If you head over to coinmetrics.io/correlations, you’ll see a new addition: time-series correlation charts. There are other places to find cryptoasset correlations: see cointrading.ninja and sifrdata, as well as the individual charts on onchainfx, but we wanted to build a tool to visualize multiple correlations of major cryptoassets on the same graph.

Why correlations?

Correlations are used frequently in portfolio construction and are a key element of many quantitative strategies. Common ideas like the notion of diversification rely on assumptions about correlation within a basket of assets. The ability to find and determine consistent correlations between assets is a key aspect of modern portfolio theory.

Harry Markowitz called diversification the only free lunch in finance. This works because holding individual assets is considered to be more risky than holding the market index. Put another way, by diversifying, you can reduce idiosyncratic risk (for instance, the risk of bankruptcy in a company whose stock you hold) and retain only systemic risk. Markowitz showed us that diversification can enhance expected returns while reducing volatility. This works because some assets have a positive expected value (i.e. you expect them to go up) while having a correlation of less than 1 – so you can in theory achieve a desired level of return with reduced risk (volatility).

Of course, for this property to hold, you have to be able to find negatively correlated or non-highly-positively correlated pairings of assets. If everything in your investable universe moves together all the time, you won’t be able to derive any meaningful benefit from diversifying.

How does it work, exactly?

A correlation coefficient is a number between -1 and 1 measuring the strength of a relationship between two variables. Here we’re measuring how much the returns of cryptoassets move together. A positive correlation means that returns move together quite a bit.

If you plotted returns of two cryptoassets on a scatterplot, dots sloping upwards and right in a diagonal line would imply a positive correlation.

The Pearson correlation coefficient here is 0.64, implying a moderate to strong correlation, especially over such a long period. You can tell that it’s positive as the dots slope upwards. This means that when Bitcoin experiences high returns (as you can tell by that exceptional 28% return day near the top right), Litecoin generally increases too (by 40%). Note that no causality is inferred. Correlation just means that “these two variables tend to move together, by this magnitude.”

The actual derivation involves taking covariance of the two variables. Covariance tells you whether two variables move together or not, but it is unbounded and unstandardized. Finding a correlation involves standardizing those arbitrarily large figures by dividing by the sample standard deviations of both variables. This reduces covariance to a range between -1 and 1, and it now is informative as to the magnitude of moves between the two assets. Put simply, correlation tells you :

whether two variables are related, and the magnitude of that inter-relatedness.

If you’re interested, we suggest reading more into the statistics and doing a derivation by hand. It can be very rewarding, and helps build intuition about the variable.

There’s another wrinkle here, which is the fact that we’re presenting you with two options for correlation: Pearson and Spearman.

So what’s the difference between Pearson and Spearman correlation?

I’ll preface this by saying that the orthodox and conventional way of doing things in finance is to take the Pearson correlation of logarithmic daily asset returns, preferably over a longer period. If you aren’t interested in getting into any additional complexity, you can stop there and use those settings on the charts, and you’ll be absolutely fine.

(A common mistake in correlating assets is to use raw prices rather than returns. This is a mistake, as prices are often trended and non-stationary, meaning that you often get spurious positive correlations.)

In the previous section, I was implicitly referring to Pearson correlation, since it is the most common way of doing things. However, Pearson correlation basically assumes that the relationship between the two variables is linear, and it measures it on this basis. If you have nonlinear yet meaningful relationships, Pearson will report a weak correlation, when in fact there may be something interesting going on behind the scenes.

One solution to this problem is using log daily returns, which helps in processing data, and has some other useful properties if the data is normally distributed. However, we felt that it was worth giving our users some more options, so we introduced Spearman correlation.

The way Spearman correlation works is it takes a ranking of all the datapoints in the sample, and then it runs a Pearson correlation on that new rankings data. It throws away the actual figures and instead compares the two variables based on how much their rankings move together. What this accomplishes is the ability to capture co-movements in datasets that are nonlinear. Spearman would find the correlation between a perfect exponential relationship as 1, whereas Pearson would declare it positive but not perfectly correlated.

For more on this, we suggest reading this excellent breakdown in the differences between the two. To put it simply: if you think your variables are linearly related, and you want to measure the strength of those co-movements, use Pearson correlation. If you want to capture variables which co-move, but not at a constant rate (as with an exponential relationship), consider Spearman correlation. Spearman makes no assumptions as to linearity but simply assesses the relationship in terms of whether one variable increases when the other increases, and vice versa.

What does the number mean?

We give you several options: spearman/pearson, log/arithmetic returns, and 90/180/360 days. Let’s say you pick log, Pearson, 180 days. This number means “in the 180 days leading up to the point on the chart you’re looking at, these two assets (that you have selected) had co-movement in their daily returns of a magnitude corresponding to x.” If x is 1: their daily returns were highly interrelated in the 180-day period, and their returns perfectly explain each other. If x is 0.3, their returns moved together more often than not, but they weren’t particularly closely linked. Remember that since you have to specify a period of time to compare returns (to get a decent sample), the number today refers to a sample of the previous 90/180/360 days.

What are some practical applications of finding correlations?

Here’s one simple example. The Litecoin / Bitcoin correlation is an interesting standout. The below chart is the spearman correlations of daily returns over a trailing 360-day period between Bitcoin and a few assets.

You can probably decipher this fairly easily: over long periods, Litecoin moved together with Bitcoin far more than other assets like Ethereum, Dash, Monero, or Ripple did. Litecoin thus offered very little diversification benefit, at least until early-mid 2017 when that correlation broke down somewhat. Even today, Litecoin is notably quite highly-correlated against Bitcoin. This means that if you’re hoping to offset Bitcoin volatility by holding Litecoin, you are probably out of luck.

Another conclusion from this analysis is just how correlated the market is. In fact, recent developments evident on the chart should give you pause. Even though we only have price data for 14 assets, we try to capture the major ones, and correlations have risen among them over the last six months.

A clear trend of increasing correlation is evident from this chart. This means that attempting to find diversification will be much more difficult in this market phase. If you have a lot of BTC or ETH, you will struggle to find a large-cap cryptoasset which can offset their volatility. This suggests that in a crash, there will probably be few or no “safe havens.” Of course this can change, and is not set in stone, but that’s a straightforward reading of this chart.

Lots of people are worried about increasing correlations in traditional asset classes, but this is nothing compared to the high correlations currently exhibited in the cryptoasset markets. We expect that as the market matures and assets decouple from Bitcoin and Ethereum, diversification may become more meaningful, and more sophisticated correlation-driven strategies will become viable.

What are the constraints of this analysis?

Attempting to predict the future by looking at historical return is always somewhat fraught. There’s no guarantee that a historical correlation will persist into the future. Because of this, we recommend looking for useful correlations over long-term periods rather than something like 30 days, which can be misleading.

However, sometimes there simply is no discernible correlation between two assets. If you look at the 90-day charts, you’ll see that they can be very unstable. Using trailing year returns neuters this and yields moderate positive correlations, which aren’t very useful. In this case, correlations between two assets don’t tell us very much. So you have to know when a correlation analysis holds little explanatory power, and should be ignored.

Things that should grab your attention: very positive correlations between two assets, especially in longer periods of time. Consistently high correlations deserve investigation. Persistent negative correlations of any sort are tremendously interesting, albeit rare. The strength of the signal increases with the quantity of historical evidence – so looking at the BTC/BCH correlation isn’t very instructive for now, but with another years’ worth of data, it might be.

Another thing to be aware of is that different market phases exist. Apparently longstanding correlations, such as the LTC/BTC relation, which hovered between 0.6 and 0.85 from 2014-16, broke down suddenly in late 2016/early 2017. Correlations across the board tightened up and finding anything inversely related to BTC became a tough task, at least in our sample. Assumptions about LTC/BTC built up in the prior two years no longer held, as LTC became more of a viable project in its own right and began to differentiate itself from BTC.

So use these with caution, and be careful not to see a signal when there is only noise. It’s also worth reading more about the statistical underpinnings of both correlation measures. If you find anything interesting or have any questions, tweet us at @coinmetrics and we can keep the discussion going.