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.

$$\rho_{AB} = \frac{\operatorname{Cov}(A, B)}{\sigma_A \, \sigma_B} \qquad\qquad r^2 = \rho_{AB}^{\,2}$$

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?

Yes — a Combined's analysis has a Correlations page, and the matrix is the table it opens with, How they move together: the lower triangle of every strategy-against-strategy pair, plus a column for each strategy against the Combined itself, all computed on daily returns. Only the lower triangle is drawn, because the upper half repeats every cell and the diagonal is 1 by definition, so neither is data. Beside it, Against the big markets sets each strategy — and the Combined — against six of the factor roster, switching between two readings of the same pair, Correlation and Adjusted beta — the second of which is the adjusted beta. A period selector above both scopes them to the whole run or to a single calendar year; a year the engine has no correlations for falls back to the whole period rather than emptying the tables.

r² is deliberately not a column. On Fincanva's figures r² is exactly the square of the correlation printed beside it, so a column of it would restate its neighbour rather than add anything — the reading in the section above is done from the correlation itself. A rolling correlation, the through-time form of the same measure, is not shown either.

The page is included from the Advanced plan, the same step as Strategy analytics: Free and Starter meet a refusal drawn over a sample strategy rather than their own figures. See what each plan includes.

Strategy analytics answers a neighbouring question one strategy at a time: tracking error says how differently a strategy moved from its parent Combined, where the matrix says how differently the strategies moved from each other.

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?.