Abstract
A retiree with a savings account balance, but without a pension, is confronted with an important investment decision that has to satisfy two conflicting objectives. Without a pension, the function of the savings is to provide post-employment income to the retiree. At the same time, most retirees want to leave an estate to their heirs. Guaranteed income can be acquired by investing in an annuity. However, that decision takes funds away from investment alternatives that might grow the estate. The decision is made even more complicated because one does not know how long one will live. A long life expectancy may require more annuities, and a short life expectancy could promote more risky investments. However there are very mixed opinions about both strategies. A framework has been developed to assess consequences and the trade-offs of alternative investment strategies. We propose a stochastic programming model to frame this complicated problem. The objective is to maximize expected estate value, subject to cash outflow constraints. The model is motivated by the Markowitz mean-variance approach, but with risk measured by CVaR and additional sophisticated constraints. The cash outflow shortages are penalized in the objective function of the problem. We use the kernel method to build position adjustment functions that control how much is invested in each asset. These adjustments nonlinearly depend upon asset returns in previous years. A case study was conducted using two variations of the model. The parameters used in this case study correspond to a typical retirement situation. The case study shows that if the market forecasts are pessimistic, it is optimal to invest in an annuity. The case study results, codes, and data are posted on our website.
Highlights
The problem of selecting optimal portfolios for retirement has unique features that are not addressed by more commonly used portfolio selection models used in trading
We developed a multi-period investment model for retirement portfolios
The parameters of the model represent a typical portfolio selection problem solved in the beginning of retirement
Summary
The problem of selecting optimal portfolios for retirement has unique features that are not addressed by more commonly used portfolio selection models used in trading. The case study showed that for scenarios of the first type, where rates are similar to the ones observed in the past, investment in annuities is not optimal. See Bayraktar and Young (2009, 2016); Gao and Ulm (2012); Milevsky (1998) While these attempts approach the problem in a variety of ways, including minimizing the chance of lifetime ruin as in Bayraktar and Young (2016) or mandating a target estate value as in Bayraktar and Young (2009), they are not directly relevant to our approach due to the more sophisticated setting involving multi-stage stochastic programming and dynamic risk management. Develop a dynamic mathematical programming model proving an optimal investment strategy for an individual investor at retirement age. Identify the percentage of capital which the investor should allocate to annuities
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