# What is Correlation and Why Does it Matter

*July 9, 2019*Howard Reisman

Contents

- More Diversification, Less Risk
- So What Exactly Is Correlation?
- Why Does Correlation Matter?
- How Does Stock Rover Calculate Correlation?
- What Is a Good Amount of Correlation?
- Exploring a Portfolio’s Correlation Profile
- Filter the Correlation Values
- Adding Benchmarks to the Correlation Matrix
- How to Find Diversifying Stocks to Add
- Adding in a Potential Buy
- Conclusion

## More Diversification, Less Risk

In this blog post we’ll explain how to make the most of Stock Rover’s powerful correlation feature to help you construct portfolios that are less risky and more resilient. And it’s easy in Stock Rover.

There are many different kinds of investment risk, but for the purposes of this blog post we are going to focus on diversification risk, which actually means having a lack of diversification. Or in other words, having a portfolio where the assets in the portfolio all behave in a similar way. We combat this problem by constructing a portfolio where the assets are **not** all strongly correlated to each other.

Before we dive into correlation, keep in mind that correlation is only one of several important factors in constructing a strong and diversified portfolio, and so should not be the only influence in deciding which stocks to buy.

## So What Exactly Is Correlation?

Correlation is a statistical relationship between asset prices. It is represented by a coefficient that measures, on a scale of -1 to 1, how likely it is that the price of two assets will move together—that is, how likely it is that they’ll both go up or that they’ll both go down. If two assets have a correlation value of 1, this means that they have perfect positive correlation—they move in the same direction (in the same proportion) 100% of the time. Perfect negative correlation has a value of -1, and it would mean that the assets move in opposite directions (in the same proportion) 100% of the time. A correlation value of 0 means that the assets move together 50% of the time. In other words, they are equally likely to move together as they are to move in opposite directions.

Correlation is based on daily returns. The daily returns of different assets are compared over a given period, typically one year. However with Stock Rover you can change the period of measurement from 10 days to 10 years.

The screenshot below shows a snippet from Stock Rover’s correlation table, where the correlation of the daily returns of three stocks (Amazon, CVS and McDonald’s) and the S&P 500 are shown over a one year period. We can see that Amazon correlates most with the S&P 500 at 0.81. The weakest correlation (though still positive) is Amazon and McDonald’s at 0.17.

## Why Does Correlation Matter?

Quite simply, using correlation information is a way to help you diversify and de-risk your portfolio. A highly correlated portfolio is a riskier portfolio. It means that when one of your stocks falls, it’s likely that all of them will fall by a similar amount. On the other hand, if your stocks are going up, then a highly correlated portfolio might feel pretty good! And while you can never eliminate risk completely, you can build a portfolio with a mix of assets that are less correlated, uncorrelated, or negatively correlated to reduce your portfolio’s overall volatility and potential maximum drawdown.

Or to put it another way, Harry Markowitz called diversification “the only free lunch in finance”. The idea is that by diversifying, an investor gets a benefit (reduced risk) at no loss in returns. Markowitz’s work expounding that notion won him a Nobel Prize and laid the foundations for Modern Portfolio Theory.

## How Does Stock Rover Calculate Correlation?

Correlation between two assets is found using regression analysis—essentially it fits a line to a scatter-plot made up of the pricing data from both assets. Stock Rover uses the standard mathematical formula for correlation, using daily dividend-adjusted price vectors. I don’t want to scare anyone off with formulas, but if you like that sort of thing, you can go here for more detail.

Note that correlation is calculated over a period of time, and therefore the coefficient can change depending on the period of the calculation. Two stocks could be strongly correlated over a longer time period—say, the past 10 years, but less correlated with a shorter time period, such as the last year. In the Stock Rover Correlation Facility, correlation values will be calculated over whichever time period you select. Generally, a 1-year time period works well.

## What Is a Good Amount of Correlation?

That depends on your tolerance of risk. If you are risk-averse, then you’d want a portfolio where the assets have as little correlation as possible. This is because a portfolio with highly correlated assets has the potential to experience big swings, both up and down. While finding perfectly uncorrelated stocks is pretty much impossible, you can aim to have a mix of stocks with varying correlations. This will reduce the volatility and the maximum drawdown of the portfolio, factors that are critical for prudent portfolio construction. It will also reduce the correlation to market benchmarks such as the S&P 500.

Within a portfolio, if you can find assets that have correlations with each other of below 0.70, that would be a good starting point. If you find that many of the assets in your portfolio are correlated at a high level, say over 0.80, you may want to rethink what the portfolio holds. You could actively search for more weakly correlated assets in order to reduce portfolio risk. If you can turn those 0.80 plus correlated assets into other assets you like, and whose correlation to most other assets in the portfolio is lower than say 0.50, that would be a big step forward.

For example, let’s consider a simple portfolio consisting of three ETFs; SPY, VNQ and XLU, which represent the S&P 500, Real Estate and Utilities respectively. This would be a portfolio where the asset correlations to each other are fairly low. In this portfolio SPY weakly correlates with VNQ at 0.51 and even more weakly with XLU at 0.21. The VNQ, XLU correlation also isn’t that strong at 0.62. Constructing an equal weighted portfolio consisting of these three assets would take on much less risk than a typical portfolio more highly correlated to the market.

When an asset has a negative correlation to the market, it’s called “hedging.” Adding hedged assets to a portfolio can be a very effective way to reduce portfolio risk. However, the hedged asset will cancel out returns in good times. This can be hard on an investor, because of the feeling of missing the party. The benefit of the approach comes some time later, when the party is over and you miss the hangover as well. It requires discipline and a long term outlook to maintain hedged assets when the good times are rolling.

## Exploring a Portfolio’s Correlation Profile

Knowing the correlation of your investments will help you manage the riskiness of your portfolio. If all of your assets are highly correlated, then when one of them takes a downturn, it’s likely that all of them will. This “diversification risk” vulnerability can be identified using Stock Rover’s Correlation Facility, found by selecting “Correlation” from the gray selector function on the left side of Stock Rover as shown below.

Here is what a correlation matrix looks like in Stock Rover using a Growth Portfolio as an example:

In the example above, we selected only the Growth Portfolio and consequently the grid displays the stocks from that portfolio, as well as the Growth Portfolio itself. You can select additional tickers, portfolios or watchlists to include in the grid via checking the boxes in the tree to the left of the correlation grid.

Within the correlation grid, each asset appears as both a row and a column. Any given cell includes the correlation coefficient for the assets in that cell’s row and column. If you lose track of which row and column you are looking at, you can just mouse over a cell to see that information in a tool tip, as shown below.

If you see a column or row with consistently high correlation, that’s a signal that that particular asset is not helping you diversify your portfolio, in which case you should ask yourself if the returns are worth the added risk.

The diagonal set of 1’s are the identity cells—these cells represent the intersection of an asset with itself in the grid. The identity cells will always contain a 1 because a stock is perfectly correlated with itself. But there is more information hidden in this cell—when you mouse over it, you get a tool tip (shown below) that tells you which assets in the current grid are the most and least correlated with the identity stock.

Let’s switch to a different correlation grid, shown below, to illustrate another feature of Correlation. You can see that some of the stocks below are shaded in varying hues of red and purple—this is called the “heat map.” Correlation above 0.50 will show in one of five shades of red—the higher the correlation, the deeper the color. Correlation below 0 will show as one of five shades of purple; deeper shades indicate more negative correlation, indicating assets that are good for hedging. Grey cells indicate coefficients that fall in the sweet spot of 0 to 0.50—considered a safe zone for the risk-averse investor.

The tool tip in the screenshot below shows that Amazon (AMZN) is negatively correlated with the utilities sectors, as represented by the ETF proxy XLU. Negative correlations are rare for most stocks and ETFs.

The heat map is an optional setting. To remove the colors, uncheck the “Heat Map” box above the grid.

## Filter the Correlation Values

You can also filter the correlation table so it only shows you the correlation coefficients that fall within a certain value range. To do this, click on the “Filter” button and fill in the filter box. Here I am setting up the grid to filter to only show correlation coefficients above 0.70.

Below is the result of applying the filter. Any column or row with a lot of red still showing signals that this stock is highly correlated with my other holdings, and I may want to examine if the stock’s returns justify its place in the portfolio. In our sample Growth Portfolio, things actually behave pretty well. There is very little red showing after applying the filter. The only issue may be Adobe (ADBE) which is highly correlated with Amazon (AMZN) and Veeva Systems (VEEV). It is also the most highly correlated stock in the portfolio to the portfolio as a whole. We may want to review Adobe to ensure that it’s still offering enough rewards in other ways.

## Adding Benchmarks to the Correlation Matrix

You can add more than tickers to the correlation matrix. Using the “Add a Quote..” box at the top, you can also add in whole benchmarks—that is, portfolios, watchlists, screeners, sectors, industries, or indices. To do this, type the name of portfolio, watchlist, industry, or index, etc., in the quote box, just as you would for a ticker, and select it from the matching results.

This allows you to see how a stock correlates with a relevant benchmark. You can use this feature to see how different portfolios correlate with each other, or see how your portfolio correlates with a specific sector.

Below I selected a few of the Stock Rover model portfolios to see how they correlate with each other. I can see for example that both the Growth Portfolio and the Dividend Growers Portfolio have the highest correlation with the S&P 500, both at or above 0.85. Interestingly, the FANG stocks (Facebook, Apple, Netflix and Google) have the lowest at 0.71. The FANG Portfolio would be diversified with almost all of the other portfolios. I wouldn’t have expected this. Also surprising, if you were looking for diversification by having a Dividend Growers and Value portfolio, which seems like they would behave differently, you wouldn’t get it, as they correlate at 0.89, which is the highest of any combination of portfolios. Again unexpected.

So using this table on my real portfolios will tell me how diversified my portfolios are to one another. If one of my portfolios experiences a downturn, I will know how likely it is that the other ones will too. Using the correlation table in this way illuminates how vulnerable I am to diversification risk across portfolios—a fact that without the correlation grid, I would only learn the hard way.

## How to Find Diversifying Stocks to Add

While there is no precise methodology for finding low-correlation investment candidates to diversify a portfolio, you can give yourself a head start by first finding a population of stocks that has a relatively low correlation to the portfolio. For example, by viewing the correlation of whole sectors or industries to your portfolio, you may get a better idea of where to start your search.

Here I’ve added in several sectors that seem promising for providing stocks that could diversify the Growth Portfolio further. First I use ETFs as proxies for the sectors. Then I would hunt for stocks via screeners within the promising sectors for additional diversification candidates. Or if I wanted to take a lazier approach, I could just add the ETFs themselves.

The sectors I am looking at are Real Estate (VNQ), Energy (XLE), Consumer Defensive (XLP), Utilities (XLU), Health (XLV) and Telecom (XTL). Of these, Utilities seems the most promising sector, basically uncorrelated at 0.02, then Consumer Defensive at 0.32 and Real Estate at 0.33. Of course I would have to check the correlation of any stocks I like from these sectors against what is already in the portfolio. But by sub-selecting from low-correlated sectors, I would have a head start in finding stocks that would increase diversification.

## Adding in a Potential Buy

Let’s say based on the prior discussion, we decide that we want to replace Adobe with a more diversified stock in our Growth Portfolio. I found it hard to find suitable growth stocks from utilities, which is the least correlated sector. However I have found a promising stock from another weakly correlated sector, Real Estate. The stock scored well in the Stock Rover Strong Growth Screener and could be a good substitute for Adobe. The ticker is ABR for Arbor Realty Trust.

Using the quote box at the top, I have added ABR into the correlation grid for the Growth Portfolio to see how it fits in with the Growth Portfolio’s correlation mix. The screenshot below highlights the correlation story by looking at the ABR column. Note you can also look at the ABR row and see the same thing. ABR looks promising as it has low correlations with every other asset in the portfolio. It could be an excellent choice for diversification if the stock, after research, looks like it is a strong buy based on its other merits.

To continue with this example, I have other stocks I have been keeping an eye on in my “Potential Buys” watchlist, and I am curious how these stocks would contribute to diversification. Below you can see how the tickers in my “Potential Buys” watchlist correlate with the Growth Portfolio and with my newly found ABR ticker. Note that in order to see this view, I’ve checked the “Potential Buys” watchlist on the left and I typed ABR and the “Growth Portfolio” into the quote box. There is a lot of grey there, which is good as far as diversification goes. All the stocks work well as potential candidates for the Growth Portfolio, with McDonald’s being the best at 0.20 and Applied Materials being the worst at 0.59, which is still not too bad.

## Conclusion

We have covered a lot of ground in this blog post. We have seen how we can use Stock Rover’s correlation facility to help diversify away risk in our portfolios. However just knowing a stock’s correlation to your other holdings is not enough. As always, further research would be needed to determine if you want to commit capital to any equity that looks promising from a diversification perspective. With that said, I hope you can see how powerful correlation is for examining the diversification risk of your portfolios. Try it out on your own and see what you find.

## Comments

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Well written. and useful. Once I log into my account can I have the blog available at the same time so I can apply the concept to my account?

Glad you liked the article. You would do that by having two browser windows side by side. One with Stock Rover and one with the blog article.

Very informative. Thanks!