It is becoming increasingly difficult to ignore the worldwide phenomenon of increased life expectancy as a consequence of improved nutrition, healthcare, and technological progress. These improvements in life expectancy are of course good news to humanity. However, the impact of improved life expectancy on retirement finances raises the level of concern for policy makers, insurers, private pension fund managers, and individuals. As improvements in mortality and life expectancy are unforeseen, uncertainty in predicting future mortality has become a significant risk when planning retirement. In this regard, longevity risk occurs when actual life expectancy is different from expected, especially when populations live longer than expected.
For pension funds and life annuity providers, longevity risk increases institutions’ liabilities to provide sufficient payments, especially to those providing defined retirement benefits. In other words, the net present value for institutions to pay promised annuity payments will be higher than expected. To alleviate such risk, more and more governments are shifting from traditional defined benefit (DB) pension plans towards defined contribution (DC) schemes over the past few decades.
In DC schemes, the accrual losses associated with DB schemes are avoided, and individual retirement savings accounts are provided as a more flexible means to manage retirement savings. The transition from DB to DC schemes reallocates risk from the corporate sector to retirees, which potentially causes retirees to rely more on the value of assets they have accumulated in their own individual accounts.
While benefiting from flexibility over participation and contribution amounts in DC schemes, retirees are exposed to both investment risk and longevity risk.
Longevity risk for individuals refers to the risk of outliving their assets, resulting in a lower standard of living and poorer quality of health care at old age. Portfolio allocation thus becomes critical for retirees to achieve their retirement goals.
Traditional life annuity provides a solution for retirees to obtain a sufficient standard of living and eliminate longevity risk. Incorporating retiree lifetime uncertainty into a standard life-cycle consumption model, Yaari (1965) demonstrates that life annuities are preferred by rational consumers without bequest motives. Davidoff et al. (2003)
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that risk-averse individuals will highly value annuities while further affirming the role of annuity products in enhancing retirement security.Nevertheless, a significant gap exists between theory and practice. In reality, very few assets are converted into annuities due to a lack of liquidity, bequest motives, and the high prices of annuities. Longevity risk also makes annuities a less attractive financial arrangement to both annuitants and annuity providers because it increases uncertainty in the value of annuities and the cost of capital for annuity providers to meet their obligations of providing fixed annuity payments, which are calculated on the policyholder’s survival rate (Stevens, 2011).
Despite the drawbacks of annuities caused by longevity risk, the annuity might still be the most ideal financial tool for retirees to maintain their lifestyles after retirement. Annuity providers thus are challenged to resolve exposure to longevity risk while fulfilling retirees’ growing demand for comprehensive retirement plans. To pursue a sustainable business, annuity providers must hedge against longevity risk, the uncertainty surrounding the life expectancy of an entire population. In recent years, there has been an increasing amount of literature on the management of longevity risk (Blake et al., 2006; Stevens, 2011; Blake et al., 2013). Together, these studies provide important insights into the role of tontine-like annuity schemes in longevity risk (e.g.
Blake, 2003; Piggott et al., 2005; Valdez et al., 2006; Goldsticker, 2007; Pitacco et al., 2009; Rotemberg, 2009; Sabin, 2010). As stated in McKeever (2009), the tontine is
“an investment scheme through which shareholders derive some form of profit or benefit while they are living, but the value of each share devolves to the other participants and not the shareholder’s heirs on the death of each shareholder.”
According to the concept of tontine, Piggott et al. (2005) demonstrated how Group Self-Annuitization (GSA) plans allow annuitants to bear a pool’s systematic risk as idiosyncratic risk is pooled together. After contributing a desired amount into the pool, individuals receive periodic benefit payments, which are adjusted according to the mortality and interest rate variations in the pool. As in a traditional tontine, the contributions of the deceased members are equally distributed to surviving members.
Though GSA plans resemble annuities in the way of payment stream, they differ from traditional annuities in that GSA plans do not utilize payment guarantees. Retirees in
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GSA plans therefore do not need to pay extra premiums for the guarantees, making GSA plans the more cost-effective option. Moreover, retirees in GSA plans face limited investment risk. GSA plans’ variable benefit payments do not create investment risk, as opposed to a variable annuity’s payment scheme, because GSA payments are generated through a benefit-sharing arrangement, not through exposure to the investment market.
Hanewald et al. (2013) show that the GSA plans play a key role in post-retirement portfolios through assessments of different individuals’ post-retirement longevity risk management strategy. The analysis includes bequests, product loadings, and solvency risk for annuity providers. Valdez et al. (2006) establish an economic choice model to analyze demand and adverse selection for GSA plans and further indicate that there exist lower levels of adverse selection in GSA plans compared to conventional annuities. The studies presented thus far provide empirical evidence that rational individuals prefer GSA plans over traditional annuities.
However, under the benefit-sharing mechanism designed by Piggott et al.
(2005), the uncertainty of mortality projections and differences between actual and expected mortality rates will lead to increasing volatility in benefit payments while human mortality improvement trends will significantly decrease benefit payments.
Pooling effectiveness is thus weakened due to the high volatility of benefit payments and low benefit payments. Furthermore, the fact that systematic longevity risk cannot be eliminated by enlarging the size of the pool limits the effectiveness of pooling.
Numerous studies have attempted to create better tontine-like schemes. In his description of a mutual fund/tontine hybrid scheme, Goldsticker (2007) proposes a new tontine-like investment vehicle: a pooled fund providing annuity-like cash flows that are set equal to fair annuity payments. Although retirees would have to bear their own investment longevity risks, the mutual fund/tontine hybrid scheme provides several advantages such as diversification of longevity risk, higher potential payments, and flexible investment options. Goldsticker (2007)’s hybrid scheme as well as the Mutual Inheritance Fund (MIF) proposed by Rotemberg (2009) require participants to contribute up-front to MIF, which are invested in a mutual fund. The benefit payments from MIF are as variable as tontines.
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Modifying the idea of fair tontine, Sabin (2010) presents the concept of Fair Tontine Annuity (FTA) to create a fair benefit payment by using a fair transfer plan.
In a fair transfer plan, members’ expected payouts depend on their proportion of contribution as well as the demographics of the membership. A similar pooling scheme known as mortality-index annuity (MIA) is presented in Richter and Weber (2011), in which payments are linked to actual mortality occurrences.
Arguing that the effects of separating the mortality adjustment factor (MEA) from the changed expectation factor (CEA) in Piggott et al. (2005) are too difficult to discern, Qiao and Sherris (2012) incorporate these two mortality factors into one single factor, known as total expectation factor (TEA), to reconcile this ambiguity.
TEA refers to a universal factor that adjusts mortality differences over consecutive periods. Furthermore, Qiao and Sherris (2012) show that the volatility of benefit payments in GSA plans can be reduced by increasing the pool size with the introduction of TEA and a yearly-modified actuarial annuity factor.
Operating public pensions as social insurance, government plays the role of an insurance company when pension fund crises appear as a result of longevity risk. As in other countries in the world, a major reform of the public pension system took place in 2005 when Taiwan first employed DC plans. The “New Labor Pension System” (DC) was introduced with characteristics like portable retirement pension accounts, minimum guaranteed dividends, and a monthly pension payment option.
Moreover, to build a more comprehensive labor insurance protection system, new annuity pension systems in the Labor Insurance Program, known as the Labor Insurance Annuity Scheme (LIAS), went into effect in 2009, providing old-age periodic payments to maintain the cost of living after retirement. While providing retirees with a basic level of income security, the Taiwan government is facing significant cost increases due to increasing longevity risk, which has seriously strained Taiwan’s public pension fund.
To examine whether tontine annuity schemes could be adopted by Taiwanese government, we will offer elaborative information on how different tontine annuity schemes work and provide a simple modeling example. Also, we will demonstrate that tontine annuity schemes are better off in Taiwan’s Labor Insurance Annuity Scheme for several major advantages. The analysis of tontine annuity schemes
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follows that in Piggott et al. (2005). However, unlike Piggott et al. (2005), we include investment risk of pension fund in this paper. Concentrating on the benefits’
comparison, we will assess the effectiveness of Piggott et al. (2005)’s tontine annuity schemes by applying historical data for the Taiwanese population.
This paper makes two contributions. First, we use stochastic mortality model considering longevity risk in a simulation study to estimate the periodic-benefit payments in tontine annuity schemes. By including longevity risk in the calculation of mortality rate for benefit payments, the expected decline over time is changed to be increase. Second, we adapt the framework of Piggott et al. (2005) to include investment risk, to show how benefit payments can be affected by the uncertainty in pool fund’s rate of return.
The remainder of this paper is organized as follows: In Section 2, we discuss the details of the classic tontine annuity scheme and its variations, as proposed by Piggott et al. (2005) and Qiao & Sherris (2012). Section 3 is the theoretical core of this paper, where a simulation of Taiwanese mortality data will be conducted to estimate the benefit payments that retirees expect to receive in tontine annuity schemes. For simplicity, we include cases with and without investment risk to highlight the effectiveness of tontine annuity schemes. The results of the analysis will also be presented in this section. Section 4 describes Taiwan’s current Labor Insurance Annuity Scheme (LIAS) and discusses the comparison of tontine annuity schemes and LIAS. Finally, Section 5 summarizes the key findings and analysis of the paper.