Build correlation matrices for portfolio assets with heat map visualization, diversification score, and efficient frontier plot.
A correlation matrix shows how much each pair of assets in your portfolio moves together, measured as the Pearson correlation of their return series, from -1 (moving in opposite directions) to +1 (moving together). The tool renders that matrix as a color-coded heat map, condenses the pairwise values into a single diversification score, and plots an efficient frontier of weight combinations. The surprise for most users: the numbers are a historical average, not a promise. Correlations measured in calm markets drift upward during selloffs, so a matrix built on quiet years will understate how your assets behave in a crash.
A concrete input and expected output from the current implementation.
Input
Asset A monthly returns (%): 4, -2, 5, 1. Asset B monthly returns (%): 3, -1, 4, 2.
Expected output
Correlation matrix (rounded to 2 decimals):
A B
A 1.00 0.98
B 0.98 1.00
Both off-diagonal cells land at the hot end of the heat map scale. Diversification score: at the poor end, since the only pair in this two-asset portfolio moves almost in lockstep. Both series average 2% a month. The summed products of the deviations from those means is 20, and the summed squared deviations are 30 and 14, so the Pearson coefficient is 20 / sqrt(30 x 14) = 0.98. The diagonal is 1.00 by definition; the off-diagonal 0.98 says the two assets moved almost in lockstep over these four months, so pairing them adds little diversification.
Each asset price history is turned into returns, then every pair is measured with the Pearson coefficient: the covariance of the two series divided by the product of their standard deviations. Cells run from -1 to +1, and the diagonal is exactly 1 by definition. The estimate depends on the window you feed in, so every pair should be measured over the same dates before you compare cells.
The diversification score condenses the matrix into one number, typically the average pairwise correlation: the lower the average, the better the score. The efficient frontier runs a mean-variance search over weight combinations, plotting expected return against volatility for each mix. Weakly correlated assets bend the frontier upward, letting the same return arrive at lower risk.
Because the diagonal compares each asset with itself, and anything compared with itself moves with itself perfectly: the Pearson coefficient of a series against its own copy is exactly 1. The diagonal carries no information about your portfolio, so read the off-diagonal cells only and ignore the 1s.
Yes. Sampling frequency changes the estimate: daily returns carry more noise, monthly returns smooth it out, and the two can disagree noticeably. Use the same frequency and date range for every asset. With only a few dozen observations the margin of error is wide, so treat the matrix as an order-of-magnitude read, not a precise measurement.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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