Inverted Withdrawal Rates And The Sequence Of Returns Bonus
May 17, 2016
by John Walton
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Providing income and preserving economic security subsequent to retirement is an important issue for an aging population. Decumulation, living off one’s assets, requires a tradeoff between preserving capital and obtaining income. This article generalizes some simple decumulation strategies and explains the strengths and weaknesses of an inverted approach.
The 4% rule, originated by Bill Bengen, is the first and most commonly studied retirement-income plan. Based on historical data, he found that if one spent 4% of the initial capital annually, adjusted for inflation, one could safely support a 30-year retirement period. The 4% rule continues to be the standard for comparing other methods for retirement-income planning.
The major problem with the 4% rule is that, since the percentage is determined by initial capital rather than ongoing portfolio value, spending does not respond to changes in value of the portfolio over time. Given the same amount of spending each year, a fraction of the current portfolio value greater than 4% is taken when the portfolio is down and less than 4% is taken when the portfolio is up. Under unfavorable markets this will rapidly deplete the portfolio and introduce sequence of returns risk. Without corrective action, a retiree using the strategy has a non-zero probability of going broke.
Another simple option is to withdraw a constant fraction of the current value of the portfolio each year, typically 4% or 5% per year, called the endowment method. In this case the portfolio never reaches zero value and the sequence of returns risk goes away.
Consider that in one case (4% rule) the annual withdrawal rate is greater than 4% when the portfolio declines and less than 4% when it increases, whereas the endowment method always uses the same constant withdrawal rate, let’s assume 4%. More generally, we can examine the spectrum of decumulation possibilities by changing the direction (“tilt”) and magnitude of how the withdrawal rate varies with changes in the portfolio balance over a range of values and examine the implications. The concept of tilt is that each year the withdrawal rate is changed (tilted) based on the value of the portfolio. Table 1 has examples of a range of tilts.
Table 1. Annual withdrawal rate options for initial $1,000,000 portfolio.
| Capital | 4% rule | -2% tilt | -1% tilt | Endowment (0% tilt) | +1% tilt | +2% tilt | +3% tilt |
| > $1M | $40,000 | 2% | 3% | 4% | 5% | 6% | 7% |
| < $1M | $40,000 | 6% | 5% | 4% | 3% | 2% | 1% |
The -2 percent tilt means that, when the portfolio balance goes above $1,000,000 (the assumed starting value), the annual withdrawal rate is decreased by 2% (from 4% to 2%) to compensate, thereby moving the annual income closer to 4% of the initial balance target. When the portfolio goes below $1,000,000, the withdrawal rate is increased from 4 to 6%, thereby stabilizing income toward the planned 4% of initial balance. The +2% tilt represents an inverted approach where, when the portfolio rises above $1,000,000, a greater portion is taken out (6% when the portfolio is greater than $1,000,000, 2% when below $1,000,000). Zero tilt is the classic endowment model where 4% of current balance is taken out each year irrespective of the balance.
The positive tilts are a mathematical formalization of how most people behave. When our portfolio has risen, we spend more (remodel the bathroom, replace the car); when the portfolio falls, we spend less (e.g., spend dividends and interest only). This makes the income more variable but tends to maintain assets near the desired level ($1,000,000 in this example). The negative tilts are closer to the 4% rule, providing a more constant income but greater risk of losing more assets. They also are similar to “floor with upside potential” withdrawal schemes. The positive tilts invert the 4% rule and other negative tilts.
The following figures represent Monte-Carlo simulations of seven different retirement-income plans with three different investment options. The investment options are labeled high, medium and low volatility (and risk). High-volatility portfolios typically have a greater fraction of stocks versus bonds, but with modern portfolios it is more complex than stocks versus bonds. The model portfolios were taken from the Research Affiliates asset allocation site, because they have a great educational treatment on the website and publish their methodologies. I neither agree nor disagree with their estimates. I merely used them as plausible numbers for my simulations. The model portfolios are (mean, annual standard deviation), (5.9, 13), (4.9, 10), (3.3, 6.5) percent.
The simulations last for 30 years; all of them are in constant (inflation-adjusted) dollars and use 4% as a basis for the tilts. The 4% rule is included in the graphics for reference. With Monte-Carlo simulations, one obtains thousands of potential future paths; each of these futures is called a realization. Statistical summaries of Monte-Carlo results have weird descriptions if one is not a statistician or practitioner of numerical uncertainty analysis. When I speak of the 10% lower results, I refer to examining all of the hypothetical future 30-year realizations and taking the worst 10%. The median of the average income means that, for all of the thousands of future 30-year realizations, I locate the point where half of the realizations are better and half are worse.
The portfolio at retirement is assumed to be $1,000,000, an easily scalable unit value. Results are shown in units of thousands of dollars. The results presented are from linear equations, meaning that the results can be directly scaled up or down based on the value of the initial portfolio of interest relative to the $1,000,000 assumed herein.
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