Methodology — Covariance & Correlation

Transparency is a feature. This page explains what covariance and correlation measure and why we compute them — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.

The covariance matrix is the shared risk input that many other tools read from. Portfolio variance, beta, tracking error and tail metrics all draw on it, so it is computed once, here, and reused. The correlation matrix is then derived from it by simple rescaling. Both are square tables: one row and one column per asset, filled in from each asset's series of simple period returns (returns expressed as decimal fractions), aligned strictly period by period.

Sample covariance

Covariance measures how two assets' returns move together — whether they tend to rise and fall in step, move in opposite directions, or move independently. A positive value means the pair tends to move the same way, a negative value means they tend to move opposite ways, and a value near zero means little co-movement; the diagonal of the matrix is each asset's own variance (its dispersion around its average). By default we use the unbiased sample estimate, which is the appropriate choice when the return history is a sample of a larger process rather than the whole population; a population variant is also available. The result is symmetric and, by construction, never implies negative risk. It reflects the frequency of the returns you feed in and is not annualized. It needs at least two periods per asset to have any variation to measure, and every asset's series must cover the same periods — mismatched lengths are rejected rather than guessed at.

Correlation from covariance

Correlation is covariance put on a standardized, unit-free scale so that different pairs can be compared directly: each covariance is divided by the two assets' own volatilities. Every off-diagonal value lies between minus one and plus one — plus one is perfect lock-step movement, minus one is perfect opposite movement, and zero is no linear relationship — while the diagonal is pinned to exactly one, since any asset is perfectly correlated with itself. It is derived from an existing covariance matrix, so it must be square. Correlation is undefined for a degenerate asset that never moves (it has no volatility to divide by), and that case is flagged rather than reported as a misleading number.