Value Of Annuity Research Articles

The Role of the Annuity's Value on the Decision (Not) to Annuitize: Evidence from a Large Policy Change

This paper presents new evidence on how the annuitization decision is affected by changes in the annuity’s value. We take advantage of an unprecedented change in policy in a number of Swiss occupational pension plans: The 20 percent reduction in the rate at which retirement capital is translated into a life-long annuity implied a net present value loss of approximately 20’000 SFR (18’000 US$) for the average affected retiree. To estimate the impact of the policy change we use administrative data from companies who did and one big company who did not change its price. Correcting for anticipation effects, we show that there was an approximately 14 percentage point decrease in the share of men choosing to annuitize their savings.

Mortality Declines, Longevity Risk and Aging

Over the past century human life expectancy has risen substantially around the world, and longevity in the modern world is largely determined by the age at which adults die. There is an ongoing, longstanding trend to higher average ages at death for both sexes in most countries. Accompanying this trend has been a decrease in the dispersion of the age of adult death which has slowed in most countries in the past five decades. Mortality forecasts can be made using the Lee-Carter method and provide stochastic projections of average longevity. We may think of the dispersion in the forecasted averages as a form of systematic risk that is important in pricing longevity risk. The dispersion around the average age at death is a form of individual risk. This individual risk certainly does matter to individuals making decisions about consumption, savings, bequests and so on. In particular it matters to economic aggregates such as population wealth, health, and savings, and to the fiscal flows in private and public pensions. Realistic models of annuity valuation are likely to be nonlinear and so annuity values are also likely to depend on the individual component of longevity risk. Analysis of the distribution of individual risk in subgroups (e.g., with high or low educational attainment) suggests that selection for low risk subgroups may be difficult to achieve.

Valuation of Mortality Risk via the Instantaneous Sharpe Ratio: Applications to Life Annuities

We develop a theory for valuing non-diversifiable mortality risk in an incomplete market by assuming that the company issuing a mortality contingent claim requires compensation for this risk in the form of a pre-specified instantaneous Sharpe ratio. We apply our method to value life annuities. One result of our paper is that the value of the life annuity is identical to the upper good deal bound of Cochrane and Saa-Requejo (2000) and of Bjork and Slinko (2006) applied to our setting. A second result of our paper is that the value per contract solves a linear partial differential equation as the number of contracts approaches infinity. One can represent the limiting value as an expectation with respect to an equivalent martingale measure, and from this representation, one can interpret the instantaneous Sharpe ratio as an annuity market's price of mortality risk.

On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee–Carter modelling

This paper provides a comparative study of simulation strategies for assessing risk in mortality rate predictions and associated estimates of life expectancy and annuity values in both period and cohort frameworks.

The choice between an annuity and a lump sum: Results from Swiss pension funds

This paper uses unique micro data from Swiss employer-based pension plans to study the annuitization decision at retirement. The administrative nature of our data, though limited with respect to individual background characteristics, allows us to analyze real choices over large retirement balances, rather than subjectively reported intentions to annuitize. We find a strong and robust impact of a utility-based measure of the annuity's value (computed within a life-cycle framework) on individual annuitization rates. Low accumulation of retirement assets is strongly associated with the choice of the lump sum, presumably due to the availability of means-tested social assistance. The sponsor's default option, in most cases the annuity, is also found to be highly influential in the decision to annuitize.

Mathematics of Asynchronous Annuities

Asynchronous annuities are defined as those in which the frequency of cash flows differs from the frequency of interest compounding. The conventional approach to calculating the present and future values of such annuities is to impute a rate of interest (or return) to a cash flow period, which is then inserted into standard annuity equations. The method produces inaccurate results when the frequency of cash flows exceeds the frequency of interest compounding. After identifying the source of those inaccuracies, this paper develops and demonstrates a new approach to accurately solving annuity problems when the frequency of cash flows exceeds the frequency of interest compounding.

Do Households Have Enough Wealth for Retirement?

Dramatic structural changes in the U.S. pension system, along with the impending wave of retiring baby boomers, have given rise to a broad policy discussion of the adequacy of household retirement wealth. We construct a uniquely comprehensive measure of wealth for households aged 51 and older in 2004 that includes expected wealth from Social Security, defined benefit pensions, life insurance, annuities, welfare payments, and future labor earnings. Abstracting from the uncertainty surrounding asset returns, length of life and medical expenses, we assess the adequacy of wealth using two expected values: an annuitized value of comprehensive wealth and the ratio of comprehensive wealth to the actuarial present value of future poverty lines. We find that most households in these older cohorts can expect to have sufficient total resources to finance adequate consumption throughout retirement, taking as given expected lifetimes and current Social Security benefits. We find a median annuity value of wealth equal to $32,000 per person per year in expected value and a median ratio of comprehensive wealth to poverty-line wealth of 3.56. About 12 percent of households, however, do not have sufficient wealth to finance consumption equal to the poverty line over their expected lifetimes, even after including the value of Social Security and welfare benefits, and an additional 9 percent can expect to be relatively close to the poverty line.

Do Households Have Enough Retirement Wealth?

Dramatic structural changes in the U.S. pension system, along with the impending wave of retiring baby boomers, have given rise to a broad policy discussion of the adequacy of household retirement wealth. We construct a uniquely comprehensive measure of wealth for households aged 51 and older in 2004 that includes expected wealth from Social Security, defined benefit pensions, life insurance, annuities, welfare payments, and future labor earnings. Abstracting from the uncertainty surrounding asset returns, length of life and medical expenses, we assess the adequacy of wealth using two expected values: an annuitized value of comprehensive wealth and the ratio of comprehensive wealth to the actuarial present value of future poverty lines. We find that most households in these older cohorts can expect to have sufficient total resources to finance adequate consumption throughout retirement, taking as given expected lifetimes and current Social Security benefits. We find a median annuity value of wealth equal to $32,000 per person per year in expected value and a median ratio of comprehensive wealth to poverty-line wealth of 3.56. About 12 percent of households, however, do not have sufficient wealth to finance consumption equal to the poverty line over their expected lifetimes, even after including the value of Social Security and welfare benefits, and an additional 9 percent can expect to be relatively close to the poverty line.

Evaluation of a contract breeding management program in Ohio dairy herds: Test day summary and economic measures

A field study was conducted to assess the impact of a contract breeding program that was offered by a breeding co-operative and featured tail chalking and daily evaluation of cows for insemination by co-operative technicians; dairy employees no longer handled estrous detection and insemination activities. From early 2002 until mid-2004, herd-level test day summary records related to production and reproduction were obtained for 32 herds identified as well-managed client herds of the breeding co-operative. Using analyses that controlled for other predictors and random herd-level effects, average days to first service were less by 13 days ( P = 0.0037) and estrous detection rate was greater by 12% ( P = 0.0011) for program than for non-program herds. Although first service conception rate was slightly less and the program herds used 0.34 more services per conception ( P = 0.1488) than non-program herds, the program herds averaged 16 fewer days before pregnancy ( P = 0.028). Test day summary information and representative estimates of feed, milk, and semen prices were used in a spreadsheet-based model to estimate a partial budget annuity value for an average cow in each herd on each test day. Value of an average cow from a contract herd did not significantly differ from a non-contract herd, even though the analyses suggested an economic benefit for the program herds; the modeling did not, however, account for costs of the program implementation. Additional analyses did not find any significant associations between technician and on days to first service, first service conception rate, estrous detection rate, services per conception, or days open.

Do Households Have Enough Wealth for Retirement?

Dramatic structural changes in the U.S. pension system, along with the impending wave of retiring baby boomers, have given rise to a broad policy discussion of the adequacy of household retirement wealth. We construct a uniquely comprehensive measure of wealth for households aged 51 and older in 2004 that includes expected wealth from Social Security, defined benefit pensions, life insurance, annuities, welfare payments, and future labor earnings. Abstracting from the uncertainty surrounding asset returns, length of life and medical expenses, we assess the adequacy of wealth using two expected values: an annuitized value of comprehensive wealth and the ratio of comprehensive wealth to the actuarial present value of future poverty lines. We find that most households in these older cohorts can expect to have sufficient total resources to finance adequate consumption throughout retirement, taking as given expected lifetimes and current Social Security benefits. We find a median annuity value of wealth equal to $32,000 per person per year in expected value and a median ratio of comprehensive wealth to poverty-line wealth of 3.56. About 12 percent of households, however, do not have sufficient wealth to finance consumption equal to the poverty line over their expected lifetimes, even after including the value of Social Security and welfare benefits, and an additional 9 percent can expect to be relatively close to the poverty line.

Modelling the joint distribution of competing risks survival times using copula functions

The problem of modelling the joint distribution of survival times in a competing risks model, using copula functions, is considered. In order to evaluate this joint distribution and the related overall survival function, a system of non-linear differential equations is solved, which relates the crude and net survival functions of the modelled competing risks, through the copula. A similar approach to modelling dependent multiple decrements was applied by Carriere [Carriere, J., 1994. Dependent decrement theory. Transactions, Society of Actuaries XLVI, 45–65] who used a Gaussian copula applied to an incomplete double-decrement model which makes it difficult to calculate any actuarial functions and draw relevant conclusions. Here, we extend this methodology by studying the effect of complete and partial elimination of up to four competing risks on the overall survival function, the life expectancy and life annuity values. We further investigate how different choices of the copula function affect the resulting joint distribution of survival times and in particular the actuarial functions which are of importance in pricing life insurance and annuity products. For illustrative purposes, we have used a real data set and used extrapolation to prepare a complete multiple-decrement model up to age 120. Extensive numerical results illustrate the sensitivity of the model with respect to the choice of copula and its parameter(s).

Actuarial values calculated using the incomplete Gamma function

The complete expectation-of-life for a person and the actuarial present value of continuous life annuities are defined by integrals. In all of them at least one of the factors is a survival function value ratio. If de Moivre’s law of mortality is chosen, such integrals can easily be evaluated; but if the Makeham survival function is adopted, they are used to be calculated numerically. For the above actuarial figures, closed form integrations are hereafter provided by means of the incomplete Gamma function.

An economic analysis of poplar based agroforestry systems in Punjab, India

The present study was undertaken to study the economics of Poplar cultivation and constraints being faced by the Poplar growers. Three types of Agroforestry systems (AFS) were studied; AFS-I (Wheat-kharif fodder), AFS-II (Sugarcane for first three years and then Wheat-kharif fodder for the successive years) and AFS-III (Potato- kharif fodder for first year and then Wheat- kharif fodder for the successive years). The highest net present value (NPV) was Rs. 116068.60 per acre in Ludhiana for AFS-II in 6th year while it was Rs. 126891.90 per acre for AFS-II in 6th year in Ropar. Annuity value (AV) was also highest for AFS-II in 6th year in both Districts. Internal rate of return (IRR) was highest for AFS-II in both the districts i.e. 53.82 per cent in Ludhiana and 51.72 per cent in Ropar District. Benefits cost ratio (BCR) was highest in 6th year i.e. 4.79 for AFS-II in Ludhiana and 5.43 for AFS-II in Ropar Districts. The most prominent production problems were the problem of interculture in block plantation of Poplar and lack of technical know-how. The major problems related to marketing of Poplars were unregulated markets of forest products and price fluctuations. It was concluded that the Poplar cultivation was a remunerative venture. However, their profitability could be further enhanced through Govt. intervention and enhanced management of Poplar plantation.

BETEL LEAF BASED FOREST FARMING BY KHASIA: TRIBES: A SUSTAINABLE SYSTEM OF FOREST MANAGEMENT IN MOULVIBAZAR DISTRICT, BANGLADESH

ABSTRACT The Khasia tribes people, living within the fringe of reserved forests of Moulvibazar district, traditionally have been growing betel leaf on naturally growing trees. Each family has been allocated 1.21 hectares of land for farming and 0.06 hectares for dwelling houses and homegardens. While deforestation is a serious concern in Bangladesh, the Khasia tribe living within the forests are protecting and conserving the biodiversity in trees through their livelihood activities in the forest—consuming and selling betel leaf, betel nuts and fruits from support trees, and firewood. The productivity of betel leaf depends on maintaining a mixture of support trees varying in age and density. The association of betel leaf with Artocarpus chaplasha has been found to be most productive in terms of cash return. However, the forests are mixtures of tree species of low commercial value, with relatively little Artocarpus chaplasha. The net present value from betel leaf, fruits and fuelwood during a 12 years rotation of betel leaf, using an interest rate of 8.5% was Taka 2,039,673 (US$34,571) with an annuity value was Taka 96,069 (US$1,628). The benefit: cost ratio for betel leaf production was 5.47, making it a both profitable and sustainable hill farming system—maintaining soil fertility, stable production and providing employment opportunities to the people living inside and outside the forests. Improvements through integrating higher value crops with betel leaf will bring additional benefit to the Khasia tribes people.

Annuity Values in Defined Contribution Retirement Systems: Australia and Singapore Compared

AbstractAnnuities promise to play an increasingly important role in countries with national defined contribution retirement systems. In this article we examine life annuities in two countries, Singapore and Australia, each of which has a national mandatory pension program. Exploiting data on annuity pricing and purchase behaviour, we compare the money's worth of life annuity products across these two nations. Our results indicate that, after controlling on administrative loadings, there are important differences in measured adverse selection. Part of the explanation may be due to the different structures of the two countries’retirement systems.

Florida's Pension Election: From DB to DC and Back

AbstractDuring the year 2002, the State of Florida's 600,000 public employees were given the choice of converting their traditional defined benefit (DB) pension plan into an individual‐account defined contribution (DC) plan with full control over asset allocation and investment decisions. To mitigate some of the risk and uncertainty in the decision, the State granted each employee electing the DC plan an additional option to switch back (i.e., change their mind once) at any point prior to retirement. This option has been labeled the 2nd election by the State and the cost of reentry is fixed at the accumulated benefit obligation of their pension entitlement, which is the present value of the life annuity. Our article presents some original analytic insights relating to the optimal time and financial value of this unique 2nd election. Although our model is deterministic in nature, we believe that it provides a number of intuitive insights that are quite robust. Our results can be contrasted with Lachance, Mitchell, and Smetters (2003). We estimate that the increase in retirement wealth that arises from having the 2nd election is equivalent to at most 30 percent in future value, and only when utilized optimally. Furthermore, for most State employees above the age of 45, the 2nd election has little economic value because the DB plan dominates the DC plan from day one. Of course, it remains to be seen what percent of Florida's 600,000 employees will elect to behave rationally with their newfound pension autonomy.

Annuities with controlled random interest rates

We derive the expected values of annuities with random interest rates modeled by a reflected Brownian motion with a switchover at some positive level at which the drift and variance parameters change. The lifetime of the annuity is assumed to be exponentially distributed. The approach can be extended to the case of several switchover levels. We also consider other related models.

Private pensions, mortality risk, and the decision to annuitize

This paper examines household decisions about whether or not to annuitize retirement resources. A life-cycle model of consumption, implemented with the use of dynamic programming techniques, is used to construct a utility-based measure of annuity value for individuals and couples in the Health and Retirement Survey. Variation in the calculated ‘annuity equivalent wealth’ arises from differences in mortality risk, marital status, risk aversion, and the presence of pre-existing annuities such as Social Security. I find that a one-percentage point increase in the annuity equivalent wealth leads to nearly a one-percentage point increase in the ex ante probability of annuitizing balances in defined contribution pension plans. However, because much of the variation in the expected annuity decision is left unexplained by the life-cycle model, other factors are also analyzed. Health status and an individual’s time horizon for financial decision making are significant determinants of the decision. There is no evidence that bequest motives are an important factor in making marginal annuity decisions.

Function space integration for annuities

We derive explicit formulas for the expected values of annuities with a random interest rate, modeled by a reflected Brownian motion at zero (RBM) stopped by certain Markov times. We consider times τ of the following kinds: (i) τ is constant, (ii) τ is a random and independent of the RBM X, (iii) τ is the first time X reaches a prespecified level, and (iv) minima of these stopping times. The case of Brownian motion without reflection is also briefly discussed.

Differential Mortality and the Value of Individual Account Retirement Annuities

This paper examines the extent of redistribution that would occur under various annuity and bequest options as part of an individual accounts retirement program. I first estimate mortality differentials by gender, race, ethnicity and level of education using the National Longitudinal Mortality Study and document substantial differences. I then use these estimates to examine the expected transfers' that would take place between socioeconomic groups under different assumptions about the structure of an annuity program. Using an expected present discounted value or money's worth' calculation as the basis for comparison, I find that the size of transfers in an individual accounts program is highly sensitive to the benefit structure. For example, mandating a single-life, real annuity can result in expected transfers of as high as 20% of the account balance, often from economically disadvantaged groups toward groups that are better off. These transfers can be substantially reduced through the use of joint life annuities, survivor provisions and bequest options. For example, the largest expected negative transfer under a joint and full survivor annuity with a fully valued 20-year guarantee option is only 2% of the account balance. However, efforts to reduce the extent of redistribution generally do so at the cost of significantly lower annuity benefits paid to the individuals who contribute to the system.