---
title: "Correlation matrix"
description: "A correlation matrix is a pair-by-pair table of how closely two return series moved together over a period, from −1 to +1, with an adjusted beta alongside."
canonical_url: "https://fincanva.com/docs/analysis/correlation-matrix"
last_updated: "2026-09-18"
md_url: "https://fincanva.com/docs/analysis/correlation-matrix.md"
---

# Correlation matrix

A correlation matrix is a pair-by-pair table of how closely two return series moved together over a period: each cell holds a correlation coefficient between −1 and +1, where +1 means the two moved in lockstep, 0 means no linear relationship, and −1 means they moved in opposite directions. Applied to a [Combined](/docs/getting-started/strategy-in-a-combined), the matrix pairs each strategy it holds with the others and with the Combined itself, and the same series are set against a handful of market factors beside it; each pair is conventionally reported alongside two companions, **r²** and an **adjusted beta** in each direction. Fincanva shows such a matrix for a Combined, computed on daily returns, on the **Correlations** page of its analysis.

**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](/docs/analysis/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](/docs/analysis/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](/docs/analysis/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](/docs/analysis/factor-roster), switching between two readings of the same pair, **Correlation** and **Adjusted beta** — the second of which is the [adjusted beta](/docs/analysis/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](/docs/analysis/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](/docs/analysis/strategy-analytics): Free and Starter meet a refusal drawn over a sample strategy rather than their own figures. See [what each plan includes](/docs/account-security/what-each-plan-includes).

[Strategy analytics](/docs/analysis/strategy-analytics) answers a neighbouring question one strategy at a time: [tracking error](/docs/analysis/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?](/docs/investing-theory/is-this-financial-advice).*