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Spurious correlations and the causation mistake

For the past twelve years, there has been a strong correlation between the average age of hedge-fund managers and the spread between large-cap and small-cap stock returns. Both have trended upward. A data scientist at a wealth-management firm notices this pattern and writes an analysis suggesting that younger hedge-fund managers have preference for small-cap stocks, driving the spread. An investment committee reads this, becomes bullish on small-cap exposure, and adjusts portfolio positioning.

This story illustrates the spurious-correlation problem in equity analysis. Two variables move together. An analyst observes the correlation, assigns causation, and builds an investment thesis. The reality is that both variables moved together due to a third factor (time, in this case) or pure coincidence. The causation story is invented, not discovered.

The mistake is nearly universal because the human brain is a causation-finding machine. We see pattern and we assign mechanism. In professional settings, this pattern-finding is dressed up in regression analysis and statistical language, but the fundamental mistake remains: seeing correlation and assuming causation.

Quick definition​

A spurious correlation is a statistical relationship between two variables that appears to exist but is not genuinely causal. Two variables can be correlated because (1) one causes the other, (2) a third variable causes both, (3) there is reverse causation, (4) the relationship is purely coincidental, or (5) the correlation is an artifact of the sample or time period studied.

Analysts often assume (1) when the data shows (2), (3), (4), or (5).

Key takeaways​

  • Correlation is easy to find, causation is hard to prove: With thousands of metrics available for analysis, you can find correlations between nearly any two series—some genuine, most spurious.
  • Reverse causation is common and invisible: Stock price moves cause analyst revisions, not the other way around, yet the regression looks the same.
  • The third variable problem: Two metrics correlate because both are driven by a common cause. The analyst attributes causation to the wrong mechanism.
  • Sample period bias disguises randomness: A strong correlation from 2005–2015 may be pure noise; expanding the sample period to 2000–2020 reveals no relationship.
  • Publication bias hides the failed correlations: Analysts publish the correlations that work and bury the ones that do not. The visible correlations are a biased sample.

Why analysts fall into the trap​

Financial analysis is inherently causal thinking. An analyst reads quarterly results and concludes: "Margin expansion drove earnings beats; this is a sign of operational improvement." This chain of reasoning requires an assumption of causation. But what if margin expansion was driven by lower input costs, which were temporary? Then the causal story (the company is improving) is incorrect.

The causal mistake is easier to make in equity analysis than in controlled experiments because you cannot rewind time and run the scenario differently. You observe the world once. If margins expanded in the same quarter that management launched a cost-reduction initiative, it is hard to prove whether the initiative caused the margin expansion or whether lower commodity prices (which would have expanded margins regardless) were the true driver.

This ambiguity is where analyst intuition fills in. The manager led a cost initiative, margins expanded, and the analyst assigns causation. This is sometimes correct, but often wrong.

In quantitative analysis, the problem is magnified. A quant analyst with access to hundreds of data points and a regression engine can test thousands of relationships. If you run 1,000 regressions testing different pairs of variables, some will show strong statistical correlation by pure chance. The analyst who reports the ones that worked—and ignores the 900+ that did not—has created a spurious relationship.

This is the multiple-comparisons problem: when you run enough tests, you will find statistical relationships that are not real. The analyst who knows this and adjusts their significance threshold is careful; the analyst who does not knows only that the p-value is less than 0.05, so the result "looks significant."

The reverse-causation trap​

One of the most subtle forms of spurious correlation is reverse causation. The analyst observes that companies with high management ownership outperform the market. The causal story: aligned management is motivated to create shareholder value. But the reverse causation is equally plausible: companies that have outperformed the market and created shareholder value gain the ability to use stock-based compensation, which increases management ownership. The stock price caused the ownership structure, not the other way around.

Or consider this: analyst upgrades are followed by stock outperformance. One causal story: the upgrade contains new information that drives the stock higher. But the reverse story is equally valid: the stock has already begun to outperform; the analyst notices this and upgrades to catch up. The stock movement caused the upgrade, not the other way around.

Identifying reverse causation requires thinking about the temporal chain of causation. Did the low analyst coverage cause the stock to underperform, or did the underperformance (due to some other factor) cause analysts to ignore the stock? These are not the same question, and they have different trading implications.

In practice, reverse causation is often overlooked because analysts do not explicitly consider it. The correlation is presented; a causal story is assumed; the thesis is built. By the time reverse causation is considered, the thesis is defended and capital has been allocated.

The third-variable problem​

Many correlations that appear to be direct causal relationships are actually mediated by a third variable. Consider this: companies with high capital expenditure tend to have higher earnings growth. An analyst concludes that capex drives growth. But capex and growth are both consequences of a third variable—the company is in a high-growth industry. In low-growth industries, capex does not produce growth; it is just a waste of capital.

If the analyst does not control for industry, the correlation is spurious. The causal mechanism (capex → growth) is wrong. The truth is (high-growth industry → capex and growth).

This problem is ubiquitous in fundamental analysis. Young companies tend to have high volatility and high growth. Does the volatility drive the growth, or does the growth (inherent in being young) create volatility? An analyst who attributes causation to volatility and predicts that high-volatility stocks will grow faster is missing the third variable: the company's life cycle stage.

Similarly, companies with high debt tend to have high ROIC. Does leverage drive ROIC, or does the market restrict leverage to high-ROIC companies? The correlation is real; the causal direction is wrong. If you try to improve returns by leveraging low-ROIC companies, you will fail. The leverage is a symptom of quality, not a driver of it.

Controlling for the third variable—through multivariate regression or stratified analysis—is the standard solution. But it requires the analyst to know which third variables to test. If you do not think to control for industry, you will miss the issue. If you do not think to control for company life cycle, you will make incorrect causal inferences.

How time period selection creates spurious correlations​

If you search across enough time periods, you will find correlations that do not exist in the broader historical context. A metric might correlate with stock returns from 2010–2015 due to some coincidental alignment of cycles. Expand the sample to 2000–2020 and the correlation disappears.

This is called data snooping. When a researcher tests many hypotheses across overlapping time windows, some will appear significant by pure chance. The analyst who finds the 2010–2015 correlation, publishes it, and uses it to guide investment decisions, without checking whether the relationship holds in other periods, has been misled by sample bias.

The antidote is out-of-sample testing: if your hypothesis is that Variable X predicts Variable Y, verify that the relationship holds in a time period different from the one in which you discovered it. An analyst who discovers a correlation from 2010–2015 should test whether it predicts returns from 2015–2020. If it does not, the original correlation was spurious.

Yet many analysts (and quants) do not have the discipline to do this. They find a correlation, build it into a model, and deploy it. When the relationship breaks down out-of-sample, they are surprised.

Real-world examples​

The small-cap value premium: For decades, academic research showed that small-cap value stocks outperformed large-cap growth stocks. The correlation was clear, and the causal story was intuitive: value investors buy cheap stocks; cheap stocks offer higher returns. But from 2010–2020, the relationship inverted. Small-cap value underperformed. What had changed? The correlation was real, but the causal mechanism was incomplete. The reason value worked from 1980–2010 was partly the rise of passive investing concentrating capital in large-cap growth. As passive investing accelerated, the causal mechanism (capital flows into growth, away from value) reversed the historical relationship. Analysts who attributed the outperformance to some inherent value-stock superiority, rather than to the causal mechanism of how capital was being allocated, were shocked by the reversal.

Technical analysis and causation: Some technical analysts observe that when a stock breaks above a moving average, it tends to continue rising. The correlation is real (at times, in some markets, in some time periods). The causal story: breaking above the moving average is a "signal" that unlocks buying pressure. But the reverse causation is equally valid: the stock is already rising (due to fundamental reasons), and when it breaks above the moving average, that is just a lagging indicator of the move that has already begun. The moving average did not cause the move; the move caused the moving average to be crossed.

Management ownership and outperformance: A study of public companies shows that those with high management ownership outperform. An intuitive causal story: aligned management works harder, creating value. But the reverse causation is strong: successful, growing companies attract owner-operators who take larger stakes; unsuccessful companies lose talented managers to other opportunities. If the causation runs from success to ownership (not ownership to success), then buying high-ownership companies does not generate alpha; it just identifies companies that are already successful.

Analyst revisions and stock performance: Every quarter, stocks that see analyst upgrades tend to outperform. The correlation is undeniable. The intuitive causal story: analyst upgrades contain new positive information. But research by Dreman and Berry found that much of the outperformance occurs before the upgrade, suggesting that analysts are following the stock price up, not leading it. The causation runs from stock price to analyst, not the reverse.

Common mistakes​

Mistake 1: Observing a correlation and assuming a single causal mechanism without considering alternatives. A metric correlates with returns. This could be causal, reverse-causal, mediated by a third variable, or spurious. Test all four possibilities before committing to a thesis.

Mistake 2: Building a thesis on a correlation without testing it out-of-sample. If your hypothesis is that high analyst coverage causes stock underperformance, test it on historical data from a period you did not use to discover the correlation. If the relationship breaks down, the original correlation was spurious.

Mistake 3: Confusing statistical significance with practical significance. A correlation might be statistically significant at the 5% confidence level but practically meaningless—explaining only 1% of the variance in returns. A statistically significant relationship might be too weak to be useful in actual trading.

Mistake 4: Ignoring confounding variables. When testing whether Variable X predicts Variable Y, control for obvious third variables that might drive both. If you do not, you risk attributing causation to X when the true driver is Z.

Mistake 5: Presenting historical correlations as forecasts without acknowledging regime change. A ratio correlated with returns for the past ten years might be uncorrelated in the next ten years if the market regime changes. Fundamental market structure changes (passive vs. active allocation, interest-rate regime, volatility regime) can break correlations that held historically.

FAQ​

Q: How can I distinguish between a genuine causal relationship and a spurious correlation?

A: Use three filters. (1) Does it make economic sense? Can you articulate a plausible mechanism by which X causes Y? (2) Does the correlation hold across time periods and sub-samples? If it only exists in 2010–2015, it is suspect. (3) Is there evidence of reverse causation? If Y could plausibly cause X, test that direction as well. If all three filters pass, the relationship is more likely to be causal.

Q: Can statistical tests like regression prove causation?

A: No. Regression can estimate the strength of correlation and test whether a relationship is likely due to chance. It cannot prove causation. Only randomized experiments (or very carefully designed natural experiments) can provide causal proof. In financial markets, such experiments are rare, so most causal claims are educated guesses, not proven facts.

Q: If I discover a correlation, should I assume it does not work because of reverse causation?

A: No. Assume it could work, but test it. Build it into a model, run it out-of-sample, and see if it predicts. If it does, use it. If it does not, abandon it or investigate why the relationship has changed. Do not assume reverse causation without evidence; instead, assume you do not know which direction the causation runs until you test.

Q: How do I control for third variables in my analysis?

A: Use multivariate regression or stratified analysis. Run a regression that includes both your proposed causal variable and potential confounding variables. If the causal variable remains significant after controlling for confounds, the relationship is more likely to be genuine. Or, divide your data by the suspected confound (e.g., by industry) and test whether the correlation holds within each stratum.

Q: Is correlation ever sufficient for making an investment decision?

A: Yes, if you acknowledge the uncertainty about causation. You can build a mean-reversion trading strategy on the correlation between a stock and its historical range without knowing the causal mechanism. But for fundamental valuations and long-term thesis development, causation matters. A thesis built on spurious correlation will break when the correlation breaks.

Q: What is the difference between finding a correlation and a factor in a factor model?

A: A factor in a factor model is a variable that predicts returns systematically across time and sub-samples, often with an economic mechanism. Not every correlation is a factor. Many researchers confuse the two, taking a correlation from a particular time period and calling it a "factor" as if the name implies durability. True factors (like value, momentum, quality) are correlations that have held across decades and geographies. Test thoroughly before calling something a factor.

  • Confounding variable: A third variable that drives both the independent and dependent variable, creating a spurious relationship.
  • Selection bias: When the sample of data is not random, correlations within that sample can be misleading. Survivorship bias is a form of selection bias.
  • Granger causality: A statistical test that checks whether past values of X help predict Y beyond Y's own history. Useful but not proof of causation.
  • Natural experiments: Real-world events that affect some entities but not others, allowing causal inference without randomization.
  • Regime change: A shift in fundamental market structure that breaks historical correlations, often due to changes in policy, technology, or market composition.

Summary​

Correlation and causation are not the same. Yet analysts constantly observe two metrics moving together, assign a causal story, and build an investment thesis. The mistake is understandable—causal thinking is natural—but expensive.

Before committing to a thesis based on a correlation, ask: (1) Is the causal mechanism plausible? (2) Could the causation run in reverse? (3) Is there a third variable driving both? (4) Does the correlation hold across different time periods and sub-samples? (5) Is the relationship statistically significant or practically meaningful?

The investor who is careful about distinguishing correlation from causation will avoid chasing spurious relationships and will be more selective about the theses they build. The investor who treats every correlation as causal will be repeatedly surprised when market conditions change and the correlation breaks.

Next​

Read the next article: Survivorship bias in analyst datasets.