More bad math from Dave RamseyArticle added by Thomas De Jong on August 9, 2011

Thomas De Jong

Sioux Center, IA

Joined: November 01, 2009

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I still can’t figure out why Dave refuses to acknowledge the difference between average annual rates of return and compounded rates of return.

​In the past few months, I’ve received two e-newsletters from Dave Ramsey. The first was titled “The 12 Percent Reality." The article defends Dave’s belief that the market has performed at a 12 percent rate over time (with no sources cited), and goes on to say how easy it is to find investments that will do the same for you by looking at past performance (again, no evidence provided).

The second e-newsletter was titled “Simple Plans Create Millionaires." The premise of the article is that investing a small amount of money and sticking with a plan will turn you into a multi-millionaire.

Here are some of Dave’s quotes from the articles (in italics), followed by my rebuttals:

When Dave says you can expect to make 12 percent on your investments, he’s using a real number that’s based on the historical average annual return of the S&P 500 … The current average annual return from 1926, the year of the S&P’s inception, through 2010 is 11.84 percent.

While the current average annual return from 1926 through 2010 is 11.95 percent, that’s the arithmetic mean, which is completely inappropriate for looking at growth rates of an investment over time. The true rate of return, the compounded rate or geometric mean from 1926-2010 was 9.89 percent. A 2 percent difference over time is enormous. Of course, this is before expenses, taxes and inflation.

I still can’t figure out why Dave refuses to acknowledge the difference between average annual rates of return and compounded rates of return.

Why is there a difference between annual average and compounded rates of return? Volatility. The higher the peaks and the lower the valleys of the market, the greater the difference between annual average returns and compounded or annualized returns.

See the rates of return for yourself by going to http://www.moneychimp.com/features/market_cagr.htm.

Here’s a simple example of the difference between annual average and compounded rates:

You start with \$10,000, and in year one you earn 100 percent. Your account balance is now \$20,000. In year two, you lose 50 percent. Your account balance is now back down to \$10,000.

What did you really earn? Nothing! Your account balance is the same as when you started.

Annual average returns say that you earned 25 percent (100 percent - 50 percent = 50 percent divided by two years = 25 percent). So you tell me? What is your true rate of return? 25 percent or 0 percent? The answer, of course, is zero.
Back to the articles:

From 1991–2010, the S&P’s average was 10.66 percent. From 1986–2010, it was 11.28 percent. In 2009, the market’s annual return was 26.46 percent. In 2010, it was 8 percent.

From 1991-2010, the S&P 500 returned an average rate of 11.04 percent, but only 9.14 percent compounded. From 1986-2010, the average rate was 11.63 percent, but only 9.97 percent compounded. In 2009, the S&P 500 grew 27.11 percent (though sources will vary slightly depending on when dividends are reinvested), and in 2010, the S&P 500 grew 14.32 percent (some sources say a little over 15 percent).

I’m not sure where Dave is getting his data, but again, he never provides any proof. I took these numbers from this moneychimp.com calculator.
From 2000–2009, the market endured a major terrorist attack and a recession. S&P 500 reflected those tough times with an average annual return of 1 percent and a period of negative returns after that, leading the media to call it the "lost decade." But that is only part of the picture. In the 10-year period right before that, 1990–1999, the S&P averaged 19 percent annually. Put the two decades together, and you get a respectable 10 percent average annual return.
More bad math. During the lost decade, the S&P 500, yes, averaged 1.21 percent, but the compounded rate of return was -0.99 percent. Also, you cannot add two decades together and divide by two to get a true rate of return … this, again, is using the arithmetic mean vs. the geometric mean. The period 1990-2009 had a compounded rate of return of 8.23 percent.
It’s not difficult to find several mutual funds that average or exceed 12 percent long-term growth, even in today’s market. An experienced investing professional can help you find good mutual funds in each of the four categories Dave recommends.
Dave’s right. It’s not difficult to find an investment that performed well in the past. However, you’ll need a time machine to go back and make sure you capture those gains.

There’s an entire body of investment research that shows that past long-term performance is a horrible predictor of future long-term performance (I do not have the room to post links here, but feel free to Google this if you’re skeptical), which is why investments must carry the disclosure “past performance is no guarantee of future returns.” The question is not “how can I find an investment that has done well in the past?” The question is “how do I identify, in advance, an investment that’s going to do well in the future?”

For the average investor (and even for the professional money manager) that has been exceedingly difficult, which is one reason why the average retail investor, over a 20 year period (ending Dec 31, 2009), earned only 3.2 percent on their investments, when the S&P 500 returned 8.2 percent (according to a DALBAR study). In the 20 years ending 2008, the gap was nearly 6.5 percent between investor and market returns.
Of course, Dave is also pushing his endorsed local providers, which are selected investment reps around the country who pay him a referral fee for being "Dave Ramsey endorsed."
Your goal is to invest 15 percent of your income, so if you make \$40,000 a year and invest 4 percent, or \$1,600, in your 401(k), you'll only need to invest \$4,400 in your Roth IRA to meet that goal. In both your 401(k) and your Roth IRA, you'll invest in mutual funds with a long track record of above-average returns.

Put 25 percent of your investment in each of these four categories: growth, aggressive growth, growth and income and international funds. The market has grown at an average annual rate of 12 percent. We'll assume your investments will do the same. A 30-year-old who follows this plan will have nearly \$6 million by the time he's 70, without ever increasing his contribution level: \$240,000 in contributions (not including 401(k) employer match + \$5.7 million in total interest = \$5.9 million for retirement). The best part about this plan is that it works for nearly everyone.
Again, more bad math. Even if you did earn 12 percent compounded returns on your investments, \$6,000 annually over 40 years at 12 percent interest equals \$5.2 million, not \$5.9 million. Also, if this works for nearly everyone, we’d have a lot more citizens with \$1 million, not to mention \$5 million.

Dave did not make his riches this way — he made them through his books, CDs, seminars, radio and television. There’s no doubt that his is a success story, but it is not one that everyone can do.

But none of this addresses why — why should we strive to have \$5 million? What’s the point of accumulating all those resources? What are you going to do with them? Indulge a temporary lifestyle? Is there more to life than money?

Wealth is not an indicator of a fulfilling life. Two things reign important here:
1) what’s the motivation for accumulating wealth, and
2) how are you going to use it.
Finances, especially regarding significant wealth accumulation, must always be purpose-driven, with a mindset far beyond simply raising a standard of living. Some may say that the errant math is not a big deal. Maybe they’re right.

But I think several dangers lie with Dave’s advice and his bad math:
• a danger that people will mistake cookie cutter financial advice for a personalized plan

• a danger that people will expect their \$240,000 in contributions to grow to nearly \$6 million

• a danger that people will be vastly under-prepared for future living expenses

• a danger that people will be investing in a manner inappropriate for their risk tolerance

• a danger that people will see accumulating wealth as the pinnacle of success in life
Again, it must be re-stated that Ramsey has put together some great material on getting out of debt, but it is for the reasons above that I urge people to be, in all things, discerning.

Disclosures:
• Dave's e-newsletters can be found online by going to: