Math Lesson in Rates of Return: Why Math Doesn’t Equal Money

A female investor uses a calculator to figure out the rates of return on her investments.

(Image credit: Getty Images)

Given the decades-long market upswing followed by the recent downturn, you may have questions about if your money is really working for you. For instance, is it possible to make an average 25% rate of return and still not make any money? The answer is “YES!” Hang with me for a math lesson in rates of return.

Investing for Retirement Income Is Different – Rethink 60/40 Rule

Understanding the simple truth that math doesn’t equal money can help you move from a passive pursuit of retirement where you only half understand what is going on – especially with all the negative news that can put you in a potential state of constant panic – to one that is an active pursuit of your retirement goals and puts you in the best position to achieve them.

A recent survey by the American Psychological Association found that issues associated with money are the top source of stress for most Americans, ranking above concerns about work, family responsibilities and even health.

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Like me, you don’t have anything against financial companies, yet they can use math to skew the numbers in their favor to make things appear better than they really are. The average rate of return on an investment is the math part of the situation, but it may not necessarily translate into money in your pocket, which in the end is what we all want — it’s what pays the bills, buys groceries and covers medical costs. We look to averages with investments to provide some sort of beacon to lean on to make the best investment choices we can.

To help you understand the concept that math does not equal money, I’ll start out using a hypothetical example with extreme numbers during four different periods of time. I will use two bull markets and two bear markets, so the results are obvious.

Here’s How a Hypothetical 25% Rate of Return Doesn’t Equal Money

Meet Tom and Debbie. They have $100,000 to invest and have a timeline of four years. They are open to growth and taking on some amount of risk. Tom and Debbie know they need to grow this money to help meet their retirement goals. They meet with a financial professional and review various portfolios and decide on a portfolio that has a historical track record of a 25% average return over their allotted time.

At the beginning of the first period, Tom and Debbie start off with $100,000 and see a bull market. They earn a 100% rate of return during that period. This will provide them with a gain on their investment of $100,000 – pretty sweet. At the end of the first bull market, they have $200,000.

They begin their second period with $200,000, but they have a bear market, and they take a 50% loss on their investment. They lose $100,000 of their $200,000. That gives them an ending balance of $100,000.

They start their third period with a balance of $100,000 and see a bull market. They earn a 100% rate of return on their investment, which is a $100,000 gain that ends the third period with a total of $200,000 – much better.

They start their fourth period with $200,000 and experience another bear market in which they take another 50% loss on their money, losing $100,000 and ending that period with a $100,000 balance in their account.

If you look at the math during these periods, Tom and Debbie gained 100% in each of the bull markets (periods one and three), and they lost 50% in each of the bear markets (periods two and four). Let’s do the math: 200% gain minus 100% loss = total gain of 100%. If they divide that 100% gain by the four periods of time, they achieve an annual average return of 25%: 100% gain divided by four periods = 25% average rate of return. That’s math!

Let’s review the money: They started with $100,000, and after four different markets, they ended with $100,000, so their actual rate of return was ZERO, right? And that’s the difference between math and money.

The big lesson is this: Math does not equal money in your pocket.

Here’s How a Rate of Return Still Doesn’t Equal Money

Let’s look at how this concept plays out in real life. Examining the average rate of return of the S&P 500 from 2000 through 2014, you can see how average returns don’t tell the full story of real money in Tom and Debbie’s pocket.

If Tom and Debbie started with $100,000 in the year 2000 and let that account grow over the next 15 years (through 2014) using the S&P 500 total return index performance, they would have an account balance of $186,430. If they add up all 15 years of gains and losses, they get 91.38%, and if they divide that total by the 15 years, they get an average rate of return of 6.09% per year.

Let’s test the math to see if the actual account balance matches the average rate of return. I’ll run a future value calculation crediting 6.09% each year on their $100,000 deposit. When I do this, their account balance is not $186,430 but is instead $242,726. That’s a 30% difference between the two account balances! The S&P 500 rate of return may be correct mathematically, but it isn’t the reality Tom and Debbie expect to see in their pocket where it counts.

Retirement Income Shouldn’t Depend on the Market; It Should Depend on Math

Living and dying by market averages depends on your timing, getting out of the market at peaks and investing at lows … but it’s impossible to predict the future! This strategy doesn’t provide you the money in your pocket that you expect. If Tom and Debbie started with $100,000 and ended with $186,430 over a 15-year period, that works out to be an actual rate of return of just 4.24%. The conclusion is that even though the S&P 500 index averaged 6.09%, the reality is the actual rate of return is only 4.24%, again proving math does not equal money.

Math Doesn’t Equal Money: The Takeaway

It is very important that, like Tom and Debbie, investors and savers understand the difference between an average rate of return and the actual return on their own investment. If you or your financial professional are doing projections using average rates of return vs. actual rates of return, it could lead to a 30% difference between what was projected for you and what your account value is when it’s time to retire.

Bottom line: Math is just a number, while money is something you can take home with you. It’s what buys the groceries, sends the kids and grandkids to college, covers your medical bills – it’s your lifestyle security.

From this day forward, my hope for you is to understand and live by this: Average rates of return should not be considered when your lifestyle security may be at risk. There are always unknown forces operating within the financial markets, and it’s impossible for anyone to predict when the next meltdown or “market correction” will occur.

The last thing you can afford is to interrupt the compounding effect of our retirement cash when it is finally time to start living out your dreams and enjoying retirement. Just hoping for the best won’t work. Gaining clarity on the reality of your approach by understanding this principle could be one step toward managing your expectations and making sure you achieve the retirement you want.

Questions You Can Ask Your Adviser to Clarify the Plan

Ask these questions to your financial adviser to get clarity:

When you provide projections, can you apply an actual rate of return vs an average?
When it’s time to start supplementing my retirement cash flow with withdrawals from my investments, what’s a realistic withdrawal rate I can count on? And how do you know that?
I notice that your projection(s) suggest I have an X% probability of success. What happens if I am unsuccessful? What’s the contingency plan?
What happens if when I retire the market happens to be in a bear or correcting state? How does that impact the cash flow we can pull out of my portfolio?

What Sort of Investment Returns Are Realistic?

Disclaimer

This article was written by and presents the views of our contributing adviser, not the Kiplinger editorial staff. You can check adviser records with the SEC or with FINRA.

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Kyle Winkfield, president of Finley Alexander Wealth Management, is a breath of fresh air to the financial industry, empowering clients and public audiences through education and straight-forward concepts. Personal finance is a topic that unnerves many Americans and the barrage of industry jargon and fast talk leaves most uncertain about what is best for them and their families. A portfolio is not a plan, and what sets Kyle’s clients apart from the rest is they have a written plan for retirement achieving financial freedom and lifestyle security.