Recently I reviewed what Dave Ramsey calls his Endorsed Local Providers (ELPs). As I was doing research for that review I learned of Dave’s view that historically the S&P 500 has returned 12%. I also learned that he believes it will continue to do so over the long run.

This was curious to me for several reasons. First, it’s common knowledge that the compound annual growth rate of the S&P 500 since 1926 is 10%, not 12% (the S&P 500 as we know it today was formed in 1957, but we can traces variations of it back further). Second, every investing expert I’ve ever read or listened to says the same thing–10%. And finally, I know of no expert or study that predicts 12% returns going forward.

So I dug into this little bit and learned from the Ramsey website that he gets very specific. He claims that from 1926 to 2011 the S&P 500 returned 11.69%. That’s not the kind of number you just make up out of thin air. It’s wrong, of course, but the better question is how he came up with it in the first place.

I literally spent days trying to reverse engineer his 11.69%. In the car one day it finally hit me. He’s taking a mathematical average of the yearly returns of the S&P 500. I checked this theory against return data and replicated his number to within a few hundredths of a percent. I emailed his company for confirmation, but have yet to receive a reply.

And that brings us to today’s topic: average annual returns vs. annualized returns (also called compound annual growth rate).

## Average Returns vs. Annualized Returns

In today’s podcast I cover the difference between average returns and annualized returns. For example, image investing $10,000 for ten years. In one scenario you earn 10% each and every year. In the second you earn 5% in year one, 15% in year two, 5% in year three, and so on. In both cases the average return is the same, 10%. The amount of money you have at the end of 10 years, however, is very different.

Listen to today’s podcast to understand why. We’ll also cover why this difference is so important. Trust me, your future retirement is at stake.

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Rob I understand the point you making about different ways to look at investment returns. I speak for the average guy when I say, “Who cares?”. I’m not an attorney with an intimate knowledge of the financial industry. In 2004 I was swimming in debt, like everyone else, but knew there was a better way to live. I read Dave’s book then paid off all my debt including the house. I’ve fully funded an IRA and Roth for the last two years. As of this year I made my first ever non-retirement investments. I used Dave’s 4 recommended mutual fund categories & I continue to fund my investments weekly. There isn’t a single person I know sweating out 10% vs 12%. Why? Because they’re busy trying to pay off all the debt on stuff they borrowed to obtain. You can split technical hairs about Dave’s advice all day but I’m a high school graduate that’s gonna have a 7 figure net worth in the next couple years. Take a look at these horrifying statistics, http://www.statisticbrain.com/retirement-statistics/ and ask yourself if it’s more important to wrangle over a couple percentage points or get debt-free and invest early and often?

BMS…you are spot on with this one…I work in finance so I totally get it Rob’s point…and in some ways he needs to set the record straight; however, at this point we are all fighting a huge fire…this discussion is like saying do I use the water hose with the metal casing or the aluminium casing…at this point it really doesn’t matter.

Last time I checked the US personal savings rate was less than 2%…everybody is drowning in credit card debt…and as a nation we are facing a looming student loan bubble…

Personally, my wife and I are focused like hawks on climbing out of debt…yeah..some will say “but each show is not for everybody” and I get that..but as you rightly pointed out..the numbers don’t lie…most of us don’t need to worry about this at all

Right now…in terms of personal finance, this is the LAST thing that the average American needs to worry about ;o)

BMS, it sounds like you are doing great. Congrats. As for why it matters, however, I describe that in the podcast. For may, it doesn’t matter at all. But when Dave recommends withdrawing 8% of your nest egg in retirement each year because in the long run you earn 12%, it matters a whole lot. It also matters when he uses the 12% figure to promote his E.L.P. program. It sounds like you ignore all of that nonsense, and good for you!

Rob you are right on. A difference of 2% a year is huge over the long run. Honestly for the Dave Ramsey crowd maybe it doesn’t matter as I think his primary audience is people who are heavily in debt. For those of us whose priority is a long term investment return, however, 2% will make a big difference. For getting out odd debt Dave is great but he should stay away from investing advice.

Regarding Dave’s 12% and investing plan: I agree with you on his ELP investing advisors. We met with one and he didn’t ask any questions and didn’t really pay attention to our interests. He did explain things (like debt, which we had none of). So fine, we are happy on eTrade, and get good advice and research there.

To explain Dave’s arguments, You need to understand his audience. These are people who generally don’t know that you need to have saved a thousand dollars in the bank. These are people who often view pay day lenders as financial advisers. So your math here would have left them far behind as soon as you mention average returns. So he has to be simple, consistent, and get people to save 15% in something that’s likely to go up, vs. having zero saved, a reverse mortgage, and a double refinanced leased car.

Many have found ways to make lots of money on the backs of stupid poor people (such as pay day lenders and reverse mortgages). Dave has found a way to make lots of money from stupid poor people, but by helping them…so even if his #s are sometimes a little iffy, I still like listening to him, even if it’s often for the voyeur value.

I can’t wait to listen to your podcast, Rob. Have to wait to get on wifi a home before I download it as I am cheap and have a $10/mo airvoice no data plan.

I used to hear 12% also – good to know that it is based on a numerical average of the yearly returns. Wow – 12% vs 10%, big difference. Maybe you mention this in your podcast, but do you know if this data is on a total return basis? That is, is it assumed any dividends are reinvested in more shares as they are paid out? That could also be a big difference in data. I’m glad you question numbers, because I do, and they can be presented to paint almost any picture you want..

Kenneth, the 10% annualized returns does include the reinvestment of dividends.

Let me say right off that I am a fan of Dave Ramsey. I read his books and enjoy his radio show. Still, I cringe when he talks about getting a good mutual fund that will produce 12%. The odds of this are very low and more likely looking for the fund that will get you 2% above the market will earn 2% below the market. And, as implied above market returns are likely to be considerably lower going forward given historically low interest rates.

Furthermore, fans of Ramsey’s would do well to read something like “The Smartest Investment Book You’ll Ever Read” by Solin or “The Investor’s Manifesto” by Bernstein after they get out of debt. In these books they will learn that a 2% difference is huge over a long period of time and that picking that mutual fund is not as simple as some people present it.

Arithmetic returns have been used since the first investment advisor came on the scene. Would you buy a fund that went from $1 to $2 and then back to $1. Average return equals 50%. If you don’t get it visit a 6th grade math teacher before you invest.

Average return would be 25%, but a good point.

You’re right. 1 to 2 is 100%, 2 to 1 is -50%, add and divide by 2 is 25%. Thanks for the correction. I guess I need the 6th grade math teacher!

Forget all the math. Here’s the most important takeaway. Dave Ramsey’s suggestion that you can withdraw 8% from a retirement portfolio reminds me of Peter Lynch (Fidelity) saying some years ago that you could withdraw 7% safely. Scott Burns dug into this particular Lynch claim and soundly refuted the 7% number so it’s safe to assume that 8% is even more incorrect. Most experts agree that if you use 7-8% withdrawal rate you will almost certainly run out of money, and I don’t think Ramsey or Lynch will bail you out!

Very interesting. I didn’t realize that the difference between these two could have such a dramatic impact. I think the more you can educate yourself about things like this, the more likely you are to enjoy success.

Pretend math is fun.

Acquired interest = Principle (P) * InterestRate (I)

Future Value (FV) = P + P*I = P*(1+I)

When I is the annual investment return and you invest for two years then:

FV = P*(1+I) * (1+i) ==> (implies) P * (1+I)^2 where ^2 is to the power of 2

If I invest for N years then FV = P(1+I)^N

So if I have invested for N years and Acquired A future value of FV then I can calculate an average growth rate by

I (average interest rate ) = e^(ln(FV/P)/N) -1

where ln is the natural logarithm function and e = ~2.71828….

Lets say I tripled my investment in 5 years then I (average) = e^(ln(3)/5) -1 = 0.2457 or 24.5%

I got the average without any adding. It is interesting. All you need is the initial value and the final value and the time the money was invested. By the way, N can include fraction of years. (for example 4.5 years)

So if my beginning investment (p) equals my final value (FV) the I = 0%

Another example would be how many years to acquire triple my investment at a given interest rate say 8%:

N= ln(FV/P)/ln(1+I) =ln(3)/ln(1.08) ==> 14.27 years

You can check the rule of 72 with this equation if you wish.