Correlation

What Is Correlation?

In investing, correlation describes how the returns of two assets tend to move in relation to each other. If two stocks usually rise and fall on the same days, they are positively correlated. If one tends to rise when the other falls, they are negatively correlated. If their movements show no consistent pattern, their correlation is close to zero.

Correlation is measured on a scale from -1 to +1. A value of +1 means the two assets move perfectly in step, -1 means they move perfectly in opposite directions, and 0 means there is no linear relationship. Most real-world pairs of stocks fall somewhere in between, often with moderate positive values, because many companies respond to the same broad economic forces.

How It Is Calculated

Correlation is most often calculated using the Pearson correlation coefficient, which divides the covariance of two return series by the product of their standard deviations:

correlation = covariance(X, Y) / (standard deviation of X × standard deviation of Y)

In practice, investors rarely do this by hand. Spreadsheet programs and data platforms compute it from historical returns, and the result depends heavily on the time period and frequency used, such as daily or monthly data.

Why It Matters to Investors

Correlation is central to diversification. Holding assets that are not closely correlated can reduce the overall swings of a portfolio, because losses in one holding may be partly offset by stability or gains in another. Assets that are highly correlated tend to move together, so owning several of them provides less protection than the number of holdings might suggest.

Correlations are not fixed. They can rise sharply during market crises, when many assets fall together, and shift over time as economic conditions change. Relationships that held during one period may weaken or reverse later, so past correlation is an imperfect guide to the future.

Limitations

Correlation measures only the strength of a linear relationship. It does not show that one asset causes another to move, and it can be distorted by outliers or by a short data sample. Two series can appear strongly correlated by coincidence, so investors often look at correlation alongside other measures of risk and the underlying reasons assets behave as they do.