Crypto Correlation and Beta: How Closely Altcoins Follow Bitcoin

Why altcoins follow bitcoin

Open several crypto charts and you often see other coins moving the same way on days bitcoin moves sharply. Several reasons overlap. First, news that changes the mood of the whole crypto market usually affects all coins together. Second, many participants treat bitcoin as the market benchmark and place orders following its moves. Third, when leverage is unwound all at once in futures markets, liquidations cascade regardless of the coin. So an altcoin's move can be split into 'the part that followed bitcoin' and 'the part driven by the coin's own reasons', and correlation and beta measure that split in numbers.

Correlation versus beta

Correlation shows, as a value from −1 to 1, whether two coins' daily returns moved in the same direction. Near 1 means almost always the same way, near 0 means no clear relationship, and negative means opposite. But correlation says nothing about size. For size, use beta. Beta is covariance(coin, BTC) ÷ variance(BTC), meaning how many percent the coin moved on average when bitcoin moved 1% in a day. For example, a beta of 1.5 means that over that period the coin moved about 1.5% on average when bitcoin moved 1%. The two are linked by beta = correlation × (coin volatility ÷ bitcoin volatility), so a very volatile coin can have a large beta even with a moderate correlation.

• High correlation and high beta: moved the same way as bitcoin, but more
• High correlation and beta near 1: moved with bitcoin by about the same amount
• Low correlation: much of the move was the coin's own; beta is also less reliable

A high beta does not mean rising more

Remembering a high-beta coin only as 'a coin that rises more when bitcoin rises' is dangerous. Beta is symmetric, so it also fell more when bitcoin fell, and if the coin's own movement drifted downward, the result can be poor even over a period when bitcoin rose. The figure below is an example built to have a beta of 1.5 and a high correlation. Its daily moves were larger than bitcoin's, yet after 90 days bitcoin was up and the altcoin was down. Beta and correlation describe how much assets move together, not which will produce the better result.

The numbers change with the period

Correlation and beta for the same two coins can differ a lot depending on whether you measure over 30, 90 or 180 days. Thirty days shows the recent relationship but has only about 30 daily returns, so a few chance days swing it a lot. 180 days is steadier but reflects a recent change late. So put short and long periods side by side, and if they differ widely, look at what has changed recently. Rolling correlation, measured over a 30-day window moved one day at a time, shows as a flow when the relationship strengthened or weakened. Also keep in mind that correlations among coins tend to rise all together in sharp sell-offs.

Common mistakes when reading the numbers

Correlation and beta are simple numbers, which makes it easy to load them with too much meaning. These are frequent misreadings. In particular, do not read a coin with low correlation as 'a safe coin unrelated to bitcoin'. Correlation may be low because thin trading makes the price move in jumps, because of a big coin-specific event such as a listing or token unlock, or because, like a stablecoin, the price barely moves at all.

• Thinking that holding several highly correlated coins is diversification
• Remembering a high-beta coin as one that only rises more
• Treating a coin as independent without checking why its correlation is low
• Trusting short-period values for a newly listed coin with too few days
• Reading correlation as causation; moving together does not mean one moved the other

Read it alongside relative performance

If correlation and beta answer 'how much did they move together', relative performance answers 'who went further in the end'. Performance relative to bitcoin is (1 + coin return) ÷ (1 + bitcoin return) − 1. For example, if over the same 30 days the coin rose 20% and bitcoin 10%, performance relative to bitcoin is about +9.1%. If beta is high but relative performance stays negative, the coin swung hard while its own trend was weak. Putting correlation, beta and relative performance on one line makes it clearer whether a coin is currently moving like bitcoin's shadow or on its own story. Changes in bitcoin's share of the market can be read alongside in the guide on bitcoin dominance and altcoin rotation.

Using the tools on this site

This site's Crypto Correlation Matrix calculates daily log returns from Binance spot daily candles for the coins you pick and shows 30-, 90- and 180-day correlations as a color matrix, plus each coin's correlation with bitcoin, beta, 30-day return, 30-day performance relative to bitcoin, the most and least similar pairs, and 30-day rolling correlation over the last 180 days. It shows no value when overlapping days are fewer than 60% of the period (at least 20 days). In Crypto Multi Chart you can put several coins' charts on one screen and compare the same day's moves by eye, and how bitcoin is linked to stocks, gold and the dollar is shown in Bitcoin vs Stocks, Gold and Dollar Correlation.

Limits and disclaimer

Correlation and beta are past relationships measured from daily candles over the chosen period, with no guarantee they will hold. The numbers can differ with the exchange, candle length, return method (simple or log) and how overlapping days are matched. The figure is an example made to show the principle, not a record of real coins. This guide explains how to read relationships between coins. It is not a forecast, does not recommend trading any coin and is not investment advice.