Correlation between stocks and why it moves

Correlation measures how closely the returns of two investments move together. It ranges from -1 to +1, and it is the number that decides how much diversification you actually get from owning both. It matters because holding many stocks does not reduce risk much if they all respond to the same forces, and because correlations are less stable than most people assume.

What the number means

Correlation(A, B) = Covariance(A, B) / (sigma_A x sigma_B)

• +1 means the two returns move in perfect lockstep (in the same direction, in proportion).
• 0 means there is no linear relationship between their returns.
• -1 means they move in exact opposite directions.

Three points are easy to miss. First, correlation is calculated on returns, not on prices. Two stocks whose prices both trend upward over time can look highly related by price while their day-to-day returns are only loosely connected. Second, correlation measures direction, not size: a stock can have a correlation of 0.9 with the market and still move much more or much less than the market does. Third, a correlation of zero does not mean the stocks are independent, only that no straight-line relationship shows up.

Correlation and beta

Beta is correlation scaled by relative volatility:

Beta = correlation(stock, market) x (sigma_stock / sigma_market)

Example (illustrative numbers): a stock has a correlation of 0.8 with the market, an annual volatility of 30%, while the market's is 15%. Its beta is 0.8 x (30 / 15) = 1.6. Two stocks can have the same correlation and different betas, and the reverse.

Typical patterns

The size of correlations varies by period and by data frequency, but some patterns are common:

The sector labels used in the GICS sector system are a useful first guide to which stocks tend to share drivers, though companies in the same sector are not identical.

Why correlations move

Correlations are estimates from past data, and they shift for real reasons:

• The dominant driver changes. In some periods interest rates drive most stocks; in others, company earnings do. When one macro force dominates, correlations rise.
• Stress raises correlations. In sharp selloffs, investors sell broadly to raise cash or cut risk, and many holdings fall together. This tendency is why diversification disappoints when it is needed most.
• Businesses change. A company that expands into a new line may start to move with a different group of stocks.
• Measurement choices matter. Daily returns, weekly returns, and monthly returns give different correlations, and so do different windows. Short windows are noisy.

Why it matters for your portfolio

The benefit of diversification comes from holdings that do not move in lockstep. If you add a stock with a correlation of 0.9 to what you already own, you have added little diversification. Adding one with a lower correlation helps more, though a low past correlation is not a promise about the future.

Correlation also affects how you interpret a position count. Four stocks in the same sector may behave like one or two larger positions during a downturn. See position sizing for how to think about that.

Common mistakes

• Treating a historical correlation as a constant. It is an average over a past window and can change quickly.
• Assuming a low correlation is a hedge. Low correlation means less co-movement on average, not an offset that pays when the other holding falls.
• Confusing correlation with causation. Two stocks can move together because of a third factor, or by coincidence in a short sample.
• Mixing up correlation and beta. Correlation tells you how tightly returns are linked; beta tells you how much one moves per unit of the other.
• Ignoring tail behavior. A pair that looks only moderately correlated in normal times can still fall together in a crash. See drawdown and risk measures.

Where to see it on StocksXray

Each stock page lists peers, and companies in the same sector often share drivers. The comparison page for Apple and Microsoft is a way to place two large technology companies side by side. Checking sector overlap among your holdings is a practical first step.

Key takeaways

• Correlation of returns ranges from -1 to +1 and sets how much diversification two holdings provide.
• It differs from beta, which also depends on relative volatility.
• Stocks in the same industry usually move together more than stocks in different sectors.
• Correlations are unstable and tend to rise in market stress.
• Treat any measured correlation as a rough guide, not a fixed property.