The correlation between STOXX600 and the S&P500

A statistical approach

This article is written by

Chiel Evertz

Most assets seem to be correlated to each other. So how does the correlation look between Europe's and United States's financial markets? In this article, we look at the correlation between the S&P500 and the STOXX600 as proxies for those financial markets. Do deviations from the normal correlations go accompanied with certain market movements?

ETF prices of S&P500 and STOXX600

I downloaded the historical adjusted closing prices of the ETFs S&P500 (SPX) and STOXX600 (STOXX) representing the United States and European financial markets, respectively, on Yahoo Finance. These ETFs are chosen as proxies for the financial markets in those regions since these are well-known, highly liquid ETFs, which give an accurate depiction of the market. Below you can see a plot of the ETF prices over time. The time series look correlated, as do many assets. We will dive a bit deeper into the correlation of these markets and inspect how this relates to the returns of these assets.

Figure 1

Correlation

I calculated the rolling correlation of the returns of the STOXX600 and S&P500 using a window of 30 days. So, on each given day we have a correlation based on the past 30 days of returns. Included in the plot is a rolling percentile band containing the last 252 observed correlations (amount of trading days in a year typically). This is chosen since we do not know the underlying distribution of the rolling correlation, so I do not want to make any assumptions about that. Besides that, fundamental changes over longer time periods could change the correlation between these markets, therefore we do not make a confidence bands based on the whole time series. You can see that the correlation mostly stays within these bounds, but sometimes breaks out of it. But why is this interesting at all? Is the correlation actually a long-term stable phenomenon? The result of a Dickey-Fuller test is included in the table below. This tests if the long-run correlation is stationary, in other words, reverting to its long-term average. I performed the test both for a longer time period (10 years) and the 3 years of data seen in the graph. We can see that in both cases we have evidence that the rolling correlation is stationary. This implies that correlation tends to move around its long-term rolling correlation and on average will return to its mean. Therefore, when the correlation is outside its normal 95% confidence bound, it has significantly diverged from the average and will likely return to the average. But does the diverging of the correlation go paired with any changes in the ETF returns?

Figure 2

When is the correlation abnormal?

To visualize when correlations are diverging from the norm I made two graphs containing indicators when the correlation is lower than the lower confidence bound and higher than the upper bound. The graph can be found below. The yellow vertical lines imply that the rolling correlation was below the 95% confidence interval, and the brown lines imply it was above. When looking at the yellow lines indicating low correlation, we see that one of both assets will outperform the other in returns shortly after the indicator. In December 2023 the correlation of the assets got below the bounds. After which the STOXX600 dipped while the S&P500 continued to rise at the start of January. We see a similar phenomenon in January 2025 where the STOXX600 rises strongly while the S&P500 goes down after low correlation has been signaled. And after may/june of 2025 the S&P500 outpermors the STOXX600 after low correlation indicators were triggered. If a low correlation shock always leads to a significant difference in short term returns is too difficult to say. But it is certainly interesting to observe that in this case.

There some moments where the correlation is very high. Just before September 2024 and in April 2025 the high correlation is accompanied with both assets going down. When both markets move down the rolling correlation suddenly becomes very high since both markets are dropping. During times of crisis the correlation between indices also goes up Sandoval and Franca (2012). This is logical, when both assets go down, they are by definition more correlated. Therefore when the whole market is trending downwards these market ETFs are higher correlated.

Figure 3

Conclusion

We found that the rolling correlation is stationary, so it revolves around its long term mean. And in our data low correlation shocks lead to either one of the assets outperforming the other in the short term after the shock. For investors holding STOXX600 and S&P500, it could be worthwhile to incorporate some indicators of the correlation between these assets. To investigate if this is a recent phenomenon due to chance or a general trend, more research is needed. Maybe an interesting short deep dive for investors with both ETFs. Potential trading strategies incorporating a correlation indicator could be interesting for this correlated financial markets.

References

Sandoval, Leonidas and Italo De Paula Franca (2012). Correlation of financial markets in times of crisis. Physica A: Statistical Mechanics and its Applications 391 (1), 187–208.