What is Correlation? Definition, Formula, and Example
Correlation is a statistical measure of how two assets move in relation to each other, ranging from -1 to +1.
What is Correlation?
Correlation is a statistical measure of the degree to which two assets move in relation to each other. It ranges from -1 to +1. A correlation of +1 means the assets move perfectly in the same direction; -1 means they move perfectly in opposite directions; 0 means there is no linear relationship. Traders use correlation to understand diversification, manage portfolio risk, and build pairs trades. It is distinct from causation: two assets can be highly correlated without one driving the other.
How Correlation is Calculated
The Pearson correlation coefficient between two assets X and Y is:
ρ(X,Y) = Cov(X,Y) / (σX × σY)
where Cov(X,Y) is the covariance of the two return series, and σX and σY are their standard deviations. Using daily returns over n periods:
ρ = Σ((Xᵢ − X̄)(Yᵢ − Ȳ)) / sqrt(Σ(Xᵢ − X̄)² × Σ(Yᵢ − Ȳ)²)
The result is bounded between -1 and +1. Rolling correlations are typically calculated over 20, 60, or 120 trading days to capture changing relationships.
Worked Example
Consider daily returns for AAPL and MSFT over 60 trading days. The covariance of their daily returns is 0.0004, the standard deviation of AAPL returns is 0.02, and the standard deviation of MSFT returns is 0.025.
ρ = 0.0004 / (0.02 × 0.025) = 0.0004 / 0.0005 = 0.8
A correlation of 0.8 indicates a strong positive relationship. On days when AAPL rises, MSFT tends to rise as well. A trader holding both stocks is not well diversified between them, because both names are exposed to similar technology-sector risk factors. If the trader adds GLD, which has a 0.2 correlation with AAPL, the portfolio’s overall correlation structure improves.
When Traders Use It
Correlation is used in portfolio construction to limit concentration risk, in pairs trading to identify mean-reverting spreads, and in risk management to estimate portfolio value at risk. It also underlies index construction and dispersion trading. During market stress, correlations often converge toward 1, reducing the benefits of diversification. Traders monitor rolling correlation to detect regime changes. the live scanner
Limitations and Common Misconceptions
Correlation measures only linear relationships and can miss non-linear dependencies. It is also time-varying; a high historical correlation does not guarantee future co-movement. Correlation does not imply causation, and two assets can move together because of a common third factor rather than a direct link. During crashes, correlations often spike even when fundamentals diverge, which can surprise traders who relied on historical diversification. Rolling window choice also materially affects the reading.
Related Terms
beta, covariance, diversification, pairs trade, implied correlation