demand for annuities,housing, and risky assets

In a life-cycle model, a retiree faces stochastic health depreciation and chooses consumption, health expenditure, and the allocation of wealth between bonds, stocks, and housing. The model explains key facts about asset allocation and health expenditure across health status and age. The portfolio share in stocks is low overall and is positively related to health, especially for younger retirees. The portfolio share in housing is negatively related to health for younger retirees and falls significantly in age. Finally, out-of-pocket health expenditure as a share of income is negatively related to health and rises in age.     

Product pricing and solvency capital requirements for long-term care insurance

This paper presents a comprehensive assessment of premiums, reserves and solvency capital requirements (SCRs) for long-term care (LTC) insurance policies using Activities of Daily Living and US data. We compare stand-alone policies, whole life insurance policies with LTC benefit riders (LTC insurance combined with whole life insurance), life care annuities (LTC insurance combined with annuities) and shared LTC insurance in terms of net premium cost and SCRs. Net premiums and best-estimate reserves for base LTC insurance policies are determined using Thiele’s differential equation. Product features such as the elimination period and the maximum benefit period are compared using a simulation-based model. We show how a maximum benefit period can reduce costs and risks for LTC insurance products. SCRs for longevity risk and disability risk are based on the Solvency II standard formula. We quantify the extent to which whole life insurance policies with LTC benefit riders and life care annuities provide lower SCRs than stand-alone LTC insurance policies.     

GMWB for life an analysis of lifelong withdrawal guarantees

In this paper, we analyze the latest guarantee feature in the variable annuities market: guaranteed minimum withdrawal benefits for life (GMWB for life) which are also called guaranteed lifelong withdrawal benefits (GLWB). This option gives the client the right to deduct a certain amount annually from the policy??s account value until death??even if a unit-linked account value drops to zero. We show how such products can be analyzed within a general framework presented in Bauer et al. (ASTIN Bull. 38(2):621?C651, 2008). We price the embedded guarantee for different product designs and parameters under both, deterministic and optimal client behavior.     

Health and Mortality Delta: Assessing the Welfare Cost of Household Insurance Choice

We develop a pair of risk measures, health and mortality delta, for the universe of life and health insurance products. A life‐cycle model of insurance choice simplifies to replicating the optimal health and mortality delta through a portfolio of insurance products. We estimate the model to explain the observed variation in health and mortality delta implied by the ownership of life insurance, annuities including private pensions, and long‐term care insurance in the Health and Retirement Study. For the median household aged 51 to 57, the lifetime welfare cost of market incompleteness and suboptimal choice is 3.2% of total wealth.