Annuity Fund Research Articles

Wealth heterogeneity in a closed pooled annuity fund

The stability of income payments in a pooled annuity fund is studied. In those funds, members receive a fluctuating income depending on their experienced mortality in exchange for their pension savings. The focus is on describing the influence of different initial savings on the ability of the fund to provide a stable income in retirement. Because of this, members coincide in their characteristics except for their initial savings. We identify a term, which we dub ‘implied number of homogeneous members’, that directly links the initial savings to the size of the income fluctuations. Our main contribution is the analysis of this term and the development of a criterion to answer the question of whether or not a given group of same-aged people should pool their funds together.

Optimal Investment Policy for Pension Annuitants in Malaysia under Economic Exposure

This research has conducted a profound evaluation into the annuity market in Malaysia from both the business and individual perspective. To a great extent, analysis is made on how the annuity insurers could better maintain the solvency level of annuity fund which is exposed under significant economic risks by obtaining an optimal fund allocation to maximise investment returns through the development of Asset-Liability Management (ALM). By adapting the concept from Wilkie model, six fundamental models including inflation rate, real interest rate, KLCI stock return, KLCI stock dividend yield, 10-year MGS return as well as Malaysian property return were formulated accordingly to the Box-Jenkins modelling approach. It concludes that the optimal weightages combination suggests that the annuity insurers should allocate 94% of the single premium such as RM100,000 which collected from the annuitant to bond market, whereas the other 5% of the fund should be invested in stock but only 1% of the premium should be allocated into the property investment.

QUANTIFYING THE TRADE-OFF BETWEEN INCOME STABILITY AND THE NUMBER OF MEMBERS IN A POOLED ANNUITY FUND

AbstractThe number of people who receive a stable income for life from a closed pooled annuity fund is studied. Income stability is defined as keeping the income within a specified tolerance of the initial income in a fixed proportion of future scenarios. The focus is on quantifying the effect of the number of members, which drives the level of idiosyncratic longevity risk in the fund, on the income stability. To do this, investment returns are held constant, and systematic longevity risk is omitted. An analytical expression that closely approximates the number of fund members who receive a stable income is derived and is seen to be independent of the mortality model. An application of the result is to calculate the length of time for which the pooled annuity fund can provide the desired level of income stability.

SINGAPORE’S LIFE PROGRAM: ACTUARIAL FRAMEWORK, LONGEVITY RISK AND IMPACT OF ANNUITY FUND RETURN

The Central Provident Fund (CPF) is a defined-contribution savings plan forming the key pillar of the pension system in Singapore. The CPF Lifelong Income For the Elderly (LIFE) program, which provides lifetime income for retirees, is a mandatory pension scheme for all Singapore residents. In this paper we construct an actuarial framework to analyze the LIFE program. We use this framework to study the plan payout outcomes with respect to changes in mortality and annuity fund return assumptions. We also examine the effects of some possible changes in the program on the payouts and bequests.

A Study on the Chinese Enterprise Annuity Replacement Rate Problem

AbstractIn this paper, the enterprise annuity replacement rate in China is discussed. The enterprise annuity replacement rate refers to the ratio of pension income and wages income before retired. It is an important indicator to measure the standard of living of the elderly population. The paper succeeded derived the equilibrium model of the enterprise annuity fund under the cost and management fee, and the enterprise annuity replacement rate is deduced. Moreover, the sensitivity analysis of each parameter is given, and the enterprise annuity rate of substitution for different gender is also obtained, which shows that the existing system of enterprise annuity unfairness to exist between men and women.

Exchanging uncertain mortality for a cost

We analyze a pooled annuity fund from a participant’s perspective by comparing it to a mortality-linked fund, a type of variable payout life annuity, that gives a return linked to the force of mortality but subject to a cost. Fixing the instantaneous volatility of return on wealth, we find that the expected return on the pooled annuity fund is higher except when the costs are very low in the mortality-linked fund. Similar results are obtained when maximizing the expected lifetime utility of consumption, assuming a constant relative risk aversion utility function. In both settings, our results indicate that a participant may be willing to accept the mortality risk of the pooled annuity fund, even when only 100 individuals are pooling their mortality in the pooled annuity fund.

Examining the provision of pension death benefits to co-habitees or life partners under the South African Pension Funds Act of 1956

The purpose of this article is to reflect on the determination in Chittenden and demonstrate its significance to the emerging jurisprudence on South African pension law relating to death benefits. Although Chittenden dates back 5 years ago, it remains important to discuss it and others for the following reasons. First, there has been no academic treatment of the determination in Chittenden and others. Second, in light of the South African Constitutional Court decision in Volks a grey area has arisen in pension law, and requires some academic treatment of the determination in Chittenden and others. According to the interpretation of the Pension Funds Act by the former Adjudicator John Murphy, the board has the discretion to accord to same sex couples and co-habitees or life partners the same rights as are accorded to heterosexual married couples. Murphy's interpretation differs from that of the recently former Adjudicator Advocate Vuyani Ngalwana who, following the recent decision in Volks held that a person who could have married a deceased pension member but chose not to should not be given the rights of a spouse of a deceased member. These conflicting interpretations have a bearing on the two-prong dependency test as developed and applied by the Adjudicator. Lastly, in light of the changing societal views regarding non-traditional relationship like cohabitation and life partnerships, it is important to examine how the pension law is adapting to these changes through the application of the dependency test. I argue in this article that the dependency test relied upon in this determination, which has been applied by the Adjudicator since 1998, should be welcomed because it advances the legislatures’ intent contained in the Pension Funds Act by requiring that death benefits payable by pension fund in the event of death of a pension member be distributed in accordance with a legislative scheme, which gives preference to need and dependency above the deceased pension member's freedom of testation. This article also argues that Chittenden (and others like it) is not undermined by Van der Merwe v. Central Retirement Annuity Fund, but remains good law in the framework of the distribution of death benefits to non-traditional couples.

Do Funds Need Governance? Evidence from Variable Annuity-Mutual Fund Twins

We study the roles of traditional governance (boards, sponsors, etc.) and market governance(investors voting with their feet) in mutual funds and variable annuities. We find that market governance is less pronounced for variable annuity investors. Using a matched sample of variable annuity-mutual fund twins, we find that variable annuity investors are less sensitive to poor performance and high fees than mutual fund investors. Given the weaker role played by market governance, we then examine the role played by traditional governance in variable annuities. Variable annuity boards and sponsors add alternative investment options and replace advisors on behalf of their investors after poor performance and high fees. These traditional governance mechanisms are, however, less effective when conflicts of interest exist between variable annuity sponsors and fund advisors.

Optimal Dynamic Consumption and Portfolio Choice for Pooled Annuity Funds

This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modeled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member's optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.

Optimal consumption and portfolio choice for pooled annuity funds

This paper presents the optimal continuous time dynamic consumption and portfolio choice for pooled annuity funds. A pooled annuity fund constitutes an alternative way to protect against mortality risk compared to purchasing a life annuity. The crucial difference between the pooled annuity fund and purchase of a life annuity offered by an insurance company is that participants of a pooled annuity fund still have to bear some mortality risk while insured annuitants bear no mortality risk at all. The population of the pool is modelled by employing a Poisson process with time-dependent hazard-rate. It follows that the pool member’s optimization problem has to account for the stochastic investment horizon and for jumps in wealth which occur if another pool member dies. In case the number of pool members goes to infinity analytical solutions are provided. For finite pool sizes the solution of the optimization problem is reduced to the numerical solution of a set of ODEs. A simulation and welfare analysis show that pooled annuity funds insure very effectively against longevity risk even if their pool size is rather small. Only very risk averse investors or those without access to small pools are more inclined to pay a risk premium to access private life annuity markets in order to lay off mortality risk completely. As even families constitute such small pools the model provides theoretical justification for the low empirical annuity demand.

Demand and adverse selection in a pooled annuity fund

In this paper, we construct a model for examining the demand for annuities together with the possible implications of adverse selection when an individual consumer has access to both a private annuity market and a market with a pooled annuity fund. An earlier paper by Piggott et al. [Piggott, J., Valdez, E.A., Detzel, B., 2005. The simple analytics of a pooled annuity fund. J. Risk Insur. 72, 497–520] provides a formal analysis of the payout adjustments from a longevity risk-pooling fund, an arrangement referred to in the paper as Group Self Annuitization (GSA). In such a pooled arrangement, the annuitants will bear their own cohorts’ systematic risk, but the cohort will share the idiosyncratic risk. The resulting return on the pooled annuity fund can be expressed as the product of a return from an ordinary annuity multiplied by a random variable that accounts for the adjustment that is due to deviations from expectation of mortality and investments. As demonstrated in this paper, a simple analysis of economic choice provides that it is possible to reduce the implications of adverse selection in a pooled annuity fund. It is well-documented that empirically, individuals do not find private annuity funds an attractive form of investment despite the potential welfare benefits that can be drawn from annuitization. A pooled annuity fund is an alternative to the conventional private annuity fund that may be considered more cost-effective.

The Simple Analytics of a Pooled Annuity Fund

AbstractThis article provides a formal analysis of payout adjustments from a longevity risk‐pooling fund, an arrangement we refer to as group self‐annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic‐benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed.

Convergence of Disturbed Martingales and a Stochastic Model for Annuity Funds

Our aim is a stochastic model for the average income of a given annuity fund. Therefore we consider a special kind of stochastic process satisfying a condition of the form: In equation (0.1) denotes the income of the annuity fund at time n+1(future) and is the information about the money market up to time n(present). We wish to find conditions under which such a stochastic process is P-almost surely convergent and to determine whether or not there is a limiting income from our annuity fund. The question of L 1-convergence is also considered

国民年金基金について 年金の動向ノート (1)

国民年金基金について 年金の動向ノート (1)

General Annuity Fund Premium Rates

SynopsisThe taxation treatment of the general annuity fund gives rise to additional variables in the calculation of premium rates. The paper discusses premium rates with particular reference to the impact of the tax structure and an attempt is made to determine a basis appropriate to a mutual life office. Some specimen rates applicable to recent conditions are then calculated and compared with market terms at the time of writing.

New Jersey's New Archival Facilities

fall New Jersey is dedicating a new State LibraryArchives Building. Together with the new State Museum, including an auditorium and planetarium, and the new Administration Building of the Department of Education, it will constitute what has come to be known as the cultural center. The decision to erect these new buildings has presented an unparalleled opportunity to develop a unified educational-cultural center for New Jersey. The new center will, in effect, serve as a permanent memorial to New Jersey's 1964 Tercentenary. From the beginning of the State Tercentenary Commission's planning, a cultural center has been the chief project among its announced goals. This goal was realized when legislation in i960 authorized the Teachers' Pension and Annuity Fund to invest some of its capital in the construction of these buildings for the Department of Education. The total expenditure for the center will be $11^2 million, and the Library-Archives Building will cost approximately $2,800,000. This article is devoted primarily to provisions concerning the archival functions of the Division of the State Library, Archives and History and to the planning of the new LibraryArchives Building. As the new building will be a multipurpose one, however, it will be necessary to present some of the functions of the entire division in order to make clear the overall planning. The most challenging aspect in planning the new LibraryArchives Building was in the very nature of the division's operations. No other State, for example, has the same combination of functions as those of the New Jersey State Library. State legislation charges the Division of the State Library, Archives and History a part of the State Department of Education with the follow-

The Impact of Income Tax on Life Assurance and Annuity Business

The original intention of this paper was to discuss the impact of income tax on annuity business only. In practice it was found impossible to discuss the impact on annuity business without at the same time discussing the impact on Life assurance business. A company transacting Ordinary life assurance, Pension annuity and General annuity business is not assessable in respect of three separate businesses; for the purpose of income tax the company conducts only one business, i.e. ‘Life Assurance and Annuity business’. Attention is drawn to this point at the outset because it is considered most important. A student coming freshly to the subject should not be misled into thinking that separate taxable units are involved because in the Income Tax Act, 1952 and the Finance Act, 1956 such terms as ‘annuity fund’ and ‘profits arising to an assurance company from pension annuity business’ are used. It may be noted that in this paper the term ‘fund’ has been avoided wherever possible, because, without precise definition on each occasion that it is used, it is liable to be misleading. It would be impracticable to discuss in one paper all the problems of a composite company which writes all classes of insurance business both at home and overseas. It is, therefore, proposed to consider only the position of a proprietary company which writes Ordinary life assurance and annuity business in the United Kingdom, values its liabilities annually and is taxed on an interest less expenses basis.

The Taxation of the Annuity Fund

In 1952 the Statutes relating to income tax were gathered together into one consolidating Statute, the Income Tax Act, 1952 and the whole system of taxation of a life office is laid down in a few sections of this Act. The position has been modified by the passing of the Finance Act, 1956, but the effect of this will be considered in the latter part of these notes. A proper understanding of the relevant sections of the 1952 Act necessitates some knowledge of the fundamental principles of income tax in general as laid down in the Act. As it is the object of these notes to try to deduce as clearly and logically as possible from the Act how a life office is taxed with special reference to its annuity fund, it will therefore be desirable to refer briefly to some of these general principles.Income is charged to tax in one of two ways, viz. by deduction of tax at the source by the payer of the income or by direct assessment on the recipient under one or other of the five Schedules A, B, C, D and E, enumerated in Section 1 of the Act.

A COMMENT ON VARIABLE ANNUITIES

Variable Annuities are the subject of considerable discussion by individuals who identify themselves with life insurance companies and security dealers. The paper by Mr. Albert Linton published in the May, 1956, issue of the Journal of Finance is a case in point. This comment does not attempt to marshall arguments for or against variable annuities, but is concerned only with the major factors determining the size of the payments to be made from a variable annuity fund during the payment period. In Mr. Linton's Table 2, the assumption is made that the variable annuity payment would follow Standard and Poor's index of stock prices.1 The other major factor influencing the size of the annuity payment, the cash dividends that will be received by and added to the annuity fund during the period of the annuity payments, is omitted. This is comparable to omitting interest on the standard annuity contract. The purpose of Table 2 was evidently to display the magnitude of the fluctuations in variable annuity payments in contrast to the absolute dollar stability of the payments made under the terms of a traditional annuity contract. Mr. Linton emphasizes that “irate and disillusioned policyholders” might write letters to insurance commissioners and even congressmen when payments fall under variable annuity contracts. Such pressure might have been (or may be) the opportunity for federal regulation of those life insurance companies that issue variable annuity contracts. Column 1, Table 1, in this comment sets forth the fixed payment of $100 per month specified by Mr. Linton, Column 2 reproduces the assumed monthly payment made under a variable annuity contract as shown by Mr. Linton in his. Table 2, and Column 3 presents a revised statement of the monthly payment under a variable annuity contract taking cognizance of the dividends received by the annuity fund during each year of the life of the annuity. The period 1926 to 1954 is the period selected by Mr. Linton. According to Mr. Linton's presentation, the payments made under the variable annuity were less than those under the traditional contract in twelve of the twenty-nine years. The revised variable annuity payments fall below the fixed monthly payments of $100 in only three years. Furthermore, the lowest payment under the revised computation is $83 per month as compared with $49 per month shown by Mr. Linton. Certainly the intensity of the remarks in the policyholders' letters would be different if the variable annuity payments fell 17 per cent rather than 51 per cent below a norm established by the payment of a fixed number of dollars under a fixed annuity contract. Fixed annuity policyholders may well complain about the opportunities missed when they compare their $100 with the more than $200 monthly income in 1954 that might have been possible under a variable annuity contract. In the computation of Column 3, Table 1, the advantages accruing to the variable annuitant during the accumulation period have been foregone. Mr. Linton recognizes this advantage in suggesting that the rate of growth of funds during the accumulation period invested in a well-selected, properly diversified group of stocks has been larger than the rate of interest achieved by the investment portfolios that are the basis for traditional annuity contracts. We believe that such higher yields on equities are not dependent on inflation given the maintenance of our long-run rate of economic growth and that this relationship is very likely to continue. This position, however, must be left undefended since the space that may be alloted to a comment is very limited. Let the case of the conservative be admitted, however. The holder of a variable annuity contract, the annuitant, would take more risk with respect to the number of dollars he will eventually receive. Life insurance companies, other financial institutions, and even the structure of the capital markets will be affected by any considerable growth in the use of variable annuities. Such changes are certain to follow whether the life insurance companies themselves or some newly developed type of financial institution handles variable valued annuities.

The Analysis of Surplus of an Annuity Fund

1. The subject of analysis of surplus has been given much study by actuaries both for the intellectual satisfaction it affords and for the practical value of the results of such inquiry. One of the earliest papers in our literature is that of G. H. Ryan in 1892 (J.I.A. 30), the first half of which was entitled ‘On a Method for determining the Gain or Loss from Mortality in an Annuity Company’. Since that date, however, attention has been devoted almost entirely to the analysis of surplus of a life fund, in view of the problems involved in its distribution, and Ryan's restricted treatment remains the only reference for students with regard to the analysis of surplus of an annuity fund. The purpose of the following notes, therefore, is to illustrate symbolically a full analysis of such a fund comprising immediate, deferred and contingent annuities, obtaining a complete reconciliation, and at the same time to indicate briefly the practical difficulties and the consequent steps in the analysis at which curtailment would be necessary in practice. Discussion of the relative importance of sources of surplus is outside the scope of these notes.