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Nanyang Business School Forum on Risk Management and Insurance

Insuring Longevity Risk and Long-Term Care: Bequest, Housing and Liquidity

by | Aug 21, 2018 | Actuarial Pricing, Economics, Long-term Care, Longevity, Valuation | 0 comments

Tags: Longevity, Long-Term Care, Liquidity, Housing, IRFRC
More from: Mengyi Xu, Michael Sherris , Jennifer Alonso-Garcia , Adam Shao

Editor’s Note: Posted by Mengyi Xu. Dr. Mengyi Xu and Professor Michael Sherris are from ARC Centre of Excellence in Population Ageing Research (CEPAR) and UNSW Business School, UNSW Sydney; Jennifer Alonso-Garcia, Professor at CEPAR and University of Groningen; Dr. Adam Shao, Milliman, Australia

Demographic changes have exposed individuals to greater challenges in financing their retirement. Longer life expectancy at 60s means retirees face a harder time allocating their financial resources across time to avoid outliving their wealth. As life expectancy at older ages increases, individuals are also likely to spend more time in disability that requires expensive healthcare costs. Given the challenges in financing retirement, there has been growing interest in retirement products such as annuities, long-term care insurance (LTCI) to address those challenges. Life annuities are an effective instrument to hedge against the risk of outliving one’s financial resources, and LTCI can alleviate the burden of healthcare costs.

When offering retirement products, it is important to recognise the diversity of retirees in their financial situations and preference that can affect their demand for products. For instance, whether retirees are homeowners can have a profound impact on product choices. Research has shown that illiquid home equity can crowd out demand for annuities and LTCI separately and can reverse the complementarity between annuities and LTCI. There is empirical evidence that home equity is generally not reduced among people who continue to own their homes and that selling the house is often associated with losing spouse or entering a nursing home. This means home equity can weaken demand for LTCI. Despite the significant role of housing, it is often excluded from the literature of optimal consumption and portfolio choice at retirement. Our paper aims to explain how homeowners’ demand for annuities and LTCI differ from that of non-homeowners.

The results show the illiquid housing wealth typically reduces demand for LTCI regardless of the availability of life annuities. This is due to the overlaps between housing liquidation and LTCI payout, creating the substitution effect. The impact of home equity on demand for life annuities depends on the availability of LTCI. When retirees have no access to LTCI, the presence of home equity generally increases the optimal annuitisation rate in a similar way that LTCI enhances demand for annuities. When LTCI is also available, the presence of home equity can make life annuities more attractive if there are sufficient liquid assets. More liquid wealth helps to better absorb the cost of purchasing LTCI, which, in turn, enhances demand for annuities.

In terms of the individual preference, a common modelling approach is to use a power utility function. It imposes an inverse relationship between risk aversion and elasticity of intertemporal substitution (EIS), which measures one’s willingness to substitute consumption over time. Contrary to such a rigid structure, experimental studies have shown that risk tolerance and the EIS are essentially uncorrelated across individual, and that individuals have relative risk aversion greater than the reciprocal of the EIS. Therefore, it is highly likely that power utility functions capture preference of only a small group of retirees. To address the drawback in the power utility function, we use the Epstein-Zin-Weil-type utility to model individual preference. Its ability to separately identify the risk aversion and EIS allows us to investigate the impact of individual preference on demand for annuities and LTCI.

We show that an individual with a higher degree of risk aversion wants more LTCI coverage and less annuities, whereas a lower level of EIS has the opposite effect. The power utility model imposes an inverse relationship on risk aversion and EIS, meaning a more risk averse individual will inevitably have a lower EIS. Such a rigid structure is unlikely to represent the preference of a large majority of retirees, so the Epstein-Zin model is more suitable to determine demand for life annuities and LTCI to accommodate individuals with various levels of risk aversion and EIS.

There is unlikely a one-size-fits-all solution when it comes to managing longevity and long-term care risks. The results show the diversity of financial situations and individual preference can have profound impact on demand for annuities and LTCI. They can provide guidance on offering tailored product menus to customers of different homeownership status and various risk preferences.

The paper can be found in Chapter 6 of the PhD thesis


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