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Lies, Damn Lies, and Statistics August 12, 2013

Posted by shaferfinancial in Uncategorized.
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Mark Twain popularized this phrase over 100 years ago, but it still has much currency today.  Neil Postman updated the idea in his chapter on “scientism” in Technopoly.  The basic idea is that statistics can be used to bolster whatever idea one is trying to push.  Most people don’t have the knowledge of statistics to counter this and just accept the statistic as is.

Average Rate of Return

The average rate of return is a generally used statistic by lay persons on blogs, financial writers, and wall street purveyers of mutual funds/ETFs and brokerage houses/insurance companies.  Recently, I have spent some of my precious time looking at blogs denouncing “permanent insurance” purchases in favor of mutual fund purchases with an asset allocation strategy.  Some of my clients regularly send me links to these blogs and ask that I “educate” those that run and post on these blogs.  Unfortunately, that is a waste of my time as I am automatically excluded from those whose opinion is important because my job and the biases it creates.  So little that I would have to say is taken seriously or even allowed to reach the general forum.  The financial ideology is such that opposing opinions can’t break through.

But if I was allowed to post and my opinion was taken seriously here is what I would point out.

You are making a fundamental [prima facie] mistake.  Until that mistake is corrected nothing you say, advice you give, analysis you offer can be useful.

You see, almost universally folks use average rate of return.  But when you use the “average rate of return” statistic for data that has negative numbers embedded, you are  overstating the return.  It’s a simple statistical concept to understand, usually covered in chapter 2 or 3 of introduction to statistics books used to teach HS and undergraduate college students.

Here’s how it works:

You invest $100,000.  The first year you lose 50% of the investment.  The second year you gain 50% on your investment.  The average rate of return on your investment is 0%.

Financial bloggers, writers, purveyors of mutual funds, etc. all report that 0% average rate of return.

The average rate of return statistic would indicate you have invested your $100,000 and two years later you have an investment worth $100,000.

Reality Bites [back hard]

Let’s run the real numbers and see how you did.

Year 1 you started with a $100,000 investment and ended with an investment worth $50,000 [100,000 X -.5].  Year two you started with an investment worth $50,000 and ended with an investment worth $75,000 [50,000 X 1.50].

What happened to the other $25,000???????

Nothing, the wrong statistic was used.  The correct statistic to use is the total return.  In the above case is was -25%.  You can then annualize total return so you can compare it to other investments that have different time ranges.  In this cash your annualized total return is -12.5% [25%/2]. This annualized annual return is called Compound Annual Growth Rate [CAGR]. Beware this is an often misused statistic too. It smooths out the variability of returns giving folks the impression that the returns are somewhat even. However this statistic can change dramatically depending on what starting date and ending date you use.
Rather than explain the math in this statistic it is easier to just use free internet calculators like this one. Click Here
Bottom line this statistic is great a comparing one investment to another in your portfolio but loses usefulness when applied to general long term returns or to try to predict what your future returns might be.

How to Fail a Statistic Test

When I taught statistics I actually used a series of questions on the first quiz that would allow students to demonstrate their understanding of this basic issue.  The majority of students would fail this quiz.  I guess some of these folks never learned this basic issue and have gone on to blog or write about financial matters!

Why This Matters

Invariably folks push their version of what is the right way to invest or save for retirement.  They always publish their opinion of what the returns have been and the expected returns should be for various strategies.  But if they use the wrong statistic that overstates historic returns [tremendously] in the strategies that they like, but doesn’t overstate historic returns for other strategies [that they don’t like] then they are lying to their readers [and probably themselves].

Bloggers and Financial Writers; Can you take their opinions seriously?

Take the most recent blog I took a look at.  This blog is dedicated to doctors’ investing.  It is typical in that the owners push investing in mutual funds/ETFs and asset allocating/rebalancing.  They also hate permanent insurance, and advise their readers to never get involved in it.  Part of the reason they hate permanent insurance is because they believe the returns inside the policy are meager compared to what they can get investing in mutual funds and that the expenses are so large as to eat up your capital.

But all over this blog is discussion and assertions of performance that use “average rate of return.”  So they are making the most basic of mistakes, a mistake that would have them flunking the first quiz in a introductory statistics course.  And ever more damning is that they then compare the “average rate of return” from the market that they expect to get with their mutual funds to the average rate of return inside whole life policies.  Whole life policies get a positive interest credit or dividend each year and never have a negative return.  So this mistake compounds, making their analysis not only wrong but misleading.  This is financial propaganda of the worst kind whether it is intentional or just ignorance.

Now these are doctors/scientist, people of high educational achievement, people who use their math skills on a daily basis to save lives, people who have to examine each case and diagnose based on statistical probability! These people are making a fundamental statistical mistake that will cost them millions of dollars!  And they are giving out financial advice to others!

What You Need to Look Out For

It is pretty simple.  Anyone that is giving you financial advise and uses “average rate of return” on market based products that go negative, instead of total return or total return annualized [CAGR] is someone that is either ignorant of his/her mistake and therefore not someone that has the ability to give advice or someone that is maliciously misleading you. RUN


1. bericm - February 13, 2014

Great advice and thanks for the post; I always get a good chuckle out of what the mutual fund industry – or what I call the Industrial Financial Complex – does with numbers.

My personal preference is for CAGR, and while it smooths out the bumpiness, it is representative of *real* growth at the end of a “period”.

(And yes, late to the party, but new the party (blogging))

2. Lies, Damned Lies, and then Statistics | The Wealth Building Society - March 30, 2014

[…] Lies, Damn Lies, and Statistics […]

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