Crypto correlation matrix

Correlation measures how closely two series of numbers move together, on a scale from -1 to 1. The matrix above uses the Pearson correlation coefficient of the daily moves of two coins: 1 is a perfect straight-line link in the same direction, -1 is the same link in opposite directions, and 0 is no straight-line link at all.

It tells how alike the moves of two coins were, not how large they were and not why they were alike. Two coins can correlate because they react to the same news or because the same traders hold both, and a high figure does not mean one coin drives the other. A figure near zero does not mean the coins are unrelated either, only that no straight line describes how their moves are linked.

Correlations are not fixed. The same pair of coins can have a different figure over a month than over a year, which is why the page shows four windows. Coins that move together add little to the spread of a portfolio, and coins that do not are the ones that spread it.

For each coin the page takes the closing price of every day from the daily bars of one exchange, named above the matrix, in the price of a dollar stablecoin. The days are UTC days, so a day is the same day for every coin, and only days that have closed are used: the day that is still going on is left out. The move of a day is the natural logarithm of its close over the close of the day before, which is close to the percentage change for a move of a day.

For each pair of coins the matrix gives the Pearson correlation coefficient of their two lists of daily moves over the window: the deviations of the two coins from their own average move, multiplied day by day and added up, over the square root of the product of their summed squared deviations. A window of 90 days holds 90 daily moves, which need 91 closes. The coefficient is worked out to four decimals and shown to two.

A coin that does not have every close a window needs is left out of that window, and the page lists it with the reason, instead of filling the gap. A coin that did not move at all in a window has no correlation with anything, and its cells say n/a. The coins are a fixed list of major ones, not a ranking that changes with the market: the matrix of one day is the matrix of the same coins as the day before.

The closes are those of the spot markets of the exchange named above the matrix, quoted in a dollar stablecoin rather than in dollars, so a stablecoin that strays from its peg moves every coin a little. The page keeps what it works out for up to an hour, and works it out again as soon as a new UTC day has closed, so the matrix changes once a day.