The Hidden Assumptions of Financial Calculators

The Median Outcome

Once upon a time, financial calculators gave the median result. If stocks were projected to gain 9% annually, the program would show that a lump-sum $10,000 investment would grow in 30 years to become $132,678. The same approach applied to more complex forecasts, such as the amount of money that a retiree would retain after making several years' worth of withdrawals.

Investors understood that reality was less precise. After all, the output would only be as accurate as the inputs. Also, even if investments did match their forecast, they would surely wobble. For that reason, financial advisors would assess their clients' risk tolerances, to ensure that investors would "stay the course."

Such was the system, and it wasn't bad. However, displaying a single long-term outcome, accompanied by warnings about volatility, fostered the impression that if investors were sufficiently patient, they would prosper. Risk, it seemed, was psychological. The primary danger was not that investments would flop over the long term but instead that shareholders would disappear along the way.

Switching to Success Rates

In 1997, Nobel laureate William Sharpe raised that objection. In a speech (later expanded into a paper entitled "Financial Planning in Fantasyland"), Professor Sharpe stated, "The software will probably point out that higher returning investments may bring higher 'short-term risk.' But there is no sign of this in the savings graph." He concluded, "One is left with the impression that a high-risk investment may go down every so often, but that it will kindly go up subsequently by a large enough amount to get the account back on its appointed track."

Sharpe's critique helped to spark a revolution in investment software. (Sharpe was not the first to offer such views, but courtesy of his Nobel Prize, he was the most prominent.) These days, thanks to Monte Carlo simulations, financial calculators routinely erect a steeper hurdle than the median, because who wants a plan that fizzles half the time? Rather than the midpoint, calculators show a relatively poor outcome, thereby delivering an answer with a high success rate.

One site's calculator, for example, defaults to a 95% success rate. That is, its initial assumption creates a plan that meets the desired goal with at least 95% of the program's trials. Schwab recommends a somewhat lower success target, at 75% to 90%. For its part, digital advisor GuidedChoice boasts that the average success rate for its customers is 90%. Like the wet head, the median is dead.

A Failure to Communicate

All well and good. There's much to be said for selecting a plan with a high success rate, as well as for using programs that convey a range of future possibilities. However, while the new approach improves upon the old, it continues to struggle at communicating the full picture of a probability distribution.

Consider last month's column, "What Retirees Get Right About Their Retirement Income," which calculated the sustainable income-withdrawal rates for retirees, assuming a 90% success rate for the program's trials. The article started with a base case, then examined how that number was affected by 1) better investment performance, 2) delaying the retirement date, or 3) permitting inflation to erode the withdrawal amounts. The results elicited many responses. However, nobody asked how the numbers would have changed had I used a different success rate.

Let's do so now. The table below depicts what happens to the base case, which was a 4% sustainable withdrawal rate, when the desired success rate is altered.

Dramatic, no? An investor who demanded a withdrawal rate that always survives the program's 1,000 trials, without exception, would be able to spend only 2.5% of the portfolio each year. (That amount grows with inflation, but again, such details are irrelevant for this column's discussion.) The withdrawal rate jumps to 3.7% when the success rate is cut to 95%, gains almost another percentage point when the success rate is established at 75%, and reaches 5.3% for the median.

With effort, investors can generally derive such results from today's financial calculators, which typically permit users to adjust the initial assumptions. However, doing so involves taking steps beyond the program's basic operations, which means that most users abstain. They input their specific situations, press the button, and await the output. Assessing how the results shift along with the desired success rate is rarely a consideration.

Open to Change

This is understandable. Tinkering with success rates feels artificial, as if gaming the system. However, it's important to recognize that a 90% success rate is no more natural or "realistic" than the previous standard of the median. In either case, that figure is merely a single point lifted from a broad distribution. It might be a more palatable single point that resists the criticism that it fails half the time, but it does not represent the whole any more accurately than does the median.

This implicit and often-overlooked decision has major implications. A generation ago, my retirement calculator would have informed retirees that they could safely spend the median computed withdrawal rate of 5.3%. Using current conventions, the calculator suggests a withdrawal rate of 4.0%. The same inputs, the same computations, the same retiree--but a substantially lower recommendation.

Is this newfound conservatism a good thing? Overall, I think the answer is yes. Better to underpromise and overdeliver than to have a bevy of disappointed retirees who created plans that proved to be overoptimistic. However, as Professor Derek Tharp writes, there are times when "higher probabilities of success could be excessively cautious" by limiting retirees' withdrawals at times when they most desire the money. There is such a thing as being too careful.

But that is a topic for another article. The point to this installment is not to sleep on a calculator's default success rate. It should be regarded as yet another tool in the investor's arsenal--and a particularly powerful tool at that.

John Rekenthaler (john.rekenthaler@morningstar.com) has been researching the fund industry since 1988. He is now a columnist for Morningstar.com and a member of Morningstar's investment research department. John is quick to point out that while Morningstar typically agrees with the views of the Rekenthaler Report, his views are his own.