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Fat Tails PDF Print E-mail
Written by John D. Buerger, CFP®   
Tuesday, 11 May 2010 14:25

John Buerger

This is a follow-up to last week's post about the 10% Myth as we continue to investigate the world of investments.

How do you behave when you don't get what you expect?

Some people can be very rude when reality doesn't match their expectations, especially when they're hungry (I could tell you horror stories from my restaurant days back in Newport, Rhode Island).

But meeting (and exceeding) expectations are the lynch pin of both business and financial success.

What is interesting is that many times, expectations can be completely out of line with reality.  The facts (data) are staring you in the face.  Your expectations were unrealistic, but you still are mad because those expectations were not met.  Bathing suits and middle age come to mind.

This is especially true with investments.

The 10% Myth

Last week we refuted the 10% Myth of the stock market - The average rate of return over the history of the stock market is NOT 10 percent (as is commonly stated by stock brokers and the media pundits on the financial pornography outlets).

The average rate of return on equities is closer to 7% (including dividends).

Now, a 7% historical return is pretty good.  It allows you to double your money in about 10 years, quadruple wealth in 20 and wind up with 8 TIMES your starting wealth after 31 years.  If you are in control of your cash flow and saving money throughout this time, you'll build wealth even faster (a little shameless plug for financial planning and cash flow management).

But what about the next two to three years?  If the average rate of return for the stock market has historically been 7% per year, how likely is it that you'll see something near that rate of return on your investments in any one of the next few years?  How likely is it that you'll see a result that is substantially different from average - a big gain or (worse yet) a huge loss?

Average is Not Normal

The answer is, "The big loss is more likely than the average return!"

Why?  Because annual returns for the stock market are highly volatile, even in time periods where everything else economically seems pretty quiet. We looked at the history of market returns since 1896 and plotted out those results in a distribution bar graph.  Here is what we found:

click on picture for a larger image

The blue line represents all the times that returns for the year were average (between 4% and 8%).  We saw average returns in less than 10% of the periods in the 112 years covered.  A loss of 8% to 12% happened 8% of the time as did a gain of 16-20% or 24-28%.

You would think that the further away from average (the more to the right or left of the blue bar) the less often you would see that kind of result, but it doesn't work that way.

Now I have been an investor since I was in high school.  Still after all those years (my kids would say "centuries") and after having seen the raw data and even the graph above, I still find it difficult to accept that normal returns for my portfolio will be anything BUT average.  But it is true.

What's going on?

Fat Tails and the Human Brain

Human beings are pattern seeking creatures.  In fact, our brains will see patterns where they do not exist.  A number of experiments have been done where participants "identified" patterns in purely random number sequences.  It's a quirk in our hard wiring and a wonderful coping mechanism that serves us well in many ways, just not in the investing world.

When we are told that the stock market has averaged a 7% rate of return over its history, our brains automatically imagine that the results next year will mostly be right around 7% with a very small chance that they will be out of the ordinary.  We develop an expectation on that assumption.

It does not matter that your recent personal experience has seen nothing but wild numbers (as we have seen), the brain still expects a lot of average results and a few outliers - what is referred to as a "bell shaped" distribution curve as represented by the gold line in the following graph:

click on picture for a larger image

The Unexpected

Do you see that really big block on the right?  That represents all the years where there was greater than a 28% gain.  And the big block on the left?  Those are all the times where the market lost more than 16%.  They both represent a pretty wild roller coaster ride ... and they happen a lot ... at least a lot more than "average" returns happen.

We call this a "fat tail" distribution curve as there are a lot of results that are at the "tail end" of the curve.

The thing is that while history is full of examples of years when returns were not average ... most people expect them to BE average.  Your brain wants average to be normal and anything that isn't average is supposed to be rare.  Unfortunately, that means a lot of people are surprised a lot of the time.  That creates stress and (often) poor financial and investment choices.

Fat Tails and Your Wealth

Besides the psychological damage that is done to investors over and over as results don't meet expectations, much of portfolio theory is built on the assumption that the stock market is a "random walk" and follows a traditional, bell-shaped distribution.

This is important to understand the next time the market goes into a tailspin (which it is likely to do again soon) and your investment portfolios and retirement accounts plummet with it.  It isn't anything unusual.  The market isn't punishing you.  The market is acting normal.  Your portfolio and how it is constructed is where the problem is.

Investment Solutions

There are a couple lessons to be learned from all of this.  The first is that your investments are exposed to more risk than you probably realize.  While we have statistics like standard deviation and semi-variance to describe risk, those numbers mean nothing to your psyche. Even if you could really get your head around those numbers, your brain circuitry will most likely discard the feedback and just expect to see the average anyway.

Secondly, most portfolios are put together by advisors who are completely ignorant of tail risk, that it exists or that it could really wreak havoc on your ability to build wealth.  Your portfolio needs to have some kind of hedge against tail risk - at least tail risk to the down side.  That hedge can be in the form of stop loss orders, futures, options or some kind of insurance contract.

Talk to a fiduciary investment professional about what kind of hedges they recommend.  If they recommend global asset allocation, they're better than most advisors but they still could do more to protect your wealth ... and meet your expectations (as unrealistic as those may be from time to time).

Now if you'll excuse me, I have a new bathing suit I want to try on.

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Comments (2)
1 Wednesday, 12 May 2010 14:46
Brett Anderson
Thank you for the very good piece. I'm trying to reconcile the graph above: you note that "A loss of 8% to 12% happened 8% of the time as did a gain of 16-20% or 24-28%", however the bars for those various returns look to be of very different lengths. And the vertical axis is a 0-100 scale versus a percentage-of-time-scale. I know I'm missing something, just need to know what!? Thanks again.
2 Thursday, 03 June 2010 16:43
John D. Buerger, CFP®
Hi Brett -

Thanks for the comment. The vertical axis represents the number of occurrences in the sample. There were about 440 data points in the sample. Each of the result marks mentioned showed 31-35 instances. Note that I did not include the 20-24% gain in that note since there were only 20 instances of that result. Hope this helps.

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Last Updated on Wednesday, 12 May 2010 01:32