Apr 16

## Average Return vs Compound Annual Growth

Every so often, it’s time to look at the terms that we use when discussing financial matters. I’d like to take a look at the terms ‘Average Return’ vs ‘Compound Annual Growth.’ These two phrases sound similar, yet the results can be quite different.

The math isn’t complex, so we’ll start with a simple example. Two years, the first year is up 20%, the second, down 20%. It’s pretty obvious that the average of +20 and -20 is zero, no surprise there. But the compound annual return is a bit different, as 1.2 * .8 = .96 and this results in -4% over a 2 year period or a true return of -2%/yr CAGR. I know that too many numbers make your eyes glaze over, so an image:

This comes from the site Money Chimp, where you can check the market return between the end of two years, and adjust for inflation if you wish. It’s one thing to see random numbers trying to illustrate a point, and quite another to see how it would actually impact your money using real data. You can see that the Compound Annual Growth of “True CAGR” as the Chimp calls it, lags the Average by a full 2%. This is a result of the volatility of returns, as in my exaggerated example, a -20 cannot simply be averaged with a +20.

I don’t know what the market will do in the future. No one can know, really. But I do know how to look at the past, and to look at this specific period, 1926-2011, and suggest it returned 12% is simply incorrect. Had we actually seen 85 years of 11.84%, the result would have been a \$13,513 return, four times the final return. Lest you think that the difference of 2% was a result of the 85 year time horizon shown, head over to the site and just enter 2001 and 2010 as the beginning and final years. You’ll learn the disparity is formed by both volatility as well as time, so even short periods are affected.

I was recently reminded of Dave Ramsey’s 12% ongoing market claim, and re-read his article The 12% Reality. In his article Dave confuses simple with compound average and stands his ground. He even discusses the so called Lost Decade; 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%. Last I checked, ten years of 1% returns would grow your money at least 10%, no? The calculator shows us a True CAGR of -.99% for a cumulative loss of 9% over the decade. Let me spell that out – You started the decade with \$10,000, and ended with \$9,100, a bit less after expenses. Dave’s claim that you’d have \$11,000 or so misses the true number by 20% for the decade.

I’ve always loved math, and find that it’s tough to argue with facts. Next time someone starts quoting market returns, remember, knowledge is power, and you’re now armed with the knowledge to help you understand the numbers and educate others.

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Feb 03

## A Superbowl XLVII Roundup

First, it’s not the same when the home team, in my case, the Patriots, aren’t in the game. I don’t have any emotional interest in the outcome, but still, I watch. Not for the football, but for the commercials. 1984. It was the Washington Redskins and the LA Raiders. I’ll admit, I didn’t remember this, I Googled it. What I do remember is the Apple commercial. When you can remember a commercial nearly thirty years later, you know they did something right.

At The Finance Buff, my friend Harry Sit described Debit Card Discounts vs Credit Card Rewards. An interesting analysis for those who want to squeeze every last cent out their potential card rewards.

At Monevator, the Investor offers Congratulations if you stayed the course with shares. He’s warned not to get frightened out of the market and time has proven that to be sage advice.

At Money Infant, the question is Are You Frugal or Just Plain Cheap? Something to ponder if your goal is to be be frugal, but sometimes get to close to crossing that line.

Mike Piper at The Oblivious Investor answers the ago old question – What to Do with a Lump Sum? An insightful article with a link to a Vanguard study from last year.

And, in case you missed it, I recently authored my first guest post at Blocktalk, the H&R Block Blog. How to Change Your W-4 Withholdings to Maximize Your Tax Refund. Most people treat their W-4 as a “set it and forget it.” If your refund or your tax due in April is too high, check out the article and get to know your W-4 again.

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May 31

## Dave Ramsey scares me

Dave had published his expectations that the market would grow 12% on average and right until 2000 there was little reason to dispute this. Only, there was something wrong with Dave’s math even then. There’s a difference between the long term CAGR (compound annual growth rate) and the average return. Let me explain. If in one year, the market is up 20% and the next year it’s down 10%, you’d be inclined to add (-10+20)= 10, then divide by 2, for a 5%/yr average return, right? But, the way to calculate the CAGR is to take the returns, and multiply, 1.2*.9= 1.08. this is over 2 years, so you take the nth root, in this case 2, and get 3.92% per year. This may seem a minor difference, but it accumulates over time, and down years of say 33%, take a 50% increase to overcome.

Now, if we run the numbers that Dave suggests, a 12% per year return tell you that you only need to save 5% per year. Wow, you think, I can really afford that, but 15% is crazy. You then find that after a decade like we just had, the compound return was a negative 1% per year. You see that by investing only 5%, you saved up about 42% (after losses) of your current income, and even if the market gets back on track, you still find you have only 15 times your final income. If the market return is a lower 8%, you retire with only six times your income, enough to withdraw less than a quarter of what you lived on prior.

On the flip side, by saving 15% as I suggest, even after this bad decade, an 8% return for the remaining time will put you at just under 18 times your final income, just a 10% shortfall. The reason Dave scares me is that even in my most optimistic days, I never assumed a 12% return long term. Not long ago, I wrote an article titled A Change of Plans, in which I looked at the S&P chart from 1980 through 2000 and extrapolate where it should have been 10 years later, in 2010:  3600, 4 times the value it actually was in 2010. Admittedly, I didn’t expect an entire decade to produce a loss, nor did I expect, as Dave did, to see 210% gains.

I’m curious what Dave’s followers did over the last ten years, have your expectations changed? Dave has only dug his heals in further, recently writing The 12% Reality. Sorry, I call it the 12% pipedream. Let me close with one question – would you rather plan for 8% and when returns are actually 12% or higher, find you can retire at 45 or 50, or would you plan for 12% and if the market stumbles even a bit, have to work till you are 70?

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Jan 27

## The 401(k) backlash

Recently I’ve read articles calling for either reform or dismantling of the retirement accounts known as 401(k). I understand Enough of human nature to know that in times when the market is shooting higher and higher there are those who will lobby for putting the Social Security Trust Fund into the stock market. Now that we are down nearly 50% depending on which index you follow, the finger is pointed at the 401(k) account. The one single point I wish to make today is that all 401(k)s are require to offer multiple investment options, one of which must be a short term bond type fund. So the choice is with the employee as to how to invest. Remember, the 401(k) is just an account designation, it’s the employee who mush choose among the available funds. I’ll revisit this thought on Thursday in my Money Merge Account Analysis series.
Joe

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Dec 29

## 2009 Tax Rates and other Tidbits

A few thoughts as the year comes to a close:
Fairmark has updated to reflect the 2009 rates, and it’s worth a look. Quite a few updates to note, personal exemption and standard deduction have both gone up, as expected, creating an \$18,700 “zero bracket” amount. If you retire today with no other taxable income this represents a 4% withdrawal rate from a sum of \$467,500 saved pretax. I’ve written a bit about the pre tax vs post tax investment discussion and this adds to that.

Next, each tax bracket has shifted, so inflation won’t add to your tax burden. See the charts.

Last item I’d point out – 401(k) limits have gone up, \$16,500 for under 50 yrs old, and \$22,000 for those 50 and older in 2009. IRA limits have not changed, \$5,000 and \$6,000 respectively.

One more post, and we say goodbye to 2009.
Joe

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