Correlation and causation

In simple terms

Two things are correlated when they tend to move together. Share prices of two banks often rise and fall on the same days; a company's sales and its profits usually grow together. Correlation is measured with a number, the correlation coefficient, which runs from −1 to +1.

Causation means one thing actually makes the other happen. Correlation can be a clue to causation, but it is never proof of it.

Seeing correlation in numbers

Why correlation is not causation

When two things move together, there are several possible explanations besides "A causes B":

1. A third factor drives both. Ice cream sales and drownings both rise in hot weather. In markets, falling interest rates can lift both property prices and share prices without either causing the other. This hidden driver is called a confounding factor.
2. The cause runs the other way. Companies with rising share prices often announce more acquisitions; the acquisitions did not necessarily cause the rise. The rise may have made the acquisitions easier.
3. Coincidence. With thousands of economic and market series available, some will line up by pure chance. Claims like "the market has risen every year that X happened" are often coincidences found by searching through many possibilities.

Only careful reasoning about how one thing could affect the other, and testing on new data, gets you closer to cause.

Small samples mislead

Correlations calculated from a handful of data points are unreliable. If you take two completely unrelated random series of just five numbers each, simulations show that roughly one pair in ten will show a correlation stronger than 0.8 in one direction or the other, purely by chance. A "strong relationship" seen over five years, or five events, may be nothing at all. The more data, and the more it covers different conditions, the more a correlation can be trusted.

Correlations change, especially in a crisis

Investors spread money across different investments partly because they do not all move together. That is the idea behind diversification. But correlations measured in calm periods are not fixed. In a panic, many investments are sold at once, by people who need cash or want to reduce risk, and correlations that looked low can jump towards +1. Diversification still helps, but less than calm-period numbers suggest, exactly when it matters most.

Why it matters

Financial news and marketing are full of claims built on correlation: a sector that "always" rises before elections, an indicator that "predicted" the last three crashes, a stock picker whose choices "beat the market" during a rising year. Asking what else could explain the pattern, and whether it has held in data it was not chosen from, is one of the most useful habits an investor can build.

Limitations

• The correlation coefficient measures straight-line relationships. Two things can be strongly related in a curved or occasional way and still show a low coefficient.
• A correlation over a whole period can hide very different behaviour in parts of it.
• Correlation describes how things moved together, not by how much. Two shares can be highly correlated while one moves twice as far as the other.

Common mistakes

• Treating correlation as cause without considering a third factor, reverse causation or chance.
• Trusting patterns from a few data points.
• Assuming correlations measured in calm markets will hold in a crisis.
• Searching through many possible indicators and believing the one that happened to fit best.

Try it yourself

1. Think of a claim you have heard, such as "markets rise when the monsoon is good". List one possible confounding factor, one way the cause could run the other way, and how you would test it with data.
2. In a spreadsheet, enter the monthly returns of two shares for a year and use the CORREL function. Then calculate it for only the first five months. How different are the results?