In recent months, I have written about common financial planning mistakes I have seen people make. As is often the case, I received several emails from readers with suggestions for more errors I could highlight. Today’s topic comes from a combination of those reader comments.

Given all the information out there about finances, why do we practitioners keep seeing some mistakes so frequently?

Today, the sheer volume of information makes it a challenge to discern what information is “good” and what to do with that information. Almost every time an error is made, I see a misunderstanding of probability, a logical fallacy, a bias, or a combination of the three.

Most people are taught little about probability and statistics in school. I won’t attempt to make up the gap here, but I will attempt to describe how failing to fully grasp basic concepts can lead to issues.

We’ll start by flipping coins. Grab a coin, a slip of paper and a pencil. The mathematics predicts that half your flips should be heads and half should be tails. Flip the coin and write down an “H” for heads and a “T” for tails. Do this twice more for a total of three flips.

I guarantee that no one engaging in this exercise had half the flips come up heads. There is nothing wrong with the mathematics of probability, yet the expected outcome is impossible.You can have zero or one or two or three but not 1½ heads.

Granted, this criticism that the expected result is impossible to achieve is a bit silly. Any odd number of flips results in the same condition. Nonetheless, I frequently see real world errors made based on similar misunderstandings. Most days you can find a story based upon the premise that because a certain result did not occur, the expectation was wrong and therefore relying on that expectation is dangerous.

I see this often with asset class comparisons. A recent example would be something like, “Academics say value stocks have higher expected returns than growth stocks, but value has lagged growth so including value in a portfolio risks falling hopelessly behind.”

In addition to the odd number of flips, another obvious flaw in our exercise is that three flips is a small sample size. Relying on a small sample seems to be a favorite of pundits, often in combination with a post hoc fallacy—because one thing happened before another, that first thing must be the cause. In the financial press, it looks something like this, “We like tech stocks here because the last five times that (fill in economic statistic here), tech stocks soared.”

We also see stories that use a reasonable description of an expectation to justify a biased conclusion. This happens when someone has an agenda. One we have been hearing for a decade or so goes something like this, “With rates low and stock valuations high, we shouldn’t expect as high a return, so clients won’t reach their goals unless they put XYZ in portfolios.”

XYZ is whatever the speaker is selling, commonly an alternative investment. It is true, of course, that rates are low and valuations high but that does not mean clients won’t reach their goals nor does it mean that XYZ would help anyway.

Another common problem with a small sample size is that all trends start with a few steps in a certin direction. The trouble is just because a few steps are taken does not mean a trend has begun.

We see a lot of investment articles that quote someone calling a change in a trend based on small sample sizes. The source will say something like, “With the dollar declining each of the last three months, XYZ is a good play for further weakness in the dollar during the balance of this year”

Sadly, we see people act on these opinions about short-term trends or streaks continuing to their detriment. For instance, they move assets to money managers profiled in the media for recent good results, ignoring weak, longer term track records, tax ramifications, or the riskiness of the manager’s strategy.

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