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Mean-Variance Analysis in Post-Retirement Planning
註釋In this study we analyze the average spending and variability of two strategies, namely, the popular “4 percent rule” and the self-annuitized spending rule. The 4 percent rule is that each year a retiree should spend 4% of her initial wealth at retirement; the spending amount grows with the rate of inflation, so in real terms it is constant. The 4 percent rule has lower average spending and little variability, while the self-annuitized spending rule has higher average spending and higher variability. The self-annuitized spending rule is based on a theoretical foundation of expected utility maximization. We demonstrate how a retiree can make an informed decision about allocating among stocks, bonds, and annuities, and whether to combine the 4 percent spending with self-annuitized rule to get higher average spending. In particular, if future returns turn out to be lower than historical returns as many experts predict, combining the 4 percent rule and self-annuitized withdrawal rule is a valid approach to reach more than 4 percent spending on average while reducing the failure rate to be less than 10 percent. Similarly, when considering mortality, we discuss how to think about combining a purchased annuity with the self-annuitized strategy.