Longevity Insurance Research Articles

Managing Systematic Mortality Risk with Group Self Pooling and Annuitisation Schemes

Group Self-annuitisation Schemes (GSAs), or Pooled Annuity Schemes, are designed to share uncertain future mortality experience including systematic improvements. They have been proposed because of the significant uncertainty of future mortality improvement on pension and annuity costs. The challenges for designing group pooled schemes include the decreasing average payments when mortality improves significantly, the decreasing numbers in the pool at the older ages and the dependence of systematic mortality improvements across different ages of members in the pool. This paper assesses the impact of systematic dependence and reducing numbers in the pool at extreme ages on the efficacy of longevity pooling. Current proposals for pooling schemes are designed to insure against idiosyncratic risk while leaving systematic risk to be borne by individuals. The paper uses a multiple-factor stochastic Gompertz-Makeham model of mortality, calibrated to Australian data, to demonstrate the significance of these issues. The model produces analytical results from extreme value theory for survival distributions and approximate annuity computations. Simulations are used to show how the pooling can be made more effective and to quantify the limitations of these pooling schemes. The results quantify the impact of pool size on risk sharing, especially at the older ages, demonstrate the significance of systematic mortality risks and dependence on pooling effectiveness, and highlight the need for reinsurance, longevity bonds and solidarity between the young and old ages in the pool to improve the effectiveness of GSAs as a longevity insurance product solution.

Valuing the Longevity Insurance Acquired by Delayed Claiming of Social Security

AbstractIndividuals can claim Social Security at any age from 62 to 70, although most claim at 62. We show that expected present value calculations substantially understate both the optimal claim age and the losses resulting from early claiming because they ignore the value of the additional longevity insurance acquired because of delay. Using numerical optimization techniques, we illustrate that the optimal claim age is between 67 and 70. We calculate that the amount by which benefits payable at suboptimal ages must be increased so that a household is indifferent between claiming at those ages and the optimal combination of ages can be as high as 19.0 percent.

Asset Demands and Consumption with Longevity Risk

In this paper we study asset demands and consumption of an individual at the end of her life cycle. We present an ideal market where complete insurance against longevity risk is available: the market consists of original assets, e.g., stocks and bonds, and annuities and life-insurance contracts linked to these assets. We also study asset demand and consumption for the other two cases: the no insurance case where there is no insurance available against longevity risk, and the partial insurance case where only bond-linked annuities exist for longevity insurance. We express asset demands in each case by using state price densities, and the expressions admit intuitive explanations. We derive consumption in analytic form and conduct comparative statics. Afterwards, we extend the model to multiple periods and show results of numerical simulation. We find the proportion of wealth invested in risky assets to total savings in the complete market case is similar to the proportion in the no insurance case. It is, however, in general larger in the complete market case than in the partial insurance case. Under reasonable conditions the optimal consumption to wealth ratio is the highest in the complete insurance market, followed by the ratio in the partial insurance case, and the smallest in the no insurance case. Furthermore, simulation results show that asset demands can change quite dramatically as the prices of annuity products change. Thus, innovations in the insurance industry which lower costs of providing personalized insurance may result in a significant shift in asset demands, particularly in the demand for risky assets. We also show that the time-old proposition that an increased mortality rate is equivalent to an increased subjective discount rate does not necessarily follow if we relax the assumption of the time-separable utility function. For a fixed relative risk aversion coefficient, comparative statics of optimal consumption yield different results depending on whether the EIS is greater or less than 1.

A tFragedy of Annuitization? Longevity Insurance in General Equilibrium

We construct a tractable discrete-time overlapping generations model of a closed economy and use it to study government redistribution of accidental bequests and private annuities in general equilibrium. Individuals face longevity risk as there is a positive probability of passing away before the retirement period. We find non-pathological cases where it is better for long-run welfare to waste accidental bequests than to give them to the elderly. Next we study the introduction of a perfectly competitive life insurance market offering actuarially fair annuities. There exists a tragedy of annuitization: although full annuitization of assets is privately optimal it is not socially beneficial due to adverse general equilibrium repercussions.

Pension Funding and Individual Accounts in Economies with Life-cyclers and Myopes

The present paper Studies the growth and efficiency consequences of pension funding with individual retirement accounts in a general equilibrium overlapping generations model with idiosyncratic lifespan and labor income uncertainty. We distinguish between economies with rational and hyperbolic consumers and compare the consequences of voluntary and mandatory retirement plans. Three major findings are derived in our study: First, we quantify the commitment effect of social security for myopic individuals by roughly 1 percent of aggregate resources. It is possible to recapture this commitment technology in IRAs, if those are annuitized. Second, despite the fact that our consumers have an operative bequest motive, the welfare gain from the (implicit) longevity insurance of the pension system is significant and amounts to roughly 0.5 percent of aggregate resources. However, mandatory annuitization reduces unintended bequests so that future generations are significantly hurt. Finally, our results highlight the importance of liquidity effects for social security analysis. These efficiency gains are only attainable if accounts are voluntary and not mandatory.

A New Strategy to Guarantee Retirement Income Using TIPS and Longevity Insurance

A New Strategy to Guarantee Retirement Income Using TIPS and Longevity Insurance

Evaluating the Advanced Life Deferred Annuity — An annuity people might actually buy

Although annuities provide longevity insurance that should be attractive to households facing an uncertain lifespan, rates of voluntary annuitization remain extremely low. We evaluate the Advanced Life Deferred Annuity, an annuity purchased at retirement, providing an income commencing in advanced old age. Using numerical optimization, we show that it would provide a substantial proportion of the longevity insurance provided by an immediate annuity, at much lower cost. At plausible levels of actuarial unfairness, households should prefer it to both immediate and postponed annuitization and an optimal decumulation of unannuitized wealth. Few households would suffer significant losses were it used as a 401(k) plan default.

Pension Funding and Individual Accounts in Economies with Life-Cyclers and Myopes

The present paper studies the growth and efficiency consequences of pension funding with individual retirement accounts in a general equilibrium overlapping generations model with idiosyncratic lifespan and labor income uncertainty. We distinguish between economies with rational and hyperbolic consumers and compare the consequences of voluntary and mandatory retirement plans. Three major findings are derived in our study: First, we quantify the commitment effect of social security for myopic individuals by roughly 1 percent of aggregate resources. It is possible to recapture this commitment technology in IRAs, if those are annuitized. Second, despite the fact that our consumers have an operative bequest motive, the welfare gain from the (implicit) longevity insurance of the pension system is significant and amounts to roughly 0.5 percent of aggregate resources. However, mandatory annuitization reduces unintended bequests so that future generations are significantly hurt. Finally, our results highlight the importance of liquidity effects for social security analysis. These efficiency gains are only attainable if accounts are voluntary and not mandatory.

Longevity Risk and Annuity Pricing with the Lee–Carter Model. Discussion Held at the Faculty of Actuaries

Longevity Risk and Annuity Pricing with the Lee–Carter Model. Discussion Held at the Faculty of Actuaries

How Much Do Households Really Lose by Claiming Social Security at Age 62?

Individuals can claim Social Security at any age from 62 to 70 although most claim at 62 or soon thereafter. Those who delay claiming receive increases that are approximately actuarially fair. We show that expected present value calculations substantially understate both the optimal claim age and the losses resulting from early claiming because they ignore the value of the additional longevity insurance acquired as a result of delay. Using numerical optimization techniques, we illustrate that for plausible preference parameters, the optimal age for non-liquidity constrained single individuals and married men to claim benefit is between 67 and 70. We calculate that Social Security Equivalent Income, the amount by which benefits payable at sub-optimal ages must be increased so that a household is indifferent between claiming at those ages and the optimal combination of ages, can be as high as 19.0 percent.

Variable payout annuities and dynamic portfolio choice in retirement

AbstractMany retirees hope to continue earning capital market rewards on their saving while avoiding outliving their funds during retirement. We model a dynamic utility maximizing investor who seeks to benefit from holding both equity and longevity insurance. She is free to adjust her portfolio allocation of her financial wealth as well as of the annuity over time, and she can purchase variable payout annuities any time and incrementally. In this setting, we show that the retiree will not fully annuitize even without bequests; rather, she will combine variable annuities with withdrawals from her liquid financial wealth so as to match her desired consumption profile. Optimal stock exposures decrease over time, both within the variable annuity and the withdrawal plan. Welfare gains from this strategy can amount to 40% of financial wealth, depending on risk parameters and other resources; additionally, many retirees will do almost as well as the fully optimized outcome if they hold variable annuities invested 60/40 in stocks/bonds.

Pension Funding and Individual Accounts in Economies with Life-Cyclers and Myopes

The present paper Studies the growth and efficiency consequences of pension funding with individual retirement accounts in a general equilibrium overlapping generations model with idiosyncratic lifespan and labor income uncertainty. We distinguish between economies with rational and hyperbolic consumers and compare the consequences of voluntary and mandatory retirement plans. Three major findings are derived in our study: First, we quantify the commitment effect of social security for myopic individuals by roughly 1 percent of aggregate resources. It is possible to recapture this commitment technology in IRAs, if those are annuitized. Second, despite the fact that our consumers have an operative bequest motive, the welfare gain from the (implicit) longevity insurance of the pension system is significant and amounts to roughly 0.5 percent of aggregate resources. However, mandatory annuitization reduces unintended bequests so that future generations are significantly hurt. Finally, our results highlight the importance of liquidity effects for social security analysis. These efficiency gains are only attainable if accounts are voluntary and not mandatory.

Evaluating the Advanced Life Deferred Annuity: An Annuity People Might Actually Buy

Although annuities provide longevity insurance that should, in theory, be attractive to risk-averse households facing an uncertain lifespan, rates of voluntary annuitization remain extremely low. We evaluate a proposed annuity product, the Advanced Life Deferred Annuity, an annuity purchased at retirement, providing an income commencing in advanced old age. Using numerical optimization techniques, we show that this product would provide a substantial proportion of the longevity insurance provided by an immediate annuity, at a small fraction of the cost. At plausible levels of actuarial unfairness, households should prefer it to both immediate and postponed annuitization, and an optimal decumulation of unannuitized wealth. We show that few households would suffer significant losses were it used as a 401(k) plan default.

A New Strategy to Maximize Retirement Withdrawals Using TIPS and Longevity Insurance

Previous studies suggest that retirees face the risk of financial ruin even with (real) withdrawal rates as low as 4%. This paper proposes a new retirement investment strategy using Treasury Inflation Protected Securities (TIPS) and longevity insurance products that would permit annual withdrawal rates in excess of 5% without any risk of ruin; this strategy does not require retirees to irrevocably commit their entire savings in an annuity at retirement. The strategy can be implemented at minimal cost by retirees and their financial advisers. Institutional providers can adapt this strategy to design and develop products that provide inflation adjusted lifetime annuities, while allowing retirees to retain control over most of their savings in retirement.

The Longevity Annuity: An Annuity for Everyone?

As of 2005, U.S. individuals had an estimated $7.4 trillion invested in IRAs and employer-sponsored retirement accounts. Many retirees will thus face the difficult problem of turning a pool of assets into a stream of retirement income. Purchasing an immediate annuity is a common recommendation for retirees trying to maximize retirement spending. The vast majority of retirees, however, are unwilling to annuitize all their assets. This research demonstrates that a “longevity annuity,” which is distinct from an immediate annuity in that payouts begin late in retirement, is optimal for retirees unwilling to fully annuitize. For a typical retiree, allocating 10–15 percent of wealth to a longevity annuity creates spending benefits comparable to an allocation to an immediate annuity of 60 percent or more.

Behavioral Obstacles to the Annuity Market

As baby boomers enter retirement, they will look to the investment industry for ways to generate retirement income from a stock of accumulated saving. A longstanding puzzle is why most retirees do not purchase insurance in the form of lifetime annuities. This question is rising in importance due to the rapid decline of defined benefit pensions, which traditionally provided such guaranteed lifetime income. This study applies the lessons of behavioral finance to understand how well-documented anomalies in decision-making under risk may affect the annuity purchase decision. We demonstrate how mental accounting - where an annuity is evaluated as a gamble distinct from the retirement spending and investment plan - can be a powerful reason for the unpopularity of annuities. We also explain the prevalence of period certain annuities which guarantee a minimum number of payouts. Finally, we show that delayed payout or longevity annuities, which are purchased today to begin payouts in the future, may be more desirable than immediate payout annuities due to the overweighting of small probabilities.

Behavioral Obstacles in the Annuity Market

As Baby Boomers enter retirement, they will look to the investment industry for ways to generate income from accumulated savings. Why most retirees do not purchase longevity insurance in the form of lifetime annuities is a long-standing puzzle. Mental accounting and loss aversion can explain the unpopularity of annuities by framing them as risky gambles where potential losses loom larger than potential gains. Moreover, behavioral anomalies can explain the prevalence of “period certain” annuities, which guarantee a minimum number of payouts. Finally, investors may prefer “longevity annuities” purchased today to begin payouts in the future to immediate annuities because investors overweight the small probability of living long enough to receive large future payouts.

Longevity Annuity: An Annuity for Everyone?

As of 2005, individuals had an estimated $7.4 trillion invested in IRAs and employer-sponsored retirement accounts. Given these investments, many retirees will face the difficult problem of turning a pool of assets into a stream of retirement income. Purchasing an immediate annuity is a common recommendation for retirees looking to maximize retirement spending. However, the vast majority of retirees are unwilling to annuitize all of their assets. This paper demonstrates that a new type of annuity, a longevity annuity, is optimal for retirees unwilling to fully annuitize. For a typical retiree, allocating 10%-15% of wealth to a longevity annuity creates spending benefits comparable to an immediate annuity allocation of 60% or more.

Longevity Risk Pricing

The uncertainty about the future mortality developments is referred to as longevity risk. This paper quanti…es the size of longevity risk premium which should be priced in various longevity-linked securities and annuity contracts. The goal of this project is to tackle the pricing di¢ culty emerged during the market innovation of the potential longevity-linked securities. Based on the equivalent utility pricing principle, we obtain the minimum risk premium required by the longevity insurance seller and the maximum acceptable risk premium by the longevity insurance buyer. Our estimated risk premium is consistent with the limited observations in the market. We show that the size of the risk premium depends on the …nancial position of the seller and buyer, and the availability of the natural hedges. One important implication for the market development of longevity-linked securities is that multiple sellers are required instead of a single seller. The paper also shows that the availability of natural hedge has signi…cant impact on the longevity risk premium required. Longevity risk is modelled by Lee-Carter (1992) model, and estimated according to the U.K. and the Dutch mortality data.

Crowd-Out, Adverse Selection and Information in Annuity Markets: Evidence from a New Retrospective Data Set in Chile

Annuitization is often considered a socially desirable payout mode from pension plans, because it provides a lifelong income stream and therefore ensures that retirees will not run out of money. However, annuitization is rare in most countries. This project examines workers' choices during the payout stage in Chile, the only country that has had mandatory personal accounts long enough to have had substantial experience with payouts. Upon retirement, workers in Chile have limited options for payouts: they must either annuitize or take gradual withdrawal. Two-thirds have annuitized. We expect that retirees are less likely to annuitize if their accumulation finances a pension in the vicinity of the minimum pension, whose value is guaranteed by the state. In that case, publicly-financed longevity insurance is likely to crowd out private annuity insurance. We expect that retirees with health problems are also less likely to annuitize, possibly leading to adverse selection. Finally, we expect that individuals with greater risk aversion, smaller time preference and better knowledge about the system are more likely to annuitize. A new retrospective data set from Chile yields evidence that is broadly consistent with these hypotheses.