The major challenge in building a sustainable retirement plan is the combination of low interest rates and stock market risk. Amplifying this challenge is the prospect of lower future equity returns and uncertainty about equity risk premium (ERP). Researchers have developed a number of different retirement withdrawal strategies to help manage investment risks; however, such strategies have not been adequately stress tested. I’ll compare strategies under stress to determine which strategies will be the most resilient.
Investment market background
Much has been written in the past few years about prospects for lowerthanhistorical future returns for both stocks and bonds. The most recent example is this McKinsey report projecting real (inflationadjusted) stock market returns, including dividends, of 4% to 5% for a lowgrowth scenario and 5.5% to 6.5% under a highergrowth scenario. (These projections are for compound or geometric returns.) By comparison, stock returns for the past 100 years have averaged 6.5%. Laurence Siegel summarized the McKinsey analysis in this recent Advisor Perspectives article and included his own projections, which were in the 4% to 4.5% range.
Bond returns are easier to predict than stock returns because current low yields exert a strong influence. For government bonds, real yields are close to zero, and both McKinsey and Siegel project future returns near zero.
Predicting stock returns is more difficult because of uncertainty about the ERP, which I discussed in this November 2015 Advisor Perspectives article. I cited extensive research by Professor Aswath Damodaran on the historical variability of the ERP, and an SSRN paper by Gordon Irlam where he analyzed the impact on asset allocation recommendations. Although Monte Carlo projections are typically done with a point estimate of the ERP, the research from Domodaran and Irlam indicates that it would be prudent to recognize a standard deviation for the ERP of two percentage points.
For this analysis, my stock return projection is approximately 1% more pessimistic than Siegel’s. Monte Carlo projections use arithmetic returns, which exceed geometric returns, and I’m projecting an arithmetic average return of 5%.[1] If I apply a 2% standard deviation to this estimate, there is a 15% to 20% probability that the “true” ERP is actually 3% or lower. Therefore I have chosen 3% for purposes of running stress tests. For bonds, I’ve used current TIPS rates to estimate a real return of 0.5%.
Example
This analysis will be based on a retired couple where the husband is age 65 and the wife is two years younger. Their life expectancies are 88 for the husband and 90 for the wife. They have $1.5 million in taxdeferred savings, which they wish to utilize to generate cash flow to support their retirement. The assumed stock/bond mix for these investments is 60/40. They also have a $400,000 unmortgaged home, which will become part of their bequest. They will be receiving $40,000 of annual inflationadjusted income from Social Security (or partly from bridge funds if they delay claiming) and their basic living expenses are $70,000 annually, also increasing with inflation. They will need to generate at least $30,000 of cash flow from savings to cover their basic needs. This will be an aftertax analysis assuming a 15% marginal tax rate.
I used these client characteristics and investment assumptions in Monte Carlo retirement simulations. I model both stock and bond returns as variable, as is typical for such simulations, but I also model the longevity of the husband and wife as variable, rather than assuming a fixed retirement period.
Return assumption impact
We’ll first assess the impact of the return assumptions used in Monte Carlo analysis. Chart 1 assumes the couple takes retirement withdrawals in accordance with the venerable 4% rule, so their withdrawals will be $60,000 per year (4% of $1.5 million) increasing with inflation, or $60,000 level in real terms.
Chart 1: Retirement projections based on 4% rule withdrawals




Scenario

Average Consumption

Volatility of Consumption

Average Shortfall

Failure Percent

Average Bequest

Historical average returns

$84,400

0.73%

$10,800

6.0%

$4,997,000

5% average real stock return

$80,400

1.39%

$70,400

33.8%

$1,415,000

3% average real stock return

$77,300

1.84%

$119,300

51.6%

$895,000

Source: Author's calculations

The first line of the chart is based on 10,000 Monte Carlo simulations and arithmetic average real returns of 9% for large company stocks and 2.4% for intermediateterm government bonds (1926 – 2015 historical averages), standard deviations of 20% for stocks and 7% for bonds, and an assumption of zero stock/bond correlation. For the second line, I kept the standard deviation and correlation assumptions and reduced the real return assumptions to my 5% estimate for stocks and 0.5% for bonds. For the third line, I lowered the stock return assumption to the stress test level of 3% and kept everything else the same.
For this chart and subsequent charts, I show some performance measures that are typical for financial planning packages, and others that are new. For each of the 10,000 Monte Carlo simulations, I calculate average consumption (Social Security plus withdrawals minus taxes) over the variable period until the last member of the couple dies. I then display the average of the 10,000 averages. (These dollar figures and all other dollar figures in the charts are based on real 2016 dollars without inflation.) The average consumption decreases as I lower the stock return assumption. With the 4% rule, real consumption stays level unless savings are depleted – due to poor investment performance and/or long life – so lowering the stock return assumption means there will be more cases where the couple depletes savings and lives their remaining years on Social Security only.
The second column shows volatility of consumption, which will become a more important measure when we analyze variable withdrawal strategies. This is a measure of the average absolute yeartoyear change in real consumption. The third column is average shortfall, which is a new measure. For the example we are using, plan failure means having consumption fall below the $70,000 needed for basic living expenses. For example, if the average failure case involved a couple living their last five years at a consumption level of $40,000, their shortfall would be $150,000, and if 50% of the couples experienced plan failure, the average shortfall measure would be $75,000. So this measure combines both probability of failure and magnitude of failure. Not surprisingly, the average shortfall increases as the stock return assumption is reduced. I also show the more commonly used failure percent measure, and this increases as well. Finally, I show the average bequest, which decreases as the average stock return is reduced.
Basically, this chart highlights that, although the 4% rule is widely used in retirement research, it is not well suited to realworld retirement planning. The first line of the chart indicates that producing an acceptably low failure percent requires a plan that on average will produce an enormous bequest – not sensible for clients lacking a strong bequest motive. And when we lower the stock return to the stress test level of 3%, more than 50% of the cases fail, and the subset that fails fall short by an average of about $230,000 ($119,300 / .516). Note that the couple in the example would still have their home equity, but the shortfall due to savings depletion would create considerable financial disruption.
So we need to look at other withdrawal strategies and see how they perform under stress.
Variable withdrawals
The pure form of the 4% rule involves establishing a withdrawal plan at the time of retirement and not deviating from the plan during retirement unless savings are depleted. At the other extreme are strategies where withdrawals during retirement are a function of the current portfolio rather than the initial portfolio. In this article in the Journal of Financial Planning, Wade Pfau describes a subset of such strategies, which he names “actuarial approaches.” The basic strategy involves resetting the withdrawal amount each year consistent with level withdrawals over the remainder of life – what economists call consumption smoothing.
In Chart 2, I compare the 4% rule under the 3% stress test from Chart 1 to an actuarial approach where each year the withdrawal amount is reset consistent with level real withdrawals over the remainder of life.
Chart 2: Effect of moving to variable withdrawals with 3% average stock return


Scenario

Average Consumption

Volatility of Consumption

Average Shortfall

Failure Percent

Average Bequest

4% rule withdrawals

$77,300

1.84%

$119,300

51.6%

$895,000

Variable withdrawals

$84,400

6.47%

$35,900

51.5%

$643,000

Source: author's calculations






The most dramatic change when we move to this variable approach is that the average shortfall is reduced by 70%. This decrease is entirely due to the magnitude of failure decreasing while the failure percent remains virtually the same, demonstrating why failure percent is an incomplete downside measure. This substantial reduction of average shortfall achieved while actually increasing consumption and leaving a smaller bequest.
The tradeoff by going to variable withdrawals is that the yeartoyear volatility of consumption increases substantially. If the savings portfolio goes up or down by X%, withdrawals change by roughly the same percentage. In terms of responding to investment performance stress, we’ve made progress by going to variable withdrawals, but we need to look for ways to dampen the volatility of consumption.
Smoothing
Chart 3 shows results for four different approaches that substantially reduce the volatility of consumption.
Chart 3: Attempts to improve on variable withdrawals with 3% average stock return


Scenario

Average Consumption

Volatility of Consumption

Average Shortfall

Failure Percent

Average Bequest

Variable withdrawals

$84,400

6.47%

$35,900

51.5%

$643,000

With 3year smoothing

$84,200

3.79%

$42,600

49.3%

$629,000

Guyton/Klinger decision rules

$80,200

2.91%

$60,600

52.0%

$736,000

Adding a SPIA to the mix

$81,200

3.29%

$0

0.0%

$464,000

More bonds instead of SPIA

$78,600

2.71%

$32,800

46.1%

$566,000

Source: author's calculations






The top line of the chart shows the variable withdrawals result from Chart 2. For the second line, I apply a simple smoothing approach where I calculate a new withdrawal amount each year as was done for variable withdrawals, but then I compare this new withdrawal amount to the prior year and only do onethird of the indicated adjustment. So withdrawals move in the indicated direction but only by onethird. We might expect volatility of consumption to be reduced to 2.16% (6.47% / 3), but we don’t achieve that much reduction because partial adjustments entail being offtarget and playing catchup. With this method, the other measures remain about the same, except there is an increase in average shortfall.
In the next line, I developed an approximation of the Guyton/Klinger decision rules that have gotten a lot of attention among financial planners. This approach developed by Jonathan Guyton and William Klinger and described in this Journal of Financial Planning article, anchors to a withdrawal rate set at inception, similar to the 4% rule approach, but uses a withdrawal rate in the 5% to 6% range. They are able to start with a higher initial rate because their method makes adjustments during retirement if withdrawals get out of line with the size of the underlying portfolio. As described in their article, Guyton and Klinger thoroughly tested and finetuned their approach and demonstrated that the method produced excellent retirement outcomes. What I have done that is different is stress test for a low return environment. They used average returns derived from 19732004 experience where real returns on stocks averaged 7.8% and bonds 3.7% (based on Ibbotson data), while my stress test had stocks averaging 3.0% and bonds 0.5%. Under my tests (using an initial withdrawal rate of 5.5%), the Guyton/Klinger rules do indeed lower consumption volatility substantially, but the tradeoff is a significant increase in average shortfall.
Next, I use $925,000 of the $1.5 million of savings to purchase a jointlife inflationadjusted single premium immediate annuity (SPIA) for the husband and wife. Based on annuity rates from the CANNEX, this SPIA will pay an inflationadjusted $37,330.13 annually in advance (4.04% payout rate). The advantage of this strategy is that we generate enough additional inflationadjusted lifetime income to cover basic living expenses, so failures are completely eliminated. The additional steady income from the SPIA also brings down consumption volatility. Consumption and bequests are reduced somewhat because SPIAs are essentially fixed income investments, so the original 60/40 stockbond mix is now effectively 23/77, assuming that savings not used for SPIA purchase stay 60/40.
In the final line of the chart, I substitute TIPS for the $925,000 SPIA purchase. Although this shift to bonds lowers consumption volatility, it produces other undesirable results – decreased consumption and significant failures. With the SPIA strategy, long lives are subsidized by short lives (mortality pooling), but when bonds are substituted for SPIAs, this mortality pooling is lost and long lives run out of money.
Conclusion
I’ve evaluated various retirement withdrawal strategies under stressful investment conditions that I consider to have a 15% to 20% chance of occurring, given the combination of bond market conditions, the prospect of lower future returns for stocks and the uncertainty about the ERP. These are not extremely rare “black swan” conditions. Strategies that work well when tested under a more favorable investment environment may not perform well under stress. Utilizing SPIAs to generate additional lifetime income performs particularly well under this stress testing.
Joe Tomlinson, an actuary and financial planner, is managing director of Tomlinson Financial Planning, LLC in Greenville, Maine. His practice focuses on retirement planning. He also does research and writing on financial planning and investment topics.
[1] The approximate relationship between these two return measures is as follows: Arithmetic return = Geometric return + 0.5 times the variance (= standard deviation squared).
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