### Combining SPIAs and Smoothing to Improve Retirement Outcomes

I’ve previously written articles about two separate techniques for improving retirement outcomes: the use of single-premium immediate annuities (SPIAs) and smoothing of year-to-year withdrawals. In this article I investigate ways to combine SPIAs and smoothing to produce even better outcomes. I’ll then broaden the discussion and briefly explain how SPIAs and smoothing fit into the wider context of ways to improve retirement outcomes.

Using a hypothetical client example, I’ll first show the effects of smoothing without using SPIAs, next introduce SPIAs and then circle back to test different smoothing approaches combined with SPIAs. I’ll base my modeling on a variable withdrawal approach (described in detail in the Appendix) that each year recalculates withdrawals with an aim of smoothing consumption over expected remaining life.

This example will be based on a 65-year-old retired female with a remaining life expectancy of 25 years and $1 million in savings split 50/50 stocks/bonds that she can dedicate to generating retirement income. (She has separate funds for unanticipated expenses.) Her basic living expenses are $50,000 per year, increasing with inflation, and she will receive an inflation-adjusted $30,000 annually from Social Security. She will utilize withdrawals from savings to cover the gap between basic living expenses and guaranteed lifetime income and take additional withdrawals for discretionary spending. Her main goal is to generate sustainable retirement income; leaving a bequest is of secondary importance. The analysis will be pre-tax.

To simplify the presentation, I’ll show a single case before-and-after comparison in each chart rather than comparing arrays of outcomes. I’ve done behind-the-scenes testing to determine the most appropriate results to display.

**Impact of smoothing**

In this May 2015 *Advisor Perspectives* article, I discussed the impact of smoothing year-to-year withdrawals. I wrote the article partly in response to an *Advisor Perspectives* article by Laurence Siegel where he proposed the ARVA (annually recalculated virtual annuity) approach for determining retirement withdrawals and spending. In his article, he argued against attempts at smoothing other than by lowering the stock allocation to reduce investment volatility. I demonstrated that an argument could be made for smoothing techniques such as averaging portfolio returns over multiple years rather than recognizing each year’s return on its own. However, in deference to Siegel, my research did indicate that multiple-year averaging did have negatives as well as positives as I show in the comparison below.

**Chart 1: Retirement performance measures--impact of smoothing**

**Variable withdrawals, no SPIAs, 50% stock allocation**

Withdrawal approach |
Average Consumption |
Cert Equiv Consumption |
Consumption Change % |
Average Bequest |
Average Shortfall |

No smoothing |
$74,784 |
$70,405 |
5.19% |
$310,694 |
-$9,938 |

Add 4-year smoothing |
$75,090 |
$69,606 |
2.48% |
$312,433 |
-$17,695 |

*Source: Author's calculations*

The performance measures I used here and in subsequent charts are defined in the Appendix. For the no-smoothing case I used a withdrawal approach that recalculates a new withdrawal amount at the start of each year based on the current value of the savings portfolio. To apply smoothing I adjust this withdrawal amount, placing a 75% weight on the prior year’s withdrawal and a 25% weight on the newly calculated withdrawal. This is roughly equivalent to using a four-year moving average return instead of the current return in coming up with a new withdrawal amount each year.

The positive impact of using this smoothing approach is that we cut the consumption volatility, as measured by the average consumption change percent, by more than half. But the offset is that the average shortfall, which measures the combined probability and magnitude of falling short of covering essential expenses, nearly doubles. So the main problem with variable withdrawals is consumption volatility; smoothing offers a partial cure, but with a side effect.

**SPIAs in place of bonds**

Before attempting to put SPIAs and smoothing together, we’ll take a quick look at the impact of adding SPIAs alone. For this example, we’ll take our 50/50 stock/bond allocation and substitute SPIAs for the bonds. The SPIA pricing is based on late November 2016 payout rates for inflation-adjusted SPIAs from Income Solutions® with annuities offered via Vanguard.

**Chart 2: Impact of substituting a SPIA for bonds without smoothing Variable withdrawals, SPIA substituted for 50% bonds, so 100% stocks for remaining savings**

**Variable withdrawals, SPIA substituted for 50% bonds, so 100% stocks for remaining savings**

Withdrawal approach |
Average Consumption |
Cert Equiv Consumption |
Consumption Change % |
Average Bequest |
Average Shortfall |

50/50 Bond stock, no SPIA |
$74,784 |
$70,405 |
5.19% |
$310,694 |
-$9,938 |

50% SPIA, 50% stocks |
$78,919 |
$74,128 |
5.99% |
$231,029 |
$0 |

*Source: Author's calculations*

The result is more complicated to explain than the smoothing impact, because every performance measure changes significantly. We see that both average consumption and the certainty equivalent, which discounts consumption variability, increase. We have substituted an annually rebalanced 50/50 portfolio for a 50/50 mix of stocks and a SPIA at inception, but the stocks grow to become more dominant in the overall stock/SPIA portfolio. Higher expected returns produce higher savings growth and higher withdrawals and consumption, since withdrawals are a percent of the savings portfolio. Consumption volatility goes up slightly, reflecting the higher allocation to more volatile stocks, and the average bequest drops, reflecting partial annuitization - if we fully annuitized, the bequest would drop to zero and here we are partially annuitized.

The most important change is that substituting a SPIA for bonds in the example produces just enough income ($20,000) to fill the gap between Social Security ($30,000) and essential expenses ($50,000). This means that there can never be a shortfall, so the average shortfall is zero.

**Combining SPIAs and smoothing**

Here’s the idea: If the main problem with smoothing is the increase in average shortfall, and SPIAs eliminate such shortfalls, why not combine smoothing and SPIAs and get the benefit of smoothing without the adverse shortfall impact? We’re looking for an ideal solution here, and in the chart below I show the effect of adding four-year smoothing to our 50/50 stock/SPIA mix.

**Chart 3: Combined impact of SPIAs and smoothing **

**Variable withdrawals, apply 4-year smoothing to withdrawals from savings after SPIA purchase**

Withdrawal approach |
Average Consumption |
Cert Equiv Consumption |
Consumption Change % |
Average Bequest |
Depleted Savings % |

50% SPIA, 50% stocks |
$78,919 |
$74,128 |
5.99% |
$231,029 |
0.0% |

Add 4-year smoothing |
$78,976 |
$73,481 |
2.78% |
$248,209 |
21.2% |

*Source: Author's calculations*

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We do indeed decrease the consumption volatility and, by virtue of generating $50,000 of guaranteed lifetime income from the SPIA and Social Security, we are assured of keeping the average shortfall at zero. However, instead of just showing a zero I’ve changed to a new performance measure - depleted savings percent. Although we no longer have cases where the client cannot pay for essential expenses, we do have a percentage of cases where the only sources of income late in life are Social Security and the SPIA. There is enough to cover essential expenses, but it would be preferable to have some cushion.

When we add smoothing to the stock/SPIA mix, we go from never depleting savings to a fifth of cases where the portion of savings dedicated to generating income is depleted. We’ve definitely improved outcomes, but not without some downside.

**A different smoothing method**

There are a variety of ways to achieve a retirement goal. The above method recognized only a portion of each year’s adjustment in calculating the amount available for consumption. Another approach, which I show below, places limits on the dollar amount of change in withdrawals from year-to-year. This is more of a guardrail approach.

*Chart 4: Impact of changing to a dollar limit on withdrawal changes*

Withdrawal approach |
Average Consumption |
Cert Equiv Consumption |
Consumption Change % |
Average Bequest |
Depleted Savings % |

4-year smoothing |
$78,976 |
$73,481 |
2.78% |
$248,209 |
21.2% |

$2,500 limit on withdrawal changes |
$76,188 |
$73,689 |
2.73% |
$392,576 |
9.9% |

*Source: Author's calculations*

Under this approach, which places a $2,500 limit on the change in withdrawals (either up or down) we see that the average consumption is less than for the four-year smoothing approach, but the certainty equivalent is higher. This indicates that the limit approach improves the utility of consumption by eliminating extremes. The consumption change percentage is about equal between the two smoothing methods, but this particular limit approach pushes more funds through to bequests. The big change is that the limit approach greatly decreases the percentage of cases where savings are depleted. Although there is certainly room for further fine tuning, the limit approach produces more favorable retirement outcomes than percentage smoothing.

**Guyton/Klinger decision rules**

There have been a variety of smoothing approaches proposed for managing withdrawals where SPIAs are not used, and perhaps the best known are the Guyton/Klinger decision rules. This approach starts with fixed withdrawals at inception (similar to the 4% rule, but typically a higher percentage) and adjustments are invoked if withdrawals get out of line with the size of the underlying portfolio. Also there is a rule that the annual inflation adjustment is foregone if the portfolio return is negative. The chart below shows outcomes based on an approximate version of the Guyton/Klinger rules where SPIAs are also utilized.

*Chart 5: Impact changing to Guyton/Klinger decision rules for withdrawals*

Withdrawal approach |
Average Consumption |
Cert Equiv Consumption |
Consumption Change % |
Average Bequest |
Depleted Savings % |

$2,500 limit on withdrawal changes |
$76,188 |
$73,689 |
2.73% |
$392,576 |
9.9% |

Guyton/Klinger decision rules w/ 5.5% initial withdrawal rate |
$75,075 |
$72,904 |
1.67% |
$418,549 |
11.3% |

*Source: Author's calculations*

Although the Guyton/Klinger rules were not developed and calibrated based on utilizing SPIAs, they still perform well in this example. In particular, they bring down the volatility of consumption considerably without significant harm to other measures. This reflects the anchoring effect of tying withdrawals to the initial withdrawal rate rather than focusing only on the current portfolio.

These rules are more complicated to apply than a simple percentage or dollar limit, but the favorable results indicate that there is potential to improve outcomes even further.

**A wider perspective**

We’ve been seeing more articles on strategies for retirement spending and withdrawals and even a few making bold claims about being the “final say” on the issue. Based on my own research, the best strategy is more likely to involve a combination of approaches and techniques rather than a single “silver bullet” strategy. In this January 2015 *Advisor Perspectives* article, I demonstrated the advantage of a dynamic withdrawal strategy over one fixed at inception. I’ve also provided a demonstration of how switching to variable withdrawals can support higher stock allocation and how adding annuities (SPIAs) can improve outcomes even further. And here I’ve attempted to show how smoothing can help overcome the problem of dynamic withdrawals making consumption too volatile.

Of course, even with these pieces fitting together, there is still the larger context of retirement planning that deals with such issues as when to retire, how to optimize Social Security, how to make the best use of home equity, and how to minimize long-term care risks. The strategies used to deal with these issues will in turn influence the best choices for withdrawal strategies. Things are much more complicated than simply choosing an ideal withdrawal strategy, but appreciating the full context will lead to better planning.

Joe Tomlinson*, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. Most of his current work involves research and writing on financial planning and investment topics.*

**Appendix**

**Investment assumptions:** For the Monte Carlo analysis, stocks are assumed to earn an arithmetic average real return of 5% with a 20% standard deviation (geometric or compound return of 3%), and bonds (TIPS) are assumed to earn an arithmetic 0.65% with a 5.5% standard deviation. These returns are significantly lower than historical averages, reflecting current interest rates and a lower-than-historical equity risk premium. Allocations are rebalanced annually to maintain the initial allocation.

**Basic variable withdrawal approach:** This approach can be described based on the Excel PMT function. The maximum allowable withdrawal is recalculated each year as a function of the current portfolio balance, estimated remaining longevity and expected investment returns. The estimated remaining longevity is updated each year based on a Gompertz mortality function calibrated to a life expectancy of age 90 for a 65-year-old. For a return assumption, I use my estimated TIPS yield of 0.65%, to be conservative, even though my assumed portfolios contain both stocks and TIPS. The key difference between this approach and traditional approaches like the 4% rule is this variable method adjusts withdrawals each year to reflect emerging investment experience, whereas traditional approaches determine the pattern of future withdrawals at the start of retirement. Smoothing techniques described in the text are used to make further adjustments to the withdrawals determined by this method.

**Guyton/Klinger decision rules:** These authors start with a fixed initial withdrawal rate similar to the classic 4% rule, but vary withdrawals to respond to future investment experience. However, they use the initial withdrawal rate as an anchor when making future adjustments. They set outer boundaries for withdrawals based on two rules: the “prosperity rule” and the “capital preservation rule.” The “prosperity rule” increases withdrawals by 10% in any year that the current withdrawal rate falls to 20% less than its initial level. The “capital preservation rule” applies during the first 15 years of retirement and cuts withdrawals by 10% if the current withdrawal rate rises to be more than 20% above its initial level. Within these boundaries, the decision rules take away the annual planned inflation adjustment if the prior year’s investment return was negative and the withdrawal rate based on the current portfolio is higher than the initial withdrawal rate. Otherwise withdrawals increase each year as under the 4% (or X %) rule.

**Modeling methodology:** For each retirement income approach that I model, I generate 10,000 simulated retirements. Withdrawals each year are determined based on the particular retirement income approach being modeled. Investment returns for each year are generated randomly based on average return and standard deviation characteristics. The date of death for each of the 10,000 simulations is randomly determined based on the Gompertz mortality function.

Although methods that determine withdrawals as a percentage of the current portfolio balance will never completely deplete savings, I use a slightly different approach. If calculated consumption is not sufficient to cover basic living expenses and there are remaining savings, I take from the savings to cover the expense gap until savings are depleted. This way I can determine the percentage of simulations where savings are depleted.

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**Performance measures**

*Average consumption: *Consumption equals Social Security income ($30,000) plus annual withdrawals. For each of the 10,000 simulations, I compute the lifetime average of the annual consumption amounts and then take the average of these averages.

*Average bequest:* Each of the 10,000 simulations produces a remaining savings at time of death, which can be zero or a positive amount. I calculate the average of the 10,000 bequest amounts.

*Failure percentage:* This represents the percentage of the 10,000 simulations where savings are insufficient to fully pay for the assumed $50,000 of basic living expenses.

*Average shortfall:* For each simulation that “fails,” I calculate the amount of additional funds that would have been needed to pay for basic living expenses until the end of life. The sum of these amounts is divided by 10,000 to determine an average shortfall for all the simulations (including those with zero shortfall). This is a more useful failure measure than failure percentage because it incorporates both frequency and magnitude, but I also show failure percentage because it is a more commonly used measure.

*Depleted savings percent*: For cases where we have used SPIAs to zero out the shortfall measure, I calculate the percentage of Monte Carlo simulations where savings are depleted before death and the client is generating retirement income from the combination of Social Security and SPIAs just sufficient to cover essential living expenses.

*Consumption change percent:* This measures the absolute value of the change in consumption from one year to the next, averaging these for each of the 10,000 simulations, then averaging these averages, and finally expressing the result as a percentage of average consumption.

*Average CE consumption: *This certainty equivalent (CE) measure 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.

For this analysis, I have assumed a medium aversion to variable consumption – an individual would be willing to accept annual consumption of a level $66,600 in trade for consumption that bounced around randomly between $60,000 and $80,000. This translates to a risk aversion coefficient of 5 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 the number of years in each iteration and convert to a CE using the inverse of the utility function.