Dave Ramsey and the farce of averagesArticle added by Tom Martin on January 22, 2016

Tom Martin

SAINT LOUIS , MO

Joined: January 07, 2005

Did you hear about the statistician that drowned crossing a river with an average depth of two feet?

Radio show host Dave Ramsey has been rightfully called out by many on this site for his misleading use of averages. But most of the criticism I've read does not go quite far enough, and the damage he inflicts upon his followers can be even greater than his critics give him credit for.

The chief complaint on his faulty mathematics revolves around the difference between mathematical average (arithmetic mean) and compound annual growth rate (geometric mean). The two numbers are not interchangeable. For example, if you have \$1,000 invested and in the first year your return was 100 percent and the following year your return was -50 percent you would have “averaged” a return of 25 percent per year. But how much money would you actually have after two years? Obviously, you would still just have \$1,000. If you actually earned 25 percent each year you would have a little over \$1,560. This would be an extreme example, but it illustrates the difference.

Without citing a specific time frame, Dave Ramsey claims the market averages 12 percent annually. Some have criticized him for being too optimistic but there are plenty of meaningful time periods where the market would have averaged such a return assuming we counted dividends. For instance, from 1983-2008 the average return of the S&P 500 including dividends was 11.95 percent. Let’s just round up to 12 percent.

Taxes, investment charges and fees can significantly eat into the returns but Dave’s world neither of these seem to exist so we will wish both of them away in the following examples.

According to Ramsey’s math, if you invested \$100,000 in the 1983-2008 market and left it alone for 25 years it would have grown to \$1.7 million. This is what you would have if your money earned exactly 12 percent each year. But the market did not deliver 12 percent each and every year. As a matter of fact, it didn’t earn 12 percent in any single year in that period. Some years were higher and some were lower but it did average 12 percent. In reality, if you had \$100,000 invested and earned the exact market rate each and every year with no taxes or fees, you would have \$1,279,000. Ramsey’s math overstates your nest egg by 33 percent even though you averaged the return he cites.

But it actually gets worse.
Most of us do not build our wealth by investing a large sum of money for 25 years; we do it by systematically investing over time. Let’s go back to my initial example of having a 100 percent return in year one followed by a 50 percent loss in year two. But rather than assuming a single deposit of \$1,000 you invested \$1,000 each year. Ramsey’s math would say you would have \$2,812.50 (\$1,000 per year compounded at 25 percent annually). In reality, you would only have \$1,500 at the end of year two. Despite “averaging” 25 percent annually, you actually lost money!

When we systematically invest over time, not all of our money earns the same rate. Over a 10-year period the first payment would receive the compound annual growth rate of the investment over 10 years. The second payment would receive the CAGR of the last nine years of the investment, and the final payment would simply receive whatever the investment did in the final year.

Let’s now apply this systematic investment to the actual performance of the market during the time frame above, and we will assume we invest \$10,000 per year. Again, this is a time period where the market “averaged” 12 percent annually. In Dave Ramsey’s world, our nest egg would be \$1,493,339 (\$10,000 per year compounded at 12 percent). But in the real world our nest egg would be worth only \$887,988. Even though we “averaged” 12 percent, Ramsey’s math overstates our nest egg by 68 percent!

But again, it gets worse…

How much are you investing today versus 25 years ago? Who generally have more to invest — the 25-year-old or the 50-year-old person? As we get older we normally earn more money and our everyday expenses consume a smaller percentage of our income. As a result, we normally have more and more to invest each year.

Now let’s take the previous example, where we were investing \$10,000 per year, but we’ll assume that we increase our deposits by 5 percent each year. Using Ramsey’s flawed math of compounding this cash flow at a constant 12 percent rate would produce a nest egg of \$2,477,504. In the real world, our nest egg would have only grown to \$1,251,388. Ramsey’s math overstates our nest egg by 98 percent even though we averaged exactly what he told us we would!

Perhaps the only salvation to the Ramsey follower is that they have gotten used to a Spartan existence of eating rice and beans and driving “beaters” that they will be able to get by on less.
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