Correlation

What is Correlation?

A statistical measure known as correlation expresses how closely two variables are related linearly. It’s a typical technique for describing straightforward connections without explicitly stating cause and consequence. In other terms, it’s the relationship between the movements of two variables. Correlation is measured on a scale of -1 to 1, where two variables with + 1.0 move in perfect synchrony, and with a correlation of -1.0 move opposite of each other. Additionally, correlation can be applied to a variety of data types. You may have guessed how certain events would link to one another in some circumstances, while you may have been surprised by the relationship in others. It’s crucial to realize that correlation does not necessarily imply causation.

Correlation can be viewed in three ways… Positive, Negative, and No Correlation, which can be seen below:

  • A positive correlation would be between 0.01 -1. This indicates that the two variables changed in the same direction, either upwards or downwards.

How Does Correlations Play a Role in Investments?

Simply said, using correlation data can assist you in diversifying and reducing the risk in your portfolio. A portfolio with high correlations can increase the risk. A high correlation in your portfolio implies that your investments will move in concert with one another. With high portfolio correlations, when times are tough for one of your investments, they’re tough for all of them.  On the other hand, if your highly correlated investments are rising, it may seem quite nice, since all your investments will be experiencing similar positive returns. And while risk can never be totally eliminated, you can lower your portfolio’s overall volatility and potential maximum drawdown (which determines the value of the lowest dip and the greatest peak preceding the trough, which together represents the biggest decrease in the investment’s value) by assembling a mix of assets that are less correlated, uncorrelated, or negatively correlated.

Ice Cream Cones and Murders

When we observe a correlation in two or more variables – lines sloping together, bars rising together, or points on a scatterplot grouping – it’s tempting to make assumptions about causes and effects. 

Unfortunately, there is a limitation to correlation known as a spurious correlation. When two variables seem to have a statistical relationship because we find a strong positive or negative correlation, but are, in fact, unrelated to each other and have no causal relationship, this is known as a spurious correlation. In other words, although it may seem that one variable’s values are causing changes in the other, this is not the case. If we are not cautious, we may encounter behavioral biases (irrational attitudes or actions that have the power to subtly affect our decision-making) by not being able to distinguish between genuine correlations and spurious correlations.

Ice Cream Sales Lead to Higher Homicide Rates is the perfect example of this. There is ample data to support the claim that rising temperatures increase crime. This is most likely because we are more prone to congregate and drink in the summer after work, which gives criminals more places to operate in the evenings. In addition, ice cream sales are greater in the hot summer months. If one were to analyze the data for murders and ice cream cone sales, they would clearly see a correlation between the two, rising through the spring and peaking in the hottest parts of the summer.  It would be tempting to argue that ice cream sales cause murders or that murderers enjoy a cool refreshing ice cream cone after committing their crime.  But alas, ice cream sales are murders are a spurious correlation and the two factors have nothing to do with one another.

Let's Get Into Some Real Data!

Figure 1: 1, 3, and 5 year Correlation Comparison for the S&P 500, Russell 2000, Nasdaq, Ethereum, Bitcoin, Facebook, and Medifast.

Getting into the data, we can see comparisons between Benchmarks (S&P, Russell 2000, NASDAQ), Crypto (Ethereum, BitCoin), and Stocks (META, MED). The goal is to track how each comparison’s correlation trends evolve over time. As we can see, some trends continue while others undergo significant shifts throughout the course of 1, 3, and 5 years.

Let’s break it down…

Comparison

Examination

Benchmark vs. Benchmark

The correlations between the 3 benchmarks are the highest (around 0.90). This indicates they are postively correlated, and the benchmarks' movement is closely related.

Crypto vs. Crypto

Both well-known cryptos display a similar pattern, with a correlation of 0.80 indicating that any movement made by ETH will be closely followed by BTC.

Stock vs. Stock

This is when things start to get interesting because stocks can come from a wide range of industries and sectors, and as was already mentioned, this is where portfolios can reduce overall volatility. The relationship between META & MED, which is roughly 0.30, is a wonderful illustration of this reduction in correlation in the attempt to diversify. According to this information, a rough earnings announcement for META should not have a significant impact on the movement of MED due to the low correlation. 

Benchmark vs. Crypto

With the 5 years having the lowest correlation, we can clearly observe a tendency between all of these benchmarks and cryptocurrencies. However, as the data becomes more recent, the correlations rise up to 0.60. This demonstrates that cryptocurrency's advantage as a means of reducing equity risk is gradually eroding.

Benchmark vs. Stock

Because benchmarks contain bundles of assets that most likely include securities in the sectors that the equities belong in, we observe comparable correlations across the board. However, the correlation trend has decreased throughout the past year of data, reaching a correlation as low as 0.30.

Crypto vs. Stock

Last but not least, some of the lowest correlations in this dataset are between cryptocurrency and the stocks in the sample. For instance. there is no association between ETH and MED, as seen by the correlation falling to as low as 0.04. This indicates that even if ETH has outstanding returns, the movement for MED shouldn't be independent of movements in ETH.

Let's Change Our Perspective!

Figure 2: Weekly return spread for ETH & SPY, NAS & SPY, META & SPY for 1 year.

There are numerous ways to view correlation. It can be visualized using a real correlation matrix and turned into a bar chart like Figure 1, for example. However, correlation in the case of Figure 2 can be observed indirectly. It can be inferred indirectly by examining the weekly spread between two assets; the difference will demonstrate the direction and magnitude of their joint movement.

It is clear to see that the sample’s ETH-SPY (Dark Blue line) has the largest magnitude. This indicates that ETH returns exhibit greater movement volatility as compared to the SPY. Figure 1, which has a correlation of about 0.60, supports this as well.

The second weekly return spread, NAS-SPY (Black Line), has the lowest magnitude in the sample. It remains stable throughout the year and demonstrates how closely the returns on both assets fluctuate.

The magnitude of META-SPY (Light Blue Line) is roughly equivalent to that of ETH-SPY. The return spread does not, however, typically exhibit the same level of extreme volatility. But what’s intriguing is that the correlation is nearly identical (around 0.50).

However… let’s look at correlation one last way.

Figure 3: 5 year weekly return plotted for the S&P500 & Nasdaq, Medifast & Facebook, S&P 500 & Ethereum, and Medifast & Ethereum

The purpose of using a scatter plot demonstrates the connection between two variables over a period of time. One variable’s values are displayed on the horizontal axis, and the other variable’s values are displayed on the vertical axis. On the graph, each data point is a representation of the returns for the two variables for a given date. The direction, shape, and intensity of the relationship can be used to define the overall pattern of a scatterplot.

Assets

Direction

Shape

Intensity

Examination

S&P 500 & Nasdaq

Positive

Straight Line

Strong

Very tight relationship with defined pattern

Medifast & Facebook

Positive

Straight Line/Clustered

Moderate

Moderate relationship with few outliers

S&P 500 & Ethereum

Positive

Clustered

Weak

Moderate relationship with outliers and faint pattern

Medifast & Ethereum

Positive

Clustered

Very Weak

Weak relationship with faint pattern

Understanding the relationship between two assets can be enhanced by shifting your perspective. Understanding the magnitude and pattern of the asset returns helps illustrate why the assets are either closely correlated or somewhat correlated in Figures 2 & 3.

Overall, there are numerous ways to represent correlation. Examples include examining the pattern in a scatter plot or the trend in a bar chart. Understanding the magnitude, pattern, and direction of the connection between two assets can be aided by statistical tools, charts, and graphs. Making investing decisions when building a portfolio to diversify and formulate a strategy can thus be aided by correlation.

There are some caveats to correlation, though. First, cause and correlation are not the same. Even while the statistics may lead us to believe there is a positive or negative link between the two assets, we must be mindful that this does not necessarily mean there is one. 

Correlation is a tool that aids us in constructing a portfolio that is diversified and reduces risk to the desired level.  However, correlation is only a tool in our toolbox and must be deployed with a variety of other portfolio construction tools. 

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