This week we will take the concept of correlation a step further and explore another technique for visualizing the relationship between assets: quantile analysis.
Rather than calculating a correlation coefficient, quantile analysis offers a more flexible and intuitive result.
Data is from 18 May 2017 to 18 May 2022 and sourced from Messari, unless otherwise stated.
Firstly, the data needs to be prepared, to compare a specific metric. In all our examples we will use daily performance of BTC/USD as the ‘base’ data and daily performance of ETH/USD as the ‘target’ data.
If we plot the entire data set versus one another, we can observe a high correlation with a few outliers.
Quintile AnalysisQuintile analysis refers to splitting the data into 5 equal parts. This means buckets of 365 daily performances, as we are using 5 years’ worth of daily data.
For the bottom 20% of BTC/USD performances, the average ETH/USD performance is -5.5%. We can see from the chart that the average daily performances are similar for each asset.
Although we have selected quintiles, any sized quantile can be used. Alternative popular quantiles include percentiles (100), deciles (10) and quartiles (4).
If we take the same data set, but split into 10 deciles:
Increasing the number of quantiles adds granularity to the analysis but needs to be balanced with ease of visual consumption.
In the presented examples, doubling the number of quantiles provides confirmation that the quintile analysis is sufficient. We can observe the positive correlation, and similarity in performance magnitude, remain true.
For the last analysis example, we look at Gold vs. BTC prices.
Gold prices are selected as the ‘base’ return for bucketing the data (no weekends). Source: World Gold Council, data from 12 May 2017 to 13 May 2022.
Looking at the scatter chart and the quintile analysis, we see weak positive correlation between gold and BTC performance. For confirmation, we can perform rolling correlation analysis.
Quantile analysis offers an interesting visualization of the relationship between data sets and is simple to calculate and understand (hopefully!).
For smaller data sets, a few large outliers could skew results due to the averaging approach. Observing different numbers of quantiles, while complementing with rolling correlation calculations, can provide a more complete picture.
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