Correlation matrix

Also seen as: correlation table; pairwise correlations.

How is correlation calculated?

Correlation is the covariance of two return series divided by the product of their standard deviations, which rescales the relationship into the fixed −1 to +1 range so any two pairs can be compared.

where $\operatorname{Cov}(A, B)$ is the covariance of the two return series, $\sigma_A$ and $\sigma_B$ are their standard deviations, $\rho_{AB}$ is the correlation coefficient, and $r^2$ is simply that coefficient squared.

What does r² add to a correlation?

r² is the correlation squared, and it says how much of one series' variation is explained by the other. A correlation of 0.9 gives an r² of 0.81 — a strong shared story; a correlation of 0.3 gives an r² of 0.09, so roughly nine tenths of the movement is unexplained by the pair. Its practical job in a matrix is to flag which cells deserve attention: a low r² means the pair's relationship is weak, so any beta-style figure reported beside it would rest on that weak relationship and should be read as noise rather than as a reliable sensitivity.

In a matrix that carries them, adjusted beta figures run in both directions — A on B and B on A — because a sensitivity is not symmetric even though the correlation is. How that adjustment is defined is documented on its own page.

How do you read a correlation matrix?

A matrix is read as a grid of pairs, and three habits make it useful:

• The diagonal is always 1 — every series is perfectly correlated with itself, so those cells carry no information.
• The matrix is symmetric, so each pair appears once: the cell for A-and-B is the cell for B-and-A.
• Where the cells are colour-graded, the intensity tracks the size of the correlation, not its usefulness — a block of deeply-shaded cells is a cluster of things that move together, and the faint cells, easy to skip past, are the ones that behave independently.

What counts as a good value?

Low correlation is what makes a group of holdings behave differently from each other; high correlation means they are, in effect, expressing the same bet in different clothing. Two cautions come with reading the number: correlation only captures the linear relationship between two series, and it is not stable — pairs that look independent in calm periods often move together in a market shock, which is precisely when their independence was supposed to help — see rolling correlation for the through-time reading of the same pair.

Does Fincanva show a correlation matrix?

No, and no other correlation view either. Analysis today covers metrics, the monthly-returns matrix, capital, allocations, positions, Strategy analytics, and start-date sensitivity; correlation is not among them.

The nearest thing the product does report is Strategy analytics, which answers a neighbouring question one strategy at a time: tracking error says how differently a strategy moved from its parent Combined, where a matrix would say how differently the strategies moved from each other. The series a correlation comparison is usually made against are the factor roster, and the time-varying form of the same measure is rolling correlation.

Worked example

A Combined holds three strategies. Strategies A and B show a correlation of 0.9: an r² of 0.81, so most of what one did the other did too — holding both bought roughly one exposure twice, and the Combined's risk is more concentrated than the count of strategies suggests. Strategy C pairs with A at 0.2, an r² of 0.04: their paths are almost unrelated, so C is the strategy actually doing something different inside the Combined. Then read the same row for a market factor: if A also correlates 0.9 with the broad market, most of A's story is the market's story, not A's.

These figures describe what a strategy would have done on historical data, not what it will do. Fincanva provides no financial advice — see Is this financial advice?.