My industry, the business of providing financial advice, should be ashamed of itself.

We’re supposed to be professionals versed in the knowledge of investments, financial markets, retirement planning, and the mathematical fundamentals behind that subject matter. We are regulated up the you-know-what. Yet, we are still allowed to provide you guidance and information that we know (or should know) with virtual certainty will be completely wrong, and we don’t tell you that.

Have you ever had one of those retirement projections done for you where a fancy software program spits out a 10-, 20-, or 30-page report full of neat-looking graphs and tables of your investments and ultimately comes to the conclusion that you will be “A-OK” in retirement?

I am going to show you today why those reports are likely more useful as fire starters than as guides for your retirement.

The problem lies in several factors:

modeling with averages rather than accounting for sequence of returns and actual volatility, the use of average market returns that are too high, advisors typing inputs into the software without understanding the mathematical principles and limitations behind the models, and advisors not adequately communicating to you the “fine print” — i.e., the inherit limitations and flaws of the models.

Instead, you are presented with a fancy and professional-looking report that gets treated like gospel because of its appearance. (As a wise uncle used to tell me, “Appearance often matters more than reality in business.”)

The Problem of Using Averages and Not Accounting for Volatility

First let’s start with the problem of using averages in retirement projections when you are withdrawing the money. I am going to show you that two different accounts can have exactly the same average compounded rate of return, and one shows you going broke in retirement while the other looks okay.

In fact, when you begin withdrawing money from your retirement accounts, you can experience nearly an infinite number of completely different outcomes, all of them having the same average compounded rate of return. I know this sounds wild, but it’s the mathematical truth. And unfortunately, I bet your advisor has not explained this concept to you.

Statistics Don’t Work When the Sample Size is One

Instead, these fancy reports that use averages typically also spit out things like probabilities, standard deviation, and other official-looking statistical information. I graduated many years ago with a degree in engineering and am a certified math geek. I took Calculus I, II, and III, differential equations, and statistics, among a myriad of other nerdy-type courses.

As an investor, standard deviation and percent probability do nothing for me and my retirement plan. And they don’t help you either, especially if you’re not a math nerd like me. Either your plan succeeds or fails. Period.

Or, as PayPal founder Peter Thiel puts it in his 2014 book Zero to One: “Statistics doesn’t work when the sample size is one.”

Telling me that my plan has a 70% to 80% chance of success with a standard deviation of +/-$250,000 is the same as the weatherman telling me it may or may not rain today. Neither one of those forecasts tells me whether I can enjoy the beach with financial peace of mind.

Let’s go through an illustration so you can understand how this freaky math wreaks havoc on your retirement. Then I will suggest a better approach to planning to increase your chances of success and peace of mind.

When You’re Not Making Withdrawals, Your Sequence of Returns Doesn’t Matter…

Suppose you had a $500,000 account at the end of 1999 and invested it in the S&P 500 (for purposes of this illustration, we’re going to assume you reinvested dividends and the index ignores fees and expenses).

During the past 15-year period, from 2000 through 2014, that account would have grown to approximately $933,000 (without withdrawals), for an average compounded rate of return of 4.25%. (By the way, it’s been a pretty wild ride just to average less than 5%, huh?)

You can download historical S&P 500 returns and obtain other useful information by visiting the S&P’s site.

When you’re not making withdrawals you could re-order the past 15 years of returns in any sequence whatsoever and you still end up at the same point. It’s the same mathematical principle that dictates that 3 x 2 is the same as 2 x 3.

To prove these couple of points to you, please refer to the illustration below where I set forth three accounts: one with the actual returns of the S&P 500 from 2000 through 2014, one with the past 15 years of S&P 500 returns in reverse order, and one with the exact average of 4.25% every year. They all end up at the same point, and therefore all three have the same average compounded rate of return of 4.25%:

But When You Start Making Withdrawals, Your Sequence of Returns (i.e., Year-to-Year Volatility) Becomes Critical

Now let’s introduce retirement withdrawals — and the entire game changes, because the mathematical equation completely changes.

When you add withdrawals, your specific sequence of returns produces a completely different result every time you change the sequence, even though each sequence has the same average compounded rate of return! And, 15 years of returns can be sequenced in more than 1.3 trillion different ways!

That means even if you knew ahead of time what the next 15 years of returns were going to be but were not given the order, you would have less than a one in 1.3 trillion chance of exactly predicting your retirement, even ignoring all the other variables such as your spending, inflation, and tax rates.

To illustrate, now that we can agree that all three accounts in my illustration above have the same average compounded rate of return, watch what happens when I add a $30,000-per-year withdrawal to each one.

After 15 years, the S&P 500 fund in reverse order would still have $489,000 remaining, and the account averaging exactly 4.25% each year would show $321,000 left. But the actual S&P 500 account would be almost broke, with only $64,000 remaining.

(By the way, BlackRock also has a good illustration of what sequence of returns does to your portfolio. Their illustration is even more dramatic, illustrating with a hypothetical set of returns on two $1 million retirement accounts. Over the course of 25 years, one account goes all the way to zero and the other finishes above $1 million, both using the same set of returns — just sequenced in different order.)

That means even if your advisor back in 2000 had correctly and exactly predicted the future market average of 4.25% and put that into your retirement prediction, your model would have been off by more than a quarter of a million dollars on a $500,000 account after just 15 years! And even worse, almost all of the models I have seen are using average returns of 6% to 7% — which, at 7%, would have predicted growth in your account to $625,000 instead of the reality of shrinking to $64,000.

Your advisor may have told you that he or she accounted for different outcomes by using a software program that does what’s called a Monte Carlo simulation. (Again, it sounds fancy so it is often treated as gospel.) A Monte Carlo simulation tries to predict different outcomes by varying the inputs into the model and then spitting out an overall probability of success of your retirement plan.

There are several problems with this. First, as I pointed out above, statistics doesn’t help you when your sample size is one. Besides, what good is it to say I might have a 25% chance of needing to look for a job in my 80s?

Second, all the Monte Carlo simulations I have seen are still based on inputting different average rates of return and do not account for sequencing and year-to-year volatility. As I just explained, you can have more than 1.3 trillion completely different outcomes with just 15 years’ worth of returns, all of which have the same average rate of return.

Over longer periods of time, the number of different outcomes goes up exponentially to numbers I can’t even pronounce. Since no one knows what the average rate of return will be in the future, let alone what the volatility and sequence of returns will be over the next 15 to 30 years, a Monte Carlo simulation isn’t of much help either.

A Word About Projected Growth Rates

In addition, as I mentioned above, most of the models I have seen are using predictions of average growth rates in the 6% to 7% range. Even if we put aside the problem of using averages without accounting for volatility, using averages of anything more than 5% is doing a disservice to investors.

As I previously mentioned, the average compounded rate of return of the S&P 500 during the past 15 years has been 4.25%, and that’s with dividends reinvested. (Without dividend reinvestment, it would have been even lower.) While it is true the S&P 500 had an average compounded return of almost 10% over the 50-year period from 1965 through the end of 2014, you must remember that we are in a much different place now than we were in 1965.

Our market and economy had a lot more room to grow in the 1960s, 70s, and 80s than they do now. The population was expanding and the baby boomers were hitting the workforce. Now our population is aging, the birth rate is declining, and the country has moved to a mature, service-based economy. Future growth rates are not likely to match the previous 50 years.

That period was also skewed by one of the greatest 18-year bull market runs in the history of financial markets from 1982 through 1999, which included the hysteria of the Internet stock market bubble. That hysterical period will also not likely be replicated any time soon.

And finally, if you don’t believe me, then please allow me to introduce Warren Buffett. Here’s what he said in his 1999 annual letter to Berkshire Hathaway shareholders:

We see growth in corporate profits as being largely tied to the business done in the country (GDP), and we see GDP growing at a real rate [i.e., nominal rate minus inflation] of about 3%. In addition, we have hypothesized 2% inflation. * * * If profits do indeed grow along with GDP, at about a 5% rate, the valuation placed on American business is unlikely to climb by much more than that.

And the next 15 years produced an average market return of 4.25%, not a bad prediction by Mr. Buffett.

For the next 15 years, I am not aware of any evidence that suggests we should expect growth in our economy any greater than what we have been seeing the past 15 years. That means retirement models using growth rates any higher than 5% are essentially crossing their fingers hoping for the best and not planning for the worst.

In addition, a proper model needs to account for advisor fees and fund expenses, which often run a total of 1% to 2% — which means that, even if the market does perform in the 5% to 7% range, your portfolio will perform in the 3% to 6% range after fees and expenses.

And if the market performs in the 4% to 5% range, as it has the past 15 years, then you as an investor are looking at 2% to 4% returns after fees and expenses. That’s a far cry from the 6% to 7% growth rates I am seeing used in retirement projections.

So What Is a Prudent Alternative for Retirement Planning?

We shouldn’t be in the business of trying to predict the future or what the market is going to do. The future is inherently uncertain. I don’t have any idea whether the next 15 years will bring more or less than 5% growth.

What we should be focused on, however, is planning for this uncertainty.

To do that I take a page out of what the banking industry is now required to do after the crash of ’08, and what well-run businesses have always done: They use stress tests.

They look at whether their banks and businesses can survive in even the worst of times, and if they can, then they know they will be just fine in average scenarios or the best of times. Why should your retirement projection be any different? Aren’t we doing a complete disservice to you if we don’t put your projection through a worst-case scenario and see if your savings can still survive retirement?

In my opinion an advisor needs to conduct a stress test in order to develop your retirement investment plan. The stress test will show how much of the portfolio needs to be protected from downside risk in order to make your plan work.

Moreover, it’s easy to look at stock market history and specifically sequence your portfolio through some of the worst and most volatile time periods to see how it would survive. So why doesn’t the industry do this?

Why Doesn’t the Industry Change How It Does Retirement Projections?

I think it’s due to a number of factors. First, I don’t believe most advisors in the industry are aware of or understand how the sequence of returns can disrupt a retirement portfolio when the retiree is making withdrawals. Certainly investors are not aware of this phenomenon, which at least means advisors are not communicating it to their clients.

Second, it seems that these projections are often used as marketing tools, and no advisor who is trying to win a new account would want to show the prospect a projection that looks bad for you, right? Moreover, I have spoken to a handful of prospective clients who said their current advisors were willing to put their credibility on the line and guaranteed them the 7% growth they needed to make their retirement plan work.

Third, as I touched on at the beginning of this article, these projections are based on software programs that look fancy and therefore are treated as gospel. The problem is that data inputs are typed into them and then an answer is spit out. I don’t believe many advisors truly understand the limitations of these models and how flawed their results can be.

So I leave you with the following question:

Would you rather plan conservatively and see if your retirement savings can survive a stress test, or are you merely hoping the market can live up to your expectations of future growth in order to make your plan work?

Tim Van Pelt is a financial planner. You can reach him at tjvanpelt@gmail.com or (608) 577-9877. This material has been prepared for informational purposes only, and is not intended to provide, and should not be relied on for, investing, tax, legal, or accounting advice. You should consult your own investment, tax, legal, and accounting advisors before engaging in any transaction.