# Let’s face it, we’re really bad at patterns and statistics

Cognitive errors

#### The hunt for the true investment guru

Most investors are aware that the money manager or investor who has beaten their benchmarks the last year or two is considered by many to be a whiz. In looking at this question we have two thorny problems as humans. We see patterns in random data. We jump to conclusions from inadequate data.

The hunt for the investment guru is the least of our problems. The title was just to get your attention. What follows is generally applicable to every decision investors make based on data. And of course, most of our decisions are based on data; think of the performance of management, a stretch of earnings, company sales or any other metric in which human endeavor and luck are both involved.

Kahneman offers this test to his readers. Look at the following three sequences where B is the births of boys and G is the births of girls born in sequence in a hospital:

BBBGGG

GGGGGG

BGBBGB

He asks the question whether the sequences are equally likely. Look at them closely. One stands out. So, what is the answer? Are the sequences equally likely? Kahneman writes: “The intuitive answer – “of course not!” – is false. Because the events are independent and because the outcomes B and G are (approximately) equally likely, then any possible sequence of six births is a likely as any other. Even now that you know this conclusions is true, it remains counterintuitive, because only the third sequence appears random.” (Kahneman, 2011)p.115.

Now change the example slightly. Look at the same three sequences. But instead we track the investment performance of three investors. B is bad performance in the stock market – underperforming the average investor. G is good performance – outperforming the average investor performance. The first investor has a track record over six years of BBBGGG, that is, they had three bad years followed by three good years. Since our benchmark is the average performance of all investors, in any given year half will underperform and half will outperform. Our second investor had six good years!

Now the same question. Are all the sequences equally likely? Instinctively we want to say the second investor is the guru. More thought is required than the birth of boys and girls. There we agree the outcomes are approximately equally likely. As well, the birth of a boy vs the birth of a girl is completely random. Because of this, the sequences are equally likely.

It might be said that given the universe of investors, it is equally likely that any investor would be above or below average in any given year, just like the chances of a girl or boy. That would be the situation where any outperformance by an investor was simply random luck.

To assess whether our GGGGGG investor is a guru we need the help of statistics. We do not ask what the chances are of outperforming six years in a row. We also need to ignore our love of patterns. To use statistics we need enough annual data so that we can say the outperformance is statistically significant. Statistics talks in terms of being 95% sure the results are not due to pure luck, i.e. is due to skill. There are millions of investors. If we asked each one to flip a coin twenty times, we can suppose that some would get 20 heads in a row. Undoubtedly amongst the millions of investors there are a large number who have outperformed the market for twenty years purely by luck. The question is how many years of cumulative outperformance is necessary to be satisfied the performance is the result of skill. Someone has apparently figured out that a fund manager would need to beat the stock market for 36 years before we would know that his performance was based on skill rather than luck! I can’t vouch for the conclusion but I could believe it’s true.

In our hunt for the investment guru we get hit with a double whammy of cognitive errors. We see patterns in random data because we, as humans, love to find causes and patterns suggest causes. And, we jump to conclusions on the basis of statistically insignificant data, again, because we love to identify causes. So, can we learn much from a few observations? Not really. But there is a high risk that we will try. Forewarned is forearmed.

Other posts on investment psychology

This post is part of a series. Readers are invited to read Investment psychology explainer for Mr. Market – introduction This will give you a better understanding of some of the terms and ideas and give you links to other posts in the series.

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