Correlation Is Not Causation
What it does and doesn't mean when two things move together, why coincidences are so common in market data, and the questions that separate a real relationship from an accident.
The short version
When two things move together there are four possible explanations: the first causes the second, the second causes the first, something else drives both, or it's chance. Market data makes chance far more likely than it feels. Anything that trends will look related to everything else that trends. With enough indicators to choose from, some will fit the past by luck. One extreme year can create a correlation out of nothing, and a relationship that held for twenty years can reverse. A correlation is a reason to ask questions. The ones that matter are whether there's a mechanism, how many other things were tried, and whether the pattern holds in data it wasn't found in.
By the end of this lesson, you'll be able to
- List the four explanations for a correlation and apply them to a claim about markets
- Explain why trends, many comparisons, small samples, and outliers produce correlations by chance
- Test a claimed relationship with questions about mechanism, selection, and out-of-sample evidence
Why this matters
Correlation, Plainly explained what correlation measures and how investors use it to build steadier portfolios. This lesson is about a different use, and a riskier one: treating a correlation as evidence that one thing drives another, and so as a way to predict. Investing is full of such claims. This indicator predicts the market. Shares with this feature outperform. Many of them rest on a pattern in past data, and a pattern in past data can mean far less than it appears to.
Four explanations
Suppose two things, A and B, have moved together. There are four ways that can come about.
| Explanation | Example of a claim | What might really be going on |
|---|---|---|
| A causes B | Lower interest rates raise the value of future profits | A real mechanism, set out in Time Value of Money and Discount Rates |
| B causes A | Companies that buy back shares see their prices rise | Companies may buy back shares because business is going well, and the price would have risen anyway |
| Something else causes both | Two retailers' shares always move together, so one must lead the other | Both respond to the same consumer spending and the same market |
| Chance | The market has risen in every year this indicator flashed | With enough indicators, one will fit by luck |
Only the first makes A useful for predicting or changing B. The rest of this lesson is about why the fourth is so much more common than intuition suggests.
Things that trend look related
Take any two things that have mostly risen over the same decades, such as a share index and the cost of living. They'll have a high correlation, and it tells you nothing about either.
To show how strong this effect is, we generated 100 series of random numbers for this lesson, each standing for 20 yearly changes, with no connection between them. Then we compared every series with every other one, 4,950 pairs in all.
| Comparing yearly changes | Comparing running totals | |
|---|---|---|
| Pairs with a correlation beyond ±0.5 | 119 (2.4%) | 1,765 (35.7%) |
| Pairs beyond ±0.7 | 2 | 719 (14.5%) |
| Pairs beyond ±0.9 | 0 | 34 |
| Strongest correlations found | +0.72 and −0.66 | +0.95 and −0.97 |
A running total is each series added up year by year, the way a price is the sum of its past changes. The yearly changes were random and mostly uncorrelated, as they should be. Their running totals look strongly related in more than a third of all pairs, and 34 pairs have a correlation beyond 0.9. Nothing connects any of them.
The practical rule: compare changes, not levels. If someone shows that two prices or two indexes have a correlation of 0.9, ask whether that's between the levels or between the yearly or monthly changes. Only the second means anything.
The rest of this lesson is for members
Still to come in this lesson: Looking at many things, Short records and single events, Relationships that change, Questions for any claimed pattern, the key takeaways, and 2 quiz questions with explanations.
Membership opens every lesson in the curriculum, the capstone projects, the interactive tools, and the members-only channels in the Hyperion Entities Discord. The first lesson of every module stays free.
Go deeper
- Present Value and Future Value FormulasMath and Statistics for Investors (depth track)
- Correlation, PlainlyPart 5: Building a Portfolio
- Contrarian and Factor InvestingPart 6: Strategy, Behavior, Accounts, and Taxes
- Overconfidence, Recency, and Narrative BiasPart 6: Strategy, Behavior, Accounts, and Taxes
Notes and sources
- Aswath Damodaran, NYU Stern School of Business. Historical Returns on Stocks, Bonds and Bills, with annual data through 2025 (updated January 2026). Checked 2026-10-12.