Optimal portfolio choice of couples with tax-deferred accounts and survival-contingent products

Abstract

Financial products for retirement planning generally have complex taxation structures and death conditions. In particular, tax-deferred accounts (TDAs) can provide tax-sheltered wealth accumulation by deferring taxes, even with the same financial products. Additionally, various survival-contingent products (SCPs), such as annuity products and life insurance contracts, have different payouts for policyholders. In this study, considering both the TDA and SCPs, we formulate and solve a couple’s lifetime portfolio choice problem using a multistage stochastic programming model. Owing to its high-dimensional state space and lifelong planning periods, stochastic dual dynamic programming (SDDP) was used to solve this problem. We find some interesting results; when both the TDA and SCPs are available, the portfolio is less concentrated in annuity holdings than when the TDA is unavailable. Moreover, the couple ends their contribution to the TA earlier than when SCPs are unavailable.

Keywords:

• Retirement planning
• Tax-deferred accounts
• Survival-contingent products
• Life insurance
• Immediate annuities
• Stochastic dual dynamic programming

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In reality, an insurance company calculates the exclusion ratio to determine the proportion of non-taxable annuity payouts for each period. The exclusion ratio is calculated by the expected value of investment (the payouts multiplied by life expectancy of the annuitant) divided by the principal. After the non-taxable parts of all distributed payouts based on the exclusion ratios exceeds the principal (that is, the annuitant outlives his or her life expectancy), the payouts become all taxable. However, to reflect the exclusion ratio, we should record the principal and exclusion ratio in each year (not the dynamics). Hence, for computational tractability, we do not calculate the exclusion ratio and the principal in each year and formulate dynamics of the non-taxable part of the principals as above. We emphasize that although the formulation is slightly different from the reality, to best of our knowledge, this is the first attempt to formulate the non-taxable parts of annuity payouts into the financial optimization problems.

2 https://www.ssa.gov/oact/STATS/table4c6_2017_TR2020.html.

3 With other parameters fixed, we replace labor income process in section 2.2 with $Y_t^i=\exp \left(f\left(t,Z_t\right)\right)P_t^i{U}_t^i$, $P_t^{\text{i}}=P_{t-1}^i{N}_t^i,i\in \left\{x,y\right\}$, $I_t=r_x{\mathbb{I}}_t^x{Y}_t^x+r_y{\mathbb{I}}_t^y{Y}_t^y$, where ${\sigma }_{u^x}={\sigma }_{u^y}=0.15$, ${\sigma }_{n^x}={\sigma }_{n^y}=0.10$. We assume that permanent and transitory shocks are iid, but allow correlation between permanent shocks of spouses (transitory shocks, respectively) as in Wu and Krueger (2021). We set correlation coefficients as ${\rho }_{n^x{n}^y}=0.08$ and ${\rho }_{u^x{u}^y}=0.31$, where the values are derived from Wu and Krueger (2021), and regenerate a scenario tree as in Appendix 2. The resulting number of branches is 20.

Additional information

Funding

This study was supported by a National Research Foundation of Korea (NRF); Korean Government (MSIT) (No. NRF-2020R1A2C101067713 and No. NRF-2022R1I1A4069163).