Causality and Statistics Traps in Investing
Every day you make decisions based on past data. What to eat for breakfast. How to approach your boss with a question. You look at what happened before and try to predict what will happen next.
The problem is, humans are pretty bad at this. Not always. But often enough to cause real damage, especially when money is involved.
Chapter 12 of Burton and Shah’s book is about the statistical traps our brains fall into. These are not exotic edge cases. These are mistakes you and I make every single day. And in financial markets, they cost real money.
Representativeness: When Stereotypes Overpower Math
Here is a classic experiment from Kahneman. Subjects were told about a guy named Tom W., a graduate student. First, they were asked to rank which department he is most likely in. Without any other info, people correctly ranked by department size. Humanities and Education is the biggest department, so Tom is most likely there. Makes sense.
Then they got a personality description. Tom is smart but not creative. Likes order and tidy systems. Writes in a dull, mechanical way. Enjoys sci-fi. Not great with people.
And people completely flipped their rankings.
Suddenly everyone said Tom must be in Computer Science or Engineering. Small departments. But here is the thing. Even after factoring in Tom’s personality, the math says he is still twice as likely to be in Humanities and Education than in Computer Science. Why? Because that department is just so much bigger. Even if a smaller percentage of Humanities students match Tom’s personality, the raw numbers still win.
But people ignored the base rates entirely. They heard “nerdy, likes order, reads sci-fi” and thought “must be computer science.” The stereotype took over.
This is called representativeness. You judge something by how much it looks like a category, and you forget about the actual probabilities.
In investing, this shows up everywhere. A stock is going up fast. It must be a tech company with strong earnings, right? Maybe. But statistically, most stocks that go up fast are just… stocks. The boring base rate matters more than the exciting narrative.
The Conjunction Fallacy: More Details, Less Likely
This one is wild. Same Tom W. experiment, but now people are asked to rank two statements:
- Tom W. is an avid gardener.
- Tom W. is an avid gardener and enjoys playing World of Warcraft.
Most people said the second statement is more likely than the first.
Stop and think about that. The second statement includes the first one plus an extra condition. It can never be more probable. Every person who is both a gardener and a WoW player is also a gardener. So “gardener” by itself is always at least as likely.
But our brains don’t work that way. People read “avid gardener” and think “nah, doesn’t sound like Tom.” Then they read “avid gardener AND plays World of Warcraft” and the WoW part feels so right that it pulls the whole statement up. They focus on the part that fits the stereotype and ignore the conjunction.
Kahneman and Tversky called this the conjunction fallacy.
For investing, imagine a stock that had a great year. Which group does it belong to?
- All common stocks.
- Technology stocks with very strong earnings.
The second group sounds more satisfying, more specific, more “right.” But it is a subset of the first group. The correct answer is always the broader category. Yet many investors pick the narrower one because it tells a better story.
Reading Into Randomness: Your Brain Finds Patterns That Don’t Exist
Your friend flips a coin ten times. Which result looks most random?
- H T H T H T H T H T
- H H H H H H H H H H
- T T T T T T T T T T
- H T T H H H H T H H
Most people say the fourth one. The first three look like obvious patterns. All heads? Alternating? Come on.
But here is the truth. There are 1,024 possible outcomes of ten coin flips, and every single one is equally likely. All heads is just as probable as any specific “random-looking” sequence. We just can’t accept that because our brains are wired to spot patterns everywhere.
And from an evolutionary perspective, this makes sense. Imagine two ancient gatherers looking at trees scattered across a field. One tries to find a pattern in where the trees grow. The other doesn’t. If there is a pattern, the first gatherer finds more food. If there isn’t a pattern, the second one gains nothing from being right. So evolution favored the pattern-seekers, even when the patterns aren’t real.
In finance, this is dangerous. Technical traders look at stock price charts and see “trends,” “support levels,” and “resistance zones.” Sometimes these are real. But often, the chart is no different from a random coin flip sequence plotted on a graph. The book shows this beautifully. If you map those four coin flip sequences as stock price movements, three of them look like obvious trends. One looks random. But they all came from the same coin.
And it gets worse. Burton Malkiel made the argument that even hedge fund track records can be explained by randomness. Start with 1,024 fund managers. Each year, about half will beat their benchmark by chance. After ten years, roughly one manager will have beaten the benchmark every single year. That manager gets on TV, writes a book, and charges 2-and-20. But their “skill” might be nothing more than surviving a coin flip tournament.
Small Sample Bias: Why Small Data Lies
Here is a fact that sounds contradictory. Smaller schools produce a disproportionate number of both the highest-achieving and the lowest-achieving senior classes. Both things are true at the same time.
How? It has nothing to do with school quality. It is pure statistics.
Think of it like coin flips again. Flip a coin four times and getting all heads has a 6% chance. Flip it twenty times and getting all heads is basically impossible, about one in a million. Small samples produce extreme results. That is just how math works.
A small school with 30 students can easily have a class that is all A-students or all struggling. A large school with 3,000 students will almost always average out.
Kahneman and Tversky called this the “law of small numbers.” People trust small samples way too much. Even scientists make this mistake. A 1962 study by Jacob Cohen showed that researchers routinely picked sample sizes so small that they had a 50% chance of their true hypothesis appearing false.
For traders, this is a real problem. You look at 10 years of earnings announcements for a stock. Sounds like a lot of data, right? But earnings come out four times a year. That is only 40 data points, and maybe 20 positive ones. Building a trading strategy on 20 observations is like deciding someone is a good basketball player after watching them take three shots.
Probability Neglect: When Scary Beats Likely
Quick quiz. What kills more people each year?
- Strokes or accidents?
- Tornadoes or asthma?
- Lightning or botulism?
Most people get all three wrong. Strokes kill more than accidents. Asthma is 20 times deadlier than tornadoes. Lightning kills 52 times more people than botulism.
Why do people get this so wrong? Because tornadoes and lightning are on the news. Asthma attacks are not. Your brain estimates probability based on how easily you can recall examples, not on actual numbers. If you can picture it vividly, it feels more likely.
Cass Sunstein calls this probability neglect. You focus on the scary outcome and forget to check how probable it actually is. When your loved one’s plane is an hour late, your mind jumps to crash images from the news. You are thinking about the numerator (number of crashes) and completely ignoring the denominator (millions of flights that land safely).
In investing, this leads to panic selling after dramatic market events and ignoring slow, boring risks that actually matter more. A headline about a market crash gets attention. The steady erosion of purchasing power from inflation does not.
Why This Matters
None of these biases are character flaws. They are features of how human brains evolved. Pattern-seeking, story-telling, shortcut-taking minds that worked great for surviving in the wild but work terribly in financial markets.
The good news from Burton and Shah is simple. Just knowing about these traps helps. You can’t eliminate them completely, but you can catch yourself. When you see a “pattern” in stock prices, ask if it could be random. When a narrative sounds too perfect, check the base rates. When a small sample gives dramatic results, remember that small samples always do.
Your brain will fight you on this every step of the way. But at least now you know what you are fighting against.
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