# How Correlation Helps You Make Better Investment Decisions

January 22, 2022

## 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.

## Why Does Diversification Work?

Diversifying a portfolio is considered the only free lunch in investing. Diversification reduces the correlation between assets within the portfolio and hence the volatility of the portfolio.

This can be best be demonstrated with a simple example. Consider two Portfolios A and B. Let’s say they have similar return, except that A is twice as volatile as B. If A goes up 20%, B goes up only 10%. But if A goes down 20%, B goes down only 10%. Let’s see what happens if we have a year where portfolio A goes up 20% followed by a year where A goes down 20%.

Assume portfolio A contains \$100,000. Then after Year 1, A is worth \$120,000. But after year 2, a 20% decline, A is reduced to \$96,000.

Note if the down year occurs first, the math works out the same. After Year 1, A has declined 20% to \$80,000. But after year 2 it rebounds 20% to \$96,000.

Now consider portfolio B. The same \$100,000 increases 10% to \$110,000 in year 1 and then is reduced by 10% or \$11,000 in year 2 to \$99,000. Portfolio B has outperformed portfolio A by \$3000 or 3%, simply by being more diversified, less correlated and less volatile than portfolio A. This improvement in return is our free lunch from diversification.

## 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 are uncorrelated. This means they move together 50% of the time. In other words, they are equally likely to move together in the same direction 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 5 days to over 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 0.57. The weakest correlation is Amazon and CVS at -0.01. It is relatively unusual to find stocks that are negatively correlated, although the value of -0.01 is so small, a more accurate statement would be that Amazon and CVS are uncorrelated.

## 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 for 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, XLE and XLU, which represent the S&P 500, Energy 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 XLE at 0.46 and even more weakly with XLU at 0.42. Even better, the XLE, XLU correlation is 0.00 meaning the two assets are completely uncorrelated. 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 first clicking on Portfolios in gray selector function on the left side of Stock Rover, This opens up the Portfolio Tool menu from where you can select “Correlation” as shown below. If you use Correlation frequently, you can bookmark it for fast access.

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

In the example above, we selected only the Dividend Growers Portfolio and consequently the grid displays the stocks from that portfolio, as well as the Dividend Growers 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. In the screenshot below, the mouse is parked over the FDX (FedEx), ACN (Accenture) cell.

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 take a look at part of the Dividend Growers Portfolio correlation grid as 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 slightly negatively correlated (-0.08) with the stock HII (Huntington Ingalls Industries, a spinoff of Northrup Grumman). 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 using the same Dividend Growers Portfolio, I am setting up the grid 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 Dividend Growers Portfolio, things actually behave reasonably well. There is not a lot of red showing after applying the filter. The highest correlation we have is CMA (Comerica) with ZION (Zions Bancorp) at 0.92. ZION is also tied with two others as the most highly correlated stock to the portfolio as a whole at 0.85. We may want to review ZION 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, at 0.76 and 0.75 respectively.

Interestingly, the FANG stocks (Facebook, Apple, Netflix and Google) have the lowest at 0.69. The FANG Portfolio would be the best choice as far as diversifying vs. all of the other portfolios, except the Growth portfolio. I wouldn’t have expected this.

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 0.93, which is the highest of any combination of portfolios. Another surprising outcome.

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 Dividend Growers Portfolio further. First I use ETFs as proxies for the sectors. Then I would hunt for stocks within the promising sectors for additional diversification candidates via screeners or via filtering columns in the Table. 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, at being only slightly correlated at 0.29, then Health at 0.44 and Staples at 0.51. 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.

Let’s say based on the prior discussion, we decide that we want to replace ZION with a more diversified stock in our Dividend Growers Portfolio. Utilities are noted for paying dividends, however they are not noted for dividend growth generally. The trick is to find a good dividend grower from utilities, which is the least correlated sector.

I was able to find a few promising candidates by using the Stock Ratings View in the Stock Rover Table. I applied filtering to the table, looking for stocks that are in the top quartile in ratings for Growth vs. Peers and Dividends vs. Peers, while still in the top half for Valuation vs. Peers. I then selected Utilities from the navigation panel, right-clicked on it and selected “Show All Stocks” from the ensuing menu. The screenshot below shows the 9 utilities out of 593 that passed the filters for this criteria.

From the 9 tickers passing the table filters, highlighted by arrows in the screenshot above, 7 are distinct companies, as two are multiple tickers for the same underlying organization. Then kicking out two of the tickers (ELP, NEP) for a lower valuation rating, leaves us with 5 promising tickers as candidates to swap for ZION. Specifically AQN (Algonquin Power), ENAKF (E.ON), KEN (Kenon Holdings), OGE (OGE Energy) and UGI (UGI Corp).

Using the quote box at the top, I have added all of the candidate tickers into the correlation grid with the Dividend Growers Portfolio to see how they fit in with the Dividend Growers Portfolio’s holdings. The screenshot below tells the story by highlighting the correlation of each of the tickers with the portfolio as a whole as well as with each other.

In the screenshot above, you can see that ENAKF (E.ON) has by far the lowest correlation with the portfolio at 0.11. I have also highlighted the ENAKF row so you can see that it weakly correlates with every stock currently held in the Dividend Growers portfolio. ENAKF looks very promising. 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. It would be my starting place for researching for a replacement candidate for ZION.

If ENAKF failed the research process, I would next research KEN (Kenon Holdings) based on its second lowest correlation score with the Dividend Growers Portfolio.

## 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.

Mel Turetzky says:

An incisive and, in my experience, a unique method of finding poorly correlated securities that still retain valuable characteristics. I compliment you on the detail and illustrations used.
It would have been valuable to show a historical example of the technique and how it might have worked in prior years over some reasonable period.
My minor contribution to this discussion is to raise the issue or upside and downside returns. It is valuable to look at the relative returns for correlated vs. uncorrrelated assets but I think it might be useful to look at the return in uptrending markets compared to the returns in falling markets, an upside/downside comparison. Maybe it is not much different than the one you made but it might be.
Also more emphasis should be placed on comparisons over several time frames, in different trending markets and with an examination of the variance exhibited in these results.

MaBoche says:

I absolutely support your precious suggestions, Mel and hope Mr. Reisman will have time and needed historical examples to reply.

Jim says:

Another good article with very valuable information. I do have a couple of ideas on how to expand the information and want to see if they make sense and are worth considering.

Looking at correlation on its own would seem to give a good but not complete indicator. Given the statement “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” implies that a correlation could be impacted by either difference in volatility ( ie moving the same way but by different proportions), or by moving in the opposite direction. Charting 2 stocks can show which is the bigger factor, but that takes some time.

One factor that could add to the understanding could be the Ratio data. I love the ratio chart, and had a spreadsheet doing this before starting Stockrover. That chart shows whether the investments go up or down together or trend consistently in one direction, eg Investment A is growing faster than B.

My use of the ratio chart has been to help understand the overall trend (is A generally growing faster over time than B), and is it a good time to move from A to B. If Ratio A/B is high (above the trend), then you will acquire more of Stock B than you will if the ratio is low (below the average).

2 views would, I believe, help look at the information on a larger scale than the charting option –

The first is a Ratio table, in exactly the format of the Correlation table, showing the ratio between each pair for a selected date. We would be able to look at the ratios on multiple dates.

The second is a Trend table, again in the same format of the Correlation table, with the regression trend between 2 dates. For example, A = mB + n over the past 5 years, indicates that A has grown faster by a factor of m.

I realize this is may be a personal way of thinking, but feel the extension of the Correlation table with these 2 views could be relatively easy and valuable in identifying where to look in more detail.

Interested in any comments, even if it makes no sense!

Howard Reisman says:

Thank you for an Interesting set of ideas, Pairing trends and ratios with correlation certainly has merit. We will give some consideration to this in a future version of Stock Rover.

Jim says:

Quick question on correlation. I looked at 4 stocks to see how correlation showed up in price charts, expecting the higher correlation number be reflected by more similar patterns on the price charts. The stocks I used were – AAPL, MSFT, ORCL, JNJ.

From the 5 year correlation –
highest was AAPL/MSFT at 0.76
Next MSFT ORCL at 0.61
Next AAPL ORCL at 0.53
Next MSFT JNJ at 0.47
Next ORCL JNJ at 0.44
Lowest AAPL JNJ at 0.41

I expected this to be borne out on a 5 year chart comparing the 4, with the higher correlated pairs being closest on shape and trajectory – ie move in the same direction and in the same proportion.

Yet if you look at the chart comparing the 4, there seems to be 2 tracks – AAPL and MSFT heading up to 250-300% on broadly similar paths, and ORCL and JNJ heading to 25-50% on more similar paths to each other.

The second lowest correlation – ORCL and JNJ at 0.44 is one of the pairs that track most closely. Much lower than MSFT/ORCL at 0.61.

Intuitively I would have considered ORCL and JNJ to be a good pair for diversification but it seems they would be more highly correlated from the chart.

Am I missing something?
Thanks,
Jim

Ken Leoni says:

Hello Jim,

Correlation looks at every day, comparing the relation of more than a thousand data points. It “correlates” movement meaning it is evaluating the tickers’ movement and how often are they moving in the same direction. It’s not a measure of how similar the returns are.

Hope this helps.

Jim says:

Ken,
thanks for the reply. I don’t want to be a pain (honestly!) but it would seem that if 2 stocks are highly correlated as defined in the article, they would tend to move the same direction and in the same proportion which “should” lead to being more similar looking in the chart and likely end up with similar price gains (returns excluding dividends?). Looked at another way, I would think lower correlation would imply the prices would diverge so be good for diversifying.

“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”

Howard Reisman says:

Looking at the data recently for a 1 year chart and a 1 year correlation, ORCL and JNJ have the lowest correlation at 0.20 and their one year chart looks to be on visual inspection not very correlated at all.

On the other hand ORCL and MSFT has the highest correlation at 0.79 and this chart looks to be far more correlated as expected.

If you run this, I expect you will see the same thing, providing you use the same time period for the correlation calculations and the chart. Correlations change over time and using different periods for the two would render the analysis invalid.