*By Joe Tomlinson*

Retirees will adjust their spending depending on investment experience. But most research uses withdrawal strategies that are fixed at inception, such as the 4% rule. I'll show that when spending can adjust each year, retirement outcomes will improve. I'll also show the gains that can be achieved by adding annuities.

Fixed strategies are straightforward to analyze. Consider the most prominent fixed strategy, the 4% rule. Here, the first year retirement withdrawal is set at 4% of the initial portfolio, and withdrawals increase at the inflation rate each year thereafter. The primary performance measure for this strategy is the failure rate – the percentage of Monte Carlo runs or historical simulations where the retiree depletes savings over a specified timeframe. Tests with different asset allocations determine the allocation that results in the lowest failure rate.

With dynamic strategies, where retirement withdrawals adjust based on realized investment performance, the asset allocation will affect the withdrawals and therefore levels of retirement consumption. Testing different asset allocations thus requires comparing not only failure rates but also levels of retirement consumption. A further complication is that more aggressive asset allocations will likely give rise to more variation in year-to-year consumption. Consumption paths that are high and variable will then need to be evaluated against others that are lower but steadier.

I'll utilize an example and begin with withdrawals based on the 4% rule as a base case. I will then switch to a dynamic withdrawal strategy to show how retirement outcomes improve. I'll expand the example by adding the option to purchase single-premium immediate annuities (SPIAs) and show how the outcomes can be further improved.

**The example**

This comparison of strategies will be based on a 65-year-old female with a 25-year life expectancy who has reached retirement with $1 million of savings that she will use to fund her retirement. She has chosen to defer Social Security to age 70 and set aside additional funds to generate income during the interim five years. She also has funds set aside for emergencies and has a plan for potential long-term-care needs that does not depend on the $I million. The $1 million can be dedicated solely to generating retirement income. Her objectives, loosely stated, are to generate a high level of retirement income with some variation from year-to-year but not too much. She doesn't care about leaving a bequest.

Her basic living expenses are $50,000 increasing with inflation each year, and she will receive an inflation-adjusted $20,000 per year from the combination of Social Security starting at 70 and five years of withdrawals from the interim funds. She needs to fill a gap of $30,000 in real dollars to meet basic living expenses, and additional withdrawals can be used for discretionary spending. Her investment options include stocks with an arithmetic real return after inflation and expense charges of 5.35% and a standard deviation of 20%, and bonds with a 0.60% real return and 5.5% standard deviation. Later we will add the option of purchasing an inflation-adjusted SPIA with an initial annualized payout rate of 4.61%.

The assumed returns are significantly lower than historical averages, reflecting current interest rates and a lower-than-historical equity risk premium. The SPIA pricing is the current rate from a direct-purchase site. Monte Carlo simulations are used to generate yearly returns, and the year of death is also modeled stochastically. The analysis is pre-tax and future dollar figures are discounted for inflation and stated in real terms.

**Fixed strategy**

I'll start with a 4% rule withdrawal strategy to establish a base case for comparison. Chart 1 shows outcomes based on different asset allocations.

*Chart 1: Comparison based on fixed withdrawal strategy (4% rule)*

Stock/Bond Mix | Average Consumption | Cert Equiv Consumption | Failure Percentage | Average Shortfall | Median Bequest |

0/100 | $55,970 | $46,551 | 44.8% | -$94,330 | $57,433 |

25/75 | $57,698 | $51,751 | 24.8% | -$52,284 | $291,975 |

50/50 | $58,014 | $53,704 | 21.0% | -$43,906 | $515,542 |

75/25 | $57,690 | $53,631 | 20.1% | -$49,022 | $724,131 |

100/0 | $56,818 | $52,156 | 23.7% | -$68,013 | $768,259 |

*Source: Author's Calculations*

The average consumption column shows the average yearly consumption based on 10,000 Monte Carlo simulations. The $20,000 of Social Security income plus 4% withdrawals from an initial $1 million of savings produces income of $60,000. However, in cases where savings are depleted, the income drops to $20,000, so average consumption is less than the upper bound of $60,000. The certainty equivalent adjusts average consumption to reflect variability (I'll provide more detail about this when we get to the dynamic strategy). I show both the failure percentage -- the standard downside measure used in retirement research -- and another measure I developed called average shortfall. Average shortfall combines the probability, magnitude, and duration of failure. The final column shows the median bequest.

There are no new revelations in this chart compared to what has been demonstrated in prior research. The failure percentages are higher than based on historical returns, as recent studies on the 4% rule have shown. The lowest failure rates are for stock allocations in the 50% to 75% range, consistent with Bill Bengen's findings 25 years ago and much of the research since. The median bequests increase as stock allocations increase, because higher returns go into bequests and not into generating higher retirement consumption.

**Dynamic withdrawals**

Chart 2 is based on a strategy where each year's withdrawal depends on the retiree's current age and remaining amount of savings. I use a pricing model to calculate an inflation-adjusted withdrawal rate consistent with aiming for level real withdrawals over remaining estimated life. If the calculated withdrawal amount plus Social Security is insufficient to meet the assumed $50,000 of basic living expenses and there are remaining savings available, I increase the withdrawal to fill the gap. The process rolls forward each year with stochastically generated returns on savings, causing the withdrawals to vary. This approach is similar to required minimum distributions (RMDs), except my calculated payout rates are higher than the RMD percentages.

*Chart 2: Comparison based on dynamic withdrawals*

Stock/Bond Mix | Average Consumption | Cert Equiv Consumption | Failure Percentage | Average Shortfall | Median Bequest |

0/100 | $56,237 | $48,612 | 37.0% | -$62,962 | $93,410 |

25/75 | $60,986 | $54,118 | 28.0% | -$41,336 | $164,228 |

50/50 | $67,252 | $58,984 | 22.9% | -$33,048 | $205,929 |

75/25 | $74,887 | $61,548 | 22.6% | -$38,932 | $241,140 |

100/0 | $83,696 | $62,763 | 24.2% | -$49,052 | $267,652 |

*Source: Author's Calculations*

Although the withdrawal approaches for Charts 1 and 2 are quite different, they produce roughly equal failure percentages. We can therefore focus on consumption columns in comparing the two charts. The certainty equivalent (CE) column is based on an economic utility calculation that converts variable year-by-year consumption into a level amount that the recipient would view as equivalent. The CE amount depends on what economists refer to as the recipient's level of risk aversion. For example, if annual consumption bounced around randomly between $60,000 and $80,000, an individual with low risk aversion would demand close to $70,000 if offered a trade to level consumption. A highly risk averse individual would be willing to accept an amount closer to $60,000. I've assumed medium/high risk aversion for this example.^{1}

We see that average consumption increases as the asset allocation gets more aggressive and fewer dollars flow into bequests than in Chart 1. This would be a preferable outcome for the client in the example, since she does not have a bequest motive. The CEs also increase as the stock percentage increases, but not as fast as the average consumption. This is because the consumption streams become more variable with more aggressive investment strategies. Switching to the dynamic approach adds 17% to CE consumption.

If we base the choice of allocation on maximizing the CE value, the most important finding is that the optimal stock allocation increases when we switch to the dynamic withdrawal approach. The optimal allocation under the 4% rule is in the range of 50% to 75% stocks, while a 100% stock allocation produces the highest CE with dynamic withdrawals.

This finding reveals a subtle but important point. Some planners attempt to build dynamic strategies by re-running fixed strategies each year with updated figures. However, this approach may repeatedly miss the optimal allocation that dynamic modeling can directly produce. Based on Chart 1, the optimal stock allocation is in the 50% to 75% range. Re-running the plan each year based on a fixed strategy would tend to keep recommending this same allocation. But, as we see from Chart 2, the optimal allocation is 100% stocks.

**Adding SPIAs**

Chart 3 is based on purchasing enough inflation-adjusted SPIA income to cover the $30,000 gap between Social Security and basic living expenses. At a 4.61% payout rate, it would require $650,759 of the $1 million savings to purchase the SPIAs, leaving $349,241 to investment.

**Chart 3: Comparison based on dynamic withdrawals plus SPIAs**

Stock/Bond Mix | Average Consumption | Cert Equiv Consumption | Failure Percentage | Average Shortfall | Median Bequest |

0/100 | $62,296 | $61,846 | 0.0% | $0 | $44,845 |

25/75 | $63,968 | $63,498 | 0.0% | $0 | $59,437 |

50/50 | $66,221 | $65,405 | 0.0% | $0 | $74,554 |

75/25 | $68,742 | $66,941 | 0.0% | $0 | $87,231 |

100/0 | $71,962 | $68,125 | 0.0% | $0 | $94,453 |

150/-50 | $80,052 | $69,000 | 0.0% | $0 | $95,387 |

*Source: Author's Calculations*

With the addition of SPIAs, we see a much narrower range in the consumption column because the amount of volatile investments has been reduced by two-thirds. The CEs are much closer to average consumption because minimum consumption has been raised from $20,000 to $50,000. The possibility of not covering basic living expenses has been eliminated, so the failure percentage and shortfall columns all contain zeros. Bequests have been reduced because there is less invested in stocks with the heavy SPIA purchases and because more consumption is being generated.

At the bottom of the chart, I show results for a 150/-50 stock/bond mix demonstrating that a leveraged stock fund might raise CEs further. This would be a "barbell" strategy with most of the $1 million used to purchase fixed income investments in the form of SPIAs and the remainder invested aggressively.

The overall impact of adding SPIAs is a 10% increase in CE consumption over dynamic withdrawals investing in stocks and bonds. The increase is 28% greater than the highest CE income based on the 4% rule. The benefit from adding SPIAs is a combination of the longevity insurance provided and attractive pricing, as this May 2014 *Advisor Perspectives* article illustrates. The percentage increases would be even higher if the $20,000 of Social Security income, common to all three charts, were stripped out in order to measure just the consumption produced from savings.

We can also use the SPIA pricing information to develop another useful comparison. If the full $1 million were invested in SPIAs with a 4.61% payout rate, it would produce $46,100 in inflation-adjusted annual income. This, added to the $20,000 of Social Security, would generate $66,100 available for consumption. There would be no variation in annual income, so this $66,100 would also be the CE. This is a higher CE than in Charts 1 and 2 not using SPIAs and has the additional advantage of eliminating failure risk. However, compared to the dynamic strategies using SPIAs in Chart 3, this all-SPIA strategy falls short of the CEs produced with a mix of SPIAs and stock-heavy investing.

**Practical implications**

I have developed a single example and demonstrated advantages for strategies that many planners would consider impractical – flexible retirement spending, stock-heavy (or even leveraged) retirement portfolios and massive purchases of SPIAs. Certainly more extensive research is needed to test these findings. Such research should include testing a variety of client wealth and spending profiles, different dynamic withdrawal strategies, and refinements to utility functions and parameters.

The utility analysis needs particular attention. CEs can provide valuable summary information combining consumption levels and consumption variability. However, more study is needed regarding retiree preferences for fixed versus variable consumption, how these preferences apply for essential versus discretionary spending, time preferences for current versus future consumption and how the level of past consumption affects the utility of future consumption.

Regardless of what we learn from additional research, there will undoubtedly always be a gap between what is financially optimal and what can be accomplished in practice. Nonetheless, if we develop a better understanding of what is financially optimal, we can better understand the financial impact of accommodating practical considerations.

- I've assumed a risk aversion coefficient of 6 based on a CRRA utility function of the form U = (1/1-RA)*C^(1-RA) to convert consumption into utility. For each of the 10,000 Monte Carlo iterations, I convert each year's consumption into utility, average the utilities based on number of years in each iteration, and convert to a CE using the inverse of the utility function. I chose the risk aversion coefficient of 6 to represent what I consider to be medium/high risk aversion, recognizing that income can fall below the amount needed to pay for basic living expenses.

**Disclosure:** None