Optimizing the equity-bond-annuity portfolio in retirement: The impact of uncertain health expenses

Abstract

JEL classification: D91 G11 I10 D14 C63 D31 H55 J32 a b s t r a c t 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.

Accounting for non-annuitization

“…21 The intuition behind this theoretical result is as follows. There are two ways to finance an annuity purchase: using financial wealth or existing annuity income.…”

The annuity puzzle remains a puzzle

“…This implies that annuities cannot be sold or borrowed against if liquidity is needed, for instance in case of breakdown of a durable consumption good or health costs. Such background risk has also been claimed to reduce demand for annuities substantially below full annuitization (Turra and Mitchell (2008) and Pang and Warshawsky (2010)). In contrast to these earlier results, we find that the annuity puzzle might be even deeper than previously thought and incomplete annuity market and background risk reduce annuity demand only slightly at most.…”

“…We assume a desire for a smooth consumption path in real terms and show that, even if only nominal annuities are available, full annuitization is still optimal. Another related paper, Pang and Warshawsky (2010), examines the effect of health cost risk, but not incomplete annuity markets, on the annuitization decision. In their model additional annuities can be bought every year and they restrict their analysis to real annuities.…”

“…Pang and Warshawsky (2010) consider that annuities represent a specific asset class with its own unique risk and return profile, hence modeling the annuitization decision essentially as a portfolio allocation decision between bonds, equity, and annuities. Since the mortality credit increases with age, an annuity bought at a later age earns a higher return than an annuity bought at age 65, without additional risk.…”

Time inconsistent preferences and the annuitization decision

“…They find that these uninsurable shocks increase the preference for liquid savings (e.g., bonds) only marginal. Also, Pang and Warshawsky (2010) find that health shock risk leads to precautionary savings and a shift from risky equities to riskless bonds. But with increasing age, annuities become superior to equity and bonds even in the presence of health shock risk.…”