The Dollar and S&P 500 Relationship Re-examined

The relationship between the dollar and the S&P 500 is a perennial concern for investors. Analysts, including ourselves, run correlations.

There are different ways to conduct the correlations. We will typically run our correlations on the basis of percent change in each variable because that is ultimately what investors are interested in: the correlation of returns.

We recently showed such a measure of correlation actually showed that over the past 60 days, the correlation between the euro-dollar exchange rate and the S&P 500 has actually been trending up since early February when it dipped below 0.25. It is near 0.41 now. The 30-day correlation is near 0.59, suggesting that in the most recent period, the correlation has gotten tighter.

However, another approach is being played up in the media. Rather than look at the euro, it looks at the Dollar Index. The Dollar Index is a basket of currencies heavily weighted to the euro and currencies, like the Swiss franc, Swedish krona, and the British pound, which move in the euro's orbit. These components account for a full three-quarters of the Dollar-Index basket.

The remainder is the Canadian dollar (9.1%) and the yen (13.65). Two of the four largest US trading partners, namely Mexico and China, are not even included. Simply put, the Dollar Index is not a trade weighted basket, but a largely speculative vehicle.

Yet the real problem with the popular approach is that it either eyeballs a correlation, which is a statistical relationship, or it uses a less rigorous methodology to demonstrate what it assumes to be the case. Conducting the correlation on the basis of level rather than (percentage change) is not very rigorous. Such an approach lends itself to spurious correlations as it makes two trending markets correlated when they are not.

Here is what the different methodologies yield.  The charts are generated on Bloomberg.  The first shows the results of our methodology--the correlation  between the Dollar Index and the S&P 500 on a 60-day rolling basis on the percentage change--over the past year.  The take away is the correlation is still inverse, though clearly less than a year ago.  

This second chart is done in the way that has been shown in some of the financial press.  It is the same rolling 60-day period, but rather than percentage change, it runs the correlation on the level of the Dollar Index and the level of the S&P 500.  Its shows two other periods in the past year where the correlation was positive, though not as much as currently.    These were false positives, if you will..  

Mathematically, our methodology is regarded as more rigorous and addresses what is important to investors- the correlation of returns not simply levels.  We need to distinguish between two time series that sometimes trend in the same direction from a two time series whose returns are correlated. 

Beware of false prophets profits