# The 5 Types of Stock Correlation — With Examples and Calculations

“The possibility of permanent loss is the risk I worry about.”

Howard Marks, The Most Important Thing

Avoiding the possibility of losing money is Buffett’s rule number one, and many value investors subscribe to that idea, including yours truly.

One way to determine the stocks’ riskiness in your portfolio is to analyze your asset construction based on its stock correlation.

By looking at your portfolio’s correlation, you can identify too closely related assets, which can hurt your returns if that asset class is underperforming.

When constructing our portfolios, it is always best to invest in stocks, bonds, ETFS, or others that are not closely correlated with each other. All of which helps avoid total portfolio meltdowns when a particular asset gets hurt.

Many portfolio managers focus more on the assets and diversification than the actual securities themselves. The theory is that uncorrelated assets move in opposite directions; for example, bonds do well when stocks perform poorly, and vice-versa.

In today’s post, we will learn:

• What is Stock Correlation?
• What Are the Five Types of Correlation?
• How Do You Calculate the Stock Correlation?
• Why Does Stock Correlation Matter?
• Examples of Portfolios with Stock Correlation

## What is Stock Correlation?

Stock correlation, according to Investopedia:

“Correlation, in the finance and investment industries, is a statistic that measures the degree to which two securities move in relation to each other.”

Many advisors use stock correlations in the more advanced portfolios, and the calculations of the stock’s correlation have a value that ranges between -1.0 and +1.0.

More on that in a moment.

Correlation, in statistics, shows the strength of the relationship between two variables. And the correlation is expressed as a statistical coefficient.

As mentioned above, the coefficient ranges between -1.0 and +1.0. A correlation coefficient of one equals a perfect positive correlation.

For stock correlations, a perfect correlation indicates that as one stock moves, either up or down, the other stock moves in tandem, in the same direction.

Likewise, a perfect negative correlation means those two stocks move in opposite directions. Bonds and stocks are thought to be in perfect negative correlation.

A correlation of zero implies no relationship at all.

Some other examples to help illustrate the point. Large-cap stocks such as Microsoft or Apple generally have a high positive correlation to the S&P 500, or nearly one.

Likewise, smaller-cap stocks such as Akero Therapeutics, Tupperware Brands, and Tootsie Roll positively correlate to the S&P 500, but it is lower, say 0.7, which means that small-cap stocks don’t move in parallel with the S&P 500.

As mentioned earlier, stocks and bonds have a negative correlation. For example, during the first half of 2008, U.S. stocks fell 25%, while Treasuries rose. And following the drawdown, stocks rebounded 8%, and Treasuries fell during the rebound.

## What Are the Five Types of Correlation?

Correlation refers to the method of determining the relationship between two variables. There are multiple methods of determining the correlation between those variables.

For our purposes, our interests lie in the correlation between two stocks, bonds, or ETFs.

Correlations occur in the world of statistics, and we are going to dive into that world briefly to find a method for determining the riskiness of our portfolios.

The idea of portfolio construction being the less correlated our portfolio, the less risk involved, and the safer our investments.

A stock correlation closer to zero, either positive or negative, implies little or no correlation between them. The coefficients move closer to a positive one, the closer the correlation to the securities.

A coefficient closer to a negative one indicates a negative correlation between the securities, with the increase in one stock tying to the other stock’s decrease.

There are three types of correlation related to our interests:

• Positive correlation – when the equity value of one security increases with respect to the other security
• Negative correlation – when the equity value of one security decreases in respect to the other security
• No correlation – when there are zero relationships between the securities

There are four different statistical methods for calculating correlation coefficients:

• Pearson correlation coefficient
• Linear correlation coefficient
• Sample correlation coefficient
• Population correlation coefficient

For our interest today, we are going to focus on the Pearson correlation coefficient.

The Pearson correlation is the most common form of coefficients and uses the values lying between -1.0 and +1.0. As mentioned earlier, when the values approach zero, the formula considers the correlation not related.

## How Do You Calculate Stock Correlation?

Now that we understand stock correlation a little, let’s start to find out how to calculate a stock correlation.

Using the Pearson Correlation Coefficient, we can determine whether two stocks correlate with each other.

Don’t worry; we will walk thru the formula, and it is not as ugly as it looks.

Inputs for the formula:

n = quantity of information

∑x = Total of the first variable

∑y = Total of the second variable

∑xy = sum of the produce of the first variable and second variable

∑x= sum of the squares of the first value

∑x3 = sum of the squares of the second value

Ok, let’s walk through a simple example to see how this works.

Let’s find the correlation between two sets of data, the home run totals of Babe Ruth and Hank Aaron from the age 29 to age 35.

X equals (47, 60, 54, 46, 49, 46, 41)

Y equals (44, 39, 29, 44, 38, 47, 38)

We have three steps to follow to find the correlation. The first step is to add up the values of each variable. The next step is to add up Y’s value and multiply each value of x by y and then add those totals to find their sums.

For example:

SUM(X) equals ( 47 + 60 + 54 + 46 + 49 + 46 + 41 ) = 343
SUM(Y) = ( 44 + 39 + 29 + 44 + 38 + 47 + 38 ) = 279

Next up, the second step:

SUM(X,Y) = (47 x 44) + (60 x 39) + (54 x 29) + (46 x 44) + (49 x 38) + (46 x 47) + (41 x 38) = 13,580

Still with me? Ok, next up the final step for this round.

For this step, we use each X value, square it, and add up all those values to find the value for SUM(x2). We will do the same with the Y values.

SUM(x2) = (47^2) + (60^2) + (54^2) + (46^2) + (49^2) + (46^2) + (41^2) = 17,039
SUM(y2) = (44^2) + (39^2) + (29^2) + (44^2) + (38^2) + (47^2) + (38^2) = 11,331

As we can see from our original data set that there are seven data inputs or n, and we can now plug all our numbers into the formula to find the coefficient for the data set.

R = (7 x 13,580 – (343 x 279) / Square Root (( 7 x 17,039 – 343^2) x ( 7 x 11,331 – 279^2))

All of which equals:

R = -907 / 9644.49 = (0.09)

Ok, now that wasn’t too horrible, was it? The formula looks scary, but if we follow the steps, the process isn’t too difficult.

Let’s try one using a real data set; how about the stock prices of two companies?

I want to compare the correlation between the stock prices of Microsoft and Apple. Let’s use the prices of each company at years end of the last five years.

Microsoft = (68.93 + 98.61 + 133.96 + 203.51 + 206.43) = 711.44
Apple = (38.53 + 56.44 + 55.99 + 115.81 + 110.44) = 377.21

The next step is to sum both Microsoft and Apple:

SUM(Microsoft, Visa) = (68.93 x 38.53) + (98.61 x 56.44) + (133.96 x 55.99) + (203.51 x 115.81) + (206.43 x 110.44) = 62,088.46

Next step, we will square each price and add those values up for each company.

SUM(Microsoft2) = (68.93^2) + (98.61^2) + (133.96^2) + (203.51^2) + (206.43^2) = 116,401.99

SUM(Apple2) = (38.53^2) + (56.44^2) + (55.99^2) + (115.81^2) + (110.4^2) = 33,409.09

Ok, now for the final step, and because we have five years of prices, n will equal 5.

R = (5 x 62088.46 – (711.44 x 377.21) / Square Root ((5 x 116401.99 – 711.442) x (5 x 33409.09 – 377.212)) = 42080.02 / 43338.48

R = 0.97

I don’t know about you, that was fun! It is interesting to see that before we began that walkthrough, I thought that the stocks would closely correlate, and lo and behold, Microsoft and Apple are closely correlated on a price basis.

Okay, I understand that not everyone wants to walk through all of that math, which is a little involved. The next question then is, how can I do this?

The simple answer is online calculators; my idea was to use a few examples to illustrate the process because I think when you understand the process, it becomes a little clearer.

Here are few links to some good online calculators I discovered while researching this post.

## Why Does Stock Correlation Matter?

Correlation is used in portfolio management as a tool to measure the amount of correlation that exists between the assets in the portfolio.

Finding assets that are not closely correlated is the goal of most financial advisors and many investors. Modern portfolio theory suggests that a portfolio full of closely correlated assets will perform poorly over time.

According to the theory, a portfolio full of assets that have less correlation to each other will perform better over time.

The process of determining correlation tells you the amount of risk you are assuming by holding assets that move in lockstep.

Where if you diversify your portfolio into uncorrelated assets, you will reduce the risk of losing money permanently in your portfolio, which, if you recall, is Buffett’s rule number one.

A great example of this is the correlation of bonds to stocks, or another example, Disney to Intel. Both of the above examples are unrelated, which in theory means that all things being equal, if one goes down, the other rises.

Now, if there is an overall market downturn, such as during March 2020, all assets dropped, with a few exceptions such as Walmart and Amazon.

## Examples of Portfolios with Stock Correlation

Let’s take a look at a few portfolios to see how closely correlated the assets are.

For our first example, I would like to look at Berkshire Hathaway’s portfolio’s top five positions. Instead of using the formula we calculated earlier, I will use one of the calculators to see the correlations.

Currently, Buffett’s top five positions are:

• Apple (AAPL)
• Bank of America (BAC)
• Coca-Cola (KO)
• American Express (AXP)
• Kraft Heinz (KHC)

I am plugging in the tickers into our calculator, and it will spit out our correlations, and it will calculate the ratios for three years of monthly returns.

For relation, consider the annualized returns of each position:

• Apple – 29.60%
• Bank of America – 7.50%
• American Express – 5.22%
• Kraft Heinz – (13.14)%
• Coca-Cola – 6.47%

So, after looking through the above chart, we can see that the top five stocks of Buffett’s portfolio are unrelated by and large.

Few are closer to each other such as Bank of America and American Express, with a ratio of 0.73. And Kraft Heinze is uncorrelated to American Express.

Much of the portfolio is correlated, but I would say mildly, and given that Apple is 49.1% of the portfolio, the less related it is, the better.

Let’s try another, shall we?

I want to examine the correlations of Ray Dalio’s portfolio; these are his top five positions:

• SPDR S&P 500 ETF Trust – SPY
• SPDR Gold Trust – GLD
• iShares Trust – iShares Core S&P 500 ETF – IVV
• Vanguard FTSE Emerging Markets ETF – VWO
• iShares Gold Trust – IAU

The three year returns for each position:

• SPY – 8.91%
• GLD – 9.50%
• IVV – 8.94%
• VWO – 6.70%
• IAU – 9.60%

We can see from the construction of Dalio’s portfolio, the top five assets are related to the stock portions, but the precious metals or gold are related to each other, but not to the stocks.

By analyzing both of the above snapshots of each portfolio, we can make a few observations.

First, the portfolio of Buffett contains more positions that are related to each other, which is by design for Buffett. He believes that investment in stocks is the best way to go. And he believes that diversifying for diversifying sake is a waste of time.

Second, Dalio’s portfolio is far more uncorrelated between the top holdings, three of the five holdings in stocks, and the remaining two holdings in gold. As you can see from the above chart, the stocks and gold are not correlated at any level.

And what all this tells us, when the markets boom Buffett will benefit from that in a big way, where Dalio will benefit as well, but to a lesser degree.

On the other side, when there are market downturns, Buffett will suffer bigger drawdowns on his positions than Dalio will, with his gold concentrations uncorrelated to the stock market.

To hammer the uncorrelation point home, let’s look at one final comparison.

Looking at two of the big Vanguard ETFs that hold the stock market and bond markets:

• Vanguard Total Stock Market ETF – VTI
• Vanguard Total Bond Market ETF – BND

The correlation ratios for both ETFs returns at 0.04, which tell us that both are uncorrelated.

## Final Thoughts

Building an investment portfolio encompasses many different ideas, such as what kind of assets you want to hold, how much risk you want to take on, and how much effort you want to put into the portfolio.

One of the tools we can use to help reduce our portfolio’s risk is looking at the correlation of our assets, particularly the stock correlations.

Stocks tend to have the best returns over the long haul. But with those higher returns, we also endure more volatility and a larger risk of losing our investments.

Comparing the two portfolios of Buffett and Dalio, I think, highlights the different ideas of building portfolios. Both are fantastic investment managers and have built portfolios that have had fantastic returns over time.

But they come at the idea of asset picking from different places. Buffett believes the stock market is the place to invest, where Dalio believes using diversification and asset allocation is the better path.

I believe they are both right, and for you, the choice is what do you believe and how much risk can you stomach. And only you can answer that question.

Using stock correlation can help you determine the amount of risk you might be taking on and balance those risks.

With that, we are going to wrap up our discussion for today.

As always, thank you for taking the time to read this post, and I hope you find something of value on your investing journey.

If I can be of any further assistance, please don’t hesitate to reach out.

Until next time, take care and be safe out there,

Dave