بهینه سازی سبد سرمایه گذاری سهام، اوراق قرضه سالیانه در دوران بازنشستگی: تاثیر نامشخص مخارج بهداشت و درمان

This paper derives optimal equity-bond-annuity portfolios for retired households who face stochastic capital market returns, differential exposures to mortality risk and uncertain uninsured health expenses, and differential Social Security and defined benefit pension coverage. The results show that the health spending risk drives household portfolios to shift from risky equities to safer assets and enhances the demand for annuities due to their increasing-with-age superiority over bonds in hedging against life-contingent health spending and longevity risks. Households with higher income have a greater incremental demand for life annuities. The annuities in turn provide greater leverage for equity investment in the remaining asset portfolios.

With the recent decline of traditional defined benefit (DB) pension plans, there has been a corresponding shift to defined contribution (DC) plans by many US corporate plan sponsors. The Social Security (SS) system may also have reductions in its scheduled benefit payouts in order to move it to sustainable solvency. Because DC plans are typically self-managed by their participants and lack the withdrawal discipline featured in the life annuity distributions of SS and most DB plans, a legitimate concern arises that many retirees may run out of their DC funds or underconsume given that the length of life is uncertain. To protect people against longevity risk, experts have suggested setting annuitization as a default or mandatory option in DC plans. Despite the superior nature of annuities as insurance against longevity, however, most retired households have historically shown relatively little interest in voluntarily annuitizing their wealth. Various factors have been cited as the potential explanations to this “annuity puzzle.” Among them, uncertain health expenses have recently gained particular attention. The literature has thus far offered inconclusive findings. Sinclair and Smetters (2004) and Turra and Mitchell (2008) find that uncertain uninsured health expenses and their negative correlation with life expectancy reduce the attractiveness of annuities. Davidoff et al. (2005), on the other hand, show that uncertain health expenses, if occurring in late life, may actually increase the demand for annuities. Our study offers a comprehensive stochastic life-cycle framework to address the major risks and choices for households in the retirement phase. We assume that annuitization can be made at any age and in any amount, in contrast to a one-time choice of annuitization upon retirement in many previous studies. We consider jointly the household investment choices of bonds, equities, and annuities. The annuitization decision is modeled as a portfolio allocation choice because a life annuity basically represents a class of financial assets with its own unique risk and return features. Specifically, households in the retirement phase optimize consumption and allocate their financial wealth among stocks, bonds and annuities, in the context of pre-existing annuities such as Social Security and DB pension coverage. Households in the model have differential exposure to mortality risks and uninsured health care costs, in addition to facing common stochastic capital market returns. They also do or do not have a bequest motive. Our key findings and the logic are as follows. The uncertainty in uninsured health expenses generally leads to precautionary savings and rational households should shift their assets from risky equities to riskless bonds for a desired level of risk exposure. The simulated optimal equity portfolio is similar to the practice of life-cycle (target-date) funds in the retirement phase. Life annuities are assumed to be as safe as bonds, though contingent on survival, provide higher returns than bonds due to the embedded survivorship premium that increases with age, and eventually dominate bonds, even with a load, for hedging against longevity risk. Occurrences of health care are also life contingent and the expected expense magnitudes increase with age, as empirically observed, which makes annuities superior to bonds in also hedging against this health spending risk. The existing annuity payouts can be rolled over to finance new annuity purchase so as to capture higher returns and provide greater old-age insurance. It is optimal for households to hold precautionary savings in the equity-bond bundle prior to annuitization when the annuity return (considering some load) has not yet exceeded the reference returns on the conventional assets. The shift to annuities also provides greater leverage than do bonds for higher-risk-and-return equity investment in the remaining asset portfolios. The health-spending-uncertainty-enhanced annuitization is compatible with the broader theory about liquidity constraints and precautionary savings because the relatively low uninsured health care costs in the early retirement years are largely buffered by the pre-existing SS and DB coverage. This paper proceeds as follows: a brief literature review, the details of the stochastic life-cycle model, the findings from the simulations (focusing on the effect of uncertain health expenses on equity-bond-annuity choices), and concluding remarks.

This paper sets up a life-cycle model and derives the optimal equity-bond-annuity portfolios for retired households, who have differential exposure, by income deciles, to mortality and uninsured health spending in addition to the uncertainty in asset returns, in the context of differential Social Security and DB plan coverage. For simplicity, we limit the annuitization choice to the joint and survival annuities whereby the same level of annuity payout continues from the annuity purchase time until the death of the last surviving spouse. With the flexible equity-bond-annuity choices, households would annuitize their wealth sometime during retirement, fully or partially depending on their bequest motive. The superiority of annuities in hedging against longevity risk is attributable to their eventually higher returns, with mortality credit incorporated, than the reference returns on conventional assets. Consistent with the findings in the literature, the uncertainty in health expenses generally leads to precautionary savings and an asset allocation shift from risky equities to riskless bonds, absent annuitization choice. The superiority of annuities over bonds in hedging against longevity risk similarly applies to the hedging against uncertain health expenses because both annuity returns and health expenses are life-contingent and rise with age. As the health spending shocks induce a portfolio shift towards safer assets, annuities are more efficient and eventually dominate bonds. This higher degree of annuitization also provides a greater leverage for more equity holdings in asset portfolios, ceteris paribus, without increasing the overall investment risk exposure. In other words, annuitization is not just a passive replacement of bonds as an insurance against risk — it is also an integral part of the asset allocation strategy for wealth creation because it accommodates higher-risk-and-return portfolios. This health-spending-uncertainty-enhanced annuitization is not contradictory to the theories about liquidity constraints and precautionary savings. On one hand, the pre-existing annuities such as SS and DB payouts to a large extent have served as a buffer against adverse shocks. On the other hand, extra savings are noticeable in the liquid equity-bond form in the retirement years when bond and equity returns are yet to be dominated by annuities. With the superiority of annuities in hedging against both longevity and health spending risks, households would be better off by eventually converting these precautionary savings, at least partially, to annuities. Life annuities support late-life consumption and significantly improve household welfare. As a limitation, our model abstracts from the consideration that major illnesses may affect life expectancy and induce preference for consumption in early life. Emphasizing the liquidity needs and reduced demand for annuities in these situations, however, would be biased without due consideration of health insurance. Holding cash as a self-insuring strategy is costly. Rather, optimizing health insurance should also be part of the portfolio choice when illnesses and mortalities are modeled to be closely linked, which is a direction for future research. Our analysis suggests the importance of annuitizing retirement wealth for households covered by DC plans or IRAs if the decline in DB plans continues or if Social Security were to be (partially) converted to personal accounts. The (offsetting) voluntary annuitization would not only utilize a life annuity’s fundamental insurance against longevity risk but also would improve household welfare by concurrently hedging against other life contingent costs such as health care expenses. This indicates the merits of embedding the annuity feature into DC-type retirement plans if they are to be the main plans. As more DC plans adopt the annuitization option and hence the annuity pool expands, and also as the development of new products such as life annuities integrated with long-term-care insurance helps circumvent market inefficiencies, one may project that there will be an increased demand for life annuities.