Thursday, February 11, 2010

The Fallacies of Safe Withdrawal Rates in Retirement

If you've given any thought to funding your retirement, chances are you've heard about a strategy for investing in stocks and bonds and spending about 4.5% of your savings “safely” throughout a long retirement. Perhaps you've used an online retirement income calculator that is based on this strategy.

The sustainable withdrawal rate (SWR) strategy is usually stated something like this quote from

Advisers typically recommend that 65-year-old retirees limit themselves to an initial draw of 4% of their portfolio, and then adjust that dollar amount for inflation each year. By doing that, they have roughly an 80% to 90% chance that their savings will last at least 30 years.

Interestingly, before the 2007 crash, SWR advocates said that a 4.5% withdrawal would provide a 95% chance of funding thirty years of retirement. Either way, let's look at what is missing from this statement.

First, an 80% to 90% chance of your savings lasting at least 30 years is another way of saying a 10% to 20% chance that they will not that the retiree will find herself flat broke before retirement ends.

A 90% chance of avoiding ruin may sound safe to some, but not when you compare it to the overall rate of bankruptcies for retirees. According to a study done by Elizabeth Warren at Harvard Law School, the overall bankruptcy rate for American households over the age of 65 was recently only about 0.5%. About 99.5% of all retirement-aged families manage to avoid bankruptcy, with or without a spending strategy. The SWR strategy promises that only 80% to 90% of retirees who use it will be as fortunate.

In other words, if you choose the 95% safe withdrawal rate, you can apparently improve your odds of avoiding bankruptcy from 95% to 99.5% just by abandoning the SWR strategy.

It is also important to note that successfully avoiding ruin in the SWR studies means dying with at least a dollar in the retiree's portfolio. Some retirees might consider this success; some would not.

Second, the strategy cannot deliver its most highly-touted benefit, that of providing a constant annual withdrawal amount with constant risk. The amount that a retiree can withdraw annually with a 95% a priori probability of not outliving his savings is a percentage of the remaining portfolio balance at that time. Furthermore, like the portfolio balance itself, the “safe withdrawal percentage” varies over time. The studies show that safe withdrawal rates for expected retirements of ten years approaches 10%, for example.

The SWR probability of success is an a priori estimate. A priori knowledge is knowledge about a process or event (like retirement), that is available before the event occurs, rather than that estimated by recent observation. It roughly translates to “at first”, or “at the start”. If a bag contains two black marbles and two white marbles and we remove one marble without looking, then before we draw there is, a priori, a 50% probability that we will remove a white marble. Once we do, the conditional probability of removing another white marble is reduced from one in two to one in three. After the first marble is removed, the fact that we used to have a 50% probability of removing a white marble is irrelevant to our future chances of drawing another.

A retiree may have a 95% probability of funding thirty years of retirement on the day she retires, but if her portfolio value drops substantially due to a market crash, her probability of successfully funding the remainder of retirement also declines dramatically. The fact that she used to have a lot more money is no longer relevant to her future success.

Here's another example. Let's say you board a plane in Los Angeles bound for Hawaii and historically, 99% of similar flights have had adequate fuel to reach the islands. Soon after takeoff, the plane's fuel tank develops a very large leak and the pilot has to decide whether to turn back. You really want him to base his decision upon conditional probabilities that take into consideration this new information and not upon historical results. The long-term success rate for similar flights may remain about 99% no matter which decision your pilot makes, but that shouldn't bring you much comfort. Suggesting that retirees can safely withdraw the same amount after a market crash is like telling you that you still have a 99% chance of reaching Hawaii after the fuel tank begins to leak.

At this point, we could dismiss the strategy as unworkable without considering the accuracy of the probabilities. After all, if a priori probabilities on the date of retirement are largely irrelevant after retirement begins, then the exact measure of that irrelevant probability is, well. . . irrelevant. Some may consider it useful that, while a constant amount cannot be withdrawn annually with constant risk, it might be safe to withdraw an annually varying 4.5% of remaining portfolio value each year. In other words, abandon the goal of constant annual income, but hold the risk constant at say, 95%.

Unfortunately, the probabilities calculated by the study are also highly suspect because they are based on a model of irrational retiree behavior.

If we gather observations about the accuracy of blindfolded dart throwers, we cannot then correctly infer that these observed results should be expected for all dart throwers, blindfolded or not. The observed sample has to be believed to be representative of the larger population before we can make that inference, and we can reasonably expect that dart throwers will perform better without a blindfold.

The models used to calculate probabilities for the sustainable withdrawal rate studies simulate a retiree who withdraws the same amount from his portfolio every year, even in the face of near-certain impending financial ruin. No rational retiree would do this, of course. When it appears that continuing one's spending pattern will soon lead to bankruptcy, rational retirees would reduce their withdrawals to avoid ruin, living on less being the preferred strategy to living on nothing. So, the percentage of rational retirees who would wind up broke using the 4% Rule strategy is likely far smaller than the 5% calculated by SWR studies, but the number who would underfund their retirement plans would almost certainly be much higher.

We can't infer the rate of ruin for rational retirees from a model of irrational retiree behavior any more than we can infer the accuracy of all dart throwers from observations of blindfolded dart throwers. Metaphorically, the retirees simulated in the sustainable withdrawal rate studies have blindfolded themselves to the reality of market risk. The SWR models simply don't represent expected retiree behavior.

In summary, the SWR strategy would be extremely risky, compared to observed bankruptcy rates for retirement-aged families, even if it were logically sound. But it isn't, and neither are the online retirement income calculators based on it. To summarize the logical flaws:
  1. A 95% probability of avoiding ruin is not “safe”; it is an order of magnitude higher than the currently-observed rate of bankruptcies among retirement-aged families,
  2. The calculated probabilities are a priori estimates. After a significant decline in a retiree's portfolio value, the retiree must either reduce spending, perhaps significantly, or accept greater risk of financial ruin, possibly much greater risk. The retiree who continues withdrawing the same amount after a major decline in portfolio value has a new probability of success that may be far less than 95%. The strategy cannot provide both constant withdrawal amounts and constant risk throughout retirement, and
  3. Rates of ruin for retirees who would reduce spending to avoid bankruptcy cannot be inferred from a model of retirees who would not.

What is the correct probability that a retiree will deplete his savings if he withdraws a fixed amount annually equal to 4.5% of his initial portfolio value? That depends entirely upon how he would behave. It's probably around 4% to 5%, as the studies indicate, if he would continue spending at the same rate right up until he was completely broke. But, that behavior seems extremely unlikely.

If he would abandon the strategy and spend less when facing potential financial ruin, a quite rational thing to do, then the probability of failure would depend on how much he reduced spending and how quickly. Unfortunately, the potential number of those scenarios is infinite and the problem is probably not solvable in a useful way. The best estimate we can make without specifying how much and at what point the retiree would reduce spending is the overall bankruptcy rate for families in this age group, which was recently about 0.5%.

SWR is not a prudent strategy for developing an individual retirement plan, nor is it a strategy built on sound logic. Withdrawing a fixed amount annually from a volatile portfolio of stocks and bonds while holding the probability of bankruptcy constant throughout retirement is not achievable.
One reliable way to estimate the amount of income a retiree might generate with a given amount of savings is to shop for fixed annuities on the web. Although most retirees seem to shy away from purchasing these insurance contracts, they tend to generate more income than the SWR strategies promise and they are the only safe way to ensure a steady income for a lifetime. Even if the retiree considers fixed annuities undesirable for other reasons, they offer a baseline from which to evaluate other strategies that promise benefits that fixed annuities can't deliver, but with greater risk.

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