Analysis
Disclaimer: This is not financial advice.
An important metric to look at when studying a token’s price is its correlation with other tokens. As an empirical metric, correlation may not be the best tool in predicting price trends or growth, but it gives valuable information about how prices of tokens have changed relative to each other historically, and how we can expect their relative relationships to continue if there are no significant changes in the market.
What is Correlation
When we talk about correlation, we are referring to the correlation coefficient, which is a scale between 1 and 1.

A correlation coefficient of 1 indicates a perfect positive correlation, which means that, historically, when the price of one token changes, the price of the other token has always changed in the same direction and by the same percentage.

A correlation coefficient of 1 indicates a perfect negative correlation, where the price of tokens have changed by the same percentage but in the opposite direction.

A correlation coefficient of 0 means that there is no correlation, so no relationship has been observed between the prices of the two tokens.
To calculate the correlation coefficient between two variables, we can use the following formula, or simply use the builtin functions in statistical or data software.
MKR Correlation Matrix
To better understand the concept of correlation, we will present an actual analysis using the MKR token. In this analysis, we are using the existing daily price data of MKR and a pool of other tokens from Sept 2019 to Sept 2021, consisting of WETH, WBTC, USDC, LINK, YFI, UNI, TUSD, MANA, renBTC and BAT. This list of tokens makes up the top 10 constituents of MKR’s multiasset collateral pool, so we can reasonably expect that some of their prices will have a high correlation with MKR prices.
Fig 1. correlation matrix of MKR and other tokens
The correlation coefficients can be presented in a correlation matrix, where we can clearly read the value for any pair of tokens. For our analysis on MKR prices, we only have to focus on the first column. We see that the correlation coefficient for all token pairs are above 0, indicating that there is a positive correlation between MKR price and other token prices. This means that when the price any of the above tokens change, the MKR price has been observed to also change in the same direction.
Analysis
Out of the 10 tokens, USDC and TUSD have the lowest correlation coefficient of 0.172 and 0.115. This is expected as these two tokens are stablecoins whose values are pegged to US Dollars, hence are unlikely to vary with the other tokens. Meanwhile, the correlation coefficients of all other tokens are above 0.8, which can be considered as a very high level of positive correlation. The highest correlation is observed from WETH at 0.973, which again is reasonable considering that WETH contributes more than 95% of the collateral value.
Conclusion
We now understand that MKR prices have a positive correlation with all of its top collaterals, and the level of correlation is generally high for nonstablecoins. However, we have to note that the correlation coefficient here is a metric calculated using historical data. It only describes the empirical observations between price movements of a pair of tokens, and does not imply any causeandeffect relationships. Although we can assume the correlation coefficients will stay at similar levels in the future (unless there is a drastic change in the market), we cannot use them to deduce the factors affecting token prices.