Asset Correlation Matrix
Compare shared monthly ETF price movements using a common date window.
How it works
Select two to eight distinct symbols from the built in list. The page requests monthly price history for each selection through the Yahoo Finance proxy. It derives a monthly return only when that month and the prior calendar month both have valid closing prices.
The matrix uses only return months shared by every selected symbol. The current incomplete month is left out, and a missing month is never skipped over to create a return. Review the common date range and number of returns above the matrix before interpreting the pairs.
Each matrix value is a Pearson correlation from negative one to positive one. The score is one minus the average absolute pairwise correlation, rounded to four decimals. It summarizes this sample only. The highest and lowest pair lists are descriptive rankings, not buy or sell signals.
Change the selection to compare another group. Data is fetched again for the new symbols. If a quote request fails, or the selected assets do not have enough shared nonconstant monthly returns, the page shows an unavailable message instead of a partial matrix.
Step by step
- Select two to eight distinct symbols
- Review the shared monthly date range and matrix
- Compare pairwise values and the descriptive score
Worked example
For a reproducible arithmetic check, use the three monthly returns in the example below: SPY 10%, 20%, 30%, and BND 10%, 30%, 20%. These are illustrative values for testing the formula, not reported ETF returns.
The sample correlation is 0.5. With one asset pair, the descriptive score is 1 minus the absolute correlation, or 0.5. Negating one complete return series changes the correlation to −0.5 and leaves this descriptive score at 0.5.
When to use this calculator
Use this matrix when you want to compare how selected ETF prices moved together over shared monthly dates. The result describes a historical sample and can help frame questions about overlap between return series.
Use a broader portfolio analysis when you need holdings weights, volatility, account level exposures, or an estimate of potential losses. Pairwise correlation alone does not provide those results.
Common mistakes
A common mistake is treating a high score or a low pair value as proof that a portfolio will lose less. Check the common sample dates, the price return definition, and other risks such as volatility, concentration, liquidity, and losses before using the matrix in a decision.
Another mistake is comparing pairs calculated over different dates. This tool uses a common month window for every selected symbol and does not fill missing months. If it reports insufficient shared history or a constant series, no matrix is shown.
The formula
Monthly price return = current month close ÷ prior calendar month close − 1. Pearson correlation: ρₓᵧ = Σ[(xᵢ − x̄)(yᵢ − ȳ)] ÷ √(Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²). Descriptive score = 1 − mean(|ρᵢⱼ|) across selected pairs.
The calculation intersects consecutive calendar month returns across all selected symbols. It excludes the incomplete current month and does not bridge missing months. Unusable provider observations are omitted, never replaced with zero. A constant series or fewer than two shared monthly returns makes the matrix unavailable. Correlation uses quote close prices, not adjusted total returns.
Limitations and assumptions
The calculation uses Yahoo quote close prices at a monthly interval, not adjusted total return data. Dividends and other distributions are not reinvested, and the provider's history can be incomplete or revised. Every selected asset must have valid prices for consecutive months and at least two return months shared by the full selection. Unusable observations are omitted, missing months are not bridged, and constant series are not assigned a correlation of zero. Pearson correlation measures linear association over this sample and can miss nonlinear or tail relationships. The score is one minus the average absolute pairwise correlation, a custom summary rather than a validated risk measure, expected return, or recommendation. Historical relationships can change and do not establish causation.
Key terms
- Pearson correlation
- A statistic from negative one to positive one that describes the direction and strength of a linear relationship between two return series.
- Common return window
- The months for which every selected symbol has a valid return from consecutive calendar month closing prices.
- Diversification score
- One minus the average absolute pairwise correlation in this matrix. It is a custom descriptive summary, not a portfolio risk measure.
Compare alternatives
Risk Parity Allocator estimates weights from asset volatility, Portfolio Temperature summarizes portfolio concentration inputs, and Lost Decade Backtester compares historical portfolio scenarios. Each answers a different question from a pairwise correlation matrix.
Use the matrix to inspect linear co movement over a shared monthly price window. Pair it with a portfolio or allocation tool when you need weights, account values, or a broader scenario analysis.
FAQ
How does the matrix calculate correlation?
For each selected pair, the tool matches monthly price return values by calendar month and calculates Pearson correlation. It uses only months present for every selected asset, so each matrix entry compares the same dates.
What market data is used?
The page requests up to ten years of monthly quote close prices through the existing Yahoo Finance proxy. The calculation uses consecutive calendar month close changes, excludes the current incomplete month, and shows the common month range and count. It uses quote close values rather than adjusted total returns, so distributions are not reinvested.
What does the diversification score mean?
It is one minus the average absolute pairwise correlation in the displayed matrix. The value ranges from zero to one. A higher value means the selected series had lower average absolute linear correlation during the displayed window. It is a descriptive summary, not a prediction of future diversification or portfolio risk.
Which assets tend to have high or low correlation?
There is no universal pairing that stays highly or weakly correlated. The displayed matrix measures the selected price series over its shared sample. Relationships can change with the market period, and correlation alone does not describe volatility, losses, or dependence during extreme events.
How many symbols can I compare?
Choose two to eight distinct symbols from the built in selector. The tool displays the full matrix, up to three highest and lowest pairs, and the descriptive score. It cannot compare arbitrary symbols.
Related tools
Use ETF Expense Ratio to compare stated fund costs, Portfolio Correlation with SPY to inspect a manually entered relationship, and Risk Parity Allocator to explore volatility based weights. Those tools use different inputs and answer separate questions.