The correlation coefficient measures the correlation between two assets. It is a statistical measure between the two asset variables that ranges between -1.0 and 1.0. The lowest correlation two assets can have between each other is -1.0 meaning as one of the two correlated assets moves up, the other moves down in the same degree; this is a perfectly negative correlation. The highest correlation two variables can have is 1.0, this is a perfectly positive correlation. In which assets will move in the same direction to the same degree. While the midrange of the correlation coefficient, 0.0 means that two assets do not have any correlation.

#### Break down and calculations

The Pearson correlation coefficient is the most common coefficient used. It measures the linear relationship, both in strength and direction or two assets. The correlation coefficient is denoted by the formula below. Where the coefficient is equal to the covariance of two assets divided by their standard deviation which are multiplied. The standard deviation of an asset can also be assessed at its risk and or used to calculate its beta in relation to a benchmark. Which denotes an assets possible volatility.

We’ve outlined the range of the correlation coefficient and its meaning, but what happens to values that fall within the range that are not 0.0? These values denote the strength of the correlation, calculated as a part of the Pearson correlation coefficient. Meaning if two assets have a correlation coefficient of 0.4 they have a slightly positive correlation. The strength of the correlation may not be as strong as a third asset that may have a 0.85 correlation with the first asset. Anything above a +0.8 correlation between two assets is considered strong, anything below -0.8 is very weak.

What is the correlation coefficient used for? Anything to do with assets! That is the easy answer, it can be used in the investing stream or trading stream as we will see shortly.

The correlation coefficient is widely used by portfolio managers to diversify portfolios and traders to trade assets based on how highly positive or highly negative correlation assets move.

## Correlation Coefficient- The Matrix

Correlation coefficients can change! The likelihood of a correlation coefficient between two assets remaining the exact same for a stretched period of time is very low. For that reason, we like to refer to the MRCI’s inter-Market correlation matrix. Click here for the website link.

Alternatively, here is a screenshot of the 60-day inter-market correlation matrix. The correlation matrix lays out futures market correlations, everything from equity markets (S&P 500-ES futures) to Orange Juice futures (JON).

The red and green highlighted numbers are correlation coefficients of futures markets that are either highly positively correlated or highly negatively correlated. Green being a correlation coefficient of 0.9 and greater, while red is a coefficient of -0.9 or lower. In the top left corner, you can see that equity markets all have a very high correlation with each other. Such as the Nasdaq futures market and the S&P 500 futures market, a correlation coefficient of 0.98. While Euro Futures and USD Futures have a highly negative correlation coefficient (-0.98) as expected.

#### Correlations change with time…

However, if you look at the past 120 days of correlations, you will see that there are discrepancies. Not to a large degree but some correlations have gone from extremely strong to just strong and vise versa.

You can see there are many differences between the 60 days of the two matrices above. The red and green colors have changed.

The matrix is important to consider, no matter what one trades or invests in. As one will see shortly. Correlation coefficients can change as seen above and it’s important to note. If most or all stocks have a high positive correlation with the benchmark market, such as was the case in 2011 in the US. When most stocks had a high correlation coefficient with the S&P 500 benchmark, there was a little possibility to outperform the market. Or even diversify investments. This pushed investors to look at index markets and ETF’s rather than investing in stocks which skewed markets.

One can be considered a time where all stocks, for all sectors, and all assets across the board time of danger. When all stocks, no matter the sector become correlated, we could experience fear in markets, and uncertainty as was the case during the 2008/09 crash.

## Correlation Coefficient- Investing

Correlation coefficients in investing and portfolio theory are important tools for many portfolio managers around the world. The main use is diversification. As mentioned above, it’s important to keep an eye on the change of correlation coefficients as diversification may become difficult during downturns in the markets. A way to mitigate this is to include assets with little to no correlation to stock markets.

Investors everywhere, not just professional portfolio managers need to consider correlation coefficients for diversification purposes. For example, the two assets will be completely diversified if their correlation coefficient is -1.0. This ensures that if one of the assets drops, the other asset will gain to the same degree, eliminating the losses of the first. Assuming asset A in this scenario losses 6%, asset B is expected to gain 6% if they have a -1.0 correlation coefficient. The tricky part is mitigating a full portfolio’s un-diversifiable risk through the diversification of correlation coefficients.

#### The Efficiency Frontier

Portfolio managers use the correlation coefficient in modern portfolio theory to maximize the return for a given risk. This is done in relation to the efficient frontier, the idea is to create a portfolio on the efficient frontier. Meaning a higher reward for the same level of risk as to the “general” made up a portfolio that is used as a benchmark. One should keep in mind that correlation coefficients can change and measures with this in mind should be taken as the portfolio’s risk profile could change.

Take the efficient frontier example below.

The diagram of the efficiency frontier outlines the most “efficient” portfolios given a certain risk or standard deviation. The black curve is the efficiency frontier with a portfolio made up of 100% bonds at the bottom in the brown circle and a portfolio made up of 100% stocks at the top of the frontier in the green circle. All directed by the legend. The individual assets are below the efficiency frontier which encompasses different risk parameters and returns, everything from bonds to stocks.

Investors look to create portfolios that lie on the efficiency frontier to max out the possible returns for the risk they take on. A lot look at correlation coefficients to diversify their portfolio structure so it can lie on the frontier.

#### What happens when everything correlates?

Such as in down-turning markets, when all sectors correlate highly with each other. Alternatively when unusually correlated assets increase correlation coefficients. This was the case when the correlation coefficient between crude oil and the S&P 500 had a correlation coefficient of 0.97 in 2016. This brought fear into the market as crude oil fell and the probability of energy companies declaring bankruptcy increased.

In general, in a bull market, an investor would mainly be long equities and higher return sectors such as tech. To mitigate this risk and to diversify, finding negative correlations to equities such as gold, bonds, and consumer goods, for example, would help increase portfolio diversification.

Market correlations help traders find discreteness between different markets that are deemed to move together naturally. That can look for profitable opportunities. Taking the matrix above as the first step of it all. Consider futures correlations that are highly correlated and those that are highly negatively correlated.

There are multiple steps to this process and a lot of things to consider. First things first, when trading futures you want to be in the most liquid market, that is the equity market and oil! On average S&P 500 futures, ES E-minis have 1 million contracts traded daily. Oil is not far behind and other equities are in the high hundreds of thousands.

### Trading equity markets with correlations

That means if you are trading the liquid equities futures, look for highly positively and negatively correlated markets! Let’s assume that you are an NQ (Nasdaq) or YM (Dow) E-mini futures trader! If you want more information on the E-minis, check out the following articles.

The highly correlated assets when trading the NQ, for example, would be the Dow Jones futures, ES futures and even Russell 2000 futures. They consistently have a correlation coefficient of 90 and above with one another. Just take a look at the correlation matrix.

The next step is looking for highly negatively, this would be, typically, bonds, gold, silver, and the yen.

The reason for looking for highly positively correlated markets through the coefficient is to see which markets are supposed to move together. So when one lags below the others, the lagging market could be seen as a discrepancy for a long opportunity to catch up to the others.

#### Positive equity correlations

For example, the positive correlation chart below. Constructed on Sierra Chart and been discussed before. The pink line represents the NQ futures, who usually lead markets. The green line is the ES futures market. The yellow is the Dow futures market. Finally, the Russell 2000 is the orange line.

In this example, Russell 2000 is seen lagging slightly, to begin with as markets are on the move higher. All other equities are pressing higher. This presents traders with the opportunity to get long the Russell 2000 futures to catch up with the rest of the markets. In the second picture, you can see that RTY futures did indeed catch up with the rest of the equity futures.

#### Negative equity correlations

Alternatively, there are markets that are negatively correlated to equities. The main ones used at TRADEPRO academy are bonds, gold, silver and the yen. These are considered risk off and ideally should move in the opposite direction to equities.

Take a look at the risk off assets below. Brown are bonds, the yellow line is gold, the grey line silver, and the red is the yen. Notice there is not much correlation between those assets that is consistent so finding trades based on a weak bond market and strong gold for a silver trade is not the highest of probability trades.

#### Combining negative and positive correlations to trade equities

Now separately they may not be as powerful as you anticipated. Equity correlations alone are a strong tool, but little can be said about risk off correlations alone. Combining the two, however, are a powerful tool.

The simplistic idea behind it is that you would like to see equities moving in the opposite direction to risk off correlations. That means everything is moving as it should. Which may rarely be the case for markets.

However, if you see equities slumping and risk off slumping and it is not a news-driven move there could be a correlation trade in the making. I’ll discuss news driven correlations in just a bit.

In the example below, equity markets are slumping, however risk off correlations are mixed. For the continuation to the downside in equity markets, we would like to see risk off rally higher all together, if that move fails to occur then we can see a reversal in equity markets higher.

Just moments later, this is what the risk off correlations looked like:

Risk off began to move higher which qualified the continued short on the equity market. Yen, silver and Bonds all caught up to the upside in risk-off assets. The inverse correlation between the two subsets of assets is a powerful tool for traders and ideally, they should move inverse of each other. When they do not traders have an opportunity to take advantage of the discrepancy. However, there is a scenario in which the two baskets move together. That is during news events such as FOMC meetings or Fed hikes we can see equities move lock step with bonds, commodities and the yen.

#### Why do risk-off and risk-on move the same during Fed news?

When the Fed takes a dovish tone, they are more accommodating and imply that rates may hold or drop. This puts upside pressure on equity markets due to more money flooding into the market, making money “cheaper” to borrow. It also puts downside pressure on the US dollar implying increased supply, which alternatively helps commodities gain ground. When rates are lowered or implied to drop, bond prices increases being sold at a premium. Finally since yen has a negative correlation with the dollar as well, the yen increases in value.

It is during such events that you can see risk-off and risk-on move in the same way. Alternatively if the Fed takes a more hawkish tone, with implied increased rates, the opposite happens. Equities decrease and so does risk off.

## Conclusion

Conclusively there is a lot of information to know in terms of the correlation coefficient. Both investors and traders alike can find value in following the correlation coefficient.

Investors are concerned with the diversification of their portfolio, and in that look for assets with opposite correlation coefficients to cancel out. Also they do often look for uncorrelated assets in events of down turning markets as we saw that when equities drop, all equities drop.

Traders are more concerned with inter-market correlations of risk off and risk on assets to find discrepancies within the two or between the two for the quick trade.