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# Statistics for crypto traders part 3: Correlation and Covariance

In the past blog posts, we covered averages, standard deviation, historical and implied volatility, and expected move.

Next, we’ll look at, covariance and correlation.

In Modern Portfolio Theory, an investor builds a collection of assets to take the least risk while maximizing their returns. In order to reduce risk, it’s necessary to diversify into other assets. The idea is that the perfect assets to diversify into are those which the price is unaffected if the other declines.

For example, if a large portion of your portfolio was held in gold, buying stock in mining companies probably would not be the best option. The reason being that if the price of gold declined severely, so too would the value of the companies mining it.

Instead, it would be best to look for assets do not share any risk, a very tricky challenge. So instead of investing in mining stock, another sector such as healthcare or tech might be better. Or it might be best to invest in other countries.

Those that subscribe to MPT are searching for what is known as the “efficient frontier,” where the greatest amount of returns is achieved with the least amount of risk.

In order to identify where the efficient frontier is, MPT uses covariance and correlation to determine how closely assets mimic each other. There are other formulas which we will not cover in this article, but these are the basics of what’s needed to start building the optimal crypto portfolio.

Covariance

Covariance measures the relationship between the returns on two crypto coins. A positive covariance means that if one asset makes a gain, so will the other. A negative covariance means that if one asset makes a gain, the other will decrease in value.

The formula is:

Where μ is the mean price for each coin.

Covariance shows the direction of the relationship between the two assets’ prices. This makes it a good tool for traders who want to hedge risks, avoid investing in two similar assets or find causal relationships between two assets’ prices.

One thing covariance doesn’t do is show the strength of a relationship. This means it’s best used with tools like correlation, covered in the section below. This way, you can know the direction and strength of any relationship between two coins’ prices.

Also note that the complex formula for covariance means it’s best calculated using Excel, Google Sheets, or an Adara widget. Taking the time to calculate covariance manually takes too long during live trading.

Here’s an example of covariance in use. Let’s say Bob learns that Ethereum and Bitcoin have a negative covariance, meaning one goes up when the other goes down. Bob can now invest in both coins simultaneously by creating a portfolio that lets him win (or break even) no matter which coin does well. He just needs to use other indicators or calculations to make sure he understands the exact relationship between the coins.

Fortunately for Bob, the next concept we’re going to cover — correlation — helps traders to just that.

Correlation

Where covariance measures the direction of the relationship between two assets’ prices, Correlation does the same for the magnitude of a relationship.

So let’s say that the trader from earlier — Bob — figures that Ethereum and Bitcoin’s prices have a negative covariance. When one goes up in value, the other goes down. This is good to know because it means Bob can use both coins to get a portfolio that gives him the exact risk and target profit he wants. However, to act on the covariance effectively, Bob needs to know the exact relationship between each asset’s prices. This is where correlation comes in.

One of the most common ways to calculate correlation is the Pearson Correlation Coefficient. Here’s the formula, wherein Cov (X,Y) is the covariance between X and Y’s prices, and σ is standard deviation.

A correlation of 1 means there’s a perfect positive correlation, i.e. a 1% price increase for one asset will increase another asset’s value by 1% as well. This is a perfectly positive correlation. On the other extreme is the perfectly negative correlation, wherein one coin’s price falls by as much as another rises.

When calculating covariance and correlation, it’s important to remember that, over short time periods, appearances can be deceiving. For example, just because 2 assets both boomed over a few days or a week doesn’t mean they’ll keep doing so in the future.

This is why we picked Ethereum and Bitcoin for our example; fundamental analysis seems to indicate that historically, one rises in value as the other falls. Still, never assume that covariance for historical data is a sure predictor of future events, especially during turbulent times.

Calculating correlation is easy using Excel, Google Sheets, and any other spreadsheet software that has the CORREL function. Alternatively, you can use Adara’s widgets and indicators to figure out the correlation between two assets automatically.

Last but not least, let’s look at an important concept that requires very little calculation: range.

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Before we close this article, let’s cover one more important thing.

All the concepts above can be used with single coins, but also to plan out portfolios. For example, there’s a single-asset and a multi-asset formula for expected moves. The same is true for standard deviation. Even covariance and correlation can extend to multiple assets. The best part is that you don’t have to memorize any of the above formulas if you’re an Adara user; our widgets and indicators do all the heavy lifting for you.

If you’d like to learn more about all these formulas and technical analysis in general, we invite you to our Intermediate trading lessons, available for free at Adara Academy. There you’ll find hours of videos covering risk management, basic and advanced calculations, patterns, indicators, and more.

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