Direction and magnitude are different
A correlation coefficient ranges from −1 to +1. Positive values indicate a tendency to move together relative to their means; negative values indicate opposite movement. A value near zero indicates little linear relationship in that sample. It does not prove the variables are independent.
Correlation also does not measure the size of returns. Two series can have the same correlation relationship while one varies much more than the other. Comparing dollar prices rather than returns can introduce another mismatch. State the measured series and frequency.
Two fictional offsetting return series
Suppose A has period returns of +2%, −2%, +4% and −4%. B has −2%, +2%, −4% and +4%. In this constructed sample, they move in exactly opposite directions with equal magnitudes. A hypothetical portfolio reset to equal weights before each period would have a zero return each period before costs.
That example is deliberately artificial. Without rebalancing, weights change through time. In real markets, exact opposite behavior should not be assumed to persist. Rebalancing costs, income and changing conditions can alter the combined path. The example explains a relationship, not a readily available hedge.
Why co-movement matters
Portfolio variation depends on both the variation of its components and how they move together. Adding another volatile asset does not automatically increase total variation by its standalone amount. Its relationship with the rest of the portfolio matters.
Covariance includes the scale of the series’ variation, while correlation standardizes the relationship. A portfolio model needs more than a correlation table to calculate risk. It also needs weights, volatility estimates and a consistent set of observations.
A measured relationship can change
Correlations depend on the chosen dates and observation frequency. Different economic conditions can change how investments respond to common shocks. A low correlation over one quiet interval is not a guarantee of protection in a later crisis.
When you see diversification claims based on correlation, check the universe, window, return convention and economic explanation. Ask what happens if the relationship weakens. Treat the estimate as evidence to stress-test, rather than as an unchanging property attached to a ticker.
Does zero correlation establish that two investments can never lose money at the same time?
Show the explanation
No. It describes a lack of linear association in the measured sample. Joint losses, nonlinear relationships and different future behavior remain possible.
Sources and editorial notes
Original explanations and hypothetical examples prepared with AI assistance. Primary references checked October 16, 2026. Numerical examples are hypothetical unless explicitly identified otherwise.
- CFA Institute: Portfolio Mathematics
Covariance, correlation and portfolio return/risk calculations; original numerical examples.