What it means
When comparing stocks, correlation describes the extent to which their returns have moved together over a chosen period. A value near +1 means their returns tended to rise and fall together; near −1 means they tended to move in opposite directions. Near zero means little linear relationship, not necessarily no relationship at all.
Correlation has no units. Its value depends on the returns used, their frequency and the observation window. For example, a correlation calculated from daily returns over one year can differ from one calculated from monthly returns over five years. Historical correlation does not establish what will happen next.
How it is calculated
Pearson correlation compares the covariance of two return series with their individual standard deviations:
r_AB = Σ[(A_i − Ā)(B_i − B̄)] / √{Σ(A_i − Ā)² × Σ(B_i − B̄)²}
r_ABis the correlation coefficient for stocks A and B, between −1 and +1.A_iandB_iare the two stocks’ returns in the same periodi, expressed consistently as percentages or decimals.ĀandB̄are their respective average returns across the observations.Σmeans add the indicated values across all matched periods.
Use returns rather than raw share prices: two prices can trend upward together even when their period-by-period returns have little relationship. If either return series has zero variation, its standard deviation is zero and this correlation is undefined. For a basket, correlations between pairs of holdings can be combined with position weights and volatilities to estimate portfolio volatility; correlation alone does not give that volatility.
Worked example
Consider two hypothetical stocks with returns measured in percentage points over four matched periods:
| Period | Stock A | Stock B |
|---|---|---|
| 1 | +1% | +2% |
| 2 | +2% | +4% |
| 3 | −1% | −2% |
| 4 | −2% | −4% |
- Average each series. Both averages are 0%.
- Multiply each pair of deviations from its average:
1 × 2 + 2 × 4 + (−1) × (−2) + (−2) × (−4) = 20squared percentage points. - Sum the squared deviations for A:
1 + 4 + 1 + 4 = 10. For B:4 + 16 + 4 + 16 = 40. - Divide:
r_AB = 20 / √(10 × 40) = 20 / 20 = +1.
B’s returns are exactly twice A’s in this artificial example, so their correlation is perfectly positive. That does not mean they have equal volatility: B’s return changes are twice as large.
Why it matters before you trade
Adding a stock to a basket does not necessarily add much diversification. If its returns closely follow those of existing holdings, the basket may remain exposed to similar movements. Conversely, a lower historical correlation can help explain why holdings sometimes offset one another, without guaranteeing protection during a downturn.
Before placing a trade, a correlation check is most useful alongside position weights, individual volatility, sector exposures and the time period examined. Correlations can change, particularly when market conditions change. A stock can also have a low correlation with another stock while both remain exposed to a broad market decline.
How PreTrAIde uses it
PreTrAIde’s stated quantitative layer does not list a pairwise correlation calculation. Its pre-trade analysis instead checks a proposed stock basket using measures including daily volatility, 1-day 95% value at risk, portfolio breakdowns by sector, country, region, currency and market capitalization, and a Herfindahl-Hirschman concentration index. These checks provide context for basket risk, but concentration by holdings or categories is not the same measure as return correlation. PreTrAIde’s GO, NO-GO and MODIFY verdicts are decision support, not investment recommendations.
Common mistakes
- Treating +1 as equal risk: Stocks can move in lockstep but have different-sized returns, as in the example.
- Treating zero as independence: Zero correlation rules out a linear relationship in the measured sample, not every possible relationship.
- Mixing periods or data types: Compare returns from matched dates and the same frequency, using consistent treatment of dividends and corporate actions.
- Assuming a fixed number: A historical estimate can shift with the observation window or future market conditions.
- Confusing correlation with concentration: Equal sector labels do not prove high correlation, and different labels do not prove low correlation.