Tools · Correlation
Diversification is a moving number.
A single correlation figure describes a whole period as though it were one thing. Rolling it through time shows something more useful: whether two series held apart when it mattered, or converged exactly when they were needed not to.
Calculator
This page is showing two example series. Their correlation over the whole period is 0.85, rolled over 12-month windows below. Enable JavaScript to paste your own; the table, chart and method on this page do not need it.
Both series must have the same number of months, and at least one more month than the window.
- Correlation
- 0.85
- whole period
- Highest rolling
- 0.94
- over the windows
- Lowest rolling
- 0.77
- over the windows
The axis runs from −1 to +1. The zero line is where the two series stopped having any linear relationship at all; distance from it in either direction is a relationship, not a quality.
| Statistic | Example series |
|---|---|
| Months in both series | 36 |
| Correlation, whole period | 0.85 |
| Rolling window | 12 months |
| Rolling windows | 25 |
| Highest rolling correlation | 0.94 |
| Lowest rolling correlation | 0.77 |
| Latest rolling correlation | 0.93 |
Method
How it is calculated.
Pearson correlation over the whole period, and the same calculation repeated on each window of the length you choose.
The coefficient
ρ = Σ(a − ā)(b − b̄) ÷ √(Σ(a − ā)² Σ(b − b̄)²)
Each series is measured against its own mean, so ρ is unaffected by the level of either series. It runs from −1 to +1 and needs at least three paired observations to mean anything.
The rolling version
Each point on the chart is the correlation of the preceding window only. The first point appears once the window is full, so a 12-month window over a series of n months gives n − 12 + 1 points. A shorter window reacts faster and is noisier; a longer one is steadier and late.
Limits
What correlation does not tell you.
- It measures a linear relationship only. Two series can be strongly related and still show a correlation near zero if the relationship bends — which is exactly what happens when one of them has an asymmetric payoff.
- It is an average over the window, so it hides the tails. Series that behave independently most of the time and fall together in stress can show a comfortable long-run figure. The rolling view exists to make that visible.
- The window choice changes the answer. A short window over a quiet stretch can produce a dramatic-looking figure from very little information.
- Correlation is not causation, and it is not stability. A pair that has held apart for years can converge in a week, and a single correlation figure gives no warning of it.
This calculator is provided for general information only and is directed to wholesale and professional investors. It is not personal advice: it does not take into account the objectives, financial situation or needs of any person, and it is not an offer, invitation or recommendation to acquire any financial product. Investing involves risk, including the possible loss of capital. Past performance is not a reliable indicator of future performance.
Definitions
Terms on this page.
Each links to the glossary entry, which states the convention the term assumes as well as what it means.
- Correlation — how closely two series have moved together.
- R² — the square of it, and what a benchmark explains.
- Benchmark — the series a portfolio is measured against.
- Volatility — what correlation does not measure.
Questions
Common questions.
Is anything I paste sent to KyperX Capital?
No. Both series are parsed and the correlations calculated in your browser. Nothing is transmitted, recorded or stored, and this website receives none of it.
What is a good correlation between two holdings?
There is no universal answer, because it depends what each holding is there to do. A lower figure means the two have tended to move apart, which is the point of holding both; it does not mean either is worth holding. What usually matters more is how the pair behaved in the worst windows, which the rolling chart shows and a single figure does not.
Why does my rolling correlation jump around so much?
Short windows contain few observations, so each new month has a large effect and one unusual month can move the figure sharply. Lengthen the window to see whether the movement is a change in relationship or noise.
Why does correlation rise in a crisis?
Because in stress, positions are often sold for reasons that have nothing to do with what they are — liquidity, margin, redemptions — so things that are otherwise unrelated move together. It is the reason diversification measured in calm conditions can be misleading about the conditions it is meant for.