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Wade Pfau’s recent article, Breaking Free from the Safe Withdrawal Paradigm, was well researched. Its goal was to accurately calculate the benefits of using single-premium immediate annuities (SPIAs) based on certain assumptions (which are explained in his article). I fear, however, that many readers may have not fully grasped the impact of a few key assumptions that drive his results. Both advisors and their clients will benefit from understanding the effect of those assumptions.
Pfau’s analysis relied on these main assumptions:
- The capital market assumptions (CMAs) of traditional stock and bond allocations and blends thereof
- The bottom 10th percentile result (which investors have 90% confidence of exceeding) as the basis for optimization of asset allocation and product blends
- The payout rate on SPIAs and, thus, the return they would deliver at varying mortality rates
Let’s examine the impact of each of these assumptions and then how they work in combination with one another to produce the results of Pfau’s analysis. It is then up to the reader to determine if those assumptions are reasonable.
Capital market assumptions
In any simulation, capital market assumptions are the key for determining the results. When telling a simulation engine what assumptions to use, you are instructing it to “draw a probability distribution that looks like this.”
Plausible but sometimes indefensible CMAs are commonplace in our industry. Despite their importance (as I highlighted in my white paper, Hunting for Black Swans), I fear most readers and journalists don’t have the time, inclination, skills or data to put the impact of CMAs in perspective. Many people will disagree on what the CMAs should be, and Pfau’s fuller published article provided some color around his notions and assumptions. Still, such assumptions are often just accepted at face value based on seemingly plausible narrative. To be fully informed and prevent unintentional consequences, is critical to have a thorough understanding of the CMAs and their cause and effect on any analysis.
Optimizing at the bottom 10% of results
Since CMAs are usually expressed in the form of an arithmetic mean and standard deviation (that results in the probability distribution shape), it is easy to lose perspective of what assumptions actually mean at any specific point in the probability distribution.
Pfau’s article also uses the bottom 10th percentile of results as the basis for calculating his optimization. The CMAs of his analysis have a huge effect in determining the percentile distributions. For our own Wealthcare Capital Management and Financeware.com CMAs, I’ve advocated using a range of the 75th to 90th percentile as a zone that defined “balanced comfort” since the early 2000s. This gives us a sense of whether a plan is overfunded or underfunded (above or below the comfort zone), and we can craft advice to prevent needless sacrifice while maintaining sufficient confidence of exceeding the currently planned goals.
Single-premium annuity payout rate
Pfau disclosed the assumed SPIA payout rate that he used in his analysis, but I could not find whether that payout rate was based on joint- or single-life payouts. For my analysis below, I assumed joint-life mortality probabilities based on David Hultstrom’s mortality calculator. If it was based on a single-life payout, the returns would obviously be lower.
It is relatively easy to calculate the assumed return of the SPIA at various ages and calculate probabilities based on the payout rate and mortality risk. These calculations expose the percentage of clients across the industry whose advisors could be recommending a product that has no chance of doing better or worse than what the SPIA contract offers. (Of course, if the returns are high on the contracts and the capital markets produce results significantly below the contract return, one might question how many insurance companies could survive that liability.)
I calculated SPIA returns using the 5.84% payout rate from the article, joint-life mortality probabilities from Hultstrom’s calculator and the base case of a 65-year-old couple. Below are the returns of the SPIA payout rate at various mortality probabilities:
| Time horizon |
SPIA % return |
% of buyers doing worse due to joint-life mortality |
| 24 Years |
2.61% |
52% |
| 30 Years |
3.93% |
84% |
| 40 Years |
4.95% |
99%+ |
A closer look
Pfau’s analysis concluded that in this base case and potentially many others, the capital markets are less efficient than blending portfolios with SPIAs. His conclusion was based on the combination of these assumptions: the CMAs, the confidence level for optimization and the SPIA payout rates combined with mortality risk. The question remains as to whether the assumptions are reasonable in combination with the approach to the analysis. I’d like to shed some light so that advisors that follow Pfau’s path have perspective they can fully disclose to their clients.
Let’s start by looking at the probability distribution of the CMAs at the 52nd percentile joint-life mortality of 24 years, which I will refer to as the “mortality point.” We’ll use an allocation with 60% domestic equities and 40% seven- to ten-year Treasury bonds1 and compare the probability distribution created by Pfau’s CMAs to 757 actual historical periods. In Exhibit 1, we use 757 different starting months, going back to 1926.
All returns are nominal throughout this paper for ease of comparison. Real returns should all be reduced by Pfau’s 2% geometric mean inflation assumption. The simulated returns throughout this article use 10,000 simulations based on Pfau’s CMAs, calculated with the Financeware.com log-normal distribution. Finally, while Pfau reduced the capital market returns based on a 20-basis-point expense, I am modeling gross returns. This allows advisors to compare the expense ratios and advisory fees of their portfolios to the returns cited.
Exhibit 1- Simulated versus historical returns based on Pfau’s CMAs
Exhibit 1’s historical returns based on monthly data recount many time periods; but those results are far more extreme than they would be if we looked at calendar years. For example, the worst month to start the plan would be October 1929, and that would produce a gross return of 4.6%.
Based on Exhibit 1, starting the plan in the worst of the 757 historical months of history (which produced a return of 4.6%) and deducting 1.5% in advisor fees and expense ratios would result in a 3.1% net return. That would still exceed the return of the SPIA by 0.50%. Due to mortality risk, 52% of the buyers of the SPIA would receive less than the SPIA’s 2.61% return at this mortality point.
Comparing the shape of the simulated (red) to the historical (blue) distribution, we observe a few key items that both advisors and clients should be aware of before implementing Pfau’s strategy. In Pfau’s CMAs simulations, 65% of all 24-year periods produce a result worse than 99% of 757 historical starting months would have produced. Conceptually, his CMAs imply an expectation for the middle of the distribution (a 50% chance) that would perform far worse than starting in the worst month of history.
Pfau may be right on that future assumption, but this strikes me as excessively conservative. Assumingthat more than half of all simulated outcomes would be worse than the worst of history is an assumption that will result in sacrifice of the client’s lifestyle.
1. Our historical database is based on seven- to ten-year Treasury bonds that optimize the blend with stocks more efficiently than Pfau’s five-year Treasury assumption. Using a less efficient bond duration for the capital markets is not material in the scheme of things. The distribution of historical returns for the seven- to ten-year Treasury has somewhat more extreme tails and a tiny increase in median return relative to the five-year Treasury when modeled without blending with stocks. But, the tails are narrower for seven-ten year Treasuries when blended with stocks due to the lower correlation to stocks and capturing greater appreciation in most market shocks due to the longer duration than five–year Treasuries.
The bottom 10th percentile for the return of the simulated balanced portfolio is 1.1%. Pfau uses this return as the basis for his optimized allocation to SPIAs for those trials that last to the 52nd percentile joint-life mortality of 24 years. This is 3.5% less than starting in the worst month of history, and 2% less if the advisor has 1.5% in advisory fees and expenses. Meanwhile, Pfau assumes that despite such low returns (which are certainly possible), the insurance company would be able to honor its obligation to deliver the payout rate that is about 1.5% higherthan what the capital markets actually produce.
Exhibit 2 focuses our attention to the upper side of this distribution tail.
Exhibit 2- Simulated versus historical returns based on Pfau’s CMAs
In Exhibit 2, we observe that the CMAs used as the basis for Pfau’s optimization imply that despite the many calamitous events that have occurred (1929 crash, Arab oil embargo, inflation spike of late 1970s and early 1980s, tech bubble burst in 2000-2002 and financial collapse of 2008), more than 81% of the 757 starting months exceeded a gross return of 8% for a balanced portfolio. The simulations based on his CMAs assume there is less than a 12% chance of an 8% return.
There is essentially no chance the SPIA would produce a return of more than 2.61% at this mortality point and current rates (unless an insurance company retroactively increased its SPIA payouts when the contract did not require it).
All 757 historical 24-year time periods produce a return of more than 4.6% gross and 3.1% net (with 1.5% in total expenses), which is 2% higher than the SPIA’s maximum gross return of 2.6%. More than 80% of the time periods also show a chance of exceeding 8% gross at this mortality point. One might ask how Pfau concludes that the optimal product blend would so heavily weigh a product that has essentially no chance of producing a return any higher than 2.6%.
The answer lies in the simulated returns at the bottom 10th percentile, the point in the distribution Pfau chose as the basis for determining his optimization. This point corresponds to an assumption of 1.1% returns for the balanced portfolio. Based on Pfau’s assumptions, you would be better off owning an SPIA that is modeled to have complete certainty of producing 2.6% returns rather than an asset that you assume will only have 1.1% returns. No surprise here. The question is whether you think that is a reasonable assumption. Does it make sense to assume a negative real net return of -0.9% over 24 years for a balanced portfolio allocation? Is it worth giving up all of the upside to lock into no more than 2.6% return with certainty (at this mortality point)?
One must question whether Pfau’s conservative CMAs were driven by his equity or his bond market assumptions. Exhibits 3 and 4 might cause one to conclude it is both. The 90th percentile (bottom 10%) nominal return for stocks is zero and Treasury bonds are assumed to return 0.25%. No matter how you blend those assumptions, comparing them to an assumed certain 2.6% SPIA return will heavily weigh the optimization to the SPIA, as his results showed.
Exhibits 3 and 4 - Simulated versus historical returns based on Pfau’s CMAs for stocks and bonds
The SPIA returns increase as one lives longer and wins the mortality lottery. While an investor with normal mortality could give up a lot of upside by investing in SPIAs, many investors fear longevity risk and are willing to pay that price for the comfort of an insurance company’s promise of continuing payouts.
In Exhibit 5, we examine the balanced portfolio allocation again, but this time for 30 years. According to David Hultstrom’s joint mortality tables, there is only a 16% chance of one member of the couple surviving after 30 years.
Exhibit 5 - Simulated versus historical returns based on Pfau’s CMAs
In this scenario, only 16% of buyers would get a 3.93% SPIA return, as compared to the 52% chance of getting a return of less than 2.6% in the twenty-four year mortality point. There is no chance of getting a higher return than 3.93% from the SPIA, while 100% of 685 different starting months in history would have produced a gross return of 6.3% or more, (4.8% net assuming 1.5% a year in total expenses).
The bottom 10th percentile return for this timeframe (the point in the distribution Pfau chose as the basis for his optimization) produces only a 1.4% return — 3.4% less than the net return of starting in the worst month in history. Pfau’s CMAs assume 81% of all results will be worse than starting in the worst month of history. Once again, one would have to question how an insurance company could honor its payments based on a 3.93% return when the capital markets produce only 1.4%.
A main benefit of annuities is protection of longevity risk. Pfau’s article used an example of 40 years, surviving to age 105, to illustrate those benefits. Hultstrom’s calculator says that there is a zero chance of both members of the couple surviving to this age, but let’s call it just above zero. Using the rolling historical analysis, there are only 565 historical time periods to consider, and returns in the middle of history are indeed used significantly more frequently than those at the beginning or end of the historical data set. Thus, the comparison to history should be taken with a bit more of a grain of salt than shorter periods.
The miniscule fraction of buyers of the SPIA that win this mortality lottery do get a significant boost to their return: It increases to 4.95%. This is still 1.4% less than the gross return of the worst historical beginning month and only 0.05% better than the net return assuming 1.5% in total expenses. Remember, there is less than a 1% chance the SPIA would produce a return this high, due to mortality risk. Exhibit 6 shows that the optimization is based on blending that 1% chance of a 4.95% SPIA return with the bottom 10th percentile 1.8% return for the capital markets. Once again, one must question how an insurance company could give this much extra return away, unless one realizes that more than 99% of all buyers of the annuity are certain to do worse than the 4.95% SPIA return.
Exhibit 5- Simulated versus historical returns based on Pfau’s CMAs
No one knows how the capital markets will perform. Pfau’s assumptions might represent the future probability distribution, despite how much lower they are relative to history. My goal here is to illustrate the conservative nature of his assumptions. Optimizing product and portfolio allocations at the bottom 10th percentile will weight the results to include the certain SPIA returns more heavily, despite their being consistently significantly worse than the worst of history.
Finally, taking a more intuitive and less objective approach, I’m suspect most clients would think that now is a better time to lock in a 30-year mortgage than a 30-year payout rate. Rates could certainly continue to go lower, but now might be a better time to be a long-term borrower (mortgage) than a long-term lender (annuity, bonds). Before signing annuity applications that locks clients’ money up for the rest of their lives, ask your clients how they feel about that question too.
A popular industry speaker, writer, consumer advocate and inventor, David B. Loeper is the CEO and founder of Wealthcare Capital Management, Inc. in Richmond, VA. He is author of the top-selling book Stop the 401(k) Rip-off!, three other books released by John Wiley & Sons (Stop the Retirement Rip-off, Stop the Investing Rip-off and The Four Pillars of Retirement Plans) and numerous whitepapers. He has appeared on CNBC, CNN, Fox Business and Bloomberg TV, served on the Investment Advisory Committee of the $30 billion Virginia Retirement System and was chairman of the Advisory Council for the Investment Management Consultants Association (IMCA). Before founding his company in 1999, he was Managing Director of Strategic Planning for Wheat First Union. He earned the CIMA® designation (Certified Investment Management Analyst) from Wharton Business School in 1990 in conjunction with IMCA.
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